# Climate Physics Dynamic Matching

arXiv: https://arxiv.org/abs/2608.26907 · HTML: https://mlsanity.com/paper/2608.26907/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 15 of its 20 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 15 of 15)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Variational Rectified Flow Matching](https://mlsanity.com/paper/2502.09616/) (2025)
- [Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Prediction](https://mlsanity.com/paper/2006.12682/) (2020)
- [Robust Hybrid Learning With Expert Augmentation](https://mlsanity.com/paper/2202.03881/) (2022)
- [Variational Grey-Box Dynamics Matching](https://mlsanity.com/paper/2602.17477/) (2026)

## Abstract (arXiv)

Deep generative models such as flow matching and diffusion models have shown potential for learning complex dynamical systems, but typically act as black boxes that neglect underlying physical structure, while physics-based models governed by partial differential equations are often incomplete due to missing source terms, or uncertain parametrisations. We present Climate Physics Dynamic Matching (ClimPhyDM), a variational simulation-free dynamics informed framework for weather forecasting that combines an advection-type physics prior with data-driven components in a variational framework. % to capture the stochasticity and multi-modality of unresolved atmospheric dynamics. On the ERA5 benchmark at hourly (42-hour) and monthly (5-month) resolutions, ClimPhyDM outperforms ClimODE, and GB-DM, keeping the lower error at extended horizon, indicating improved temporal stability and resistance to error accumulation, while its simulation-free paradigm also enables training on a single modest 12 GB consumer GPU.