mlsanityData to 7 Oct 2026

GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems

arXiv 2109.00092 ↗First posted 31 Aug 2021math.DS cs.LGcited by 48

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Abstract (arXiv)

We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprise two modules, each of which contains two components. We model each component using a neural network whose architecture is designed to satisfy the required conditions. The component-wise architecture design provides flexible ways of leveraging available physics information into neural networks. We prove theoretically that GFINNs are sufficiently expressive to learn the underlying equations, hence establishing the universal approximation theorem. We demonstrate the performance of GFINNs in three simulation problems: gas containers exchanging heat and volume, thermoelastic double pendulum and the Langevin dynamics. In all the examples, GFINNs outperform existing methods, hence demonstrating good accuracy in predictions for both deterministic and stochastic systems.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). Builds on 18 of its 46 references that are in the map. First posted on arXiv 31 Aug 2021.

Builds on

18 of 46 references.

References · 18

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6 more
  1. 2020Structure-preserving neural networkscited by 54
  2. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
  3. 2020Deep learning of thermodynamics-aware reduced-order models from datacited by 38
  4. 2020Learning Poisson systems and trajectories of autonomous systems via Poisson neural networkscited by 37
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 8; 2023: 6; 2024: 8; 2025: 14; 2026: 12.

48 papers.

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  1. 2022Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systemscited by 54
  2. 2023Correcting model misspecification in physics-informed neural networks (PINNs)cited by 33
  3. 2022Thermodynamics-informed graph neural networkscited by 31
  4. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  5. 2024tLaSDI: Thermodynamics-informed latent space dynamics identificationcited by 23
  6. 2024A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modelingcited by 22
  7. 2024Efficiently Parameterized Neural Metriplectic Systemscited by 18
  8. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 17
  9. 2022Exact conservation laws for neural network integrators of dynamical systemscited by 15
  10. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  11. 2022Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systemscited by 11
  12. 2022Thermodynamics of learning physical phenomenacited by 10
36 more
  1. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  2. 2022SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problemscited by 9
  3. 2022A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluidscited by 9
  4. 2023Lie-Poisson Neural Networks (LPNets): Data-Based Computing of Hamiltonian Systems with Symmetriescited by 9
  5. 2024DynGMA: a robust approach for learning stochastic differential equations from datacited by 8
  6. 2025Thermodynamically Consistent Latent Dynamics Identification for Parametric Systemscited by 8
  7. 2026MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanicscited by 8
  8. 2023Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-netscited by 6
  9. 2024Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous mediacited by 5
  10. 2024SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classificationcited by 4
  11. 2024Thermodynamics-informed super-resolution of scarce temporal dynamics datacited by 3
  12. 2024Learning Macroscopic Dynamics from Partial Microscopic Observationscited by 3
  13. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  14. 2025Identifiable learning of dissipative dynamicscited by 3
  15. 2025Equilibrium Conserving Neural Operators for Super-Resolution Learningcited by 2
  16. 2025SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertaintycited by 2
  17. 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
  18. 2025Meta-learning Structure-Preserving Dynamicscited by 2
  19. 2023Pseudo-Hamiltonian system identificationcited by 1
  20. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  21. 2026Structure-Aware Variational Learning of a Class of Generalized Diffusionscited by 1
  22. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  23. 2026Hypothesis-driven construction of mesoscopic dynamicscited by 1
  24. 2025Learning thermodynamic master equations for open quantum systemscited by 0
  25. 2025Variational Neural Networks for Observable Thermodynamics (V-NOTS)cited by 0
  26. 2025THINNs: Thermodynamically Informed Neural Networkscited by 0
  27. 2025Scalable learning of macroscopic stochastic dynamicscited by 0
  28. 2025Can Transformers overcome the lack of data in the simulation of history-dependent flows?cited by 0
  29. 2025GIMLET: Generalizable and Interpretable Model Learning through Embedded Thermodynamicscited by 0
  30. 2026Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modelingcited by 0
  31. 2026An Invariant Compiler for Neural ODEs in AI-Accelerated Scientific Simulationcited by 0
  32. 2026A Comparative Investigation of Thermodynamic Structure-Informed Neural Networkscited by 0
  33. 2026WGFINNs: Weak formulation-based GENERIC formalism informed neural networkscited by 0
  34. 2026GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operatorscited by 0
  35. 2026CoSynFlow: Conformal Symplectic Neural Flows for Cross-System Prediction of Dissipative Hamiltonian Dynamicscited by 0
  36. 2026Structure-preserving uncertainty quantification for GENERIC dynamicscited by 0