Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems
This work addresses efficient modeling of complex physical systems for researchers in computational physics and engineering, representing an incremental improvement by integrating thermodynamics principles into existing methods.
The authors tackled the problem of reduced-order modeling for parametric nonlinear dynamical systems by proposing a thermodynamics-informed latent space dynamics identification framework, achieving up to 3,528x speed-up with 1-3% relative errors and reducing training and inference costs by 50-90% and 57-61%, respectively.
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.