Deep learning has become a cornerstone in numerous applications, such as robotics, augmented reality, and autonomous systems, where accurate 6D pose estimation – determining an object’s position and orientation in 3D space – is critical. Despite its success, designing optimal neural architectures and tuning hyperparameters remain computationally expensive and challenging, especially in high-variance and data-intensive domains like 6D pose estimation. To address this, we investigate the application of a Neural Architecture Search (NAS) technique guided by classical Machine Learning-based performance predictors. As these predictors estimate final model performance using early-stage training data, we demonstrate that leveraging such a strategy allows for efficient exploration of the hyperparameter space, significantly reducing the computational burden of exhaustive search while still achieving improved performance. Building on an existing NAS method, we introduce a novel modification that enhances the efficiency of the search process, further accelerating convergence by nearly 71% without sacrificing accuracy. Through extensive experimentation on the LineMOD dataset, we demonstrate that our method consistently discovers high-performing configurations of an Augmented Autoencoder for 6D pose estimation, outperforming benchmark models by almost 15% in pose accuracy and 42% in reconstruction loss. These results underscore the potential of predictor-based NAS as a powerful and computationally efficient tool for neural architecture optimization in complex, real-world tasks.

We consider a class of nonlinear integro-differential equations whose leading operator is modeled on a superposition of (−∆_p)^s and (−∆_p)^t, where 0 < s < t < 1 < p < ∞, weighted via two possibly degenerate coefficients a(·, ·) ≥ 0 and b(·, ·) ≥ 0, respectively. We prove local boundedness and Hölder regularity of its weak solutions under natural assumptions on the coefficients a(·, ·), b(·, ·) and the powers s, t, p. Moreover, when a(·, ·) ≡ 1, we also prove a Harnack inequality for weak solutions.

Plasticity with softening and fracture mechanics lead to ill-posed mathematical problems due to the loss of monotonicity. Multiple co-existing solutions are possible when softening elements are coupled together, and solutions cannot be continued beyond the point of complete degradation of the set of admissible stresses. We present a state-dependent sweeping process which solves the evolution of elasto-plastic Lattice Spring Models with arbitrary placement of softening, hardening and perfectly plastic springs. Using numerical simulations of regular grid lattices with softening, we demonstrate the emergence of non-symmetric shear bands with strain localization. At the same time, in toy examples it is easy to analytically derive multiple co-existing solutions. These solutions correspond to fixed points in the implicit catch-up algorithm and we observe a discontinuous bifurcation with the exchange of stability of those fixed points.

In this paper, we investigate the spectral stability of two biharmonic Steklov problems under domain perturbation. We provide optimal conditions on the boundary perturbations ensuring the stability of both eigenvalues and eigenfunctions. To highlight the optimality of those conditions, we present alternative assumptions on the boundary perturbations that lead to either a degeneration of the spectrum or to the appearance of a strange term in the limiting problem. In particular, these phenomena are discussed for a boundary homogenization problem exhibiting a trichotomy in the asymptotic behaviour.

We pursue a computational analysis of the biomedical problem on the identification of cancerous tumors at an early stage of development based on the Electrical Impedance Tomography (EIT) and optimal control of elliptic partial differential equations. Relying on the fact that the electrical conductivity of the cancerous tumor is significantly higher than that of healthy tissue, we consider an inverse EIT problem for identifying the conductivity map in the complete electrode model based on m current-to-voltage measurements on the boundary electrodes. A variational formulation as a PDE-constrained optimal control problem is introduced based on the novel idea of increasing the size of the input data by adding “voltage-to-current” measurements through various permutations of the single “current-to-voltage” measurement. The idea of permutation preserves the size of the unknown parameters at the expense of an increase in the number of PDE constraints. We apply a gradient projection method (GPM) based on the Fr´echet differentiability in Besov-Hilbert spaces. Numerical simulations of 2D and 3D model examples demonstrate the sharp increase in the resolution of the cancerous tumor by increasing the number of measurements from m to m².