Machine learning can discover governing equations from data, but trustworthy model discovery for non-equilibrium systems requires more than reproducing observed trajectories. Learned models should obey the laws of thermodynamics, remain robust to scarce or noisy data, and quantify epistemic uncertainty associated with incomplete knowledge and extrapolation. Moreover, uncertainty quantification should not compromise the physical constraints encoded in a structure-preserving model.
This talk presents a sequence of scientific machine learning approaches developed toward these goals. The first builds on Onsager’s variational principle, extending the learning of free-energy and dissipation-potential densities to a probabilistic formulation that is robust to noisy observations, quantifies epistemic uncertainty, and satisfies the second law by construction. A second line of work concerns particle-to-continuum coarse-graining, where fluctuation–dissipation relations help resolve the non-identifiability of free energy and dissipative kinetics from macroscopic dynamics alone. This framework learns long-time continuum behavior from short-time particle simulations and quantifies uncertainty in both the inferred thermodynamic components and continuum predictions. Finally, recent work extends these ideas to the nonlinear General Equation for Non-Equilibrium Reversible–Irreversible Coupling (GENERIC) formalism, which couples reversible Hamiltonian dynamics with a generalized, potentially non-quadratic dissipation potential. Its thermodynamic building blocks are learned subject to the first and second laws, while structure-preserving uncertainty quantification ensures that every predictive realization remains thermodynamically admissible and conformal calibration provides coverage guarantees.