Convergence rate of DeepONets for learning operators arising from advection-diffusion equations
Analysis of PDEs
2021-03-18 v2 Numerical Analysis
Numerical Analysis
Abstract
We present convergence analysis of operator learning in [Chen and Chen 1995] and [Lu et al. 2020], where continuous operators are approximated by a sum of products of branch and trunk networks. In this work, we consider the rates of learning solution operators from both linear and nonlinear advection-diffusion equations with or without reaction. We find that the convergence rates depend on the architecture of branch networks as well as the smoothness of inputs and outputs of solution operators.
Keywords
Cite
@article{arxiv.2102.10621,
title = {Convergence rate of DeepONets for learning operators arising from advection-diffusion equations},
author = {Beichuan Deng and Yeonjong Shin and Lu Lu and Zhongqiang Zhang and George Em Karniadakis},
journal= {arXiv preprint arXiv:2102.10621},
year = {2021}
}