An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator

Arda Mavi, Ali Can Bekar, Ehsan Haghighat, Erdogan Madenci

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a convolutional filter for evaluating derivatives the field variable. The NN captures the time-dynamics in smaller latent space through encoder–decoder layers with a Convolutional Long–short Term Memory (ConvLSTM) layer between them. The ConvLSTM architecture is modified by employing a novel activation function to improve the predictive capability of the learning architecture for physics with periodic behavior. The physics is invoked in the form of governing equations at the output of the NN and in the latent (reduced) space. By considering a few benchmark PDEs, we demonstrate the training performance and extrapolation capability of this novel NN architecture by comparing against Physics Informed Neural Networks (PINN) type solvers. It is more capable of extrapolating the solution for future timesteps than the other existing architectures.

Original languageEnglish (US)
Article number115944
JournalComputer Methods in Applied Mechanics and Engineering
Volume407
DOIs
StatePublished - Mar 15 2023

Keywords

  • Convolutional-recurrent learning
  • Deep learning
  • Peridynamic differential operator

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications

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