mlsanityData to 7 Oct 2026

Constraint-based graph network simulator

arXiv 2112.09161 ↗First posted 16 Dec 2021cs.LGcited by 27

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Abstract (arXiv)

In the area of physical simulations, nearly all neural-network-based methods directly predict future states from the input states. However, many traditional simulation engines instead model the constraints of the system and select the state which satisfies them. Here we present a framework for constraint-based learned simulation, where a scalar constraint function is implemented as a graph neural network, and future predictions are computed by solving the optimization problem defined by the learned constraint. Our model achieves comparable or better accuracy to top learned simulators on a variety of challenging physical domains, and offers several unique advantages. We can improve the simulation accuracy on a larger system by applying more solver iterations at test time. We also can incorporate novel hand-designed constraints at test time and simulate new dynamics which were not present in the training data. Our constraint-based framework shows how key techniques from traditional simulation and numerical methods can be leveraged as inductive biases in machine learning simulators.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 29 of its 56 references that are in the map. First posted on arXiv 16 Dec 2021.

Builds on

29 of 56 references.

References · 29

  1. 2016Layer Normalizationcited by 5,579
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  4. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  6. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  7. 2019Hamiltonian Neural Networkscited by 702
  8. 2019Deep Equilibrium Modelscited by 603
  9. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
  10. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 503
  11. 2021Machine learning accelerated computational fluid dynamicscited by 461
  12. 2020Lagrangian Neural Networkscited by 388
17 more
  1. 2018Graph networks as learnable physics engines for inference and controlcited by 242
  2. 2018Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluidscited by 219
  3. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
  4. 2019Towards Physics-informed Deep Learning for Turbulent Flow Predictioncited by 203
  5. 2019Latent ODEs for Irregularly-Sampled Time Seriescited by 182
  6. 2021DC3: A learning method for optimization with hard constraintscited by 181
  7. 2019SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solvercited by 173
  8. 2020Multiscale Deep Equilibrium Modelscited by 149
  9. 2019Symplectic Recurrent Neural Networkscited by 148
  10. 2018Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flowscited by 147
  11. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
  12. 2019Hamiltonian Graph Networks with ODE Integratorscited by 107
  13. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 102
  14. 2018Flexible Neural Representation for Physics Predictioncited by 91
  15. 2018Reviving and Improving Recurrent Back-Propagationcited by 69
  16. 2017Application of Convolutional Neural Network to Predict Airfoil Lift Coefficientcited by 26
  17. 2020Learning Physical Constraints with Neural Projectionscited by 19

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 7; 2023: 5; 2024: 7; 2025: 5; 2026: 3.

27 papers.

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  1. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  2. 2022Learning rigid dynamics with face interaction graph networkscited by 43
  3. 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 38
  4. 2024Learning Iterative Reasoning through Energy Diffusioncited by 36
  5. 2022Learning Iterative Reasoning through Energy Minimizationcited by 32
  6. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  7. 2022Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Networkcited by 22
  8. 2023MTP-GO: Graph-Based Probabilistic Multi-Agent Trajectory Prediction with Neural ODEscited by 19
  9. 2023Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformercited by 18
  10. 2023Graph Neural Network-based surrogate model for granular flowscited by 16
  11. 2024A review of graph neural network applications in mechanics-related domainscited by 14
  12. 2025FlashMD: long-stride, universal prediction of molecular dynamicscited by 11
15 more
  1. 2022A composable machine-learning approach for steady-state simulations on high-resolution gridscited by 8
  2. 2025AMR-Transformer: Enabling Efficient Long-range Interaction for Complex Neural Fluid Simulationcited by 7
  3. 2022Equilibrium Aggregation: Encoding Sets via Optimizationcited by 5
  4. 2023Inferring Relational Potentials in Interacting Systemscited by 5
  5. 2023Equivariance Is Not All You Need: Characterizing the Utility of Equivariant Graph Neural Networks for Particle Physics Taskscited by 5
  6. 2024EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutionscited by 4
  7. 2024DEL: Discrete Element Learner for Learning 3D Particle Dynamics with Neural Renderingcited by 4
  8. 2024Learning Physical Simulation with Message Passing Transformercited by 2
  9. 2025Generalizable Reasoning through Compositional Energy Minimizationcited by 2
  10. 2024MBDS: A Multi-Body Dynamics Simulation Dataset for Graph Networks Simulatorscited by 1
  11. 2025Thickness-aware E(3)-Equivariant 3D Mesh Neural Networkscited by 1
  12. 2025EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulatorcited by 1
  13. 2026Exactness Matters for Physical Rule Enforcementcited by 0
  14. 2026Enabling Structure-Only Initialization and Out-of-Distribution Generalization in GNN-based Molecular Dynamics Simulatorscited by 0
  15. 2026TRACE: A spatiotemporal contact memory graph network simulator for granular dynamicscited by 0