A Convolutional Dispersion Relation Preserving Scheme for the Acoustic Wave Equation
This addresses the challenge of numerical accuracy in wave propagation simulations for computational physics or engineering, but appears incremental as it combines existing optimized schemes with machine learning.
The authors tackled the problem of approximating solutions to the 2D acoustic wave equation by developing a numerical scheme that uses machine learning to find stencils effective for high wavenumbers, resulting in an accurate method.
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.