mlsanityData to 14 Oct 2026

Machine learning structure preserving brackets for forecasting irreversible processes

arXiv 2106.12619 ↗First posted 23 Jun 2021physics.comp-ph cs.LGcited by 52

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Abstract (arXiv)

Forecasting of time-series data requires imposition of inductive biases to obtain predictive extrapolation, and recent works have imposed Hamiltonian/Lagrangian form to preserve structure for systems with reversible dynamics. In this work we present a novel parameterization of dissipative brackets from metriplectic dynamical systems appropriate for learning irreversible dynamics with unknown a priori model form. The process learns generalized Casimirs for energy and entropy guaranteed to be conserved and nondecreasing, respectively. Furthermore, for the case of added thermal noise, we guarantee exact preservation of a fluctuation-dissipation theorem, ensuring thermodynamic consistency. We provide benchmarks for dissipative systems demonstrating learned dynamics are more robust and generalize better than either "black-box" or penalty-based approaches.

Key facts. Cited by 52 papers in the map (data through 14 Oct 2026). Builds on 24 of its 60 references that are in the map. First posted on arXiv 23 Jun 2021.

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24 of 60 references.

References · 24

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12 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 10; 2023: 5; 2024: 6; 2025: 12; 2026: 16.

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  1. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
  2. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  3. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 38
  4. 2022Thermodynamics-informed graph neural networkscited by 33
  5. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  6. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  7. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 26
  8. 2024tLaSDI: Thermodynamics-informed latent space dynamics identificationcited by 23
  9. 2024A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modelingcited by 22
  10. 2022Scalable algorithms for physics-informed neural and graph networkscited by 21
  11. 2024Efficiently Parameterized Neural Metriplectic Systemscited by 19
  12. 2022Exact conservation laws for neural network integrators of dynamical systemscited by 15
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  4. 2022A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluidscited by 9
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  6. 2022Learning Neural Hamiltonian Dynamics: A Methodological Overviewcited by 8
  7. 2025Thermodynamically Consistent Latent Dynamics Identification for Parametric Systemscited by 8
  8. 2023Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Modelscited by 5
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  10. 2022AdamNODEs: When Neural ODE Meets Adaptive Moment Estimationcited by 3
  11. 2024Thermodynamics-informed super-resolution of scarce temporal dynamics datacited by 3
  12. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  13. 2025Identifiable learning of dissipative dynamicscited by 3
  14. 2025Equilibrium Conserving Neural Operators for Super-Resolution Learningcited by 2
  15. 2025SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertaintycited by 2
  16. 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
  17. 2025Meta-learning Structure-Preserving Dynamicscited by 2
  18. 2026Metriplector: From Field Theory to Neural Architecturecited by 2
  19. 2026Hypothesis-driven construction of mesoscopic dynamicscited by 2
  20. 2022Mining Causality from Continuous-time Dynamics Models: An Application to Tsunami Forecastingcited by 1
  21. 2025Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structurescited by 1
  22. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  23. 2026Parameterized Temporal Extrapolation of PDEs via Disentangled Latent Dynamics Manifold Fusioncited by 1
  24. 2026Structure-Aware Variational Learning of a Class of Generalized Diffusionscited by 1
  25. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  26. 2026GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operatorscited by 1
  27. 2023Climate Intervention Analysis using AI Model Guided by Statistical Physics Principlescited by 0
  28. 2025Modeling Neural Networks with Privacy Using Neural Stochastic Differential Equationscited by 0
  29. 2025Learning thermodynamic master equations for open quantum systemscited by 0
  30. 2025Variational Neural Networks for Observable Thermodynamics (V-NOTS)cited by 0
  31. 2025Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Driftscited by 0
  32. 2026WGFINNs: Weak formulation-based GENERIC formalism informed neural networkscited by 0
  33. 2026Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physicscited by 0
  34. 2026Physics-conforming Latent Twinscited by 0
  35. 2026Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamicscited by 0
  36. 2026Structure-preserving uncertainty quantification for GENERIC dynamicscited by 0
  37. 2026Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysiscited by 0
  38. 2026Conservation Buys Stability and Factoring Buys Counterfactuals in Physical World Modelscited by 0

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