THINNs: Thermodynamically Informed Neural Networks
This work addresses the challenge of enhancing accuracy and consistency in PINNs for physics simulations, though it appears incremental as it builds on existing PINN frameworks with a specific extension.
The authors tackled the problem of improving Physics-Informed Neural Networks (PINNs) for non-equilibrium fluctuating systems by proposing a thermodynamically consistent penalization method based on large deviations principles, resulting in THINNs that show empirical improvements over heuristic strategies.
Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that is consistent with the underlying fluctuation structure, as characterized by a large deviations principle. This approach yields a novel formulation of PINNs in which the penalty term is chosen to penalize improbable deviations, rather than being selected heuristically. The resulting thermodynamically consistent extension of PINNs, termed THINNs, is subsequently analyzed by establishing analytical a posteriori estimates, and providing empirical comparisons to established penalization strategies.