On the approximation of rough functions with deep neural networks
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Date
2020-01
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Report
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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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published
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2020-07
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Seminar for Applied Mathematics, ETH Zurich
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Subject
ENO; Deep nets; Subcell
Organisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
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770880 - Computation and analysis of statistical solutions of fluid flow (EC)