The paper introduces beignet, a neural field architecture that replaces the random Fourier feature embedding in physics-informed neural networks with a trainable multi‑resolution Fourier feature pyramid. By using Fourier interpolation and spectral derivatives, beignet efficiently computes spatial derivatives and scales accuracy through the feature pyramid rather than the neural network size. Experiments show that beignet achieves more accurate PDE solutions with fewer parameters than existing PINN methods and can reach machine‑precision residuals on the inviscid Burgers blowup problem using the Adam optimizer.
By Brandon Zhao, Yixuan Wang, Jonathan T. Barron, Katherine L. Bouman, Dor Verbin, Pratul P. Srinivasan
arXiv:2607. 13566v1 Announce Type: cross Abstract: For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy.
By Tianchi Yu, Ivan Oseledets
arXiv:2606. 25753v1 Announce Type: new Abstract: Gradient-based inverse lithography technology~(ILT) for extreme ultraviolet~(EUV) masks is presented.
By Vasiliy A. Es'kin, Egor V. Ivanov
The paper presents a method for training single‑step neural surrogates that can handle wave‑scattering inverse problems with tens of thousands of controllable variables. By dynamically generating training examples through gradient ascent and using a replay dataset with normalization, the authors achieve a surrogate that accurately models two‑dimensional wave scattering for up to 41,772 variables and can generalize to over 3 million variables without retraining. The surrogate demonstrates comparable or better performance than traditional FDTD simulations for large‑scale forward simulations and inverse design of photonic devices, achieving speedups up to 26.5×.
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.
By Yutong Du, Zicheng Liu, Bo Qi, Yali Zong, Peixian Han
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
The paper presents a method for training single‑step neural surrogates that can handle wave‑scattering problems with tens of thousands of controllable variables. By dynamically generating training examples that highlight surrogate errors and using a replay dataset with normalization, the authors achieve a surrogate that accurately simulates two‑dimensional wave scattering for up to 41,772 variables and generalizes to over 3 million variables without retraining. The surrogate is applied to forward simulations and inverse design of freeform beam splitters and gradient‑index lenses, achieving speedups up to 26.5× compared to traditional FDTD methods.
By Charles Dove, Laura Waller
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
The paper introduces a coordinate-residual physics-driven neural network (CRPDNN) for 3‑D electromagnetic inverse scattering. CRPDNN models the unknown contrast distribution using normalized spatial coordinates and a residual convolutional network, optimizing parameters by enforcing consistency between measured and predicted scattered fields. It eliminates the need for preliminary reconstruction, achieving lower relative error and significant speedups compared to existing methods, while maintaining stability under noisy measurements and showing promise in practical imaging experiments.
By Yutong Du, Zicheng Liu, Bo Qi, Yali Zong, Peixian Han
arXiv:2609. 38023v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) embed governing equations into deep learning, but enforce them only through loss residuals, leaving highly oscillatory wave behavior to be discovered by optimization.
By Huiwen Zhang, Feng Ye, Chu Ma
arXiv:2609.08594v1 Announce Type: new
Abstract: This paper proposes a level-set-based physics-driven neural network solver (LSPDNN) for 3-D electromagnetic inverse scattering. To mitigate boundary bl...
By Yutong Du, Zicheng Liu, Bo Qi, Yali Zong, Peixian Han
arXiv:2605. 08318v2 Announce Type: replace Abstract: We study the problem of \emph{architecture selection} for deep learning models trained to solve partial differential equations (PDEs), asking when transformer-based architectures with learned attention outperform Fourier-domain neural operators.
By Brandon Yee, Pairie Koh, Jack Rodriguez, Mihir Tekal