mlsanityData to 14 Oct 2026

Thermodynamics-informed graph neural networks

arXiv 2203.01874 ↗First posted 3 Mar 2022cs.LG cs.CE math.DScited by 33

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Abstract (arXiv)

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting integration scheme. The first is achieved with Graph Neural Networks, which induces a non-Euclidean geometrical prior with permutation invariant node and edge update functions. The second bias is forced by learning the GENERIC structure of the problem, an extension of the Hamiltonian formalism, to model more general non-conservative dynamics. Several examples are provided in both Eulerian and Lagrangian description in the context of fluid and solid mechanics respectively, achieving relative mean errors of less than 3% in all the tested examples. Two ablation studies are provided based on recent works in both physics-informed and geometric deep learning.

Key facts. Cited by 33 papers in the map (data through 14 Oct 2026). Builds on 31 of its 51 references that are in the map. First posted on arXiv 3 Mar 2022.

Builds on

31 of 51 references.

References · 31

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2017Graph Attention Networkscited by 8,923
  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  5. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,223
  6. 2018Relational inductive biases, deep learning, and graph networkscited by 1,360
  7. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  8. 2021E(n) Equivariant Graph Neural Networkscited by 965
  9. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  10. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  11. 2019Hamiltonian Neural Networkscited by 712
  12. 2019Graph U-Netscited by 492
19 more
  1. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 344
  2. 2018Neural Relational Inference for Interacting Systemscited by 339
  3. 2020Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloudcited by 335
  4. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  5. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 183
  6. 2018GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphscited by 165
  7. 2019Symplectic Recurrent Neural Networkscited by 150
  8. 2019Mish: A Self Regularized Non-Monotonic Activation Functioncited by 141
  9. 2019Hamiltonian Graph Networks with ODE Integratorscited by 108
  10. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 67
  11. 2021ForceNet: A Graph Neural Network for Large-Scale Quantum Calculationscited by 58
  12. 2020Structure-preserving neural networkscited by 55
  13. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 52
  14. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
  15. 2020Deep learning of thermodynamics-aware reduced-order models from datacited by 38
  16. 2019ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modelingcited by 19
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  18. 2021A Deep Emulator for Secondary Motion of 3D Characterscited by 16
  19. 2021Physics perception in sloshing scenes with guaranteed thermodynamic consistencycited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 4; 2023: 5; 2024: 7; 2025: 7; 2026: 10.

33 papers.

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  1. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  2. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 26
  3. 2022Scalable algorithms for physics-informed neural and graph networkscited by 21
  4. 2023Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Predictioncited by 17
  5. 2022Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systemscited by 11
  6. 2022Thermodynamics of learning physical phenomenacited by 10
  7. 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
  8. 2026MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanicscited by 10
  9. 2022Thermodynamics-informed neural networks for physically realistic mixed realitycited by 9
  10. 2024Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous mediacited by 5
  11. 2024A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networkscited by 4
  12. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
21 more
  1. 2025On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL conditioncited by 4
  2. 2024Thermodynamics-informed super-resolution of scarce temporal dynamics datacited by 3
  3. 2024A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problemscited by 3
  4. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  5. 2025Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticitycited by 2
  6. 2025Parameter-Efficient Conditioning for Material Generalization in Graph-Based Simulatorscited by 2
  7. 2026Metriplector: From Field Theory to Neural Architecturecited by 2
  8. 2024Learning Paradigms and Modelling Methodologies for Digital Twins in Process Industrycited by 1
  9. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  10. 2023Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systemscited by 0
  11. 2023On the Interplay of Subset Selection and Informed Graph Neural Networkscited by 0
  12. 2025Learning thermodynamic master equations for open quantum systemscited by 0
  13. 2025Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variablescited by 0
  14. 2025Constraint Breeds Generalization: Temporal Dynamics as an Inductive Biascited by 0
  15. 2026Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEscited by 0
  16. 2026Graph-Instructed Neural Networks for parametric problems with varying boundary conditionscited by 0
  17. 2026Variational Graph Neural Networks for Uncertainty Quantification in Inverse Problemscited by 0
  18. 2026Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networkscited by 0
  19. 2026A Graph Neural Network approach to zero-shot Digital Twinscited by 0
  20. 2026ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flowscited by 0
  21. 2026Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solverscited by 0