Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems

TL;DR

This paper introduces a thermodynamics-informed latent space modeling framework for parametric nonlinear systems, combining autoencoders, physics-informed neural networks, and active learning to achieve fast, accurate reduced-order models that respect physical laws.

Contribution

It develops a novel thermodynamics-consistent neural network approach for parametric system modeling, integrating active learning for improved efficiency and physical insight.

Findings

Achieves up to 3,528x speed-up with 1-3% relative error.

Reduces training and inference costs significantly.

Reveals thermodynamic behavior in latent space dynamics.

Abstract

We propose an efficient thermodynamics-informed latent space dynamics identification (tLaSDI) framework for the reduced-order modeling of parametric nonlinear dynamical systems. This framework integrates autoencoders for dimensionality reduction with newly developed parametric GENERIC formalism-informed neural networks (pGFINNs), which enable efficient learning of parametric latent dynamics while preserving key thermodynamic principles such as free energy conservation and entropy generation across the parameter space. To further enhance model performance, a physics-informed active learning strategy is incorporated, leveraging a greedy, residual-based error indicator to adaptively sample informative training data, outperforming uniform sampling at equivalent computational cost. Numerical experiments on the Burgers' equation and the 1D/1V Vlasov-Poisson equation demonstrate that the proposed method achieves up to 3,528x speed-up with 1-3% relative errors, and significant reduction in training (50-90%) and inference (57-61%) cost. Moreover, the learned latent space dynamics reveal the underlying thermodynamic behavior of the system, offering valuable insights into the physical-space dynamics.