We study inverse problems consisting on determining space-time structures using the responses to probing waves (e.g. acoustic waves, gravitational waves etc.) 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. We also discuss the depth and number of units of the network and their quantitative dependence on the complexity of medium structures. The talk is based on joint work with G. Uhlmann.
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