Sound speed profile prediction using a multi-parameter, single-layer residual LSTM approach

Abstract

Temporal variation errors in ocean sound speed constitute a critical factor affecting underwater navigation and positioning accuracy. However, real-time and large-scale measurement of ocean sound speed remains challenging. Therefore, the inversion of the sound speed profile (SSP) is essential for obtaining ocean sound speed field data at high spatiotemporal resolution. Because the ocean SSP inversion function is relatively complex, neural network-based inversion models demonstrate clear advantages over conventional SSP inversion methods. This study presents a multi-parameter, single-layer residual long short-term memory network (Res-LSTM) for SSP prediction. The proposed model enhances prediction accuracy and generalization capability in complex marine environments. It introduces residual connections within the traditional long short-term memory (LSTM) hidden layer, utilizing skip connections to form identity mappings. This architecture learns residuals between the inputs and outputs while integrating key influencing factors, such as temperature, salinity, and depth. The approach achieves high-precision SSP prediction through these technical innovations. To evaluate the performance of the Res-LSTM model, this study utilizes Copernicus Marine reanalysis data. The proposed model is systematically compared against benchmark methods, including generalized regression neural networks (GRNN), radial basis function networks (RBF), and standard LSTM architectures. Experimental results indicate that at four representative points, the root mean square error (RMSE) of the Res-LSTM decreased by 62.4%, 46.0%, and 32.9% compared with GRNN, RBF, and LSTM, respectively. Furthermore, in tests conducted across different time scales, the RMSE of Res-LSTM consistently remained the lowest. Ablation experiments further indicate that the introduction of residual connections is a key factor in the model’s performance improvement. Therefore, the Res-LSTM is an effective method for predicting SSP and can further improve prediction accuracy and stability.

Keywords

Sound speed profile (SSP) / Residual connection / Long short-term memory (LSTM) / Generalized regression neural networks (GRNN) / Radial basis function (RBF)

References

[1] Bianco M, Gerstoft P. Compressive acoustic sound speed profile estimation. J Acoust Soc Am, 2016, 139(3): EL90-EL94

[2] Bianco M, Gerstoft P. Dictionary learning of sound speed profiles. J Acoust Soc Am, 2017, 141(3): 1749-1758

[3] Bianco M, Gerstoft P, Traer J, Ozanich E, Roch MA, Gannot S, et al.. Machine learning in acoustics: theory and applications. J Acoust Soc Am, 2019, 146(5): 3590-3628

[4] Chen X, Yang S, Wang YF. Application of genetic neural network in PQF rolling process design. J Tianjin Univ Sci Technol, 2012, 27(5): 74-79

[5] Choo Y, Seong W. Compressive sound speed profile inversion using beamforming results. Remote Sens, 2018, 10(5): Article ID: 704

[6] Ge ZX, Sun ZQNeural network theory and MATLAB R2007 implementation, 2007BeijingPublishing House of Electronics Industry

[7] He KM, Zhang XY, Ren SQ, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, pp 770–778. https://doi.org/10.1109/CVPR.2016.90

[8] Hochreiter S, Schmidhuber J. Long short-term memory. Neural Comput, 1997, 9(8): 1735-1780

[9] Hu J, Xiao YW, Zhang DB, Leng LL. Inversion prediction method for sound speed profile. Adv Mar Sci, 2019, 37(2): 245-254

[10] Huang W, Gao F, Wang JT, Xu TH. A review on the construction of underwater sound speed fields. J Harbin Eng Univ, 2023, 44(11): 2005-2017

[11] Li M (2023) Interpretability learning and application of multivariate time series wind speed prediction model. PhD thesis, Lanzhou University, Lanzhou. https://d.wanfangdata.com.cn/thesis/D03411682

[12] Li HC, Li M, Chen X, Mao KF, Wang PH, Liu YH. Fast reconstruction of sound speed profile based on machine learning and empirical orthogonal function method. Oceanologia Limnol Sin, 2025, 56(1): 101-111

[13] Liu YY, Chen W, Chen Y, et al.. Research progress on methods for constructing underwater sound speed profile. Inf Countermeas Technol, 2024, 3(5): 1-18

[14] Liu ZY, Wang ZJ, Wang ZZ. A stepwise construction method for refined sound velocity field. Eng Surv Mapp, 2025, 34(1): 30-38

[15] Mackenzie KV. Nine-term equation for sound speed in the oceans. J Acoust Soc Am, 1981, 70(3): 807-812

[16] Munk W, Wunsch C. Ocean acoustic tomography: a scheme for large-scale monitoring. Deep-Sea Res Part A-Oceanogr Res Pap, 1979, 26(2): 123-161

