Work

Convergence rate of DeepONets for learning operators arising from advection-diffusion equations

Year: 2021

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2102.10621

Authors: Deng, Beichuan, Shin, Yeonjong, Lu, Lu, Zhang, Zhongqiang, Karniadakis, George Em

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: U.S. Department of Energy, Defense Advanced Research Projects Agency

Awards: G5703010195, G604497219

OpenAlex ID: W3129610195

Cites: 37

Cited by: 11

Related to: 10