mlsanityData to 7 Oct 2026

Continuous PDE Dynamics Forecasting with Implicit Neural Representations

arXiv 2209.14855 ↗First posted 29 Sep 2022cs.LG cs.AI cs.NEcited by 71

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Abstract (arXiv)

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE's flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.

Key facts. Cited by 71 papers in the map (data through 7 Oct 2026). Builds on 38 of its 58 references that are in the map. First posted on arXiv 29 Sep 2022.

Builds on

38 of 58 references.

References · 38

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 12; 2024: 24; 2025: 20; 2026: 15.

71 papers.

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  1. 2023Operator Learning with Neural Fields: Tackling PDEs on General Geometriescited by 80
  2. 2024AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fieldscited by 38
  3. 2023Domain Agnostic Fourier Neural Operatorscited by 36
  4. 2024Wavelet Diffusion Neural Operatorcited by 28
  5. 2025Generative Latent Neural PDE Solver using Flow Matchingcited by 28
  6. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 27
  7. 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulationcited by 25
  8. 2024Grounding Continuous Representations in Geometry: Equivariant Neural Fieldscited by 19
  9. 2024Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responsescited by 18
  10. 2024Space-Time Continuous PDE Forecasting using Equivariant Neural Fieldscited by 18
  11. 2023Time Series Continuous Modeling for Imputation and Forecasting with Implicit Neural Representationscited by 16
  12. 2023Inducing Point Operator Transformer: A Flexible and Scalable Architecture for Solving PDEscited by 16
38 more
  1. 2025Geometric Operator Learning with Optimal Transportcited by 15
  2. 2024Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEscited by 14
  3. 2024On latent dynamics learning in nonlinear reduced order modelingcited by 14
  4. 2023How to Train Neural Field Representations: A Comprehensive Study and Benchmarkcited by 12
  5. 2024CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equationscited by 12
  6. 2024Vectorized Conditional Neural Fields: A Framework for Solving Time-dependent Parametric Partial Differential Equationscited by 11
  7. 2023A Hierarchical Spatial Transformer for Massive Point Samples in Continuous Spacecited by 10
  8. 2023Latent assimilation with implicit neural representations for unknown dynamicscited by 8
  9. 2023Reduced-order modeling for parameterized PDEs via implicit neural representationscited by 7
  10. 2024Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular gridscited by 7
  11. 2024Space and Time Continuous Physics Simulation From Partial Observationscited by 6
  12. 2024Advancing Generalization in PINNs through Latent-Space Representationscited by 5
  13. 2025A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometriescited by 5
  14. 2023INFINITY: Neural Field Modeling for Reynolds-Averaged Navier-Stokes Equationscited by 4
  15. 2024Heterogeneous Peridynamic Neural Operators: Discover Biotissue Constitutive Law and Microstructure From Digital Image Correlation Measurementscited by 4
  16. 2024Physics-informed reduced order model with conditional neural fieldscited by 4
  17. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 4
  18. 2025PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modelingcited by 4
  19. 2025Breaking the Discretization Barrier of Continuous Physics Simulation Learningcited by 4
  20. 2023Learning Space-Time Continuous Neural PDEs from Partially Observed Statescited by 3
  21. 2024Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularizationcited by 3
  22. 2025A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEscited by 3
  23. 2025FlowKac: An Efficient Neural Fokker-Planck solver using Temporal Normalizing Flows and the Feynman-Kac Formulacited by 3
  24. 2025SCENT: Robust Spatiotemporal Learning for Continuous Scientific Data via Scalable Conditioned Neural Fieldscited by 3
  25. 2025Neural Entropy-stable conservative flux form neural networks for learning hyperbolic conservation lawscited by 3
  26. 2026SMART: Scalable Mesh-free Aerodynamic Simulations from Raw Geometries using a Transformer-based Surrogate Modelcited by 3
  27. 2023CONFIDE: Contextual Finite Differences Modelling of PDEscited by 2
  28. 2024Learning Spatiotemporal Dynamical Systems from Point Process Observationscited by 2
  29. 2024Learning Lagrangian Interaction Dynamics with Sampling-Based Model Order Reductioncited by 2
  30. 2024Accelerate Coastal Ocean Circulation Model with AI Surrogatecited by 2
  31. 2025Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solverscited by 2
  32. 2025RONOM: Reduced-Order Neural Operator Modelingcited by 2
  33. 2025Conditional neural field for spatial dimension reduction of turbulence data: a comparison studycited by 2
  34. 2025Unified all-atom molecule generation with neural fieldscited by 2
  35. 2025Efficient Generative Transformer Operators For Million-Point PDEscited by 2
  36. 2026Latent Generative Solvers for Generalizable Long-Term Physics Simulationcited by 2
  37. 2023Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformerscited by 1
  38. 2024PDETime: Rethinking Long-Term Multivariate Time Series Forecasting from the perspective of partial differential equationscited by 1

50 most cited of 71 All 71 (JSON)