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We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in…

Machine Learning · Computer Science 2025-02-14 Vivek Oommen , Aniruddha Bora , Zhen Zhang , George Em Karniadakis

Accurate knowledge of acoustic surface admittance or impedance is essential for reliable wave-based simulations, yet its in situ estimation remains challenging due to noise, model inaccuracies, and restrictive assumptions of conventional…

Machine Learning · Computer Science 2026-04-10 Jonas M. Schmid , Johannes D. Schmid , Martin Eser , Steffen Marburg

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

Analysis of PDEs · Mathematics 2018-12-03 Heping Dong , Jun Lai , Peijun Li

In this paper, we propose Neumann Series Neural Operator (NSNO) to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions. Helmholtz equation is a crucial partial differential…

Numerical Analysis · Mathematics 2024-01-25 Fukai Chen , Ziyang Liu , Guochang Lin , Junqing Chen , Zuoqiang Shi

Frequency estimation is a fundamental problem in signal processing, with applications in radar imaging, underwater acoustics, seismic imaging, and spectroscopy. The goal is to estimate the frequency of each component in a multisinusoidal…

Machine Learning · Computer Science 2021-02-04 Gautier Izacard , Sreyas Mohan , Carlos Fernandez-Granda

Wavefield reconstruction inversion (WRI) formulates a PDE-constrained optimization problem to reduce cycle skipping in full-waveform inversion (FWI). WRI often requires expensive matrix inversions to reconstruct frequency-domain wavefields.…

Geophysics · Physics 2022-05-04 Chao Song , Tariq Alkhalifah

In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the…

Numerical Analysis · Mathematics 2024-12-31 Zhilin You , Zhenli Xu , Wei Cai

Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the…

Computational Engineering, Finance, and Science · Computer Science 2025-06-16 Stefan Schoder , Aneta Furmanová , Viktor Hruška

A fast method is proposed for solving the high frequency Helmholtz equation. The building block of the new fast method is an overlapping source transfer domain decomposition method for layered medium, which is an extension of the source…

Numerical Analysis · Mathematics 2015-07-10 Wei Leng

In this paper, the frequency-domain sound field is regarded as an element of some band-limited function space, and a representation of the field as a linear combination of the reproducing kernel in that space is proposed. This model has the…

Sound · Computer Science 2024-05-24 Takahiro Iwami , Akira Omoto

Full-waveform inversion (FWI) with extended sources first computes wavefields with data-driven source extensions, such that the simulated data in inaccurate velocity models match the observed counterpart well enough to prevent cycle…

Geophysics · Physics 2023-03-03 Gaoshan Guo , Stephane Operto , Ali Gholami , Hossein S. Aghamiry

We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…

Numerical Analysis · Mathematics 2022-01-14 Anton Arnold , Sjoerd Geevers , Ilaria Perugia , Dmitry Ponomarev

Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees…

Optics · Physics 2024-04-02 Charles Dove , Jatearoon Boondicharern , Laura Waller

Full waveform inversion (FWI) is one of a family of methods that allows the reconstruction of earth subsurface parameters from measurements of waves at or near the surface. This is a numerical optimization problem that uses the whole…

Numerical Analysis · Mathematics 2022-01-25 Mauricio A. Londoño , Francisco J. Rodríguez-Cortés

We consider the wave scattering and inverse scattering in an inhomogeneous medium embedded a homogeneous droplet with a small size, which is modeled by a constant mass density and a small bulk modulus. Based on the Lippmann-Schwinger…

Numerical Analysis · Mathematics 2026-04-06 Zhe Wang , Ahcene Ghandriche , Jijun Liu

For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent)…

Numerical Analysis · Mathematics 2024-03-06 A. Gibbs , S. Langdon

This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…

Analysis of PDEs · Mathematics 2017-06-14 Jiaqing Yang , Bo Zhang , Haiwen Zhang

The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…

Numerical Analysis · Mathematics 2022-04-19 Elwin van 't Wout , Seyyed R. Haqshenas , Pierre Gélat , Timo Betcke , Nader Saffari

High frequency estimates for the Dirichlet-to-Neumann and Neumann-to-Dirichlet operators are obtained for the Helmholtz equation in the exterior of bounded obstacles. These a priori estimates are used to study the scattering of plane waves…

Mathematical Physics · Physics 2013-07-18 Evgeny Lakshtanov , Boris Vainberg

We develop efficient and high-order accurate solvers for the Helmholtz equation on complex geometry. The schemes are based on the WaveHoltz algorithm which computes solutions of the Helmholtz equation by time-filtering solutions of the wave…

Numerical Analysis · Mathematics 2025-04-07 Daniel Appelo , Jeffrey W. Banks , William D. Henshaw , Donald W. Schwendeman