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

arXiv: https://arxiv.org/abs/2404.10024 · HTML: https://mlsanity.com/paper/2404.10024/

## Key facts

- Cited by 82 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 48 references that are in the map.
- First posted on arXiv 15 Apr 2024.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Gradients are Not All You Need](https://mlsanity.com/paper/2111.05803/) (2021)
- [Sub-seasonal forecasting with a large ensemble of deep-learning weather prediction models](https://mlsanity.com/paper/2102.05107/) (2021)
- [Learning continuous-time PDEs from sparse data with graph neural networks](https://mlsanity.com/paper/2006.08956/) (2020)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [Interpretable Polynomial Neural Ordinary Differential Equations](https://mlsanity.com/paper/2208.05072/) (2022)

## Built on by (most cited first, 30 of 82)

- [Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold](https://mlsanity.com/paper/2408.14608/) (2024)
- [Continuous Ensemble Weather Forecasting with Diffusion models](https://mlsanity.com/paper/2410.05431/) (2024)
- [Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems](https://mlsanity.com/paper/2410.19892/) (2024)
- [Generalizing Weather Forecast to Fine-grained Temporal Scales via Physics-AI Hybrid Modeling](https://mlsanity.com/paper/2405.13796/) (2024)
- [DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction](https://mlsanity.com/paper/2504.19496/) (2025)
- [Topological Neural Networks go Persistent, Equivariant, and Continuous](https://mlsanity.com/paper/2406.03164/) (2024)
- [Deep Learning and Foundation Models for Weather Prediction: A Survey](https://mlsanity.com/paper/2501.06907/) (2025)
- [CirT: Global Subseasonal-to-Seasonal Forecasting with Geometry-inspired Transformer](https://mlsanity.com/paper/2502.19750/) (2025)
- [ClimateLLM: Efficient Weather Forecasting via Frequency-Aware Large Language Models](https://mlsanity.com/paper/2502.11059/) (2025)
- [Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme](https://mlsanity.com/paper/2506.01502/) (2025)
- [Feedback Favors the Generalization of Neural ODEs](https://mlsanity.com/paper/2410.10253/) (2024)
- [ARROW: An Adaptive Rollout and Routing Method for Global Weather Forecasting](https://mlsanity.com/paper/2510.09734/) (2025)
- [CaFA: Global Weather Forecasting with Factorized Attention on Sphere](https://mlsanity.com/paper/2405.07395/) (2024)
- [CoDiCast: Conditional Diffusion Model for Global Weather Prediction with Uncertainty Quantification](https://mlsanity.com/paper/2409.05975/) (2024)
- [Mitigating Time Discretization Challenges with WeatherODE: A Sandwich Physics-Driven Neural ODE for Weather Forecasting](https://mlsanity.com/paper/2410.06560/) (2024)
- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [HR-Extreme: A High-Resolution Dataset for Extreme Weather Forecasting](https://mlsanity.com/paper/2409.18885/) (2024)
- [Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning](https://mlsanity.com/paper/2410.06074/) (2024)
- [Towards Principled Test-Time Adaptation for Time Series Forecasting](https://mlsanity.com/paper/2605.17250/) (2026)
- [PhysMetrics.Weather: An Evaluation Framework for Physical Consistency in ML Weather Models](https://mlsanity.com/paper/2606.10642/) (2026)
- [ClimateBench-M: A Multi-Modal Climate Data Benchmark with a Simple Generative Method](https://mlsanity.com/paper/2504.07394/) (2025)
- [Position: Biology is the Challenge Physics-Informed ML Needs to Evolve](https://mlsanity.com/paper/2510.25368/) (2025)
- [Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting](https://mlsanity.com/paper/2601.21151/) (2026)
- [Synthetic Datasets for Machine Learning on Spatio-Temporal Graphs using PDEs](https://mlsanity.com/paper/2502.04140/) (2025)
- [Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecasting](https://mlsanity.com/paper/2505.14555/) (2025)
- [Neuro-Spectral Architectures for Causal Physics-Informed Networks](https://mlsanity.com/paper/2509.04966/) (2025)
- [WIND: Weather Inverse Diffusion for Zero-Shot Atmospheric Modeling](https://mlsanity.com/paper/2602.03924/) (2026)
- [PINT: Physics-Informed Neural Time Series Models with Applications to Long-term Inference on WeatherBench 2m-Temperature Data](https://mlsanity.com/paper/2502.04018/) (2025)
- [FuXi-RTM: A Physics-Guided Prediction Framework with Radiative Transfer Modeling](https://mlsanity.com/paper/2503.19940/) (2025)
- [Physics-Informed Teleconnection-Aware Transformer for Global Subseasonal-to-Seasonal Forecasting](https://mlsanity.com/paper/2506.08049/) (2025)

## 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.