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Anthony Gruber

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3 papers

2 author rows

TMLR Journal 2026 Journal Article

Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems

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

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.

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ICLR Conference 2025 Conference Paper

Efficiently Parameterized Neural Metriplectic Systems

Anthony Gruber
Kookjin Lee
Haksoo Lim
Noseong Park
Nathaniel Trask

Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic operators. In addition to being provably energy-conserving and entropy-stable, the proposed neural metriplectic systems (NMS) approach includes approximation results that demonstrate its ability to accurately learn metriplectic dynamics from data, along with an error estimate that indicates its potential for generalization to unseen timescales when the approximation error is low. Examples are provided to illustrate performance both with full state information available and when entropic variables are unknown, confirming that the NMS approach exhibits superior accuracy and scalability without compromising on model expressivity.

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NeurIPS Conference 2023 Conference Paper

Reversible and irreversible bracket-based dynamics for deep graph neural networks

Anthony Gruber
Kookjin Lee
Nathaniel Trask

Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing. The role of these physics is unclear, however, with successful examples of both reversible (e. g. , Hamiltonian) and irreversible (e. g. , diffusion) phenomena producing comparable results despite diametrically opposed mechanisms, and further complications arising due to empirical departures from mathematical theory. This work presents a series of novel GNN architectures based upon structure-preserving bracket-based dynamical systems, which are provably guaranteed to either conserve energy or generate positive dissipation with increasing depth. It is shown that the theoretically principled framework employed here allows for inherently explainable constructions, which contextualize departures from theory in current architectures and better elucidate the roles of reversibility and irreversibility in network performance. Code is available at the Github repository \url{https: //github. com/natrask/BracketGraphs}.

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