mlsanityData to 7 Oct 2026

ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs

arXiv 2404.10024 ↗First posted 15 Apr 2024cs.AI cs.ET cs.LGcited by 78

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Abstract (arXiv)

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts. However, they often act as data-driven black-box models that neglect the underlying physics and lack uncertainty quantification. We address these limitations with ClimODE, a spatiotemporal continuous-time process that implements a key principle of advection from statistical mechanics, namely, weather changes due to a spatial movement of quantities over time. ClimODE models precise weather evolution with value-conserving dynamics, learning global weather transport as a neural flow, which also enables estimating the uncertainty in predictions. Our approach outperforms existing data-driven methods in global and regional forecasting with an order of magnitude smaller parameterization, establishing a new state of the art.

Key facts. Cited by 78 papers in the map (data through 7 Oct 2026). Builds on 27 of its 48 references that are in the map. First posted on arXiv 15 Apr 2024.

Builds on

27 of 48 references.

References · 27

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  2. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
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  5. 2018Neural Ordinary Differential Equationscited by 3,733
  6. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  7. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  8. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  9. 2019Hamiltonian Neural Networkscited by 702
  10. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
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15 more
  1. 2023ClimaX: A foundation model for weather and climatecited by 325
  2. 2021Skillful Precipitation Nowcasting using Deep Generative Models of Radarcited by 308
  3. 2020WeatherBench: A benchmark dataset for data-driven weather forecastingcited by 272
  4. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  5. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 230
  6. 2023WeatherBench 2: A benchmark for the next generation of data-driven global weather modelscited by 227
  7. 2022Forecasting Global Weather with Graph Neural Networkscited by 165
  8. 2019Graph Neural Ordinary Differential Equationscited by 153
  9. 2020Dissecting Neural ODEscited by 150
  10. 2022Clifford Neural Layers for PDE Modelingcited by 91
  11. 2021Gradients are Not All You Needcited by 82
  12. 2021Sub-seasonal forecasting with a large ensemble of deep-learning weather prediction modelscited by 76
  13. 2020Learning continuous-time PDEs from sparse data with graph neural networkscited by 53
  14. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  15. 2022Interpretable Polynomial Neural Ordinary Differential Equationscited by 24

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 13; 2025: 37; 2026: 28.

78 papers.

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  1. 2024Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifoldcited by 41
  2. 2024Continuous Ensemble Weather Forecasting with Diffusion modelscited by 27
  3. 2024Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systemscited by 25
  4. 2024Generalizing Weather Forecast to Fine-grained Temporal Scales via Physics-AI Hybrid Modelingcited by 23
  5. 2025DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic predictioncited by 21
  6. 2024Topological Neural Networks go Persistent, Equivariant, and Continuouscited by 15
  7. 2025Deep Learning and Foundation Models for Weather Prediction: A Surveycited by 15
  8. 2025CirT: Global Subseasonal-to-Seasonal Forecasting with Geometry-inspired Transformercited by 13
  9. 2025ClimateLLM: Efficient Weather Forecasting via Frequency-Aware Large Language Modelscited by 9
  10. 2024Feedback Favors the Generalization of Neural ODEscited by 8
  11. 2025ARROW: An Adaptive Rollout and Routing Method for Global Weather Forecastingcited by 8
  12. 2024CaFA: Global Weather Forecasting with Factorized Attention on Spherecited by 6
38 more
  1. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 6
  2. 2026Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operatorscited by 6
  3. 2024CoDiCast: Conditional Diffusion Model for Global Weather Prediction with Uncertainty Quantificationcited by 5
  4. 2024HR-Extreme: A High-Resolution Dataset for Extreme Weather Forecastingcited by 5
  5. 2024Scalable Mechanistic Neural Networks for Differential Equations and Machine Learningcited by 5
  6. 2024Mitigating Time Discretization Challenges with WeatherODE: A Sandwich Physics-Driven Neural ODE for Weather Forecastingcited by 5
  7. 2025ClimateBench-M: A Multi-Modal Climate Data Benchmark with a Simple Generative Methodcited by 4
  8. 2025Position: Biology is the Challenge Physics-Informed ML Needs to Evolvecited by 4
  9. 2026Towards Principled Test-Time Adaptation for Time Series Forecastingcited by 4
  10. 2025Synthetic Datasets for Machine Learning on Spatio-Temporal Graphs using PDEscited by 3
  11. 2025Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecastingcited by 3
  12. 2025Neuro-Spectral Architectures for Causal Physics-Informed Networkscited by 3
  13. 2026PhysMetrics.Weather: An Evaluation Framework for Physical Consistency in ML Weather Modelscited by 3
  14. 2025Physics-Informed Teleconnection-Aware Transformer for Global Subseasonal-to-Seasonal Forecastingcited by 2
  15. 2025A Gravity-informed Spatiotemporal Transformer for Human Activity Intensity Predictioncited by 2
  16. 2025Numerical PDE solvers outperform neural PDE solverscited by 2
  17. 2026Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecastingcited by 2
  18. 2026Position: The Inevitable End of One-Architecture-Fits-All-Domains in Time Series Forecastingcited by 2
  19. 2026WIND: Weather Inverse Diffusion for Zero-Shot Atmospheric Modelingcited by 2
  20. 2026Variational Grey-Box Dynamics Matchingcited by 2
  21. 2026Probabilistic Precipitation Nowcasting with Rectified Flow Transformerscited by 2
  22. 2025PINT: Physics-Informed Neural Time Series Models with Applications to Long-term Inference on WeatherBench 2m-Temperature Datacited by 1
  23. 2025FuXi-RTM: A Physics-Guided Prediction Framework with Radiative Transfer Modelingcited by 1
  24. 2025A Physics-preserved Transfer Learning Method for Differential Equationscited by 1
  25. 2025Physics-Assisted and Topology-Informed Deep Learning for Weather Predictioncited by 1
  26. 2025Sonnet: Spectral Operator Neural Network for Multivariable Time Series Forecastingcited by 1
  27. 2025PointODE: Lightweight Point Cloud Learning with Neural Ordinary Differential Equations on Edgecited by 1
  28. 2025SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecastingcited by 1
  29. 2025Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transportcited by 1
  30. 2025Generalising Traffic Forecasting to Regions without Traffic Observationscited by 1
  31. 2025FlowCast-ODE: Continuous Hourly Weather Forecasting with Dynamic Flow Matching and ODE Solvercited by 1
  32. 2025Breaking Scale Anchoring: Frequency Representation Learning for Accurate High-Resolution Inference from Low-Resolution Trainingcited by 1
  33. 2026Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equationscited by 1
  34. 2026Super-Resolving Coarse-Resolution Weather Forecasts With Flow Matchingcited by 1
  35. 2026Neural Stochastic Processes for Satellite Precipitation Refinementcited by 1
  36. 2026RainODE: Continuous-Time Precipitation Forecasting with Latent Neural ODEscited by 1
  37. 2026VeinCast: Physics-Guided Dynamic Field Graphs with Graph-Conditioned Fusion for Global Medium-Range Weather Forecastingcited by 1
  38. 2024Spatial Shortcuts in Graph Neural Controlled Differential Equationscited by 0

50 most cited of 78 All 78 (JSON)