mlsanityData to 7 Oct 2026

Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems

arXiv 2211.01873 ↗First posted 3 Nov 2022cs.LG cs.AI math.DScited by 11

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Abstract (arXiv)

We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy, non-negative entropy production), we modify accordingly the port-Hamiltonian formalism so as to achieve a port-metriplectic one. We show that the constructed networks are able to learn the physics of complex systems by parts, thus alleviating the burden associated to the experimental characterization and posterior learning process of this kind of systems. Predictions can be done, however, at the scale of the complete system. Examples are shown on the performance of the proposed technique.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 28 of its 66 references that are in the map. First posted on arXiv 3 Nov 2022.

Builds on

28 of 66 references.

References · 28

  1. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  2. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
  3. 2019Hamiltonian Generative Networkscited by 136
  4. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  5. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 77
  6. 2020Structure-preserving neural networkscited by 54
  7. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
  8. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 48
  9. 2020Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Datacited by 40
  10. 2020Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Controlcited by 38
  11. 2020Deep learning of thermodynamics-aware reduced-order models from datacited by 38
  12. 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 38
16 more
  1. 2022Physical Design using Differentiable Learned Simulatorscited by 37
  2. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  3. 2022Thermodynamics-informed graph neural networkscited by 31
  4. 2020LagNetViP: A Lagrangian Neural Network for Video Predictioncited by 24
  5. 2020Machine Learning and Computational Mathematicscited by 22
  6. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 17
  7. 2021Learning ground states of quantum Hamiltonians with graph networkscited by 12
  8. 2021Physics perception in sloshing scenes with guaranteed thermodynamic consistencycited by 10
  9. 2022Thermodynamics of learning physical phenomenacited by 10
  10. 2022A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluidscited by 9
  11. 2022Learning Neural Hamiltonian Dynamics: A Methodological Overviewcited by 8
  12. 2018Robust port-Hamiltonian representations of passive systemscited by 4
  13. 2021A unified framework for Hamiltonian deep neural networkscited by 4
  14. 2020Machine Learning a Molecular Hamiltonian for Predicting Electron Dynamicscited by 3
  15. 2020Mastering high-dimensional dynamics with Hamiltonian neural networkscited by 3
  16. 2021Lagrangian Neural Network with Differentiable Symmetries and Relational Inductive Biascited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 3; 2026: 5.

11 papers.

  1. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  2. 2026MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanicscited by 8
  3. 2025On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL conditioncited by 4
  4. 2024Physics informed cell representations for variational formulation of multiscale problemscited by 1
  5. 2024Thermodynamics-informed graph neural networks for real-time simulation of digital human twinscited by 1
  6. 2026Metriplector: From Field Theory to Neural Architecturecited by 1
  7. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  8. 2025SALSA-RL: Stability Analysis in the Latent Space of Actions for Reinforcement Learningcited by 0
  9. 2025Learning thermodynamic master equations for open quantum systemscited by 0
  10. 2026A Graph Neural Network approach to zero-shot Digital Twinscited by 0
  11. 2026An Energy-Based Conservative-Dissipative Latent Neural Evolution Operator for Magnetization Dynamicscited by 0