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

Alina Chertock; Christopher Leonard; Semyon Tsynkov

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

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arxiv 2202.05768 v1 pith:E62ZBHCF submitted 2022-02-11 math.NA cs.NA

Alina Chertock , Christopher Leonard , Semyon Tsynkov This is my paper · ORCID

classification math.NAcs.NA

keywords lacunaenetworkshapeequationfullyneuralwaveapply

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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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