mlsanityData to 7 Oct 2026

Graph Element Networks: adaptive, structured computation and memory

arXiv 1904.09019 ↗First posted 18 Apr 2019cs.LG stat.MLcited by 41

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Abstract (arXiv)

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational process defined on the graph to model the relationship between an initial function defined over a space and a resulting function in the same space. We use GNNs as a computational substrate, and show that the locations of the nodes in space as well as their connectivity can be optimized to focus on the most complex parts of the space. Moreover, this representational strategy allows the learned input-output relationship to generalize over the size of the underlying space and run the same model at different levels of precision, trading computation for accuracy. We demonstrate this method on a traditional PDE problem, a physical prediction problem from robotics, and learning to predict scene images from novel viewpoints.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Apr 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 11; 2022: 13; 2023: 10; 2024: 4; 2025: 1; 2026: 2.

41 papers.

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  1. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  2. 2021Choose a Transformer: Fourier or Galerkincited by 333
  3. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  4. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  5. 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 82
  6. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  7. 2022Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Networkcited by 45
  8. 2021Simulating Continuum Mechanics with Multi-Scale Graph Neural Networkscited by 39
  9. 2021Reinforcement Learning for Adaptive Mesh Refinementcited by 37
  10. 2022Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditionscited by 33
  11. 2021Noether Networks: Meta-Learning Useful Conserved Quantitiescited by 26
  12. 2024HAMLET: Graph Transformer Neural Operator for Partial Differential Equationscited by 24
29 more
  1. 2021Learning Connectivity with Graph Convolutional Networks for Skeleton-based Action Recognitioncited by 20
  2. 2021Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networkscited by 18
  3. 2022Learning the Solution Operator of Boundary Value Problems using Graph Neural Networkscited by 17
  4. 2023Neural Relational Inference with Fast Modular Meta-learningcited by 16
  5. 2023Grounding Graph Network Simulators using Physical Sensor Observationscited by 15
  6. 2022A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulationscited by 14
  7. 2021Convergent Graph Solverscited by 11
  8. 2022Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networkscited by 11
  9. 2023GNN-based physics solver for time-independent PDEscited by 10
  10. 2023Better Neural PDE Solvers Through Data-Free Mesh Moverscited by 9
  11. 2022A composable machine-learning approach for steady-state simulations on high-resolution gridscited by 8
  12. 2022Learning time-dependent PDE solver using Message Passing Graph Neural Networkscited by 7
  13. 2024Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular gridscited by 7
  14. 2022Quasi-optimal hp-finite element refinements towards singularities via deep neural network predictioncited by 6
  15. 2022REMuS-GNN: A Rotation-Equivariant Model for Simulating Continuum Dynamicscited by 3
  16. 2023An Implicit GNN Solver for Poisson-like problemscited by 3
  17. 2023Inductive biases in deep learning models for weather predictioncited by 3
  18. 2023Learning Space-Time Continuous Neural PDEs from Partially Observed Statescited by 3
  19. 2023Learning Efficient Surrogate Dynamic Models with Graph Spline Networkscited by 2
  20. 2024LatticeGraphNet: A two-scale graph neural operator for simulating lattice structurescited by 2
  21. 2024G-Adaptivity: optimised graph-based mesh relocation for finite element methodscited by 2
  22. 2025Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flowscited by 2
  23. 2021Skeleton-based Hand-Gesture Recognition with Lightweight Graph Convolutional Networkscited by 1
  24. 2021Learning Chebyshev Basis in Graph Convolutional Networks for Skeleton-based Action Recognitioncited by 0
  25. 2021An FEA surrogate model with Boundary Oriented Graph Embedding approachcited by 0
  26. 2022Inference from Real-World Sparse Measurementscited by 0
  27. 2023SURF: A Generalization Benchmark for GNNs Predicting Fluid Dynamicscited by 0
  28. 2026WeatherNext 3: Increasing resolution and performance of global weather models with raw observationscited by 0
  29. 2026Where to Compute and How to Interact: Operator-Readable Adaptation with Gauge-Aware Transportcited by 0