[17] Sun WC, Bao JY, Jin SH, Xiao FM, Cui Y. Inversion of sound velocity profiles by correcting the terrain distortion. Geomat Inf Sci Wuhan Univ, 2016, 41(3): 349-355

[18] Tang A, He KF, Wu Y, Wang S. Construction of sound velocity field based on deep learning combined with WOA18 temperature and salinity model. Adv Mar Sci, 2024, 42(4): 816-829

[19] Tang JF, Yang SE. Sound speed profile in ocean inverted by using travel time. J Harbin Eng Univ, 2006, 27(5): 733-736

[20] Tolstoy A, Diachok O, Frazer LN. Acoustic tomography via matched field processing. J Acoust Soc Am, 1991, 89(3): 1119-1127

[21] Wang J, Li Y, Jiang XC, Lyu XX, Xiao HQ. Named entity recognition of LSTM based on hierarchical residual connection. J Jiangsu Univ, 2022, 43(4): 446-452

[22] Wang JT, Xu TH, Huang W, Zhang LP, Shu JX, Liu YF, et al.. Underwater sound speed field forecasting based on the least square support vector machine. J Mar Sci Eng, 2024, 12(3): Article ID: 480

[23] Wang T, Su L, Ren QY, Wang WB, Jia YQ, Ma L. Full-sea depth sound speed profiles prediction using RNN and attention mechanism. J Electron Inf Technol, 2022, 44(2): 726-736

[24] Wang T, Su L, Ren QY, Wang WB, Ma L. Application of the sound speed profile and sound source location in shallow waters. J Harbin Eng Univ, 2021, 42(8): 1133-1139

[25] Wang ZH, Wang ZJ, Nie ZX, Zhang YF. Research on the sampling depth in the EOF reconstruction of the sound speed profile. Mar Sci, 2021, 45(6): 126-134

[26] Yan XP, Bu XH, Liu HX, Xin MZ, Yang FL. Application of sound velocity profile interpolation methods in multibeam echosounding. J Shandong Univ Sci Technol, 2017, 36(2): 27-33

[27] Yan X, Li QQ, Yang FL, Peng DD, Juan ZH, Li Q. Time-series prediction of shallow water sound speed profiles in the presence of internal waves based on deep transfer learning. Acta Acust, 2025, 50(1): 23-31

[28] Yu XK (2021) Research on the construction of ocean sound velocity field and theadjustment method of seafloor geodetic network. Master thesis, Chang'an University, Xi'an. https://doi.org/10.26976/d.cnki.gchau.2021.002038

[29] Yu XK, Xu TH, Wang JT (2020) Sound velocity profile prediction method based on RBF neural network. In: China Satellite Navigation Conference (CSNC) 2020 Proceedings. Springer, Singapore, pp 475–487. https://doi.org/10.1007/978-981-15-3715-8_43

[30] Yuan H, Zhang JL. Radar target classification and recognition method based on residual-connected LSTM. Comput Meas Control, 2022, 30(4): 182-189

[31] Zhang L, Ye S, Zhou SD, Liu F, Han YQ. Review of measurement techniques for temperature, salinity and depth profile of sea water. Mar Sci Bull, 2017, 36(5): 481-489

[32] Zhang W, Yang SE, Huang YW, Li L. Inversion of sound speed profile in shallow water with irregular seabed. AIP Conf Proc, 2012, 1495: 392-399

[33] Zhang ZM (2005) The study for sound speed inversion in shallow water on application of genetic and simulated annealing algorithm. Master thesis, Harbin Engineering University, Harbin

[34] Zhang ZM, Liu BS. Simulation study of sound speed profile inversion in shallow water using genetic simulated annealing algorithm. J Harbin Eng Univ, 2006, 27(4): 505-508

[35] Zhou FJ, Yang HB, Dong NP (2024a) A low flow forecasting model based on recession curve and long short-term memory (LSTM) network. Water Resour Hydropower Eng 55(9):99–107. https://doi.org/10.13928/j.cnki.wrahe.2024.09.009

[36] Zhou KM, Cheng K, Zeng SX, Ding Z, Yu S, Feng ZG. Prediction of shield attitude using deep residual long short-term memory model. Tunnel Constr, 2024, 44(8): 1643-1651

Funding

the National Key Research and Development Program of China(2024YFB3909701)

the National Natural Science Foundation of China(42304011)

the Shandong Provincial Natural Science Foundation(ZR2023QD163)

the Shandong Provincial Natural Science Foundation(ZR2023QF128)

State Key Laboratory of Spatial Datum(SKLSD2025-KF-05)

RIGHTS & PERMISSIONS

The Author(s)