On the approximation of rough functions with deep neural networks

被引：0

作者：

De Ryck T. ^{[1
]}

Mishra S. ^{[1
]}

Ray D. ^{[2
]}

机构：

[1] Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, Zurich

[2] University of Southern California, Los Angeles

来源：

SeMA Journal | 2022年 / 79卷 / 3期

基金：

欧盟地平线“2020”;

关键词：

Data compression; Deep ReLU networks; ENO; Interpolation; Rough functions;

D O I：

10.1007/s40324-022-00299-w

中图分类号：

学科分类号：

摘要：

The essentially non-oscillatory (ENO) procedure and its variant, the ENO-SR procedure, are very efficient algorithms for interpolating (reconstructing) rough functions. We prove that the ENO (and ENO-SR) procedure are equivalent to deep ReLU neural networks. This demonstrates the ability of deep ReLU neural networks to approximate rough functions to high-order of accuracy. Numerical tests for the resulting trained neural networks show excellent performance for interpolating functions, approximating solutions of nonlinear conservation laws and at data compression. © 2022, The Author(s).

引用

页码：399 / 440

页数：41

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