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
收藏
页码：399 / 440
页数：41
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