On the approximation of rough functions with deep neural networks

Tim De Ryck; Siddhartha Mishra; Deep Ray

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arXiv · 1912.06732

On the approximation of rough functions with deep neural networks

Tim De Ryck·Siddhartha Mishra·Deep Ray

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Abstract

Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions. We prove that at any order, the ENO interpolation procedure can be cast as a deep ReLU neural network. This surprising fact enables the transfer of several desirable properties of the ENO procedure to deep neural networks, including its high-order accuracy at approximating Lipschitz functions. Numerical tests for the resulting neural networks show excellent performance for approximating solutions of nonlinear conservation laws and at data compression.

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Tim De Ryck, Siddhartha Mishra, Deep Ray. 2019-12-13. On the approximation of rough functions with deep neural networks. https://arxiv.org/abs/1912.06732

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