A Convolutional Dispersion Relation Preserving Scheme for the Acoustic Wave Equation

TL;DR

This paper introduces a novel convolutional scheme that leverages machine learning to accurately solve the 2D acoustic wave equation, especially at high wavenumbers, by integrating physical principles into the optimization process.

Contribution

It presents a new machine learning-based convolutional scheme that preserves dispersion relations for the acoustic wave equation, enhancing accuracy at high wavenumbers.

Findings

Improved accuracy in approximating acoustic wave solutions.

Effective handling of high wavenumber scenarios.

Integration of physical principles into machine learning optimization.

Abstract

We propose an accurate numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to find a stencil suitable even in the presence of high wavenumbers. The proposed scheme incorporates physically informed elements from the field of optimized numerical schemes into a convolutional optimization machine learning algorithm.