Finding the Shape of Lacunae of the Wave Equation Using Artificial Neural Networks

TL;DR

This paper demonstrates that a fully connected neural network can accurately determine the shape of lacunae in wave equation solutions from simulated data, including complex enclosed configurations.

Contribution

It introduces a neural network approach to reconstruct lacunae shapes in wave solutions, a novel application in this context.

Findings

Neural network accurately reconstructs lacunae shapes.

Method works for fully enclosed lacunae.

Effective with simulated data.

Abstract

We apply a fully connected neural network to determine the shape of the lacunae in the solutions of the wave equation. Lacunae are the regions of quietness behind the trailing fronts of the propagating waves. The network is trained using a computer simulated data set containing a sufficiently large number of samples. The network is then shown to correctly reconstruct the shape of lacunae including the configurations when it is fully enclosed.