# A Convolutional Dispersion Relation Preserving Scheme for the Acoustic Wave Equation

arXiv: https://arxiv.org/abs/2205.10825 · HTML: https://mlsanity.com/paper/2205.10825/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 29 references that are in the map.
- First posted on arXiv 22 May 2022.

## Builds on (most cited first, 1 of 1)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)

## Built on by (most cited first, 1 of 1)

- [LLT: Local Linear Transformer for PDE Operator Learning](https://mlsanity.com/paper/2607.07718/) (2026)

## Abstract (arXiv)

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.