mlsanityData to 7 Oct 2026

Climate Modeling with Neural Diffusion Equations

arXiv 2111.06011 ↗First posted 11 Nov 2021cs.LG cs.AIcited by 20

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Abstract (arXiv)

Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design a novel climate model based on the two concepts, the neural ordinary differential equation (NODE) and the diffusion equation. Many physical processes involving a Brownian motion of particles can be described by the diffusion equation and as a result, it is widely used for modeling climate. On the other hand, neural ordinary differential equations (NODEs) are to learn a latent governing equation of ODE from data. In our presented method, we combine them into a single framework and propose a concept, called neural diffusion equation (NDE). Our NDE, equipped with the diffusion equation and one more additional neural network to model inherent uncertainty, can learn an appropriate latent governing equation that best describes a given climate dataset. In our experiments with two real-world and one synthetic datasets and eleven baselines, our method consistently outperforms existing baselines by non-trivial margins.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 25 of its 57 references that are in the map. First posted on arXiv 11 Nov 2021.

Builds on

25 of 57 references.

References · 25

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2019Simplifying Graph Convolutional Networkscited by 1,470
  4. 2015Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcastingcited by 1,428
  5. 2019Hamiltonian Neural Networkscited by 702
  6. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  7. 2020Lagrangian Neural Networkscited by 388
  8. 2018Graph networks as learnable physics engines for inference and controlcited by 242
  9. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 230
  10. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
  11. 2017Deep Learning for Precipitation Nowcasting: A Benchmark and A New Modelcited by 180
  12. 2019Continuous Graph Neural Networkscited by 114
13 more
  1. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 102
  2. 2017Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledgecited by 95
  3. 2018Neural networks for post-processing ensemble weather forecastscited by 95
  4. 2020Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODEcited by 76
  5. 2020SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimatescited by 75
  6. 2021Dissecting the Diffusion Process in Linear Graph Convolutional Networkscited by 58
  7. 2019Neural Dynamics on Complex Networkscited by 38
  8. 2016Application of Deep Convolutional Neural Networks for Detecting Extreme Weather in Climate Datasetscited by 31
  9. 2018Exascale Deep Learning for Climate Analyticscited by 28
  10. 2019Differentiable Physics-informed Graph Networkscited by 25
  11. 2019Neural Networks with Cheap Differential Operatorscited by 18
  12. 2018A test case for application of convolutional neural networks to spatio-temporal climate data: Re-identifying clustered weather patternscited by 15
  13. 2021Numerical Weather Forecasting using Convolutional-LSTM with Attention and Context Matcher Mechanismscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 7; 2024: 3; 2025: 5; 2026: 2.

20 papers.

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  1. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  2. 2022Blurring-Sharpening Process Models for Collaborative Filteringcited by 35
  3. 2024Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systemscited by 25
  4. 2023Graph Neural Rough Differential Equations for Traffic Forecastingcited by 14
  5. 2024PANDA: Expanded Width-Aware Message Passing Beyond Rewiringcited by 10
  6. 2025ClimateLLM: Efficient Weather Forecasting via Frequency-Aware Large Language Modelscited by 9
  7. 2023Learnable Path in Neural Controlled Differential Equationscited by 8
  8. 2023Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-time Dynamicscited by 8
  9. 2023Continuous-time Autoencoders for Regular and Irregular Time Series Imputationcited by 6
  10. 2024Generating Physical Dynamics under Priorscited by 6
  11. 2023Do We Need an Encoder-Decoder to Model Dynamical Systems on Networks?cited by 3
  12. 2023RDGCL: Reaction-Diffusion Graph Contrastive Learning for Recommendationcited by 3
8 more
  1. 2026ODEBrain: Continuous-Time EEG Graph for Modeling Dynamic Brain Networkscited by 3
  2. 2022Mining Causality from Continuous-time Dynamics Models: An Application to Tsunami Forecastingcited by 1
  3. 2023Long-term Time Series Forecasting based on Decomposition and Neural Ordinary Differential Equationscited by 1
  4. 2025PointODE: Lightweight Point Cloud Learning with Neural Ordinary Differential Equations on Edgecited by 1
  5. 2025Generalising Traffic Forecasting to Regions without Traffic Observationscited by 1
  6. 2025A Causality-Aware Spatiotemporal Model for Multi-Region and Multi-Pollutant Air Quality Forecastingcited by 1
  7. 2025SSTODE: Ocean-Atmosphere Physics-Informed Neural ODEs for Sea Surface Temperature Predictioncited by 0
  8. 2026Generalizing Dynamics Modeling More Easily from Representation Perspectivecited by 0