TY - JOUR
T1 - Generalization Error in the Deep Ritz Method with Smooth Activation Functions
AU - Siipola , Janne
JO - Communications in Computational Physics
VL - 3
SP - 761
EP - 815
PY - 2024
DA - 2024/04
SN - 35
DO - http://doi.org/10.4208/cicp.OA-2023-0253
UR - https://global-sci.org/intro/article_detail/cicp/23059.html
KW - Deep learning, Deep Ritz method, Poisson’s equation, residual neural networks, shallow neural networks, generalization.
AB - <p style="text-align: justify;">Deep Ritz method is a deep learning paradigm to solve partial differential
equations. In this article we study the generalization error of the Deep Ritz method.
We focus on the quintessential problem which is the Poisson’s equation. We show that
generalization error of the Deep Ritz method converges to zero with rate $\frac{C}{\sqrt{n}},$ and we
discuss about the constant $C.$ Results are obtained for shallow and residual neural
networks with smooth activation functions.</p>