Dawning of a new era in gravitational wave data analysis: Unveiling cosmic mysteries via artificial intelligence — A systematic review

Abstract

Gravitational wave data analysis (GWDA) faces significant challenges due to high-dimensional parameter spaces and non-Gaussian, non-stationary artifacts in the interferometer background, which traditional methods have made significant progress in addressing but continue to face limitations. Artificial intelligence (AI), particularly deep learning (DL) algorithms, offers potential advantages, including computational efficiency, scalability, and adaptability, which may complement traditional approaches in tackling these challenges more effectively. In this review, we explore AI-driven approaches to GWDA, covering every stage of the pipeline and presenting first explorations in waveform modeling and parameter estimation. This work represents the most comprehensive review to date, integrating the latest AI advancements with practical GWDA applications. Our meta-analysis reveals insights and trends, highlighting the transformative potential of AI in revolutionizing gravitational wave research and paving the way for future discoveries.

Graphical abstract

Keywords

gravitational wave / artificial intelligence / deep learning / astrophysics / data analysis

1 Introduction

In today’s rapidly evolving world, artificial intelligence (AI) stands as a beacon of transformation, seamlessly integrating into every facet of our lives. From the convenience of face recognition [1] unlocking our devices to the magic of speech synthesis [2] that brings virtual assistants to life, AI’s influence is omnipresent. Diving deeper into the world of language, large language models (LLMs) like ChatGPT (GPT-3.5 and GPT-4) [3] and Llama 2 [4] have revolutionized our interaction with digital content. These advanced language models are now being harnessed for creative endeavors, such as co-writing novels, generating art-inspired poetry [5], and even composing music [6]. They are also playing pivotal roles in bridging communication gaps, offering real-time translations for diplomats and global travelers, and assisting in preserving endangered languages by generating rich linguistic content [3]. Beyond these linguistic marvels, AI’s imprint extends to personalized healthcare, where it crafts treatments tailored to individual genetic profiles [7], and to our cities, optimizing the ebb and flow of traffic [8]. Venturing into the domain of scientific inquiry, AI emerges as a powerful ally, reshaping our methodologies and accelerating the pace of discovery [9]. Innovations like self-supervised learning are reimagining how we interpret complex datasets [10], while generative AI techniques are forging new pathways in diverse fields, from drug design [11] to the creation of advanced materials [12]. Delving into specific achievements, tools like AlphaFold2 [13] have unraveled the intricate puzzle of protein folding, offering unprecedented insights into the very fabric of biological life. Similarly, in the vast cosmos, AI assists astrophysicists in deciphering the myriad signals from the universe, unveiling celestial phenomena that were once shrouded in mystery [14]. As we journey further into this decade, AI promises to be more than just a technological marvel — it is poised to be the compass guiding our quest for knowledge, reshaping our world, and expanding the horizons of what’s possible [15].

In 2015, the detection of gravitational waves (GWs) provided a monumental breakthrough in astrophysics [16], validating Einstein’s century-old theoretical prediction [17] and introducing a new window to probe the universe’s mysteries [18, 19]. gravitational wave data analysis (GWDA) is a complex endeavor that consist of many stages. Given the sensitivity of detectors like the Laser Interferemeter Gravitational Wave Observatory (LIGO) [20], Virgo [21] and KAGRA [22], it is imperative to differentiate genuine GW signals from terrestrial interference [23]. This involves rigorous data quality labeling [24], glitch classification to categorize transient noise events [25], and noise suppression techniques to enhance the clarity of potential signals [26]. In addition to these ground-based efforts, upcoming space-based observatories like Laser Interferometer Space Antenna (LISA) [27], Taiji [28, 29], and TianQin [30] will open another detection window by targeting sources such as massive black hole binary (MBHB), extreme-mass-ratio inspiral (EMRI), galactic binary (GB), and stochastic gravitational wave background (SGWB). With cleaner data in hand, the focus then shifts to signal detection. For example, template-based methods rely on accurate waveform modeling to predict gravitational-wave signals from sources such as black hole mergers [31] and employ matched filtering to detect these signals [32]. However, signal detection also encompasses template-free approaches — such as excess power searches and coherent analyses for SGWBs and unmodeled signals — that identify statistically significant features in the data without relying on precomputed templates [33]. Following a successful detection, the pipeline culminates in parameter estimation, where the goal is to decipher the astrophysical properties of the GW sources [34]. Each stage of the GWDA process, from data pre-processing to scientific discoveries, presents its unique set of challenges. Real-time analysis is essential to enable timely communication of detections to the external astronomical community, ensuring that follow-up observations and coordinated multi-messenger campaigns can be initiated promptly. Real-time data analysis necessitates maintaining high data quality because it allows for robust and reliable prompt detections [35, 36]. When it comes to signal detection, the non-stationary and non-Gaussian nature of the noise poses significant hurdle, as traditional matched filters are optimized for Gaussian noise [37]. To adopt matched filtering in non-Gaussian cases, advanced techniques like adaptive power spectral density (PSD) estimation need to be employed [38]. The generation of waveform templates, crucial for signal searching and parameter estimation, is computationally expensive and time-consuming when relying on classical methods [39, 40], resulting in full parameter estimation taking several hours [41, 42].

GWDA is confronted with challenges stemming from the high-dimensional parameter space and the presence of non-Gaussian, non-stationary artifacts in the interferometer background [43]. The introduction of AI, particularly deep learning (DL) algorithms, offers a promising avenue to address these challenges [14, 44] (Fig.1). These algorithms are characterized by their computational efficiency, leveraging accelerated hardware for rapid solutions [45]. Their scalability ensures they can handle extensive datasets, providing reliable model performance estimates [46]. The modular nature of these algorithms facilitates adaptability, allowing for the streamlined incorporation of new methodologies [47]. Furthermore, the generalization capabilities of DL models ensure consistent performance across varied GWDA scenarios [48]. Several recent reviews have explored the applications of AI in GWDA. Notably, Refs. [14, 44, 45] focus primarily on ground-based, detectors, while Ref. [49] offers a more comprehensive overview of the field without providing an overall statistical analysis of the literature (Fig.2). In light of these advancements, our review undertakes:

　● The paper reviews various AI-driven approaches to GWDA, covering every stage of the entire compact binary coalescences search pipeline, from waveform modeling to scientific discoveries.

　● We offer the review of AI’s application in gravitational waveform modeling, showcasing novel methodologies and their accuracy.

　● We also present the review of AI’s role in dramatically accelerating parameter estimation within gravitational wave studies.

　● This paper presents the most comprehensive review to date, seamlessly integrating the latest advancements in AI with their practical applications in the field of GWDA.

　● Our study culminates in a meta-analysis, synthesizing insights and trends from diverse AI applications in GWDA, discussing the fusion of AI and GWDA, and opening new avenues for insights and future research directions.

With this exploration, we aim to offer a panoramic view, intertwining the intricacies of AI with the mysteries of GWs, underscoring the transformative potential of their collaboration.

The remainder of this review is structured to provide a comprehensive overview of the intersection between AI and GWDAs (Fig.3). In Section 2, we briefly introduce the development of DL. In Section 3, we delve into waveform modeling, discussing both traditional methods and the advancements brought about by DL. Section 4 is dedicated to data quality management, encompassing topics from data quality labeling to noise suppression. Signal detection, a pivotal stage in the analysis, is covered in Section 5, where we explore various methods and their implications. Parameter estimation, a complex yet crucial aspect, is dissected in Section 6. Moving beyond the technicalities, Section 7 sheds light on the broader scientific discoveries enabled by these methodologies. Lastly, in Section 8, we offer a meta-analysis of the literature, discuss futuristic insights, and chart potential directions for the field.

2 Deep learning

With AlexNet’s unprecedented performance in the ImageNet challenge, 2012 marked an important turning point in AI [86]. This accomplishment demonstrated the potential of neural networks for complex visual tasks. Convolutional neural networks (CNNs) rapidly ascended as the benchmark in image processing, leveraging spatial hierarchies through convolutional layers and pooling operations [87]. However, as network architectures deepened, the vanishing gradient problem became evident. Residual network (ResNet) addressed this, introducing skip connections to facilitate gradient flow [88]. Concurrently, for sequential data, recurrent neural networks (RNNs) emerged as a promising approach [89]. Their capacity to retain state was notable, but challenges with long-term dependencies persisted. WaveNet [90], designed for raw audio generation, addressed this by employing dilated convolutions, expanding the receptive field. In the unsupervised learning domain, AutoEncoders [91], with their encoder−decoder structure, excelled at deriving efficient data representations without relying on labels. Together, these innovations post-AlexNet have shaped the trajectory of DL, setting the stage for subsequent advancements.

Contrasted with discriminative models that have been the mainstay of DL, generative modeling has carved its own niche, offering unique capabilities [92]. Generative adversarial networks (GANs) [93] emerged as a groundbreaking approach, where two neural networks, a generator and a discriminator, engage in a game-theoretic framework [94]. The generator crafts synthetic data, while the discriminator discerns between real and generated samples. This adversarial process results in the generator producing increasingly realistic data [95]. Variational autoencoders (VAEs) [96] offered another perspective, framing generative modeling as a probabilistic graphical model where the encoder and decoder networks are conditioned on latent variables. Normalizing flows [97] and Diffusion models [98] further enriched the generative landscape, providing mechanisms to transform simple distributions into complex data distributions. These generative models have been instrumental in the rise of artificial intelligencegenerated content (AIGC) [99], enabling the synthesis of high-fidelity images [100], videos [101], and even art [102]. The ability of these models to generate content that is often indistinguishable from real-world data has opened new avenues in digital media [103], virtual reality [104], and beyond.

As the field of DL progressed, the Transformer architecture emerged as a groundbreaking innovation, particularly for sequence-based tasks. Introduced by Vaswani et al. [105], the Transformer discarded the recurrent layers that characterized RNNs, instead relying on self-attention mechanisms to process input data. This self-attention allows the model to weight the significance of different parts of an input sequence, regardless of their positional distance, enabling it to capture long-range dependencies in the data with ease [106]. Unlike CNNs, which uses fixed-size filters to process data in local receptive fields, the Transformer’s self-attention mechanism provides it with a dynamic receptive field, adjusting based on the content of the input [107]. This flexibility allows Transformers to excel in tasks where the importance of data points varies contextually [108]. Furthermore, while RNNs processes sequences step-by-step, leading to potential issues with long sequences due to vanishing and exploding gradients, transformers process all sequence elements in parallel. This parallel processing not only speeds up training but also alleviates the gradient issues associated with long sequences [109]. Building on the foundational transformer architecture, LLMs like BERT [110] and GPT [111] have set new benchmarks in natural language processing. ChatGPT, encompassing iterations like GPT-3.5 and GPT-4 [3], epitomizes the rapid evolution and capabilities of LLMs. These models, with their ability to understand, generate, and reason with text, have showcased the superiority of the transformer architecture over traditional CNNs and RNNs in handling sequence data [112].

While supervised learning and generative models have made significant strides, another paradigm, reinforcement learning from human feedback (RLHF), has emerged as a potent tool in the AI arsenal [113]. At its core, reinforcement learning is an approach where an agent learns to maximize rewards by interacting with an environment, much like how one might learn a game through trial and error [114]. However, designing suitable reward functions for complex tasks can be challenging. RLHF, sidesteps these challenges by leveraging human feedback as a primary source of reward signals [115]. This approach allows models to learn more complex behaviors without the need for explicit reward shaping. OpenAI’s fine-tuning of models like GPT-4 using RLHF is a testament to the power of this approach [3]. By collecting comparison data, ranking different model responses, and using proximal policy optimization, models can be fine-tuned to produce safer and more useful outputs [116]. Simultaneously, the field of multi-agent systems is undergoing substantial development [117]. As AI models become more sophisticated, there is a growing interest in how they interact in shared environments [118]. Multi-agent systems, where multiple AI entities collaborate or compete, offer insights into emergent behaviors, cooperation strategies, and even the evolution of communication [119]. The fusion of LLMs with multi-agent setups is particularly intriguing [120, 121]. Imagine agents equipped with the linguistic prowess of LLMs negotiating, strategizing, and evolving their communication protocols in real-time. Such advancements hint at a future where AI entities do not just operate in isolation but actively learn from, compete with, and collaborate with other AI entities, paving the way for more dynamic and adaptive AI ecosystems [122].

3 Waveform modeling

GW astronomy has experienced significant progress in recent years, with the numerical modeling of compact binary coalescence — including BBH, BNS, and NSBH — which has been a key component in developing accurate waveform templates [123]. The journey of these cosmic phenomena is typically segmented into three phases: the inspiral, merger, and ringdown, with the potential for tidal disruptions in systems involving neutron stars [124]. Moreover, burst signals arising from events such as core-collapse supernovae or tidal disruption events contribute another class of short-duration waveforms, which, despite their less predictable morphology, are crucial for a complete understanding of GW sources. The accurate depiction of these stages through gravitational waveforms is vital for the detection of GW signals and the interpretation of the celestial narratives they unveil [125, 126].

