Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems

Xiaolong He, Yeonjong Shin, Anthony Gruber, Sohyeon Jung, Kookjin Lee, Youngsoo Choi

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 the 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 2,495x speed-up over the full-order numerical baseline with 1-3% relative errors, as well as significant reductions 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. Code is available at the repository: https://github.com/xiaolong7/pGFINN-tLaSDI.

Certifications: J2C Certification

Submission Length: Regular submission (no more than 12 pages of main content)

Code: https://github.com/xiaolong7/pGFINN-tLaSDI

Assigned Action Editor: ~Yoshinobu_Kawahara1

Submission Number: 6018