Evaluating Operators for Acoustic Wave Simulation Correction

2026-06-07

AI Summary

This study addresses the numerical dispersion artifacts arising from finite difference methods in two-dimensional anisotropic acoustic wave simulations. Building upon the Deep Finite Difference framework, it systematically introduces and evaluates multiple neural operator architectures—including the Fourier Neural Operator—for the first time to correct errors in fourth-order finite difference solutions. A unified ten-fold cross-validation benchmark is established across 27,000 heterogeneous velocity models to comprehensively assess the performance of twelve correction models. The experiments encompass finite difference and pseudospectral reference solutions alongside various data-driven approaches such as convolutional neural networks and linear regression, establishing the first large-scale, reproducible performance benchmark and delivering effective solutions for numerical error correction in acoustic wave equation modeling.

Abstract

Correcting numerical dispersion artifacts from Finite Difference solvers is a well-identified challenge in computational wave physics, but existing approaches evaluate only a restricted family of CNN-based architectures and have been applied exclusively to the elastic wave equation. We instantiate the Deep Finite Difference framework on two-dimensional anisotropic acoustic wave propagation, pairing a fourth-order Finite Difference proxy with a Pseudo-Spectral reference over 27,000 heterogeneous velocity fields. We benchmark twelve correction architectures, from linear regression to Fourier Neural Operators, under a unified 10-fold cross-validation protocol.

Problem

• numerical dispersion
• acoustic wave simulation
• Finite Difference
• correction operators
• anisotropic media

Innovation

• Deep Finite Difference
• acoustic wave propagation
• numerical dispersion correction
• Fourier Neural Operator
• cross-validation benchmarking