The creation of waveform templates is an essential aspect of GW data analysis. These templates act as blueprints for expected GW signals from diverse astrophysical origins and are crucial for the comparison with data collected by GW observatories. However, the production of these templates, particularly for intricate systems, poses significant computational challenges. The computational demands and the sparse nature of numerical relativity (NR) waveforms necessitate the use of more practical approaches. To this end, a variety of approximate waveform models have been developed, such as the \mathrm{I}\mathrm{M}\mathrm{R}\mathrm{P}\mathrm{h}\mathrm{e}\mathrm{n}\mathrm{o}\mathrm{m} [129–131] and \mathrm{S}\mathrm{E}\mathrm{O}\mathrm{B}\mathrm{N}\mathrm{R} [132–134] families, which are calibrated against NR simulations to ensure accuracy and efficiency in GW data analysis.

In parallel with these developments, the field of waveform modeling is undergoing a transformative phase with the introduction of DL techniques. DL offers a promising pathway to expedite the generation of waveform templates by employing neural networks that are potentially capable of quickly synthesizing the complex dynamics of compact binary mergers. This innovative approach could speed up the process of generating waveforms, potentially overcoming some of the computational bottlenecks of traditional methods. For a detailed overview of the advancements in waveform modeling facilitated by DL, refer to Tab.1.

Although the evolution of GW waveforms is fundamentally deterministic and governed by differential equations, forecasting in the deep learning context refers to training a model to implicitly learn the waveform evolution from data [135]. This data-driven approach enables rapid predictions that are useful for real-time analysis [51]. DL models, particularly transformers, have the potential to revolutionize waveform forecasting. Khan et al. [51] stands as a testament to this potential, showcasing the capabilities of DL in predicting the evolution of GW signals.

In GW astronomy, the imperative for swift and accurate waveform modeling is ever-present [136]. DL presents a promising pathway, but the intricate parameter space of GW signals can be daunting [137]. Surrogate models, trained on NR waveforms, integrate DL techniques to expedite traditional waveform calculations [55]. These models stand as rapid waveform generators, adeptly spanning the vast GW parameter space [128]. Typically, the speed-up factor achieved through surrogate models is greater than 100, making them significantly faster than traditional methods [138]. Recent investigations indicate that surrogate models may substantially enhance computational efficiency, offering a promising approach to align traditional GW methodologies with the capabilities of AI [139].

4 Data quality management

Ensuring high data quality is essential in GW astronomy, where detecting these subtle spacetime ripples depends on precise measurements. This section examines the critical aspects of data quality management, including accurate data labeling, robust glitch classification, and effective denoising. Each of these procedures is vital for maintaining data integrity and reliability, which are fundamental to successful GW detection.

4.1 Data quality labeling

The detection of GW is a complex task, primarily due to the challenge of distinguishing these faint cosmic signals from background noise. The sensitivity of GW detectors is such that they pick up a myriad of noises, ranging from seismic activities to instrumental glitches [140]. This noise can often mimic or obscure the actual GW signals, making the task of identifying genuine events extremely challenging [141, 142]. The intricate nature of GW signals, often buried deep within the noise, requires sophisticated methods to accurately separate signals from noise. This complexity is a fundamental difficulty in GW detection, necessitating advanced techniques for noise analysis and signal extraction [61].

The quality of the data plays a crucial role in the successful detection and analysis of GW signals. High-quality data ensures that the signals extracted are accurate representations of astrophysical events. To achieve this, it is essential to label and categorize the data effectively [24]. Traditional methods of data quality monitoring involve manual labeling, which, while thorough, can be time-consuming and subject to human error [143]. The vast volume of data generated by GW detectors adds to the complexity, as each data segment needs to be meticulously analyzed to determine its quality. This process is vital as it directly impacts the reliability of signal detection and the subsequent astrophysical interpretations [24].

DL has emerged as a powerful tool in addressing the challenges of data quality labeling in GW astronomy [56, 59]. DL algorithms, particularly neural networks, have the capability to automate the process of data quality assessment, offering both efficiency and accuracy [144]. These algorithms can process large volumes of data rapidly, identifying patterns and anomalies that may indicate issues with data quality [145]. Several studies have demonstrated the effectiveness of DL in automating the data quality labeling process, significantly reducing the time and effort required while maintaining, if not improving, the accuracy of the labels [36, 49, 146]. By ensuring that only high-quality data is fed into analysis pipelines, DL contributes significantly to the robustness and reliability of GW signal detection and analysis [24].

4.2 Glitch classification

Glitches, or transient noise artifacts, are a recurring challenge in GW data analysis. These anomalies can significantly impede signal detection processes (see Fig.4), necessitating their accurate classification and understanding [147]. The impact of glitches is twofold: they can either mimic authentic GW signals, leading to false positives, or they can obscure genuine signals, resulting in missed detections [148]. This dual nature of glitches makes them a critical focus in GW data analysis, as their presence can skew the results and interpretations of GW observations.

Traditionally, the classification of glitches has relied on a variety of methods. Notable initiatives in this realm are the Gravity Spy and GWitchHunters project, which have been instrumental in tackling the glitch challenge [57, 149]. This project has compiled a comprehensive dataset that serves as a crucial resource for the classification of glitches. Traditional methods often involve manual inspection or semi-automated techniques, where analysts use witness data—auxiliary information from the detectors — to help identify and categorize these glitches. These methods, while effective, can be time-consuming and may not always capture the subtle nuances of different glitch types [150].

The advent of DL has introduced a new paradigm in glitch classification, offering more efficient approaches [146]. Some of these techniques directly analyze time-series data from GW detectors, identifying patterns that are characteristic of specific types of glitches [159]. Another innovative approach involves transforming time-series data into visual formats, allowing CNNs to classify glitches based on their visual signatures [59, 146, 152, 153]. This method leverages the pattern recognition capabilities of CNNs to discern between different glitch types effectively. Looking ahead, the integration of DL in glitch classification is poised to play a pivotal role in the future of GW data analysis, potentially leading to more accurate detections and a deeper understanding of the cosmos [149]. For a detailed exploration of these DL methods, refer to Tab.2.

4.3 Data denoising

In the realm of GW astronomy, noise is an unavoidable and challenging factor that significantly impacts signal detection [148]. The presence of noise in the data result in a low signal-to-noise ratio (SNR), leading to difficulties in identifying genuine GW events [32]. Effective denoising is therefore crucial, as it not only improves the SNR but also decreases the false alarm rate (FAR), making it easier to distinguish real signals from noise. Additionally, denoising plays a vital role in the convergence of Markov-chain Monte Carlo (MCMC) parameter estimation processes. By suppressing the noise, denoising methods help in faster and more accurate extraction of signal from the noisy data, thereby enhancing the overall efficiency and reliability of GW signal analysis [61].

Traditional denoising methods in GW astronomy have focused on direct noise suppression techniques, encompassing a variety of approaches [160–162]. These include variational-based methods [160], wavelet-based methods, and techniques utilizing the Hilbert-Huang transform [163]. Each of these strategies aims to remove noise components while preserving the integrity of potential GW signals. For instance, variational-based methods apply mathematical optimization techniques to filter out noise [164], while wavelet-based methods use wavelet transformations to reconstruct signals from data [165, 166]. The Hilbert-Huang transform, a novel approach, is particularly effective for non-linear and non-stationary data [163]. While effective in certain scenarios, these traditional approaches can be limited in their ability to handle the complex and dynamic nature of noise in GW data without the help of data from witness channel [167].

Although DL-based denoising methods are not yet integrated into current detection pipelines, research has shown that they have advanced signal extraction techniques in GWDA. These include dictionary learning [168], which employs basis waveforms for signal representation; WaveNet [169] for its sequential data handling capabilities; denoising autoencoders [170] for reconstructing signals from noisy data; and RNN [171] for capturing temporal dependencies. Notably, the transformer-based model, as discussed in Refs. [61, 62], has been applied to both ground-based and space-based GW denoising and detection (Fig.5), showcasing its potential in handling complex GW data, the transformer-based approach demonstrated measurable improvements in sensitivity and a reduction in false alarm rates compared to traditional methods, thereby underscoring its practical utility in real-world applications.

5 Signal detection

5.1 BBH

The detection of GWs, is a formidable task, primarily due to the subtlety of these signals against a backdrop of overwhelming instrumental and terrestrial noise. The advent of interferometric detectors, notably LIGO and Virgo, has revolutionized GW astronomy by enabling the first direct detection of GW event. However, the increased sensitivity and observational bandwidth of these instruments have also introduced intricate data analysis challenges. A cornerstone of GWDA has been matched filtering [32], a technique that cross-correlates observed data with theoretical waveform templates. Given the high-dimensional parameter space associated with potential astrophysical sources, this method, while powerful, is computationally demanding, especially in the context of real-time analysis.

Machine learning, particularly deep learning, has emerged as a potential tool for addressing the computational challenges in GW detection [63, 64]. The initial forays into integrating DL algorithms with mock LIGO data underscored the viability and promise of these approaches [63, 64, 172–174]. These models, trained on simulated waveforms, were subsequently tested on synthetic data. Impressively, their performance in discerning potential GW signatures from noise was on par with traditional matched filtering-based techniques, highlighting an important step forward in GWDA [65], Tab.3 lists out some related works, and their area under the curve (AUC) for detailed performance comparison corresponding receiver operating characteristic (ROC) curve is depicted in Fig.6.

In light of the proven effectiveness of machine learning on simulated LIGO datasets, the subsequent logical step was its application to genuine observational data. This transition presented inherent complexities, primarily attributed to the non-Gaussian and non-stationary nature of the noise, which elevated false alarm rates. Addressing these challenges, Wang et al. [66] integrated a matched filtering sensing layer prior to the CNN, showcasing its performance on O1 data. Building upon foundational research [60, 177], Huerta et al. [46] employed a hardware-accelerated WaveNet to probe for GW signals within a month-long span of LIGO data. Concurrently, Wang et al. [61] proposes WaveFormer, a deep learning-based data quality enhancement method for real observational gravitational wave processing, achieving state-of-the-art noise suppression performance, which paves a solid foundation for future strides in GW data processing and search [178, 179]. See Tab.4 for a detailed performance comparison of FAR.

As the GW community approaches a transformative phase, the ongoing development of space-based and third-generation ground-based detectors heralds a new observational epoch. These advanced instruments, set to provide unparalleled observational capabilities, also bring forth intricate data analysis challenges, particularly due to overlapping GW signals [180]. Recent endeavors on LISA [27] and Einstein Telescope (ET) [181] mock data have shown promising results [62, 67, 182]. The ongoing advancement and incorporation of machine learning techniques remain crucial for effectively addressing these challenges in the forthcoming era.

5.2 EMRI

EMRIs are among the most intriguing astrophysical phenomena in the universe. These events occur when a stellar-mass compact object, such as a neutron star or a stellar-mass black hole, spirals into a supermassive black hole found at the center of galaxies [186]. The detection of EMRIs holds significant scientific objectives [27]. Firstly, they provide a unique probe into the spacetime geometry around supermassive black holes, allowing for precise tests of general relativity (GR) in strong-field regimes [187]. Secondly, EMRIs can offer insights into the evolution and demographics of compact objects in galactic centers, shedding light on the formation and growth of supermassive black holes over cosmic time [187].

From a technical perspective, detecting EMRIs poses substantial challenges. The GW signals produced by EMRIs are weak and buried in the noise of space-based GW detectors. Their waveform patterns are intricate due to the complex interplay of relativistic effects, making them difficult to model accurately [188]. Furthermore, the long duration of EMRI signals demands efficient and robust data analysis techniques to comb through vast amounts of data. Advanced computational methods, including machine learning and deep neural networks, are being explored to enhance the detection capabilities, such as Zhang et al. [68], Yun et al. [70], Zhao et al. [189] detecting EMRI signals using CNNs, achieving rapid detection of EMRIs with high accuracy in time domain, frequency domain, and time-frequency domain. These advancements are poised to play a pivotal role in the forthcoming era of GW astronomy, where space-based detectors like LISA [27], Taiji [28, 29], and TianQin [30] will offer unprecedented observational capabilities for EMRI detection.

5.3 GB

GW studies have revealed a range of astrophysical sources, each with distinct signal characteristics and associated detection challenges. Among these, continuous GWs emitted by GBs or isolated neutron stars—offer valuable insights into the dynamics of compact objects. In this section, we review the characteristics of continuous signals from galactic binaries, focusing on detection strategies and the innovative techniques employed to resolve these overlapping signals from noisy data.

