Identifiable learning of dissipative dynamics.

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 govern their behavior but are difficult to quantify from data. Here, we introduce a universal and identifiable neural framework that learns non-degenerate stochastic dissipative dynamics directly from trajectories while ensuring interpretability, expressiveness, and uniqueness. Our method identifies a unique energy landscape, separates reversible from irreversible motion, and allows direct computation of the entropy production, providing a principled measure of irreversibility and deviations from equilibrium. Applications to polymer stretching in elongational flow and to stochastic gradient Langevin dynamics reveal characteristic scaling behaviors, 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. Our methodology thus provides a data-driven approach to discovering and interpreting non-equilibrium dynamics.