THINNs: Thermodynamically Informed Neural Networks

• URL: http://arxiv.org/abs/2509.19467v1
• Date: Tue, 23 Sep 2025 18:22:47 GMT
• Title: THINNs: Thermodynamically Informed Neural Networks
• Authors: Javier Castro, Benjamin Gess,
• Abstract summary: 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.<n> Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that is consistent with the underlying fluctuation structure.<n>This approach yields a novel formulation of PINNs in which the penalty term is chosen to penalize deviations, rather than being selected improbableally.
• Score: 1.2031796234206138
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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