mlsanityData to 14 Oct 2026

Reversible and irreversible bracket-based dynamics for deep graph neural networks

arXiv 2305.15616 ↗First posted 24 May 2023cs.LGcited by 26

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Abstract (arXiv)

Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing. The role of these physics is unclear, however, with successful examples of both reversible (e.g., Hamiltonian) and irreversible (e.g., diffusion) phenomena producing comparable results despite diametrically opposed mechanisms, and further complications arising due to empirical departures from mathematical theory. This work presents a series of novel GNN architectures based upon structure-preserving bracket-based dynamical systems, which are provably guaranteed to either conserve energy or generate positive dissipation with increasing depth. It is shown that the theoretically principled framework employed here allows for inherently explainable constructions, which contextualize departures from theory in current architectures and better elucidate the roles of reversibility and irreversibility in network performance.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). Builds on 44 of its 74 references that are in the map. First posted on arXiv 24 May 2023.

Builds on

44 of 74 references.

References · 44

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32 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 5; 2025: 11; 2026: 8.

26 papers.

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  1. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  2. 2024Efficiently Parameterized Neural Metriplectic Systemscited by 19
  3. 2024PANDA: Expanded Width-Aware Message Passing Beyond Rewiringcited by 10
  4. 2026MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanicscited by 10
  5. 2025Thermodynamically Consistent Latent Dynamics Identification for Parametric Systemscited by 8
  6. 2025Structure-Preserving Digital Twins via Conditional Neural Whitney Formscited by 8
  7. 2023Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftingscited by 6
  8. 2024A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networkscited by 4
  9. 2024SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classificationcited by 4
  10. 2025On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL conditioncited by 4
  11. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  12. 2025Meta-learning Structure-Preserving Dynamicscited by 2
14 more
  1. 2025Data-efficient Kernel Methods for Learning Hamiltonian Systemscited by 2
  2. 2026Metriplector: From Field Theory to Neural Architecturecited by 2
  3. 2025Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networkscited by 1
  4. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  5. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  6. 2026GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operatorscited by 1
  7. 2024Learning Nonholonomic Dynamics with Constraint Discoverycited by 0
  8. 2025Modeling Neural Networks with Privacy Using Neural Stochastic Differential Equationscited by 0
  9. 2025Learning thermodynamic master equations for open quantum systemscited by 0
  10. 2025Variational Neural Networks for Observable Thermodynamics (V-NOTS)cited by 0
  11. 2025Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheetscited by 0
  12. 2026Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physicscited by 0
  13. 2026Stable and Counterfactually Robust Physical World Models from Imposed Structure and Learned Physicscited by 0
  14. 2026Poisson-GENERIC Neural Operators: Exact Metriplectic Structure in Function Space via Casimir Entropiescited by 0