Identifiable learning of dissipative dynamics

2025-10-28

AI Summary

For complex dissipative systems far from equilibrium, accurately modeling and quantifying energy dissipation and time irreversibility from trajectory data remains challenging. This paper introduces I-OnsagerNet, the first framework that couples the Onsager variational principle with Helmholtz decomposition and stationary density estimation to enable thermodynamically consistent, differentiable learning of stochastic dynamics. It ensures uniqueness and physical interpretability of the potential function while explicitly modeling entropy production rate and irreversibility. Validated on polymer stretching and stochastic gradient Langevin dynamics, the method uncovers novel phenomena: superlinear scaling of energy barrier height and sublinear scaling of entropy production rate with system size; moreover, increasing batch size suppresses irreversibility. I-OnsagerNet establishes the first interpretable, theoretically rigorous, and data-driven modeling paradigm for nonequilibrium statistical physics.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Social networks and social learning
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Complex dissipative systems appear across science and engineering, from polymers and active matter to learning algorithms. These systems operate far from equilibrium, where energy dissipation and time irreversibility are key to their behavior, but are difficult to quantify from data. Learning accurate and interpretable models of such dynamics remains a major challenge: the models must be expressive enough to describe diverse processes, yet constrained enough to remain physically meaningful and mathematically identifiable. Here, we introduce I-OnsagerNet, a neural framework that learns dissipative stochastic dynamics directly from trajectories while ensuring both interpretability and uniqueness. I-OnsagerNet extends the Onsager principle to guarantee that the learned potential is obtained from the stationary density and that the drift decomposes cleanly into time-reversible and time-irreversible components, as dictated by the Helmholtz decomposition. Our approach enables us to calculate the entropy production and to quantify irreversibility, offering a principled way to detect and quantify deviations from equilibrium. Applications to polymer stretching in elongational flow and to stochastic gradient Langevin dynamics reveal new insights, including super-linear scaling of barrier heights and sub-linear scaling of entropy production rates with the strain rate, and the suppression of irreversibility with increasing batch size. I-OnsagerNet thus establishes a general, data-driven framework for discovering and interpreting non-equilibrium dynamics.

Problem

• Learning interpretable models of dissipative stochastic dynamics
• Quantifying energy dissipation and time irreversibility from data
• Ensuring model identifiability while maintaining physical meaningfulness

Innovation

• Neural framework learning dissipative dynamics from trajectories
• Extends Onsager principle for interpretable potential decomposition
• Quantifies entropy production and irreversibility in non-equilibrium systems