mlsanityData to 7 Oct 2026

A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networks

arXiv 2404.01060 ↗First posted 1 Apr 2024cs.LGcited by 4

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Abstract (arXiv)

The development of inductive biases has been shown to be a very effective way to increase the accuracy and robustness of neural networks, particularly when they are used to predict physical phenomena. These biases significantly increase the certainty of predictions, decrease the error made and allow considerably smaller datasets to be used. There are a multitude of methods in the literature to develop these biases. One of the most effective ways, when dealing with physical phenomena, is to introduce physical principles of recognised validity into the network architecture. The problem becomes more complex without knowledge of the physical principles governing the phenomena under study. A very interesting possibility then is to turn to the principles of thermodynamics, which are universally valid, regardless of the level of abstraction of the description sought for the phenomenon under study. To ensure compliance with the principles of thermodynamics, there are formulations that have a long tradition in many branches of science. In the field of rheology, for example, two main types of formalisms are used to ensure compliance with these principles: one-generator and two-generator formalisms. In this paper we study the advantages and disadvantages of each, using classical problems with known solutions and synthetic data.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 17 of its 39 references that are in the map. First posted on arXiv 1 Apr 2024.

Builds on

17 of 39 references.

References · 17

  1. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  2. 2019Hamiltonian Neural Networkscited by 702
  3. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  4. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  5. 2020Lagrangian Neural Networkscited by 388
  6. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  7. 2020Structure-preserving neural networkscited by 54
  8. 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 46
  9. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  10. 2020Deep learning of thermodynamics-aware reduced-order models from datacited by 38
  11. 2020OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principlecited by 35
  12. 2020Hamiltonian neural networks for solving equations of motioncited by 33
5 more
  1. 2022Thermodynamics-informed graph neural networkscited by 31
  2. 2023Self-Supervised Learning with Lie Symmetries for Partial Differential Equationscited by 29
  3. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  4. 2018Model Reduction with Memory and the Machine Learning of Dynamical Systemscited by 19
  5. 2022Thermodynamics of learning physical phenomenacited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 1.

4 papers.

  1. 2024Thermodynamics-informed graph neural networks for real-time simulation of digital human twinscited by 1
  2. 2025Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systemscited by 1
  3. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  4. 2025Can Transformers overcome the lack of data in the simulation of history-dependent flows?cited by 0