tLaSDI: Thermodynamics-informed latent space dynamics identification

We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based mode...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2024-09, Vol.429, p.117144, Article 117144
Main Authors: Park, Jun Sur Richard, Cheung, Siu Wun, Choi, Youngsoo, Shin, Yeonjong
Format: Article
Language:English
Subjects:
Autoencoder
Error estimates
MATHEMATICS AND COMPUTING
Nonlinear-manifold ROM
Reduced order modeling
Thermodynamics
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Summary:We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2024.117144