The paper introduces a simplified Physics-Informed Neural Network (PINN) that uses trainable Gabor basis functions to better capture the localized, oscillatory nature of acoustic wavefields, addressing the low‑frequency bias of traditional PINNs. By redefining the network’s task as learning a nonlinear mapping to a custom Gabor coordinate system, the method absorbs Gabor parameters into the mapping, reducing computational complexity and eliminating manual hyperparameter tuning. Numerical experiments on various velocity models demonstrate faster convergence, higher accuracy, and greater robustness compared to conventional PINNs and earlier Gabor‑based approaches, with the implementation made publicly available for reproducibility.
By Mohammad Mahdi Abedi, David Pardo, Tariq Alkhalifah
The paper evaluates the robustness of Physics‑Informed Neural Networks (PINNs) against noisy data in inverse problems, comparing them to a finite element method (FEM) plus optimizer baseline. Experiments on viscosity identification in 1D Burgers’ equation and 2D/3D Taylor‑Green Vortex with additive Gaussian noise show that PINNs, while requiring less human expertise, are outperformed by the traditional FEM approach in accuracy (e.g., RMSE 0.01 vs. 0.0013 for 2D Taylor‑Green with σ=1). PINNs do, however, exhibit better scaling with problem complexity, and the study highlights specific training failures that must be addressed for PINNs to become more competitive.
By Aleksandra Jekic, Afroditi Natsaridou, Signe Riemer-S{\o}rensen, Helge Langseth, Odd Erik Gundersen
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.
By Ali AlHadi Kalout, Pablo Tejerina-P\'erez, Konstantin Karchev, Pedro Taranc\'on-\'Alvarez, Leonid Sarieddine, Raul Jimenez, Max Engelstein, Guy David
arXiv:2606. 16575v2 Announce Type: replace Abstract: Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors.
By Yong Wang, Tao Zhou, Xuhui Meng
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.
By Sonal Ankush Chibire, Jenn-Terng Gau, Bo Zhang
arXiv:2602.08515v3 Announce Type: replace-cross
Abstract: This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partia...
By Muhammad Luthfi Shahab, Imam Mukhlash, Hadi Susanto
arXiv:2502. 07209v4 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning.
By Shaghayegh Fazliani, Zachary Frangella, Madeleine Udell
The paper proposes Domain-aware Fourier Features (DaFFs) for Physics-Informed Neural Networks (PINNs), embedding domain-specific geometry and boundary conditions into the positional encoding. DaFFs eliminate the need for explicit boundary loss terms, simplify optimization, and reduce training cost, leading to orders-of-magnitude lower errors and faster convergence compared to vanilla PINNs and RFF-based PINNs. An LRP-based explainability framework further shows that DaFFs produce more physically consistent relevance attributions, improving interpretability.
By Alberto Mi\~no Calero, Luis Salamanca, Konstantinos E. Tatsis
arXiv:2109.08813v1 Announce Type: cross
Abstract: Seismic wave velocity of underground rock plays important role in detecting internal structure of the Earth. Rock physics models have long been the f...
By Weitao Sun
The article discusses how automatic differentiation (AD) enables neural networks to compute derivatives of governing equations to machine precision, forming the backbone of physics-informed machine learning. However, the author argues that numerical exactness does not guarantee physical fidelity, as AD lacks awareness of the physical structure a solution must satisfy. The paper highlights that many physical constraints—such as convection directionality, diffusion, dispersion, conservation, thermodynamic consistency, symmetry, symplectic structure, positivity, monotonicity, and boundedness—are overlooked by AD, suggesting a need to rethink how PDE-driven neural surrogates are built.
By Ameya D. Jagtap
The paper investigates when frequency decomposition aids Physics-Informed Neural Networks (PINNs) by introducing a dual‑branch, spectrally‑gated architecture (DBSG‑PINN) that separates low‑ and high‑frequency components. Experiments on five one‑dimensional PDE benchmarks show that frequency decomposition significantly reduces error—up to 59.2% on a multimodal wave problem—when the target solution is spectrally complex, but offers little improvement on smoother problems and can even worsen performance on a simple 1D wave benchmark. The adaptive gate’s effectiveness scales with the spectral richness of the solution, suggesting it exploits frequency structure rather than adding noise.
By Shubham Rai
arXiv:2606. 01110v1 Announce Type: cross Abstract: Full waveform inversion (FWI) reconstructs heterogeneous material properties from receiver data but remains computationally demanding.
By Hoang Anh Nguyen, Divakar Vashisth, Ali Tura