Continuous GWs, unlike their transient counterparts, persist over extended observation periods [190]. These waves, often emanating from sources like rapidly rotating neutron stars, present a distinct challenge due to their weak amplitude [191]. Traditional data analysis methods often grapple with the intricacies of these continuous signals [190]. However, the advent of DL has ushered in a new era of possibilities. Neural networks, with their ability to learn intricate patterns from vast amounts of data, have shown promise in detecting and analyzing these weak, continuous GW signals [192]. Several DL models have been proposed, aiming to enhance the detection capabilities by leveraging the power of convolutional and recurrent architectures [71, 72, 74, 192–194]. Although current pipelines for continuous signals rely predominantly on traditional signal processing methods, early studies suggest that deep learning could enhance the speed of these searches [73]. Ongoing research continues to assess the potential of these methods to complement traditional techniques in the pursuit of continuous GW detection [195, 196].

LISA is set to revolutionize our understanding of GWs from space. However, one of the inherent challenges LISA faces is the confusion noise. This noise arises from the superposition of countless unresolved sources, primarily binary systems, creating a cacophony that can mask potential signals. Addressing this requires sophisticated data analysis strategies and a deep understanding of the galactic GW foreground.

Gaussian processes (GP) have emerged as a powerful tool in the realm of GW research, particularly for GB GW separation [75]. By leveraging the non-parametric nature of GPs, researchers can model the statistical properties of GBs, effectively separating it from potential signals [197]. This technique holds promise, especially in scenarios with overlapping signals or in the presence of non-Gaussian noise, offering a robust method to extract meaningful information from the data [198].

6 Parameter estimation

The extraction of astrophysical source properties from observed GW signals, a process integral to GW astronomy, is known as parameter estimation (PE). At the heart of PE lies the MCMC algorithm, a statistical method that has been instrumental in the field [199]. MCMC operates on the principle of building Markov chains, which are sequences of random samples that, over time, approximate the desired distribution of the parameters being estimated (see Fig.7 for detail). This method is particularly effective in exploring high-dimensional parameter spaces, making it widely used in GWDA [200].

Despite the effectiveness of MCMC in providing detailed insights into complex data sets, it comes with its own set of challenges. The primary concerns are its computational intensity and occasional struggles with convergence, especially in scenarios involving intricate and voluminous data. Moreover, global fitting — which aims to jointly estimate parameters for all overlapping signals in extremely high-dimensional spaces — is particularly challenging for space-based missions and third-generation ground-based detectors, significantly increasing the computational demands and speed requirements for parameter estimation [203]. These limitations become increasingly significant as the complexity of GW data escalates and the demand for rapid analysis grows [200].

In response to these challenges, the field of gravitational-wave astronomy has begun to explore deep learning models as a complementary approach to traditional parameter estimation methods such as MCMC. Several studies have demonstrated that machine learning-based methods can offer potential improvements in processing large datasets and reducing computational time [42, 78, 204]. These methods are still under active development, and further research is needed to validate and refine them for operational use.

6.1 Point estimation

Fast PE by MLP. One of the initial forays into DL for PE involved the use of Multi-Layer Perceptrons (MLP). These architectures, designed to provide a direct “point estimate” for each parameter, have the advantage of speed. Capable of delivering estimates in near-real-time. Although MLPs are not currently a standard component of the production pipelines for multimessenger searches, early studies suggest that they could potentially be valuable in scenarios where rapid response is required [77].

Localization. Beyond the realm of intrinsic parameters, DL models have also been proposed to address extrinsic parameters. For instance, exploratory studies have suggested that DL-based approaches could be used to estimate both sky location and distance, potentially providing rapid source localization estimates for future multi-messenger observations [205].

6.2 Posterior distribution

While point estimates are invaluable for quick insights, a deeper understanding of source properties necessitates the exploration of the full posterior distribution. To this end, several DL models have been proposed:

Flow-based models. Flow-based architectures, which are known for their ability to model complex distributions (Fig.7), have been a popular choice for density estimation and posteriors. Green et al. [206] and Shen et al. [207] first demonstrated the efficacy of these models in GW PE by proposing toy models for the low-dimensional parameter sub-space of binary black hole (BBH), then Green and Gair [208] extended the work to the full parameter space of BBH and evaluated on GW150914. Subsequently, Wang et al. [209] accelerated the convergence speed by intergrating domain knowledge into prior distribution. Recently, Dax et al. [42, 78, 79], Wildberger et al. [210], Williams et al. [211, 212], Bhardwaj et al. [213] have further refined these models, showcasing their performance on a variety of GW events. Wong et al. [214–216] developed a \mathrm{J}\mathrm{a}\mathrm{x}-based [217] framework for rapid PE. The ability of these models to capture the nuances of the posterior distribution, especially in scenarios with complex degeneracy, has been a key factor in their success. Furthermore, the computational efficiency of these models, coupled with their ability to generate samples, has potential in addressing the challenges of traditional PE methods.

Conditional variational autoencoders (CVAE). Another promising avenue is the use of CVAE. As demonstrated by Gabbard et al. [218] and Green et al. [206], CVAEs, by conditioning on observed data, can generate samples that align closely with the true posterior distribution, offering a probabilistic perspective on source parameters.

Gaussian processes (GP). For specialized sources such as GBs and EMRIs, GP have been employed, as seen in Refs. [75, 219]. Tailored to the unique signatures of these sources, GPs provides refined posterior estimates, enriching our comprehension of these intriguing astrophysical systems.

7 AI for GW science

GW astronomy has opened a new window to the universe, allowing us to probe extreme astrophysical and cosmological phenomena. With the increasing complexity and volume of GW data, AI has emerged as a powerful tool to address various challenges and unlock new scientific potential in the field.

7.1 Fundamental physics

GWs, ripples in the fabric of spacetime, have emerged as a revolutionary tool for astrophysical exploration. These waves, produced by cataclysmic events such as the merger of black holes or neutron stars, provide a pristine medium to probe the universe’s most enigmatic phenomena [223]. Unlike electromagnetic radiation, which can be obscured or altered by intervening matter, GWs travels undisturbed, offering a direct and unadulterated glimpse into their sources. The detection of GWs has opened a new avenue to explore the strong-field regime of GR [224]. Traditional electromagnetic observations, while invaluable, often fall short in this domain, especially when it comes to events like black hole mergers. GW detections, on the other hand, allow scientists to test Einstein’s theory under extreme conditions, shedding light on the intricate dance of massive celestial bodies and the spacetime they warp [224].

The promise of space-based observatories, particularly LISA, is immense. Positioned far from Earth’s noisy environment, LISA aims to access the low-frequency GW spectrum [225]. This capability is anticipated to unveil events like supermassive black hole mergers, which have remained elusive to ground-based detectors, offering a new observational window into the dynamics of galactic centers [226]. The GW community eagerly anticipates the advent of third-generation observatories, such as the ET. These state-of-the-art facilities promise enhanced sensitivity and a broader frequency range [181]. With these advancements, scientists expect to detect a diverse array of sources, from the dramatic death throes of massive stars in core-collapse supernovae to potential signals from exotic compact objects. The enriched catalog of detections will undoubtedly deepen our understanding of the universe’s violent processes.

While GR has withstood a century of scrutiny, GW observations offer a unique platform to test its predictions and probe potential deviations. The precision of these observations might reveal subtle signatures hinting at alternative theories of gravity, pushing the boundaries of our current understanding and opening doors to new realms of physics (Fig.8). The synergy of advanced detector networks has been instrumental in refining parameter estimation techniques. As detectors’ sensitivity improves, so does the accuracy with which we can determine the properties of GW sources. This precision not only allows for a more detailed understanding of individual events but might also offer subtle hints of new physics lurking in the shadows. Among the most tantalizing prospects in GW science is the detection of the SGWB. This omnipresent hum, a relic from the early universe, holds the potential to offer insights into primordial processes and interactions, painting a picture of the cosmos’s infancy. Interdisciplinary efforts, merging the expertise of astrophysicists, general relativists, and data scientists, promise to usher in a new era of GW science. As technology advances and our observational capabilities expand, so too will our understanding of the cosmos, revealing its mysteries one GW at a time.

7.2 Cosmology

GWs offer a unique lens to probe the cosmos, and their potential in cosmological studies is gradually being realized. One pressing issue in cosmology is the Hubble tension—the discrepancy between the Hubble constant values derived from cosmic microwave background radiation and those from local distance ladder measurements [227]. While traditional methods have presented conflicting results, AI-driven analyses of GW data could provide an independent and precise measurement of the Hubble constant [228]. By analyzing the GW signals from binary mergers, AI can help refine our understanding of the universe’s expansion rate, offering a potential resolution to the Hubble tension. This synergy between GW astronomy and AI not only underscores the interdisciplinary nature of modern astrophysics but also promises to address some of the most perplexing challenges in the field [82].

7.3 Astrophysics

GWs emanate from some of the most violent and energetic processes in the universe, making them invaluable tools for astrophysical studies [229]. Neutron stars, the remnants of massive stellar explosions, are laboratories for extreme physics. Their equation of state (EoS) remains one of the outstanding puzzles in astrophysics [230]. AI-driven methods can assist in classifying different EoS models based on the GW signals emitted during neutron star mergers [83–85, 231]. Furthermore, core-collapse supernovae (CCSN) are cataclysmic events marking the end of a massive star’s life. The EoS governing the processes inside these explosive events can be probed using GWs [232]. AI can aid in deciphering the intricate signals from CCSN, providing insights into the underlying physics [233]. As the number of GW detections grows, there’s an increasing interest in understanding the population properties of the sources, be it BBHs, neutron stars (BNSs), or other exotic objects [234]. AI can assist in population synthesis studies, helping to unravel the formation and evolution histories of these compact objects [215].

8 Discussion

As the application of DL techniques to GW analysis matures, several key themes and challenges emerge [45]. This section delves into a meta-analysis of the current landscape, discusses the prospects of waveform forecasting [235], highlights the importance of gap imputation [236], and underscores the significance of multi-modality [237] and interpretability [51] in DL models.

8.1 Meta-analysis

The intersection of GW astronomy and DL has generated a growing body of research. Our meta-analysis, presented in Fig.1 and Fig.2, provides a quantitative overview of publication trends and the evolution of training dataset sizes within this field. Fig.1 illustrates two key trends: the increase in average training dataset size over time and the rising number of publications — both peer-reviewed articles and preprints on platforms like arXiv. This analysis highlights how the availability of large datasets is associated with a corresponding increase in research output, which in turn supports the development of DL models for GW applications. Each data point in these figures marks progress in the field, reflecting improvements in detector technology and data processing methods, as well as the expansion of the research community. In Fig.2, the breakdown into subdomains — such as waveform modeling, signal detection, and parameter estimation — demonstrates the diversity of research efforts and their interconnections within the GW and AI.

While our meta-analysis offers a retrospective view of the past decade, the trends observed may also help inform future research directions and resource allocation. We acknowledge that these figures represent a limited perspective of a complex field; however, they serve as a useful overview of the evolving landscape at the intersection of GW astronomy and DL.

8.2 Waveform forecasting

GW astronomy has ushered in a new era of understanding the universe, with waveform modeling playing a pivotal role in deciphering the signals from astrophysical cataclysms. Waveform forecasting, a subset of this modeling, focuses on predicting the evolution of these waveforms (Fig.9), especially in scenarios where only a fragment of the waveform is known or computationally feasible to generate.

The importance of efficient waveform modeling cannot be overstated. Traditional waveform modeling, particularly for systems exhibiting higher modes or precession, demands significant computational resources [134]. The ability to forecast a waveform, rather than compute it in its entirety, offers a promising avenue to mitigate these computational challenges [238]. As the GW community moves towards real-time detections, the need for rapid template generation becomes essential [239]. Waveform forecasting can expedite this process, ensuring that potential GW events are not missed during live observations. Some astrophysical systems present intricate waveforms that are computationally intensive to model [240]. Forecasting provides a mechanism to capture the essence of these systems, offering a balance between accuracy and computational feasibility.

While traditional methods have laid the groundwork for waveform forecasting, they come with inherent limitations, especially when dealing with complex astrophysical systems [241]. Enter DL. Drawing inspiration from its successes in other domains, particularly sequence forecasting, DL holds the promise of revolutionizing waveform forecasting in GW astronomy [242]. The potential benefits include enhanced accuracy, reduced computational overhead, and the ability to handle a broader range of astrophysical systems.

However, the journey of integrating DL into waveform forecasting is not without challenges. The complexity of GW signals, the omnipresent detector noise, and the need for vast training datasets to train robust models are but a few of the hurdles to overcome [235].

In conclusion, as we stand on the cusp of a new frontier in GW astronomy, the symbiosis between DL and waveform forecasting is poised to play a transformative role. Collaborative efforts between the AI and GW communities will be instrumental in navigating this exciting journey ahead.

