On the approximation of rough functions with deep neural networks
| Autor: | Tim De Ryck, Siddhartha Mishra, Deep Ray |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Numerical Analysis Control and Optimization Applied Mathematics Machine Learning (stat.ML) Numerical Analysis (math.NA) Machine Learning (cs.LG) Deep ReLU networks ENO Interpolation Rough functions Data compression Statistics - Machine Learning Modeling and Simulation FOS: Mathematics Mathematics - Numerical Analysis |
| Zdroj: | SeMA Journal, 79 (3) |
| DOI: | 10.3929/ethz-b-000570908 |
| Popis: | 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. SeMA Journal, 79 (3) |
| Databáze: | OpenAIRE |
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