# Neural network augmented wave-equation simulation

arXiv: https://arxiv.org/abs/1910.00925 · HTML: https://mlsanity.com/paper/1910.00925/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2019.

## Built on by (most cited first, 3 of 3)

- [QuasiSim: Parameterized Quasi-Physical Simulators for Dexterous Manipulations Transfer](https://mlsanity.com/paper/2404.07988/) (2024)
- [j-Wave: An open-source differentiable wave simulator](https://mlsanity.com/paper/2207.01499/) (2022)
- [Solving Maxwell's Equation in 2D with Neural Networks with Local Converging Inputs](https://mlsanity.com/paper/2302.02860/) (2023)

## Abstract (arXiv)

Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of Laplacian in simulation of wave equation via finite-difference method. We exploit intrinsic one-to-one similarities between timestepping algorithm with Convolutional Neural Networks (CNNs), and propose to intersperse CNNs between low-fidelity timesteps. Augmenting neural networks with low-fidelity timestepping algorithms may allow us to take large timesteps while limiting the numerical dispersion artifacts. While simulating the wave-equation with low-fidelity timestepping algorithm, by correcting the wavefield several time during propagation, we hope to limit the numerical dispersion artifact introduced by a poor discretization of the Laplacian. As a proof of concept, we demonstrate this principle by correcting for numerical dispersion by keeping the velocity model fixed, and varying the source locations to generate training and testing pairs for our supervised learning algorithm.