8.3 Gap imputation

In the realm of time series data analysis, especially when dealing with time series data, the presence of gaps or missing data points can pose significant challenges [243]. These gaps can arise due to a myriad of reasons, from instrumental downtime to environmental disturbances or even data transmission issues [244]. GW data, with their intricate patterns and crucial reliance on continuity, are no exception to this challenge [245].

GW observations, by their nature, require continuous and uninterrupted data streams for accurate data analysis [246]. Any gaps in this data can lead to biases in parameter estimation (Fig.10) [236]. Traditional methods employed in other fields to address missing data, such as linear interpolation or mean imputation, often fall short when applied to the complexities of GW signals [247]. These methods, while simple, may not capture the intricate patterns and dependencies inherent in GW data, leading to inaccuracies [248].

DL is a paradigm that has shown remarkable success in various domains, including gap imputation in time series data [249]. DL models, with their ability to learn and capture intricate patterns in data, hold significant promise for addressing the gap imputation challenge in GW data [250]. The potential benefits are manifold, from improved accuracy in imputation to the capability to handle large gaps that traditional methods might struggle with. However, the application of DL to GW data for gap imputation is not without its challenges. The non-stationary nature of GW data, combined with the noise, necessitates careful consideration and design of DL models [251]. Additionally, it is essential to ensure that the integration of imputed data does not lead to biases or inaccuracies in further analytical processes [252].

In conclusion, while DL offers a promising avenue for gap imputation in GW data, the field is ripe for research and exploration. Collaborative efforts between the AI and GW communities could pave the way for innovative solutions, ensuring that our observations of the universe remain as accurate and uninterrupted as possible.

8.4 Multi-modality

The realm of AI, particularly in the domain of DL, has witnessed a surge in the exploration and application of multi-modal techniques [253, 254]. These techniques harness information from multiple data sources or modalities, aiming to provide a more comprehensive understanding of the underlying phenomena. In many AI applications, multi-modality has proven to be transformative. For instance, in medical imaging, combining visual data from MRI scans with textual patient records has enhanced diagnostic accuracy and predictive modeling [255]. Similarly, in natural language processing, the fusion of textual, auditory, and visual cues in multi-modal sentiment analysis models has led to more nuanced and context-aware interpretations [256].

GW astronomy, while primarily reliant on signal data, has the potential to benefit from a multi-modal approach. As a starting point, one can combine raw time series data with their time-frequency representations — such as spectrograms — to capture complementary features. This initial idea, though relatively simple, forms the basis for more sophisticated multi-modal analyses (Fig.11). Consider the richness of information available: beyond the GW signals, there are electromagnetic signals, neutrino observations, and more [257]. Each modality offers a unique perspective on astrophysical events. While current GW analyses have not yet integrated such diverse data streams, the success of multi-modal techniques in other AI domains suggests potential avenues for exploration. One can envision a future where GW detections are enhanced by concurrent observations from electromagnetic or neutrino observatories [258]. DL models, adept at handling multi-modal data, could be trained to extract features from each modality and then fuse these features to improve event characterization, source localization, and parameter estimation [259].

However, the integration of multi-modal data in GW analysis is not without challenges. The synchronization of data streams, the handling of disparate data resolutions and formats, and the development of fusion techniques tailored to the specificities of GW events are all areas that would require meticulous research and innovation [237]. Yet, the potential rewards are significant. A successful multi-modal approach could provide a more holistic view of astrophysical events, bridging gaps in our understanding and opening new frontiers in GW astronomy [259].

8.5 Interpretability

Interpretability in machine learning has garnered significant attention [260], especially when models are applied to complex scientific domains [261]. In the realm of GW analysis, understanding the decision-making process of models is not just a luxury but a necessity. This ensures that the predictions and insights derived are both reliable and scientifically meaningful. GW signals, with their intricate patterns and the profound astrophysical phenomena they represent, pose a unique challenge for DL models [76]. While these models can achieve impressive performance metrics, deciphering their decision-making process in the context of such complex signals remains a formidable task [51].

Recent works have made strides in bridging this interpretability gap. For instance, Khan et al. [51] delved into creating models that not only detect but also elucidate the characteristics of GW signals. Similarly, the studies by Shi et al. [52] and Zhao et al. [62] have contributed to enhancing the transparency of models, especially Transformers, ensuring that their predictions can be traced back to understandable reasoning. An interpretable model in GW analysis offers more than just reliable predictions (see Fig.12). It provides a window into the astrophysical processes that generate these ripples in spacetime. By understanding how a model discerns between different types of signals, researchers can gain deeper insights into the astrophysical events behind these waves, potentially unlocking new facets of our universe.

As the field progresses, there is a palpable need for more research dedicated to enhancing interpretability. The fusion of traditional astrophysical knowledge with transparent machine learning models holds the promise of richer, more profound insights into the cosmos.

References

[1] F. Schroff,D. Kalenichenko,J. Philbin, FaceNet: A unified embedding for face recognition and clustering, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), IEEE, Boston, MA, USA, 2015

[2] Seamless Communication, SeamlessM4T — massively multilingual & multimodal machine translation, arXiv: 2308.11596 (2023)

[3] A. I. Open, GPT-4 technical report, OpenAI, arXiv: 2303.08774 (2023)

[4] H. Touvron,L. Martin,K. Stone,P. Albert,A. Almahairi, ., Llama2: Open foundation and fine-tuned chat models, arXiv: 2307.09288 (2023)

[5] M. Stinger, AI poetry: Artificially generated poems written by the latest in AI technology, 2023 (Independently published)

[6] J. Copet,F. Kreuk,I. Gat,T. Remez,D. Kant, ., Simple and controllable music generation, arXiv: 2306.05284 (2023)

[7] G. Eysenbach, The role of ChatGPT, generative language models, and artificial intelligence in medical education: A conversation with ChatGPT and a call for papers, JMIR Med. Educ. 9, e46885 (2023)

[8] Y. Djenouri, A. Belhadi, G. Srivastava, and J. C. W. Lin, Hybrid graph convolution neural network and branch-and-bound optimization for traffic flow forecasting, Future Gener. Comput. Syst. 139, 100 (2023)

[9] H. Wang, T. Fu, Y. Du, W. Gao, K. Huang, . Scientific discovery in the age of artificial intelligence, Nature 620(7972), 47 (2023)

[10] B. A. Olshausen and D. J. Field, Emergence of simple-cell receptive field properties by learning a sparse code for natural images, Nature 381(6583), 607 (1996)

[11] C. V. Theodoris, L. Xiao, A. Chopra, M. D. Chaffin, Z. R. Al Sayed, M. C. Hill, H. Mantineo, E. M. Brydon, Z. Zeng, X. S. Liu, and P. T. Ellinor, Transfer learning enables predictions in network biology, Nature 618(7965), 616 (2023)

[12] A. Suwardi, F. Wang, K. Xue, M. Y. Han, P. Teo, P. Wang, S. Wang, Y. Liu, E. Ye, Z. Li, and X. J. Loh, Machine learning-driven biomaterials evolution, Adv. Mater. 34(1), 2102703 (2022)

[13] J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, . Highly accurate protein structure prediction with AlphaFold, Nature 596(7873), 583 (2021)

[14] E. A. Huerta,Z. Zhao, Advances in machine and deep learning for modeling and real-time detection of multi-messenger sources, in: Handbook of Gravitational Wave Astronomy, edited by C. Bambi, S. Katsanevas, and K. D. Kokkotas, Springer, Singapore, 2021, pp 1793–1820

[15] S. Lucci,S. M. Musa,D. Kopec, Artificial Intelligence in the 21st Century, 3rd Ed., Mercury Learning and Information, Duxbury, 2022

[16] B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, . Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116(6), 061102 (2016)

[17] B. P. Abbott, et al. (LIGO Scientific Collaboration, and Virgo Collaboration), . Tests of general relativity with GW150914, Phys. Rev. Lett. 116(22), 221101 (2016)

[18] B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, . GW150914: The advanced LIGO detectors in the era of first discoveries, Phys. Rev. Lett. 116(13), 131103 (2016)

[19] G. González, A. Viceré, and L. Wen, Gravitational wave astronomy, Front. Phys. (Beijing) 8(6), 771 (2013)

[20] J. Aasi, B. P. Abbott, R. Abbott, T. Abbott, M. R. Abernathy, . Advanced LIGO, Class. Quantum Gravity 32(7), 074001 (2015)

[21] F. Acernese, M. Agathos, K. Agatsuma, D. Aisa, and N. Allemandou, . Advanced Virgo: A second-generation interferometric gravitational wave detector, Class. Quantum Gravity 32(2), 024001 (2015)

[22] T. Akutsu, M. Ando, K. Arai, Y. Arai, S. Araki, . KAGRA: 2.5 generation interferometric gravitational wave detector, Nat. Astron. 3(1), 35 (2019)

[23] D. V. Martynov, E. D. Hall, B. P. Abbott, R. Abbott, T. D. Abbott, . The sensitivity of the advanced LIGO detectors at the beginning of gravitational wave astronomy, Phys. Rev. D 93(11), 112004 (2016)

[24] D. Davis,B. Hughey,T. Massinger,L. Nuttall,A. Stuver, ., Data quality vetoes applied to the analysis of LIGO data from the third observing run, Tech. Rep. LIGO-T2100045-v2, LIGO, 2021

[25] K. Mogushi, Reduction of transient noise artifacts in gravitational-wave data using deep learning, Tech. Rep. LIGO-P2100159, LIGO, 2021, arXiv: 2105.10522

[26] F. Matichard, B. Lantz, R. Mittleman, K. Mason, J. Kissel, . Seismic isolation of advanced LIGO: Review of strategy, instrumentation and performance, Class. Quantum Gravity 32(18), 185003 (2015)

[27] P. Amaro-Seoane,H. Audley,S. Babak, J. Baker,E. Barausse, ., Laser interferometer space antenna, arXiv: 1702.00786 (2017)

[28] W. R. Hu and Y. L. Wu, The Taiji Program in Space for gravitational wave physics and the nature of gravity, Natl. Sci. Rev. 4(5), 685 (2017)

[29] Z. Ren, T. Zhao, Z. Cao, Z. K. Guo, W. B. Han, H. B. Jin, and Y. L. Wu, Taiji data challenge for exploring gravitational wave universe, Front. Phys. (Beijing) 18(6), 64302 (2023)

[30] J. Luo, L. S. Chen, H. Z. Duan, Y. G. Gong, S. Hu, J. Ji, Q. Liu, J. Mei, V. Milyukov, M. Sazhin, C. G. Shao, V. T. Toth, H. B. Tu, Y. Wang, Y. Wang, H. C. Yeh, M. S. Zhan, Y. Zhang, V. Zharov, and Z. B. Zhou, TianQin: A space-borne gravitational wave detector, Class. Quantum Gravity 33(3), 035010 (2016)

[31] T. Zhao,Z. Cao,C. Y. Lin,H. J. Yo, Numerical relativity for gravitational wave source modelling, in: Handbook of Gravitational Wave Astronomy, edited by C. Bambi, S. Katsanevas, and K. D. Kokkotas, Springer Singapore, Singapore, 2020, pp 1347–1376

[32] L. S. Finn, Detection, measurement, and gravitational radiation, Phys. Rev. D 46(12), 5236 (1992)

[33] N. Karnesis,M. Lilley,A. Petiteau, Assessing the detectability of a stochastic gravitational wave background with LISA, using an excess of power approach, Class. Quantum Grav. 37, 215017 (2020), arXiv: 1906.09027

[34] E. Poisson and C. M. Will, Gravitational waves from inspiraling compact binaries: Parameter estimation using second-post-Newtonian waveforms, Phys. Rev. D 52(2), 848 (1995)

[35] M. D. Caballero-Garcia, Astrophysical transients in time domain and multi-messenger astronomy: A review, arXiv: 2409.15554 (2024)

[36] R. Essick, P. Godwin, C. Hanna, L. Blackburn, and E. Katsavounidis, iDQ: Statistical inference of nongaussian noise with auxiliary degrees of freedom in gravitational-wave detectors, Mach. Learn. Sci. Technol. 2(1), 015004 (2020)

[37] P. Jaranowski and A. Królak, Gravitational-wave data analysis. Formalism and sample applications: The Gaussian case, Living Rev. Relativ. 15(1), 4 (2012)

[38] B. Zackay, T. Venumadhav, J. Roulet, L. Dai, and M. Zaldarriaga, Detecting gravitational waves in data with non-stationary and non-Gaussian noise, Phys. Rev. D 104(6), 063034 (2021)

