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THINNs: Thermodynamically Informed Neural Networks

arXiv 2509.19467 ↗First posted 23 Sep 2025cs.LG cs.NA math.NAcited by 0

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Abstract (arXiv)

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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References · 16

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
  3. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 583
  4. 2017Solving high-dimensional partial differential equations using deep learningcited by 556
  5. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  6. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  7. 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEscited by 116
  8. 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 87
  9. 2022Error estimates for physics informed neural networks approximating the Navier-Stokes equationscited by 63
  10. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
  11. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 39
  12. 2024Numerical analysis of physics-informed neural networks and related models in physics-informed machine learningcited by 39
4 more
  1. 2022wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation lawscited by 29
  2. 2022Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustrationcited by 21
  3. 2021The Deep Minimizing Movement Schemecited by 15
  4. 2021Error Estimates for the Deep Ritz Method with Boundary Penaltycited by 14

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