mlsanityData to 7 Oct 2026

Structure-preserving neural networks

arXiv 2004.04653 ↗First posted 9 Apr 2020cs.LG physics.comp-ph stat.MLcited by 54

Not on the map. Why?

Abstract (arXiv)

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC [M. Grmela and H.C Oettinger (1997). Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E. 56 (6): 6620-6632]. The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that include conservative as well as dissipative systems, discrete as well as continuous ones.

Key facts. Cited by 54 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Apr 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 7; 2023: 2; 2024: 10; 2025: 14; 2026: 16.

54 papers.

Sort:

By area:

  1. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
  2. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 48
  3. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
  4. 2022Thermodynamics-informed graph neural networkscited by 31
  5. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  6. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  7. 2024tLaSDI: Thermodynamics-informed latent space dynamics identificationcited by 23
  8. 2024A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modelingcited by 22
  9. 2022The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systemscited by 21
  10. 2024Efficiently Parameterized Neural Metriplectic Systemscited by 18
  11. 2024Space-Time Continuous PDE Forecasting using Equivariant Neural Fieldscited by 18
  12. 2022Exact conservation laws for neural network integrators of dynamical systemscited by 15
38 more
  1. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  2. 2022Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systemscited by 11
  3. 2021Physics perception in sloshing scenes with guaranteed thermodynamic consistencycited by 10
  4. 2022Thermodynamics of learning physical phenomenacited by 10
  5. 2022A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluidscited by 9
  6. 2022Thermodynamics-informed neural networks for physically realistic mixed realitycited by 9
  7. 2026MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanicscited by 8
  8. 2024A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networkscited by 4
  9. 2024PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEscited by 4
  10. 2025On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL conditioncited by 4
  11. 2024Thermodynamics-informed super-resolution of scarce temporal dynamics datacited by 3
  12. 2024Structure-Preserving Operator Learningcited by 3
  13. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  14. 2025Physics-informed sensor coverage through structure preserving machine learningcited by 3
  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. 2025A Mechanistic Analysis of Transformers for Dynamical Systemscited by 2
  19. 2026Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectivescited by 2
  20. 2023Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variablescited by 1
  21. 2024Thermodynamics-informed graph neural networks for real-time simulation of digital human twinscited by 1
  22. 2025Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systemscited by 1
  23. 2026Metriplector: From Field Theory to Neural Architecturecited by 1
  24. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  25. 2026Geometry-Conditioned Fourier Neural Operators for Cubic Nonlinear Schrodinger Dynamics on Periodic Domainscited by 1
  26. 2026CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systemscited by 1
  27. 2024Data-Driven Computing Methods for Nonlinear Physics Systems with Geometric Constraintscited by 0
  28. 2025A Structure-Preserving Framework for Solving Parabolic Partial Differential Equations with Neural Networkscited by 0
  29. 2025Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variablescited by 0
  30. 2025Augmented Structure Preserving Neural Networks for cell biomechanicscited by 0
  31. 2025Hybrid twinning using PBDW and DeepONet for the effective state estimation and prediction on partially known systemscited by 0
  32. 2025Can Transformers overcome the lack of data in the simulation of history-dependent flows?cited by 0
  33. 2026Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modelingcited by 0
  34. 2026Sampling Boltzmann distributions via normalizing flow approximation of transport mapscited by 0
  35. 2026A Comparative Investigation of Thermodynamic Structure-Informed Neural Networkscited by 0
  36. 2026WGFINNs: Weak formulation-based GENERIC formalism informed neural networkscited by 0
  37. 2026Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physicscited by 0
  38. 2026GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operatorscited by 0

50 most cited of 54 All 54 (JSON)