Approximation rates of DeepONets for learning operators arising from advection–diffusion equations

Deng, Beichuan; Shin, Yeonjong; Lu, Lu; Zhang, Zhongqiang; Karniadakis, George Em

doi:10.1016/j.neunet.2022.06.019

Approximation rates of DeepONets for learning operators arising from advection–diffusion equations

Journal Article · Sat Jun 25 00:00:00 EDT 2022 · Neural Networks

DOI:https://doi.org/10.1016/j.neunet.2022.06.019· OSTI ID:1977482

^[1]; Shin, Yeonjong ^[2]; ^[3]; ^[4]; ^[2]

Worcester Polytechnic Institute, MA (United States); OSTI
Brown University, Providence, RI (United States)
University of Pennsylvania, Philadelphia, PA (United States)
Worcester Polytechnic Institute, MA (United States)

Here we present the analysis of approximation rates of operator learning in Chen and Chen (1995) and Lu et al. (2021), 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 approximation rates depend on the architecture of branch networks as well as the smoothness of inputs and outputs of solution operators.

View Accepted Manuscript (DOE)

Research Organization:: Brown University, Providence, RI (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Air Force Office of Scientific Research (AFOSR); Defense Advanced Research Projects Agency (DARPA)

Grant/Contract Number:: SC0019453

OSTI ID:: 1977482

Alternate ID(s):: OSTI ID: 1960880

Journal Information:: Neural Networks, Journal Name: Neural Networks Journal Issue: C Vol. 153; ISSN 0893-6080

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Approximation rates of DeepONets for learning operators arising from advection–diffusion equations

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