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

2022/02/11 by Alina Chertock, Chertock, Alina, Christopher S. Leonard +3 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Neural Networks and Applications #Numerical Analysis (math.NA) #Optical Polarization and Ellipsometry #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2202.05768

openalex publication_date 2022/02/11 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

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.

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