The paper introduces a neural surrogate model for ultrasonic wave propagation in heterogeneous media, addressing limitations of existing Fourier Neural Operator (FNO) and U‑Net approaches. While FNOs fail to capture key signal features like reflections, U‑Net methods lack cross‑scale information transfer. The proposed hybrid model combines FNOs with local‑integral resampling within a U‑Net architecture, enabling accurate, noise‑robust predictions trained on limited data across spatial scales.
By Burla Nur Korkmaz, Petro Moilanen, Ari Salmi, Harsha Vardhan Tetali, Arto Klami
arXiv:2508. 20650v2 Announce Type: replace Abstract: Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framework.
By Juncai He, Xinliang Liu, Jinchao Xu
The paper addresses the spectral bias of Fourier Neural Operators (FNO) in predicting underwater acoustic transmission loss. It introduces a Spectral‑Spatial Residual Learning (S2RL) framework that first uses a spectral global propagator for coarse predictions and then a spatial local refiner to recover high‑frequency details. Experiments on a South China Sea dataset show that S2RL outperforms FNO baselines while keeping inference times in the millisecond range.
By Yifan Sun, Shikai Fang, Chao Zhang, Lei Cheng, Jianlong Li, Peter Gerstoft
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.
By Han Zhang, Alexander Ogren, Cynthia Rudin, Johann Guilleminot, L. Catherine Brinson
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
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: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...
By Davide Staub, Ben Moseley
arXiv:2608. 05839v1 Announce Type: cross Abstract: Deep neural networks have shown great empirical success in the solution of a wide variety of ill-posed inverse problems in imaging.
By Alexander Auras, Martin Burger, Samira Kabri, Michael Moeller, Michael Schopf-Kuester
arXiv:2604.06433v2 Announce Type: replace-cross
Abstract: The impact of wave-induced forcing on the mean water level and nearshore currents is typically modeled through excess momentum fluxes, also k...
By Shukai Cai, Sourav Dutta, Mark Loveland, Eirik Valseth, Peter Rivera-Casillas, Corey Trahan, Clint Dawson
Acoustic impedance imaging is a fundamental yet severely ill-posed problem in subsurface analysis: the seismic wavelet is unknown, observations are band-limited, and labeled well-log samples are extremely scarce (typically <1% of all traces). Existing semi-supervised deep learning methods mitigate few-shot problem by incorporating forward modeling, yet they either rely on inaccurate prior wavelet assumptions or introduce auxiliary networks, leading to unstable optimization and degraded performance.
ROMNet is a hybrid reduced‑order modeling and machine‑learning framework designed to improve waveform inversion for acoustic waves. It replaces the costly nonlinear mapping from a reduced‑order model (ROM) matrix to wave speed with a neural network that outputs a simpler ROM matrix, thereby reducing computational effort. The method is validated on two training datasets—random Gaussian‑based media and the GeoFWI benchmark—and compared against direct ROM inversion and two deep‑learning FWI approaches, Fourier‑DeepONet and InversionNet.
By Liliana Borcea, Alexander Mamonov, Kui Ren, Haizhao Yang, Chugang Yi
arXiv:2606. 18305v1 Announce Type: cross Abstract: Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing.
By Kuilin Qin, Lianfang Wang, Xu Sun, Jiwei Jia, Yu Wang, Yong Wang, Yuping Duan