[39] A. Bohé, L. Shao, A. Taracchini, A. Buonanno, S. Babak, I. W. Harry, I. Hinder, S. Ossokine, M. Pürrer, V. Raymond, T. Chu, H. Fong, P. Kumar, H. P. Pfeiffer, M. Boyle, D. A. Hemberger, L. E. Kidder, G. Lovelace, M. A. Scheel, and B. Szilágyi, Improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors, Phys. Rev. D 95(4), 044028 (2017)

[40] V. Varma, S. E. Field, M. A. Scheel, J. Blackman, L. E. Kidder, and H. P. Pfeiffer, Surrogate model of hybridized numerical relativity binary black hole waveforms, Phys. Rev. D 99(6), 064045 (2019)

[41] G. Ashton, M. Hübner, P. D. Lasky, C. Talbot, K. Ackley, S. Biscoveanu, Q. Chu, A. Divakarla, P. J. Easter, B. Goncharov, F. H. Vivanco, J. Harms, M. E. Lower, G. D. Meadors, D. Melchor, E. Payne, M. D. Pitkin, J. Powell, N. Sarin, R. J. E. Smith, and E. Thrane, Bilby: A user-friendly Bayesian inference library for gravitational-wave astronomy, Astrophys. J. Suppl. Ser. 241(2), 27 (2019)

[42] M. Dax, S. R. Green, J. Gair, J. H. Macke, A. Buonanno, and B. Schölkopf, Real-time gravitational wave science with neural posterior estimation, Phys. Rev. Lett. 127(24), 241103 (2021)

[43] P. B. Covas, A. Effler, E. Goetz, P. M. Meyers, A. Neunzert, . Identification and mitigation of narrow spectral artifacts that degrade searches for persistent gravitational waves in the first two observing runs of advanced LIGO, Phys. Rev. D 97(8), 082002 (2018)

[44] E. Cuoco,A. Iess,F. Morawski,M. Razzano, Machine learning for the characterization of gravitational wave data, in: Handbook of Gravitational Wave Astronomy, edited by C. Bambi, S. Katsanevas, and K. D. Kokkotas, Springer Singapore, Singapore, 2020, pp 1769–1792

[45] V. Benedetto, F. Gissi, G. Ciaparrone, and L. Troiano, AI in gravitational wave analysis, an overview, Appl. Sci. (Basel) 13(17), 9886 (2023)

[46] E. A. Huerta, A. Khan, X. Huang, M. Tian, M. Levental, R. Chard, W. Wei, M. Heflin, D. S. Katz, V. Kindratenko, D. Mu, B. Blaiszik, and I. Foster, Accelerated, scalable and reproducible AI-driven gravitational wave detection, Nat. Astron. 5(10), 1062 (2021)

[47] C. Ma, W. Wang, H. Wang, and Z. Cao, Ensemble of deep convolutional neural networks for real-time gravitational wave signal recognition, Phys. Rev. D 105(8), 083013 (2022)

[48] J. McGinn, C. Messenger, M. J. Williams, and I. S. Heng, Generalised gravitational wave burst generation with generative adversarial networks, Class. Quantum Gravity 38(15), 155005 (2021)

[49] E. Cuoco,M. Cavaglià,I. S. Heng, D. Keitel,C. Messenger, Applications of machine learning in gravitational wave research with current interferometric detectors, arXiv: 2412.15046 (2024)

[50] C. H. Liao and F. L. Lin, Deep generative models of gravitational waveforms via conditional autoencoder, Phys. Rev. D 103(12), 124051 (2021)

[51] A. Khan, E. A. Huerta, and H. Zheng, Interpretable AI forecasting for numerical relativity waveforms of quasicircular, spinning, nonprecessing binary black hole mergers, Phys. Rev. D 105(2), 024024 (2022)

[52] R. Shi,Y. Zhou,T. Zhao,Z. Cao,Z. Ren, Compact binary systems waveform generation with generative pre-trained transformer, arXiv: 2310.20172 (2023)

[53] V. Varma, D. Gerosa, L. C. Stein, F. Hébert, and H. Zhang, High-accuracy mass, spin, and recoil predictions of generic black-hole merger remnants, Phys. Rev. Lett. 122(1), 011101 (2019)

[54] V. Varma, S. E. Field, M. A. Scheel, J. Blackman, D. Gerosa, L. C. Stein, L. E. Kidder, and H. P. Pfeiffer, Surrogate models for precessing binary black hole simulations with unequal masses, Phys. Rev. Res. 1(3), 033015 (2019)

[55] T. Islam, S. E. Field, S. A. Hughes, G. Khanna, V. Varma, M. Giesler, M. A. Scheel, L. E. Kidder, and H. P. Pfeiffer, Surrogate model for gravitational wave signals from nonspinning, comparable-to large mass-ratio black hole binaries built on black hole perturbation theory waveforms calibrated to numerical relativity, Phys. Rev. D 106(10), 104025 (2022)

[56] P. Godwin, Low-Latency Statistical Data Quality in the Era of Multi-Messenger Astronomy, Ph.D. Thesis, The Pennsylvania State University, University Park, PA, USA, 2020

[57] M. Zevin, S. Coughlin, S. Bahaadini, E. Besler, N. Rohani, S. Allen, M. Cabero, K. Crowston, A. K. Katsaggelos, S. L. Larson, T. K. Lee, C. Lintott, T. B. Littenberg, A. Lundgren, C. Østerlund, J. R. Smith, L. Trouille, and V. Kalogera, Gravity Spy: Integrating advanced LIGO detector characterization, machine learning, and citizen science, Class. Quantum Gravity 34(6), 064003 (2017)

[58] L. Vazsonyi and D. Davis, Identifying glitches near gravitational-wave signals from compact binary coalescences using the Q-transform, Class. Quantum Gravity 40(3), 035008 (2023)

[59] M. Razzano and E. Cuoco, Image-based deep learning for classification of noise transients in gravitational wave detectors, Class. Quantum Gravity 35(9), 095016 (2018)

[60] W. Wei and E. A. Huerta, Gravitational wave denoising of binary black hole mergers with deep learning, Phys. Lett. B 800, 135081 (2020)

[61] H. Wang, Y. Zhou, Z. Cao, Z. Guo, and Z. Ren, WaveFormer: Transformer-based denoising method for gravitational-wave data, Mach. Learn. Sci. Technol. 5(1), 015046 (2024)

[62] T. Zhao, R. Lyu, H. Wang, Z. Cao, and Z. Ren, Space-based gravitational wave signal detection and extraction with deep neural network, Commun. Phys. 6(1), 212 (2023)

[63] D. George and E. A. Huerta, Deep learning for real-time gravitational wave detection and parameter estimation: Results with advanced LIGO data, Phys. Lett. B 778, 64 (2018)

[64] D. George and E. A. Huerta, Deep neural networks to enable real-time multimessenger astrophysics, Phys. Rev. D 97(4), 044039 (2018)

[65] H. Gabbard, M. Williams, F. Hayes, and C. Messenger, Matching matched filtering with deep networks in gravitational-wave astronomy, Phys. Rev. Lett. 120(14), 141103 (2018)

[66] H. Wang, Z. Cao, X. Liu, S. Wu, and J. Y. Zhu, Gravitational wave signal recognition of O1 data by deep learning, Phys. Rev. D 101(10), 104003 (2020)

[67] W. H. Ruan, H. Wang, C. Liu, and Z. K. Guo, Rapid search for massive black hole binary coalescences using deep learning, Phys. Lett. B 841, 137904 (2023)

[68] X. T. Zhang, C. Messenger, N. Korsakova, M. L. Chan, Y. M. Hu, and J. Zhang, Detecting gravitational waves from extreme mass ratio inspirals using convolutional neural networks, Phys. Rev. D 105(12), 123027 (2022)

[69] T. Zhao,Y. Zhou,R. Shi,Z. Cao,Z. Ren, DECODE: Dilated convolutional neural network for detecting extreme-mass-ratio inspirals, arXiv: 2308.16422 (2023)

[70] Q. Yun,W.B. Han,Y.Y. Guo,H. Wang,M. Du, Detecting extreme-mass-ratio inspirals for space-borne detectors with deep learning, arXiv: 2309.06694 (2023)

[71] C. Dreissigacker, R. Sharma, C. Messenger, R. Zhao, and R. Prix, Deep-learning continuous gravitational waves, Phys. Rev. D 100(4), 044009 (2019)

[72] C. Dreissigacker and R. Prix, Deep-learning continuous gravitational waves: Multiple detectors and realistic noise, Phys. Rev. D 102(2), 022005 (2020)

[73] B. Beheshtipour and M. A. Papa, Deep learning for clustering of continuous gravitational wave candidates, Phys. Rev. D 101(6), 064009 (2020)

[74] B. Beheshtipour and M. A. Papa, Deep learning for clustering of continuous gravitational wave candidates. II. Identification of low-SNR candidates, Phys. Rev. D 103(6), 064027 (2021)

[75] M. Falxa, S. Babak, and M. Le Jeune, Adaptive kernel density estimation proposal in gravitational wave data analysis, Phys. Rev. D 107(2), 022008 (2023)

[76] A. Khan, E. A. Huerta, and A. Das, Physics-inspired deep learning to characterize the signal manifold of quasicircular, spinning, non-precessing binary black hole mergers, Phys. Lett. B 808, 135628 (2020)

[77] P. G. Krastev, K. Gill, V. A. Villar, and E. Berger, Detection and parameter estimation of gravitational waves from binary neutron-star mergers in real LIGO data using deep learning, Phys. Lett. B 815, 136161 (2021)

[78] M. Dax,S. R. Green,J. Gair,M. Deistler,B. Schökopf, ., Group equivariant neural posterior estimation, in International Conference on Learning Representations (ICLR), OpenReview.net, Virtual, 2022

[79] M. Dax, S. R. Green, J. Gair, M. Pürrer, J. Wildberger, J. H. Macke, A. Buonanno, and B. Schölkopf, Neural importance sampling for rapid and reliable gravitational-wave inference, Phys. Rev. Lett. 130(17), 171403 (2023)

[80] I. Liodis,E. Smirniotis,N. Stergioulas, A neuralnetwork-based surrogate model for the properties of neutron stars in 4D Einstein-Gauss-Bonnet gravity, arXiv: 2309.03991 (2023)

[81] S. Bhagwat and C. Pacilio, Merger-ringdown consistency: A new test of strong gravity using deep learning, Phys. Rev. D 104(2), 024030 (2021)

[82] F. Stachurski,C. Messenger,M. Hendry, Cosmological inference using gravitational waves and normalising flows, arXiv: 2310.13405 (2023)

[83] Y. Fujimoto, K. Fukushima, and K. Murase, Mapping neutron star data to the equation of state using the deep neural network, Phys. Rev. D 101(5), 054016 (2020)

[84] F. Morawski and M. Bejger, Neural network reconstruction of the dense matter equation of state derived from the parameters of neutron stars, Astron. Astrophys. 642, A78 (2020)

[85] M. C. Edwards, Classifying the equation of state from rotating core collapse gravitational waves with deep learning, Phys. Rev. D 103(2), 024025 (2021)

[86] A. Krizhevsky,I. Sutskever,G. E. Hinton, ImageNet classification with deep convolutional neural networks, in: Advances in Neural Information Processing Systems (NeurIPS), Vol. 25, edited by F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger, Curran Associates, Inc., Lake Tahoe, NV, USA, 2012

[87] K. Simonyan,A. Zisserman, Very deep convolutional networks for large-scale image recognition, in: 3rd International Conference on Learning Representations (ICLR), edited by Y. Bengio and Y. LeCun, Computational and Biological Learning Society, San Diego, CA, USA, 2015, pp 1–14, arXiv: 1409.1556

[88] K. He,X. Zhang,S. Ren,J. Sun, Deep Residual Learning for Image Recognition, in: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), IEEE, Las Vegas, NV, USA, 2016, pp 770–778

[89] K. Cho,B. van Merrienboer,Ç. Gülçehre,D. Bahdanau,F. Bougares, ., Learning phrase representations using RNN encoder-decoder for statistical machine translation, in: Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), edited by A. Moschitti, B. Pang, and W. Daelemans, ACL, Doha, Qatar, 2014, pp 1724–1734

[90] A. van den Oord,S. Dieleman,H. Zen, K. Simonyan,O. Vinyals, ., WaveNet: A generative model for raw audio, in: Proc. 9th ISCA Workshop on Speech Synthesis Workshop (SSW 9), ISCA, Sunnyvale, CA, USA, 2016, p. 125, arXiv: 1609.03499

[91] G. E. Hinton and R. R. Salakhutdinov, Reducing the dimensionality of data with neural networks, Science 313(5786), 504 (2006)

[92] D. Ganguli,D. Hernandez,L. Lovitt,A. Askell,Y. Bai, ., Predictability and Surprise in Large Generative Models, in: 2022 ACM Conference on Fairness, Accountability, and Transparency, ACM, Seoul, Republic of Korea, 2022, pp 1747–1764

