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×.