arXiv:2606. 28119v1 Announce Type: cross Abstract: We introduce a physics-constrained neural network (PCNN) for the rapid prediction of rigorous coupled-wave analysis (RCWA) outputs in the form of Jones matrices.
The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces.
arXiv:2607. 07682v1 Announce Type: new Abstract: The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces.
arXiv:2609.07983v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) have recently emerged as a promising approach for solving Partial Differential Equations (PDEs), offering a me...
arXiv:2608. 09382v1 Announce Type: cross Abstract: Electromagnetic inverse scattering is a nonlinear and ill-posed problem, where accurate reconstruction is challenging due to measurement limitations, noise, and high computational costs, especially for 3-D imaging.
The paper presents Finite Basis Physics-Informed Neural Networks (FBPINNs) and their multilevel extensions as a new approach to solving the Helmholtz equation. By decomposing the computational domain into overlapping sub‑domains, each governed by a local neural network, the method aims to improve accuracy and computational efficiency for high‑frequency wave problems in complex two‑dimensional domains. The authors evaluate the technique on the homogeneous Helmholtz case, showing its potential to overcome limitations of traditional finite difference and finite element methods.
arXiv:2607. 13574v1 Announce Type: cross Abstract: We develop a convergent scheme to train neural networks involving analytic activation functions based on gradient flows.
arXiv:2607. 06479v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) provide a promising framework for solving partial differential equations while embedding the underlying physical laws directly into the learning process.
arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.
Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems. Two factors underlie this difficulty: spectral bias, the tendency of neural networks to underfit high-frequency features; and representation-coefficient coupling, the entanglement of representation learning and coefficient fitting within a single nonconvex optimization objective.
arXiv:2608. 05892v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems.
The paper introduces a method that combines Fourier Neural Operators with wavelet-based encodings to learn and predict multiple eigenmodes of the elastic wave equation in metamaterials. By encoding PDE inputs with wavelets, the model can deterministically select eigenmodes for both continuous and binary geometries, and it explains how prediction accuracy depends on geometric discontinuities. The surrogate model achieves a three‑order‑of‑magnitude speedup over finite element analysis while maintaining high fidelity, offering a powerful tool for accelerating metamaterial design.
arXiv:2606. 28158v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have recently emerged as a promising framework for addressing the Calder\'on inverse problem from limited boundary data.