[93] I. Goodfellow,J. Pouget-Abadie,M. Mirza,B. Xu,D. Warde-Farley, ., Generative adversarial nets, in: Advances in Neural Information Processing Systems (NeurIPS), Vol. 27, edited by Z. Ghahramani, M.Welling, C. Cortes, N. Lawrence, and K. Weinberger, Curran Associates, Inc., Montreal, Canada, 2014

[94] C. Bowles,L. Chen,R. Guerrero,P. Bentley,R. N. Gunn, ., GAN augmentation: Augmenting training data using generative adversarial networks, arXiv: 1810.10863 (2018)

[95] K. Shmelkov,C. Schmid,K. Alahari, How good is my GAN? In: Proceedings of the European Conference on Computer Vision (ECCV), Springer, Munich, Germany, 2018, pp 213–229

[96] D. P. Kingma,M. Welling, Auto-encoding variational bayes, in: 2nd International Conference on Learning Representations (ICLR), edited by Y. Bengio and Y. LeCun, OpenReview.net, Banff, AB, Canada, 2014

[97] D. Rezende,S. Mohamed, Variational inference with normalizing flows, in: Proceedings of the 32nd International Conference on Machine Learning (ICML), Proceedings of Machine Learning Research, Vol. 37, edited by F. Bach and D. Blei, PMLR, Lille, France, 2015, pp 1530–1538

[98] J. Ho,A. Jain,P. Abbeel, Denoising diffusion probabilistic models, in: Advances in Neural Information Processing Systems (NeurIPS), Vol. 33, edited by H. Larochelle, M. Ranzato, R. Hadsell, M. Balcan, and H. Lin, Curran Associates, Inc., Vancouver, Canada, 2020, pp 6840–6851

[99] Y. Cao,S. Li,Y. Liu,Z. Yan,Y. Dai, ., A comprehensive survey of AI-generated content (AIGC): A history of generative AI from GAN to ChatGPT, arXiv: 2023)

[100] J. Xiang,J. Yang,Y. Deng,X. Tong, GRAM-HD: 3D-consistent image generation at high resolution with generative radiance manifolds, in: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), IEEE, Paris, France, 2023, pp 2195–2205

[101] Y. Gao,Y. Zhou,J. Wang,X. Li,X. Ming, ., High-fidelity and freely controllable talking head video generation, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), IEEE, Vancouver, Canada, 2023, pp 5609–5619

[102] J. Oppenlaender, The creativity of text-to-image generation, in: Proceedings of the 25th International Academic Mindtrek Conference, ACM, Tampere Finland, 2022, pp 192–202

[103] S. Karnouskos, Artificial intelligence in digital media: The era of deepfakes, IEEE Trans. Technol. Soc. 1(3), 138 (2020)

[104] R. M. Geraci,A. I. Apocalyptic, Visions of Heaven in Robotics, Artificial Intelligence, and Virtual Reality, Oxford University Press, Oxford, UK, 2010

[105] A. Vaswani,N. Shazeer,N. Parmar,J. Uszkoreit,L. Jones, ., Attention is all you need, in: Advances in Neural Information Processing Systems (NeurIPS), Vol. 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, et al., Curran Associates, Inc., Long Beach, CA, USA, 2017

[106] K. M. Choromanski,V. Likhosherstov,D. Dohan,X. Song,A. Gane, ., Rethinking attention with performers, in: International Conference on Learning Representations (ICLR), OpenReview.net, Virtual, 2023

[107] A. M. P. Brasoveanu,R. Andonie, Visualizing transformers for NLP: A brief survey, in: 2020 24th International Conference Information Visualisation (IV), IEEE, Melbourne, Australia, 2020, pp 270–279

[108] S. Garg,D. Tsipras,P. Liang,G. Valiant, What can transformers learn in-context? A case study of simple function classes, in: Advances in Neural Information Processing Systems (NeurIPS), edited by A. H. Oh, A. Agarwal, D. Belgrave, and K. Cho, Curran Associates, Inc., Virtual, 2022

[109] T. Dao, FlashAttention-2: Faster attention with better parallelism and work partitioning, arXiv: 2307.08691 (2023)

[110] J. Devlin,M. Chang,K. Lee,K. Toutanova, BERT: pre-training of deep bidirectional transformers for language understanding, in: Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT), edited by J. Burstein, C. Doran, and T. Solorio, Association for Computational Linguistics, Minneapolis, MN, USA, 2019, pp 4171–4186

[111] A. Radford,J. Wu,R. Child,D. Luan,D. Amodei, ., Language models are unsupervised multitask learners, 2019

[112] S. Karita,N. Chen,T. Hayashi,T. Hori,H. Inaguma, ., A Comparative Study on Transformer vs RNN in Speech Applications, in: 2019 IEEE Automatic Speech Recognition and Understanding Workshop (ASRU), 2019, pp 449–456

[113] R. Ramamurthy,P. Ammanabrolu,K. Brantley,J. Hessel,R. Sifa, ., Is reinforcement learning (Not) for natural language processing: Benchmarks, baselines, and building blocks for natural language policy optimization, in: The Eleventh International Conference on Learning Representations (ICLR), OpenReview.net, Virtual, 2022

[114] M. J. Mataric, Reward functions for accelerated learning, in: Machine Learning Proceedings 1994, Elsevier, New Brunswick, NJ, USA, 1994, pp 181–189

[115] S. Griffith,K. Subramanian,J. Scholz,C. L. Isbell,A. L. Thomaz, Policy shaping: Integrating human feedback with reinforcement learning, in: Advances in Neural Information Processing Systems (NeurIPS), Vol. 26, Curran Associates, Inc., Lake Tahoe, NV, USA, 2013

[116] Y. Gu, Y. Cheng, C. L. P. Chen, and X. Wang, Proximal policy optimization with policy feedback, IEEE Trans. Syst. Man Cybern. Syst. 52(7), 4600 (2022)

[117] K. Zhang,Z. Yang,T. Başar, Multi-agent reinforcement learning: A selective overview of theories and algorithms, in: Handbook of Reinforcement Learning and Control, Vol. 325, edited by K. G. Vamvoudakis, Y. Wan, F. L. Lewis, and D. Cansever, Springer International Publishing, Cham, 2021, pp 321–384

[118] F. Christianos,L. Schäer,S. Albrecht, Shared experience actor-critic for multi-agent reinforcement learning, in: Advances in Neural Information Processing Systems, Vol. 33, Curran Associates, Inc., Virtual, 2020, pp 10707–10717

[119] T. T. Nguyen, N. D. Nguyen, and S. Nahavandi, Deep reinforcement learning for multiagent systems: A review of challenges, solutions, and applications, IEEE Trans. Cybern. 50(9), 3826 (2020)

[120] C. M. Chan,W. Chen,Y. Su,J. Yu,W. Xue, ., ChatEval: Towards better LLM-based evaluators through multi-agent debate, arXiv: 2308.07201 (2023)

[121] Q. Wu,G. Bansal,J. Zhang,Y. Wu,B. Li, ., Auto-Gen: Enabling next-gen LLM applications via multi-agent conversation, arXiv: 2308.08155 (2023)

[122] Y. Talebirad,A. Nadiri, Harnessing the power of intelligent LLM agents, arXiv: 2306.03314 (2023)

[123] F. Pretorius, Evolution of binary black-hole spacetimes, Phys. Rev. Lett. 95(12), 121101 (2005)

[124] M. Shibata,K. Uryū, Simulation of merging binary neutron stars in full general relativity: Γ=2 case, Phys. Rev. D 61, 064001 (2000), arXiv: gr-qc/9911058

[125] J. G. Baker, J. Centrella, D. I. Choi, M. Koppitz, and J. Van Meter, Gravitational-wave extraction from an inspiraling configuration of merging black holes, Phys. Rev. Lett. 96(11), 111102 (2006)

[126] M. Campanelli, C. O. Lousto, P. Marronetti, and Y. Zlochower, Accurate evolutions of orbiting black-hole binaries without excision, Phys. Rev. Lett. 96(11), 111101 (2006)

[127] M. Pürrer and C. J. Haster, Gravitational waveform accuracy requirements for future ground-based detectors, Phys. Rev. Res. 2(2), 023151 (2020)

[128] E. A. Huerta, C. J. Moore, P. Kumar, D. George, A. J. K. Chua, R. Haas, E. Wessel, D. Johnson, D. Glennon, A. Rebei, A. M. Holgado, J. R. Gair, and H. P. Pfeiffer, Eccentric, nonspinning, inspiral, Gaussianprocess merger approximant for the detection and characterization of eccentric binary black hole mergers, Phys. Rev. D 97(2), 024031 (2018)

[129] S. Khan, S. Husa, M. Hannam, F. Ohme, M. Pürrer, X. J. Forteza, and A. Bohé, Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era, Phys. Rev. D 93(4), 044007 (2016)

[130] G. Pratten, C. García-Quirós, M. Colleoni, A. Ramos-Buades, H. Estellés, M. Mateu-Lucena, R. Jaume, M. Haney, D. Keitel, J. E. Thompson, and S. Husa, Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes, Phys. Rev. D 103(10), 104056 (2021)

[131] H. Yu,J. Roulet,T. Venumadhav,B. Zackay,M. Zaldarriaga, IMRPhenomXODE: An accurate and efficient waveform model for precessing binary black holes, arXiv: 2306.08774 (2023)

[132] W. B. Han and Z. Cao, Constructing effective one-body dynamics with numerical energy flux for intermediate mass-ratio inspirals, Phys. Rev. D 84(4), 044014 (2011)

[133] Z. Cao and W. B. Han, Waveform model for an eccentric binary black hole based on the effective-one-body numerical-relativity formalism, Phys. Rev. D 96(4), 044028 (2017)

[134] D. P. Mihaylov,S. Ossokine,A. Buonanno,H. Estelles,L. Pompili, ., pySEOBNR: A software package for the next generation of effective-one-body multipolar waveform models, arXiv: 2303.18203 (2023)

[135] E. Fons,A. Sztrajman,Y. El-Laham,A. Iosifidis,S. Vyetrenko, HyperTime: Implicit neural representations for time series, in: NeurIPS 2022 Workshop on Synthetic Data for Empowering ML Research, 2022

[136] A. Gamboa,A. Buonanno,R. Enficiaud,M. Khalil,A. Ramos-Buades, ., Accurate waveforms for eccentric, aligned-spin binary black holes: The multipolar effective-one-body model SEOBNRv5EHM, arXiv: 2412.12823 (2024)

[137] S. Khan and R. Green, Gravitational-wave surrogate models powered by artificial neural networks, Phys. Rev. D 103(6), 064015 (2021)

[138] R. Shi, Y. Zhou, T. Zhao, Z. Wang, Z. Ren, and Z. Cao, Rapid eccentric spin-aligned binary black hole waveform generation based on deep learning, Phys. Rev. D 111(4), 044016 (2025)

[139] O. G. Freitas,A. Theodoropoulos,N. Villanueva,T. Fernandes,S. Nunes, ., NRSurNN3dq4: A deep learning powered numerical relativity surrogate for binary black hole waveforms, arXiv: 2412.06946 (2024)

[140] D. Davis and M. Walker, Detector characterization and mitigation of noise in ground-based gravitational-wave interferometers, Galaxies 10(1), 12 (2022)

[141] C. Pankow, K. Chatziioannou, E. A. Chase, T. B. Littenberg, M. Evans, J. McIver, N. J. Cornish, C. J. Haster, J. Kanner, V. Raymond, S. Vitale, and A. Zimmerman, Mitigation of the instrumental noise transient in gravitational-wave data surrounding GW170817, Phys. Rev. D 98(8), 084016 (2018)

[142] S. B. Coughlin, S. Bahaadini, N. Rohani, M. Zevin, O. Patane, M. Harandi, C. Jackson, V. Noroozi, S. Allen, J. Areeda, M. Coughlin, P. Ruiz, C. P. L. Berry, K. Crowston, A. K. Katsaggelos, A. Lundgren, C. Østerlund, J. R. Smith, L. Trouille, and V. Kalogera, Classifying the unknown: Discovering novel gravitational-wave detector glitches using similarity learning, Phys. Rev. D 99(8), 082002 (2019)

[143] A. J. Bekker,J. Goldberger, Training deep neural networks based on unreliable labels, in: 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, Shanghai, China, 2016, pp 2682–2686

[144] J. Glanzer, S. Banagiri, S. B. Coughlin, S. Soni, M. Zevin, C. P. L. Berry, O. Patane, S. Bahaadini, N. Rohani, K. Crowston, V. Kalogera, C. Østerlund, L. Trouille, and A. Katsaggelos, Data quality up to the third observing run of advanced LIGO: Gravity Spy glitch classifications, Class. Quantum Gravity 40(6), 065004 (2023)

