Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations

Wuzhe Xu, Yulong Lu, Li Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it provides an efficient approach to predict the evolution equations in a finite time horizon. Nevertheless, the vanilla DeepONet suffers from the issue of stability degradation in the longtime prediction. This paper proposes a transfer-learning aided DeepONet to enhance the stability. Our idea is to use transfer learning to sequentially update the DeepONets as the surrogates for propagators learned in different time frames. The evolving DeepONets can better track the varying complexities of the evolution equations, while only need to be updated by efficient training of a tiny fraction of the operator networks. Through systematic experiments, we show that the proposed method not only improves the long-time accuracy of DeepONet while maintaining similar computational cost but also substantially reduces the sample size of the training set.

Original languageEnglish (US)
Title of host publicationAAAI-23 Technical Tracks 9
EditorsBrian Williams, Yiling Chen, Jennifer Neville
PublisherAAAI press
Pages10629-10636
Number of pages8
ISBN (Electronic)9781577358800
StatePublished - Jun 27 2023
Event37th AAAI Conference on Artificial Intelligence, AAAI 2023 - Washington, United States
Duration: Feb 7 2023Feb 14 2023

Publication series

NameProceedings of the 37th AAAI Conference on Artificial Intelligence, AAAI 2023
Volume37

Conference

Conference37th AAAI Conference on Artificial Intelligence, AAAI 2023
Country/TerritoryUnited States
CityWashington
Period2/7/232/14/23

Bibliographical note

Publisher Copyright:
Copyright © 2023, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

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