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A Comparative Investigation of Thermodynamic Structure-Informed Neural Networks

arXiv 2603.26803 ↗First posted 26 Mar 2026cs.LG stat.MLcited by 0

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Abstract (arXiv)

Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are incorporated. In this work, we present a systematic comparison of different thermodynamic structure-informed neural networks by incorporating various thermodynamics formulations, including Newtonian, Lagrangian, and Hamiltonian mechanics for conservative systems, as well as the Onsager variational principle and extended irreversible thermodynamics for dissipative systems. Through comprehensive numerical experiments on representative ordinary and partial differential equations, we quantitatively evaluate the impact of these formulations on accuracy, physical consistency, noise robustness, and interpretability. The results show that Newtonian-residual-based PINNs can reconstruct system states but fail to reliably recover key physical and thermodynamic quantities, whereas structure-preserving formulation significantly enhances parameter identification, thermodynamic consistency, and robustness. These findings provide practical guidance for principled design of thermodynamics-consistency model, and lay the groundwork for integrating more general nonequilibrium thermodynamic structures into physics-informed machine learning.

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References · 19

  1. 2016On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minimacited by 1,352
  2. 2017Visualizing the Loss Landscape of Neural Netscited by 1,130
  3. 2019Hamiltonian Neural Networkscited by 712
  4. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  5. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  6. 2017Sharp Minima Can Generalize For Deep Netscited by 466
  7. 2020Lagrangian Neural Networkscited by 398
  8. 2016Entropy-SGD: Biasing Gradient Descent Into Wide Valleyscited by 359
  9. 2017Train longer, generalize better: closing the generalization gap in large batch training of neural networkscited by 279
  10. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 222
  11. 2017Generalization in Deep Learningcited by 146
  12. 2020Structure-preserving neural networkscited by 55
7 more
  1. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
  2. 2020OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principlecited by 37
  3. 2023An operator preconditioning perspective on training in physics-informed machine learningcited by 27
  4. 2023Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regressioncited by 25
  5. 2023Improving physics-informed neural networks with meta-learned optimizationcited by 19
  6. 2023Exactly conservative physics-informed neural networks and deep operator networks for dynamical systemscited by 13
  7. 2024Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structurecited by 6

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  3. 2023Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs
  4. 2026Neither Precision Nor Architecture Alone: Controlled Tests of Failure Remedies for Physics-Informed Neural Networks
  5. 2025Sub-Sequential Physics-Informed Learning with State Space Model
  6. 2025Training thermodynamic computers by gradient descent
  7. 2026Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators
  8. 2025KD-PINN: Knowledge-Distilled PINNs for ultra-low-latency real-time neural PDE solvers