SeMA Journal

Journal: SeMA Journal

Springer

2254-3902
2281-7875

Publications 1 - 2 of 2

On the approximation of rough functions with deep neural networks
De Ryck, Tim; Mishra, Siddhartha; Ray, Deep (2022)
SeMA Journal
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.
Nonlocal minimal surfaces: recent developments, applications, and future directions
Serra, Joaquim (2023)
SeMA Journal
Recently, we have found that nonlocal minimal surfaces enjoy notably stronger regularity estimates than classical minimal surfaces. This survey paper discusses these findings and their exciting applications in phase transitions and minimal surfaces.

Publications 1 - 2 of 2