Deep autoencoders for physics-constrained data-driven nonlinear materials modeling

Xiaolong He, Qizhi He, Jiun Shyan Chen

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains difficult to deal with high-dimensional applications and extrapolative generalization. This paper introduces deep learning techniques under the data-driven framework to address these fundamental issues in nonlinear materials modeling. To this end, an autoencoder neural network architecture is introduced to learn the underlying low-dimensional representation (embedding) of the given material database. The offline trained autoencoder and the discovered embedding space are then incorporated in the online data-driven computation such that the search of optimal material state from database can be performed on a low-dimensional space, aiming to enhance the robustness and predictability with projected material data. To ensure numerical stability and representative constitutive manifold, a convexity-preserving interpolation scheme tailored to the proposed autoencoder-based data-driven solver is proposed for constructing the material state. In this study, the applicability of the proposed approach is demonstrated by modeling nonlinear biological tissues. A parametric study on data noise, data size and sparsity, training initialization, and model architectures, is also conducted to examine the robustness and convergence property of the proposed approach.

Original languageEnglish (US)
Article number114034
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Nov 1 2021
Externally publishedYes

Bibliographical note

Funding Information:
The support of this work by the National Science Foundation under Award Number CCF-1564302 to University of California, San Diego, is greatly appreciated. Q. H. acknowledges support from Pacific Northwest National Laboratory (PNNL) under the Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PhILMs) project. PNNL is operated by Battelle for the DOE under Contract DE-AC05-76RL01830 .

Publisher Copyright:
© 2021 The Author(s)


  • Autoencoders
  • Biological material
  • Convexity-preserving reconstruction
  • Data-driven computational mechanics
  • Deep learning


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