[145] R. Biswas, L. Blackburn, J. Cao, R. Essick, K. A. Hodge, E. Katsavounidis, K. Kim, Y.M. Kim, E.O. Le Bigot, C.H. Lee, J. J. Oh, S. H. Oh, E. J. Son, Y. Tao, R. Vaulin, and X. Wang, Application of machine learning algorithms to the study of noise artifacts in gravitational-wave data, Phys. Rev. D 88(6), 062003 (2013)

[146] T. S. Fernandes,S. J. Vieira,A. Onofre,J. C. Bustillo,A. Torres-Forné, ., Convolutional neural networks for the classification of glitches in gravitational-wave data streams, arXiv: 2303.13917 (2023)

[147] J. D. Merritt, B. Farr, R. Hur, B. Edelman, and Z. Doctor, Transient glitch mitigation in advanced LIGO data, Phys. Rev. D 104(10), 102004 (2021)

[148] A. H. Nitz, Distinguishing short duration noise transients in LIGO data to improve the PyCBC search for gravitational waves from high mass binary black hole mergers, Class. Quantum Gravity 35(3), 035016 (2018)

[149] M. Razzano,F. Di Renzo,F. Fidecaro,G. Hemming,S. Katsanevas, GWitchHunters: Machine learning and citizen science to improve the performance of gravitational wave detector, Nucl. Instrum. Methods Phys. Res. A 1048, 167959 (2023), arXiv: 2301.05112

[150] S. Mukherjee, R. Obaid, and B. Matkarimov, Classification of glitch waveforms in gravitational wave detector characterization, J. Phys. Conf. Ser. 243, 012006 (2010)

[151] N. Mukund, S. Abraham, S. Kandhasamy, S. Mitra, and N. S. Philip, Transient classification in LIGO data using difference boosting neural network, Phys. Rev. D 95(10), 104059 (2017)

[152] J. Powell, D. Trifiro, E. Cuoco, I. S. Heng, and M. Cavaglia, Classification methods for noise transients in advanced gravitational-wave detectors, Class. Quantum Gravity 32(21), 215012 (2015)

[153] J. Powell, A. Torres-Forné, R. Lynch, D. Trifirò, E. Cuoco, M. Cavaglià, I. S. Heng, and J. A. Font, Classification methods for noise transients in advanced gravitational-wave detectors II: Performance tests on advanced LIGO data, Class. Quantum Gravity 34(3), 034002 (2017)

[154] J. Powell, L. Sun, K. Gereb, P. D. Lasky, and M. Dollmann, Generating transient noise artifacts in gravitational-wave detector data with generative adversarial networks, Class. Quantum Gravity 40(3), 035006 (2023)

[155] S. Bahaadini, V. Noroozi, N. Rohani, S. Coughlin, M. Zevin, J. R. Smith, V. Kalogera, and A. Katsaggelos, Machine learning for Gravity Spy: Glitch classification and dataset, Inf. Sci. 444, 172 (2018)

[156] S. Soni, C. P. L. Berry, S. B. Coughlin, M. Harandi, C. B. Jackson, K. Crowston, C. Østerlund, O. Patane, A. K. Katsaggelos, L. Trouille, V.G. Baranowski, W. F. Domainko, K. Kaminski, M. A. L. Rodriguez, U. Marciniak, P. Nauta, G. Niklasch, R. R. Rote, B. Téglás, C. Unsworth, and C. Zhang, Discovering features in gravitational wave data through detector characterization, citizen science and machine learning, Class. Quantum Gravity 38(19), 195016 (2021)

[157] Y. Sakai, Y. Itoh, P. Jung, K. Kokeyama, C. Kozakai, K. T. Nakahira, S. Oshino, Y. Shikano, H. Takahashi, T. Uchiyama, G. Ueshima, T. Washimi, T. Yamamoto, and T. Yokozawa, Unsupervised learning architecture for classifying the transient noise of interferometric gravitational-wave detectors, Sci. Rep. 12(1), 9935 (2022)

[158] D. George, H. Shen, and E. A. Huerta, Classification and unsupervised clustering of LIGO data with deep transfer learning, Phys. Rev. D 97(10), 101501 (2018)

[159] G. Vajente, Y. Huang, M. Isi, J. C. Driggers, J. S. Kissel, M. J. Szczepańczyk, and S. Vitale, Machine-learning non-stationary noise out of gravitational wave detectors, Phys. Rev. D 101(4), 042003 (2020)

[160] A. Torres-Forné, E. Cuoco, A. Marquina, J. A. Font, and J. M. Ibáñez, Total-variation methods for gravitational-wave denoising: Performance tests on advanced LIGO data, Phys. Rev. D 98(8), 084013 (2018)

[161] N. J. Cornish and T. B. Littenberg, BayesWave: Bayesian inference for gravitational wave bursts and instrument glitches, Class. Quantum Gravity 32(13), 135012 (2015)

[162] S. Klimenko, I. Yakushin, A. Mercer, and G. Mitselmakher, Coherent method for detection of gravitational wave bursts, Class. Quantum Gravity 25(11), 114029 (2008)

[163] A. Akhshi, H. Alimohammadi, S. Baghram, S. Rahvar, M. R. R. Tabar, and H. Arfaei, A template-free approach for waveform extraction of gravitational wave events, Sci. Rep. 11(1), 20507 (2021)

[164] A. Torres, A. Marquina, J. A. Font, and J. M. Ibáñez, Total-variation-based methods for gravitational wave denoising, Phys. Rev. D 90(8), 084029 (2014)

[165] N. J. Cornish, T. B. Littenberg, B. Bécsy, K. Chatziioannou, J. A. Clark, S. Ghonge, and M. Millhouse, BayesWave analysis pipeline in the era of gravitational wave observations, Phys. Rev. D 103(4), 044006 (2021)

[166] S. Klimenko, G. Vedovato, M. Drago, F. Salemi, V. Tiwari, G. A. Prodi, C. Lazzaro, K. Ackley, S. Tiwari, C. F. Da Silva, and G. Mitselmakher, Method for detection and reconstruction of gravitational wave transients with networks of advanced detectors, Phys. Rev. D 93(4), 042004 (2016)

[167] B. P. Abbott, R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, . A guide to LIGO–Virgo detector noise and extraction of transient gravitational-wave signals, Class. Quantum Gravity 37(5), 055002 (2020)

[168] A. Torres-Forné, A. Marquina, J. A. Font, and J. M. Ibáñez, Denoising of gravitational wave signals via dictionary learning algorithms, Phys. Rev. D 94(12), 124040 (2016)

[169] W. Wei and E. A. Huerta, Gravitational wave denoising of binary black hole mergers with deep learning, Phys. Lett. B 800, 135081 (2020)

[170] H. Shen,D. George,E. A. Huerta,Z. Zhao, Denoising gravitational waves with enhanced deep recurrent denoising auto-encoders, in: 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, Brighton, UK, 2019, pp 3237–3241, arXiv: 1711.09919

[171] C. Chatterjee, L. Wen, F. Diakogiannis, and K. Vinsen, Extraction of binary black hole gravitational wave signals from detector data using deep learning, Phys. Rev. D 104(6), 064046 (2021)

[172] M. Q. Jiang, N. Yang, and J. Li, Identify real gravitational wave events in the LIGO-Virgo catalog GWTC-1 and GWTC-2 with convolutional neural network, Front. Phys. (Beijing) 17(5), 54501 (2022)

[173] X. Li, W. Yu, X. Fan, and G. J. Babu, Some optimizations on detecting gravitational wave using convolutional neural network, Front. Phys. (Beijing) 15(5), 54501 (2020)

[174] H. M. Luo, W. Lin, Z. C. Chen, and Q. G. Huang, Extraction of gravitational wave signals with optimized convolutional neural network, Front. Phys. (Beijing) 15(1), 14601 (2020)

[175] H. Xia, L. Shao, J. Zhao, and Z. Cao, Improved deep learning techniques in gravitational-wave data analysis, Phys. Rev. D 103(2), 024040 (2021)

[176] P. G. Krastev, Real-time detection of gravitational waves from binary neutron stars using artificial neural networks, Phys. Lett. B 803, 135330 (2020)

[177] W. Wei, A. Khan, E. Huerta, X. Huang, and M. Tian, Deep learning ensemble for real-time gravitational wave detection of spinning binary black hole mergers, Phys. Lett. B 812, 136029 (2021)

[178] V. Skliris,M. R. K. Norman,P. J. Sutton, Real-time detection of unmodelled gravitational-wave transients using convolutional neural networks, arXiv: 2009.14611 (2021)

[179] V. Skliris, Machine Learning to Extract Gravitational Wave Transients, Ph.D. Thesis, Cardiff University, Cardiff, UK, 2021

[180] L. Speri, N. Karnesis, A. I. Renzini, and J. R. Gair, A roadmap of gravitational wave data analysis, Nat. Astron. 6(12), 1356 (2022)

[181] M. Maggiore, C. V. D. Broeck, N. Bartolo, E. Belgacem, D. Bertacca, . Science case for the Einstein telescope, J. Cosmol. Astropart. Phys. 2020, 050 (2020)

[182] W. Alhassan, T. Bulik, and M. Suchenek, Detection of Einstein Telescope gravitational wave signals from binary black holes using deep learning, Mon. Not. R. Astron. Soc. 519(3), 3843 (2023)

[183] Y. Zhang, H. Xu, M. Liu, C. Liu, Y. Zhao, and J. Zhu, Deep learning model based on a bidirectional gated recurrent unit for the detection of gravitational wave signals, Phys. Rev. D 106(12), 122002 (2022)

[184] M. Tian,E. A. Huerta,H. Zheng, Physics-inspired spatiotemporal-graph AI ensemble for gravitational wave detection, arXiv: 2306.15728 (2023)

[185] M. B. Schäfer and A. H. Nitz, From one to many: A deep learning coincident gravitational-wave search, Phys. Rev. D 105(4), 043003 (2022)

[186] Z. Pan and H. Yang, Formation rate of extreme mass ratio inspirals in active galactic nuclei, Phys. Rev. D 103(10), 103018 (2021)

[187] S. Babak, J. Gair, A. Sesana, E. Barausse, C. F. Sopuerta, C. P. L. Berry, E. Berti, P. Amaro-Seoane, A. Petiteau, and A. Klein, Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals, Phys. Rev. D 95(10), 103012 (2017)

[188] J. R. Gair, S. Babak, A. Sesana, P. Amaro-Seoane, E. Barausse, C. P. L. Berry, E. Berti, and C. Sopuerta, Prospects for observing extreme-massratio inspirals with LISA, J. Phys. Conf. Ser. 840, 012021 (2017)

[189] T. Zhao, Y. Zhou, R. Shi, Z. Cao, and Z. Ren, Dilated convolutional neural network for detecting extreme-mass ratio inspirals, Phys. Rev. D 109(8), 084054 (2024)

[190] T. B. Littenberg, N. J. Cornish, K. Lackeos, and T. Robson, Global analysis of the gravitational wave signal from Galactic binaries, Phys. Rev. D 101(12), 123021 (2020)

[191] T. B. Littenberg, Detection pipeline for Galactic binaries in LISA data, Phys. Rev. D 84(6), 063009 (2011)

[192] C. Dreiβigacker, Searches for Continuous Gravitational Waves: Sensitivity Estimation and Deep Learning as a Novel Search Method, Ph.D. Thesis, Leibniz Universität Hannover, Hannover, Germany, 2020

[193] J. Bayley, C. Messenger, and G. Woan, Robust machine learning algorithm to search for continuous gravitational waves, Phys. Rev. D 102(8), 083024 (2020)

[194] T. S. Yamamoto and T. Tanaka, Use of an excess power method and a convolutional neural network in an all-sky search for continuous gravitational waves, Phys. Rev. D 103(8), 084049 (2021)

[195] P. M. Joshi and R. Prix, Large-kernel convolutional neural networks for wide parameter-space searches of continuous gravitational waves, Phys. Rev. D 110(12), 124071 (2024)

[196] R. Tenorio,J. R. Mérou,A. M. Sintes, A one-stop strategy to search for long-duration gravitational-wave signals, arXiv: 2411.18370 (2024)

[197] S. H. Strub, L. Ferraioli, C. Schmelzbach, S. C. Stähler, and D. Giardini, Bayesian parameter estimation of Galactic binaries in LISA data with Gaussian process regression, Phys. Rev. D 106(6), 062003 (2022)

[198] S. H. Strub, L. Ferraioli, C. Schmelzbach, S. C. Stähler, and D. Giardini, Global analysis of LISA data with Galactic binaries and massive black hole binaries, Phys. Rev. D 110(2), 024005 (2024)

