mlsanityData to 14 Oct 2026

Space-Time Continuous PDE Forecasting using Equivariant Neural Fields

arXiv 2406.06660 ↗First posted 10 Jun 2024cs.LG cs.AI cs.NEcited by 18

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Abstract (arXiv)

Recently, Conditional Neural Fields (NeFs) have emerged as a powerful modelling paradigm for PDEs, by learning solutions as flows in the latent space of the Conditional NeF. Although benefiting from favourable properties of NeFs such as grid-agnosticity and space-time-continuous dynamics modelling, this approach limits the ability to impose known constraints of the PDE on the solutions -- e.g. symmetries or boundary conditions -- in favour of modelling flexibility. Instead, we propose a space-time continuous NeF-based solving framework that - by preserving geometric information in the latent space - respects known symmetries of the PDE. We show that modelling solutions as flows of pointclouds over the group of interest G improves generalization and data-efficiency. We validated that our framework readily generalizes to unseen spatial and temporal locations, as well as geometric transformations of the initial conditions - where other NeF-based PDE forecasting methods fail - and improve over baselines in a number of challenging geometries.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Builds on 42 of its 55 references that are in the map. First posted on arXiv 10 Jun 2024.

Builds on

42 of 55 references.

References · 42

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30 more
  1. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  2. 2019Hamiltonian Neural Networkscited by 712
  3. 20233DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Modelscited by 458
  4. 2019General E(2)-Equivariant Steerable CNNscited by 446
  5. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  6. 2022Message Passing Neural PDE Solverscited by 386
  7. 2017Meta-SGD: Learning to Learn Quickly for Few-Shot Learningcited by 379
  8. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 326
  9. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  10. 2020Learned Initializations for Optimizing Coordinate-Based Neural Representationscited by 242
  11. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  12. 2020MetaSDF: Meta-learning Signed Distance Functionscited by 214
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  14. 2019B-Spline CNNs on Lie Groupscited by 97
  15. 2022Clifford Neural Layers for PDE Modelingcited by 92
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  17. 2023Spatial Functa: Scaling Functa to ImageNet Classification and Generationcited by 57
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  20. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 41
  21. 2022Variable-Input Deep Operator Networkscited by 25
  22. 2024Clifford-Steerable Convolutional Neural Networkscited by 25
  23. 2021Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groupscited by 22
  24. 2024Grounding Continuous Representations in Geometry: Equivariant Neural Fieldscited by 19
  25. 2024Mechanistic Neural Networks for Scientific Machine Learningcited by 16
  26. 2022Learning reversible symplectic dynamicscited by 11
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 11; 2026: 6.

18 papers.

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  1. 2025AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformerscited by 53
  2. 2024NeuralDEM -- Real-time Simulation of Industrial Particulate Flowscited by 10
  3. 2025Platonic Transformers: A Solid Choice For Equivariancecited by 10
  4. 2025Geometry aware inference of steady state PDEs using Equivariant Neural Fields representationscited by 6
  5. 2025Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogatescited by 6
  6. 2025A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometriescited by 5
  7. 2025Breaking the Discretization Barrier of Continuous Physics Simulation Learningcited by 4
  8. 2026SMART: Scalable Mesh-free Aerodynamic Simulations from Raw Geometries using a Transformer-based Surrogate Modelcited by 4
  9. 2025A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEscited by 3
  10. 2025A Circular Argument : Does RoPE need to be Equivariant for Vision?cited by 3
  11. 2025Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spacescited by 1
  12. 2025EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulatorcited by 1
6 more
  1. 2026Recursive Flow Matchingcited by 1
  2. 2026Neural Field Tokenizations with Hierarchy and Spatial Locality Priorscited by 1
  3. 2025Physics-based machine learning for mantle convection simulationscited by 0
  4. 2026FlowForge: A Staged Local Rollout Engine for Flow-Field Predictioncited by 0
  5. 2026A Deep Learning-based surrogate model for Severe Accidents in nuclear reactors using ASTECcited by 0
  6. 2026Function-Space Transformer with Adaptive Anchorscited by 0