tLaSDI: Thermodynamics-informed latent space dynamics identification

TL;DR

tLaSDI is a novel method that embeds thermodynamic principles into latent space dynamics identification using autoencoders and neural networks, enabling robust and extrapolative modeling of complex systems.

Contribution

The paper introduces tLaSDI, a thermodynamics-informed latent space modeling approach that integrates physical laws into neural network-based dynamics identification.

Findings

Effective in capturing latent dynamics with thermodynamic consistency

Demonstrates robust generalization and extrapolation capabilities

Empirically observes correlation between latent space quantities and full-state behaviors

Abstract

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.