[199] N. Christensen and R. Meyer, Markov chain Monte Carlo methods for Bayesian gravitational radiation data analysis, Phys. Rev. D Part. Fields 58(8), 082001 (1998)

[200] J. S. Speagle, A conceptual introduction to Markov chain Monte Carlo methods, arXiv: 1909.12313 (2019)

[201] S. Chib and E. Greenberg, Understanding the Metropolis–Hastings algorithm, Am. Stat. 49(4), 327 (1995)

[202] J. Lee, W. Sung, and J. H. Choi, Metamodel for efficient estimation of capacity-fade uncertainty in Li-ion batteries for electric vehicles, Energies 8(6), 5538 (2015)

[203] T. B. Littenberg and N. J. Cornish, Prototype global analysis of LISA data with multiple source types, Phys. Rev. D 107(6), 063004 (2023)

[204] M. Dax,J. Wildberger,S. Buchholz,S. R. Green,J. H. Macke, ., Flow matching for scalable simulation-based inference, arXiv: 2305.17161 (2023)

[205] S. Sasaoka, Y. Hou, K. Somiya, and H. Takahashi, Localization of gravitational waves using machine learning, Phys. Rev. D 105(10), 103030 (2022)

[206] S. R. Green, C. Simpson, and J. Gair, Gravitational wave parameter estimation with autoregressive neural network flows, Phys. Rev. D 102(10), 104057 (2020)

[207] H. Shen, E. A. Huerta, E. O’Shea, P. Kumar, and Z. Zhao, Statistically-informed deep learning for gravitational wave parameter estimation, Mach. Learn. Sci. Technol. 3(1), 015007 (2022)

[208] S. R. Green and J. Gair, Complete parameter inference for GW150914 using deep learning, Mach. Learn. Sci. Technol. 2(3), 03L (2021)

[209] H. Wang, Z. Cao, Y. Zhou, Z. K. Guo, and Z. Ren, Sampling with prior knowledge for high-dimensional gravitational wave data analysis, Big Data Min. Anal. 5(1), 53 (2022)

[210] J. Wildberger, M. Dax, S. R. Green, J. Gair, M. Pürrer, J. H. Macke, A. Buonanno, and B. Schölkopf, Adapting to noise distribution shifts in flow-based gravitational-wave inference, Phys. Rev. D 107(8), 084046 (2023)

[211] M. J. Williams, J. Veitch, and C. Messenger, Importance nested sampling with normalising flows, Mach. Learn. Sci. Technol. 4(3), 035011 (2023)

[212] M. J. Williams, J. Veitch, and C. Messenger, Nested sampling with normalizing flows for gravitational-wave inference, Phys. Rev. D 103(10), 103006 (2021)

[213] U. Bhardwaj,J. Alvey,B. K. Miller,S. Nissanke,C. Weniger, Peregrine: Sequential simulationbased inference for gravitational wave signals, arXiv: 2304.02035 (2023)

[214] K. W. K. Wong, G. Franciolini, V. De Luca, V. Baibhav, E. Berti, P. Pani, and A. Riotto, Constraining the primordial black hole scenario with Bayesian inference and machine learning: The GWTC-2 gravitational wave catalog, Phys. Rev. D 103(2), 023026 (2021)

[215] K. W. K. Wong,M. Cranmer, Automated discovery of interpretable gravitational-wave population models, in: International Conference on Machine Learning (ICML), PMLR, Baltimore, MD, USA, 2022

[216] K. W. K. Wong,M. Isi,T. D. P. Edwards, Fast gravitational wave parameter estimation without compromises, arXiv: 2302.05333 (2023)

[217] J. Bradbury,R. Frostig,P. Hawkins,M. J. Johnson,C. Leary, ., JAX: Composable transformations of Python+NumPy programs, 2018

[218] H. Gabbard, C. Messenger, I. S. Heng, F. Tonolini, and R. Murray-Smith, Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy, Nat. Phys. 18(1), 112 (2022)

[219] M. Liu,X. D. Li,A. J. K. Chua, Improving the scalability of Gaussian-process error marginalization in gravitational-wave inference, arXiv: 2307.07233 (2023)

[220] F. Nielsen, On the Jensen–Shannon symmetrization of distances relying on abstract means, Entropy (Basel) 21(5), 485 (2019)

[221] J. Langendorff, A. Kolmus, J. Janquart, and C. Van Den Broeck, Normalizing flows as an avenue to studying overlapping gravitational wave signals, Phys. Rev. Lett. 130(17), 171402 (2023)

[222] P. Bull,Y. Akrami,J. Adamek,T. Baker,E. Bellini, ., Beyond ΛCDM: Problems, solutions, and the road ahead, Phys. Dark Universe 12, 56 (2016), arXiv: 1512.05356

[223] L. Bian, R. G. Cai, S. Cao, Z. Cao, H. Gao, Z.K. Guo, K. Lee, D. Li, J. Liu, Y. Lu, S. Pi, J.M. Wang, S.J. Wang, Y. Wang, T. Yang, X.Y. Yang, S. Yu, and X. Zhang, The gravitational-wave physics II: Progress, Sci. China Phys. Mech. Astron. 64(12), 120401 (2021)

[224] K. G. Arun, E. Belgacem, R. Benkel, L. Bernard, E. Berti, . New horizons for fundamental physics with LISA, Living Rev. Relativ. 25(1), 4 (2022)

[225] M. Bailes, B. K. Berger, P. R. Brady, M. Branchesi, K. Danzmann, . Gravitational-wave physics and astronomy in the 2020s and 2030s, Nat. Rev. Phys. 3(5), 344 (2021)

[226] E. Barausse,A. Lapi, Massive black-hole mergers, in: Handbook of Gravitational Wave Astronomy, edited by C. Bambi, S. Katsanevas, and K. D. Kokkotas, Springer Singapore, Singapore, 2020, pp 1–33

[227] W. L. Freedman, Measurements of the Hubble constant: Tensions in perspective, Astrophys. J. 919(1), 16 (2021)

[228] B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, . A gravitational-wave standard siren measurement of the Hubble constant, Nature 551(7678), 85 (2017)

[229] B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, . GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119(16), 161101 (2017)

[230] B. P. Abbott, R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, . GW190425: Observation of a compact binary coalescence with tocM ⊙, Astrophys. J. Lett. 892(1), L3 (2020)

[231] S. Soma, L. Wang, S. Shi, H. Stöcker, and K. Zhou, Reconstructing the neutron star equation of state from observational data via automatic differentiation, Phys. Rev. D 107(8), 083028 (2023)

[232] A. Saiz-Pérez, A. Torres-Forné, and J. A. Font, Classification of core-collapse supernova explosions with learned dictionaries, Mon. Not. R. Astron. Soc. 512(3), 3815 (2022)

[233] M. L. Portilla, I. Di Palma, M. Drago, P. Cerda-Duran, and F. Ricci, Deep learning for core-collapse supernova detection, Phys. Rev. D 103(6), 063011 (2021)

[234] R. Qiu, P. Krastev, K. Gill, and E. Berger, Deep learning detection and classification of gravitational waves from neutron star-black hole mergers, Phys. Lett. B 840, 137850 (2023)

[235] R. Shi, Y. Zhou, T. Zhao, Z. Cao, and Z. Ren, Compact binary systems waveform generation with a generative pretrained transformer, Phys. Rev. D 109(8), 084017 (2024)

[236] A. Blelly, J. Bobin, and H. Moutarde, Sparse data inpainting for the recovery of Galactic-binary gravitational wave signals from gapped data, Mon. Not. R. Astron. Soc. 509(4), 5902 (2021)

[237] E. Cuoco,B. Patricelli,A. Iess,F. Morawski, Multimodal analysis of gravitational wave signals and gamma-ray bursts from binary neutron star mergers, arXiv: 2110.09833 (2021)

[238] Y. Nie,N. H. Nguyen,P. Sinthong,J. Kalagnanam, A time series is worth 64 words: Long-term forecasting with transformers, in: The Eleventh International Conference on Learning Representations (ICLR), Open-Review.net, Virtual, 2022

[239] B. P. Abbott, R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, . Low-latency gravitational-wave alerts for multimessenger astronomy during the second advanced LIGO and Virgo observing run, Astrophys. J. 875(2), 161 (2019)

[240] M. L. Katz, A. J. K. Chua, L. Speri, N. Warburton, and S. A. Hughes, Fast extreme-mass-ratio-inspiral waveforms: New tools for millihertz gravitational-wave data analysis., Phys. Rev. D 104(6), 064047 (2021)

[241] J. Durbin,S. J. Koopman, Time Series Analysis by State Space Methods, 2nd Ed., Oxford Statistical Science Series No. 38, Oxford University Press, Oxford, UK, 2012

[242] A. Gu,K. Goel,C. Re, Efficiently modeling long sequences with structured state spaces, in: International Conference on Learning Representations (ICLR), OpenReview.net, 2022

[243] W. C. Lin, C. F. Tsai, and J. R. Zhong, Deep learning for missing value imputation of continuous data and the effect of data discretization, Knowl. Base. Syst. 239, 108079 (2022)

[244] L. Diener,S. Sootla,S. Branets,A. Saabas,R. Aichner, ., INTERSPEECH 2022 audio deep packet loss concealment challenge, arXiv: 2204.05222 (2022)

[245] Q. Baghi,N. Korsakova, LISA data challenge: Spritz, Tech. Rep., ESA, 2022

[246] Q. Baghi, J. I. Thorpe, J. Slutsky, J. Baker, T. D. Canton, N. Korsakova, and N. Karnesis, Gravitational-wave parameter estimation with gaps in LISA: A Bayesian data augmentation method, Phys. Rev. D 100(2), 022003 (2019)

[247] J. Blackman, B. Szilagyi, C. R. Galley, and M. Tiglio, A sparse representation of gravitational waves from precessing compact binaries, Phys. Rev. Lett. 113(2), 021101 (2014)

[248] A. Blelly, H. Moutarde, and J. Bobin, Sparsity based recovery of galactic binaries gravitational waves, Phys. Rev. D 102(10), 104053 (2020)

[249] T. Emmanuel, T. Maupong, D. Mpoeleng, T. Semong, B. Mphago, and O. Tabona, A survey on missing data in machine learning, J. Big Data 8(1), 140 (2021)

[250] N. Li,X. Zheng,C. Zhang,L. Guo,B. Yu, Endto-end multi-loss training for low delay packet loss concealment, in: Interspeech 2022, ISCA, Brno, Czech Republic, 2022, pp 585–589

[251] L. P. Le,X.H. N. Thi,T. Nguyen,M. A. Riegler,P. Halvorsen, ., Missing data imputation for noisy time-series data and applications in healthcare, arXiv: 2412.11164 (2024)

[252] E. Castelli,Q. Baghi,J. G. Baker, J. Slutsky,J. Bobin, ., Extraction of gravitational wave signals from LISA data in the presence of artifacts, arXiv: 2411.13402 (2024)

[253] G. Rani, M. G. Oza, V. S. Dhaka, N. Pradhan, S. Verma, and J. J. P. C. Rodrigues, Applying deep learning-based multi-modal for detection of coronavirus, Multimedia Syst. 28(4), 1251 (2022)

[254] X. Pei, K. Zuo, Y. Li, and Z. Pang, A review of the application of multi-modal deep learning in medicine: Bibliometrics and future directions, Int. J. Comput. Intell. Syst. 16(1), 44 (2023)

[255] E. Korot, Z. Guan, D. Ferraz, S. K. Wagner, G. Zhang, X. Liu, L. Faes, N. Pontikos, S. G. Finlayson, H. Khalid, G. Moraes, K. Balaskas, A. K. Denniston, and P. A. Keane, Code-free deep learning for multi-modality medical image classification, Nat. Mach. Intell. 3(4), 288 (2021)

[256] S. Zhao, M. Gong, H. Fu, and D. Tao, Adaptive context-aware multi-modal network for depth completion, IEEE Trans. Image Process. 30, 5264 (2021)

[257] P. Mészáros, D. B. Fox, C. Hanna, and K. Murase, Multi-messenger astrophysics, Nat. Rev. Phys. 1(10), 585 (2019)

[258] B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, . Multi-messenger observations of a binary neutron star merger, Astrophys. J. 848, L12 (2017)

[259] C. Hoy, C. R. Weaving, L. K. Nuttall, and I. Harry, A rapid multi-modal parameter estimation technique for LISA, Class. Quantum Gravity 41(24), 245012 (2024)

[260] Z. C. Lipton, The mythos of model interpretability: In machine learning, the concept of interpretability is both important and slippery, ACM Queue 16(3), 31 (2018)

[261] F. Doshi-Velez,B. Kim, Towards a rigorous science of interpretable machine learning, arXiv: 1702.08608 (2017)

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