Adaptive Deep Learning Approximation for Allen-Cahn Equation

Huiying Xu, Jie Chen*, Fei Ma

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingConference Proceedingpeer-review

3 Citations (Scopus)


Solving general non-linear partial differential equations (PDE) precisely and efficiently has been a long-lasting challenge in the field of scientific computing. Based on the deep learning framework for solving non-linear PDEs physics-informed neural networks (PINN), we introduce an adaptive collocation strategy into the PINN method to improve the effectiveness and robustness of this algorithm when selecting the initial data to be trained. Instead of merely training the neural network once, multi-step discrete time models are considered when predicting the long time behaviour of solutions of the Allen-Cahn equation. Numerical results concerning solutions of the Allen-Cahn equation are presented, which demonstrate that this approach can improve the robustness of original neural networks approximation.

Original languageEnglish
Title of host publicationComputational Science - ICCS 2022, 22nd International Conference, Proceedings
EditorsDerek Groen, Clélia de Mulatier, Valeria V. Krzhizhanovskaya, Peter M.A. Sloot, Maciej Paszynski, Jack J. Dongarra
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783031087592
Publication statusPublished - 2022
Event22nd Annual International Conference on Computational Science, ICCS 2022 - London, United Kingdom
Duration: 21 Jun 202223 Jun 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13353 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference22nd Annual International Conference on Computational Science, ICCS 2022
Country/TerritoryUnited Kingdom


  • Adaptive collocation
  • Allen-Cahn equation
  • Deep learning
  • Discrete time models
  • Physics informed neural networks


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