tLaSDI: Thermodynamics-informed latent space dynamics identification
This work addresses the challenge of preserving thermodynamic laws in reduced-order models for computational physics, representing an incremental improvement with a novel hybrid approach.
The authors tackled the problem of modeling complex physical systems by proposing tLaSDI, a method that embeds thermodynamic principles into latent space dynamics identification, achieving robust generalization and an empirically observed correlation between latent space quantities and full-state solution behaviors.
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.