Papers › Climate Modeling with Neural Diffusion Equations

Climate Modeling with Neural Diffusion Equations

11 Nov 2021arXiv:2111.06011archive 2025-07-28

Jeehyun Hwang, Jeongwhan Choi, Hwangyong Choi, Kookjin Lee, Dongeun Lee, Noseong Park

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.

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Tasks

Weather Forecasting

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Weather Forecasting LA NDE MSE (t+1) 0.2621 ± 0.0026 #3 of 4 Archive leaderboard report
Weather Forecasting LA NDE MSE (t+6) 0.7594 ± 0.0225 #3 of 4 Archive leaderboard report
Weather Forecasting NOAA Atmospheric Temperature Dataset NDE MAE (t+1) 0.2975 ± 0.0062 #2 of 5 Archive leaderboard report
Weather Forecasting NOAA Atmospheric Temperature Dataset NDE MAE (t+10) 1.6337 ± 0.0467 #2 of 5 Archive leaderboard report
Weather Forecasting SD NDE MSE (t+1) 0.3561 ± 0.0055 #3 of 10 Archive leaderboard report
Weather Forecasting SD NDE MSE (t+6) 0.7301 ± 0.0048 #3 of 10 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

Diffusion

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