Convolutional neural networks in phase space and inverse problems

TL;DR

This paper introduces a deep convolutional neural network designed to classify and reconstruct medium properties from wave responses, leveraging wave propagation understanding and nonlinear interactions.

Contribution

It presents a novel neural network architecture tailored for inverse wave problems, with theoretical analysis of its depth and size relative to medium complexity.

Findings

Network effectively classifies medium properties.

Reconstruction accuracy depends on network depth and units.

Theoretical bounds relate network size to medium complexity.

Abstract

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we construct a deep convolutional neural network in which the parameters are used to classify and reconstruct the coefficients of nonlinear wave equations that model the medium properties. Furthermore, for given approximation accuracy, we obtain the depth and number of units of the network and their quantitative dependence on the complexity of the medium.