GB-DM: Grey-Box Dynamic Matching for Weather Forecasting

Introduced in the paper Variational Grey-Box Dynamics Matching, accepted at AISTATS 2026.

Authors: Gurjeet Sangra Singh, Frantzeska Lavda, Giangiacomo Mercatali, and Alexandros Kalousis.

$$ \begin{equation*} \frac{\partial u}{\partial t} = -\underbrace{\textcolor{blue}{v_t^\phi}(u_t, \nabla u_t, z_t, \psi) \cdot \nabla u_t}{\textcolor{blue}{\text{transport}}} - \underbrace{u_t,(\nabla \cdot \textcolor{blue}{v_t^\phi}(u_t, \nabla u_t, z_t, \psi))}{\text{compression}} + \underbrace{\textcolor{orange}{s_t^\phi}(u_t, \nabla u_t, \psi)}_{\textcolor{orange}{\text{source}}} \end{equation*} $$

This model is the monthly time embedding checkpoint of GB-DM (Grey-Box Dynamic Matching), a grey-box (physics-informed) deep learning model for medium-range weather forecasting.

If you are looking for an hourly climate model, refer to the Hourly HF model card.

Overview

GB-DM combines incomplete physics models with data-driven deep learning in a simulation-free framework inspired by Flow Matching. Rather than relying on expensive ODE solvers at training time, it learns to correct and augment a known physics prior using neural networks — enabling scalable, stable forecasting of high-dimensional atmospheric dynamics.

Key properties:

Physics-informed: integrates known atmospheric physics as a structural prior.
Simulation-free training: no ODE solvers needed during training.
ERA5-based: trained on WeatherBench ERA5 reanalysis data at 5.625° resolution.
This checkpoint uses monthly temporal embeddings.
Runs on mid-range GPUs (≥12 GB VRAM) with batch size 16–32.

Forecasted Variables

The model forecasts five meteorological variables from the ERA5 reanalysis dataset:

Variable	Description
`z500`	Geopotential at 500 hPa
`t2m`	2-metre ground temperature
`t850`	Atmospheric temperature at 850 hPa
`u10`	Eastward wind component at 10 m
`v10`	Northward wind component at 10 m

Usage

This model was uploaded using the PyTorchModelHubMixin. To load and use it:

1. Install the package

git clone https://github.com/DMML-Geneva/VGB-DM
cd VGB-DM
pip install -e .

2. Load the model from the Hub

from src.grey_box_clim.fm_phys_func import Climate_GBDM_Monthly as GBDMModel # adjust import and alias

model = GBDMModel.from_pretrained("GurjeetSinghSangra/climate_GB_FM_Monthly")
model.eval()

3. Code and Model Usage

Please refer to the README - Climate Section for further details about training, evaluation and usage.

Citation

If you find this work useful, please cite:

@inproceedings{
  singh2026variational,
  title={Variational Grey-Box Dynamics Matching},
  author={Gurjeet Sangra Singh and Frantzeska Lavda and Giangiacomo Mercatali and Alexandros Kalousis},
  booktitle={The 29th International Conference on Artificial Intelligence and Statistics},
  year={2026},
  url={https://openreview.net/forum?id=NMuUPLBc84}
}

Links

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