Climate Physics Dynamic Matching

Gurjeet Sangra Singh; Frantzeska Lavda; Alexandros Kalousis

stat.APAug 27, 2026

Climate Physics Dynamic Matching

Authors: Gurjeet Sangra Singh, Frantzeska Lavda, Alexandros Kalousis

Organizations: University of Geneva, Geneva, Switzerland · HES-SO Geneva, Geneva, Switzerland

Abstract

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.

Figures & tables

Figure 1: Vector field decomposition . Term-wise visualization of ClimPhyDM’s learned PDE components from Eq. equation 1 at a single forecast step.

Figure 2: Hourly forecasting performance. Latitude-weighted RMSE (top, lower is better) and ACC (bottom, higher is better) over 42 hours.

Figure 3: Residual maps for weather forecasting . Visualization of absolute error maps between ground truth and predicted fields for five meteorological variables.

Figure 4: 5-month forecast horizon. Latitude-weighted RMSE (lower is better).

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Type	Variable name	Abbrev.	ECMWF ID	Levels
Static	Land-sea mask	lsm	172
Single	2 metre temperature	t2m	167
Single	10 metre U wind component	u10	165
Single	10 metre V wind component	v10	166
Atmospheric	Geopotential	z	129	500
Atmospheric	Temperature	t	130	850

Appendix

Table A1 : ECMWF data variables from ERA5 used in our dataset. Static variables are time-independent, Single represents surface-level variables, and Atmospheric represents time-varying atmospheric properties at chosen altitudes.

Figure A5 : Example of Climate forecasting using ClimPhyDM over $42$ hours.

Weather Forecasting

Weather forecasting predicts future atmospheric conditions, from local storms to global patterns, using physical models, observations, and machine learning.

See all 172 papers

Variational Grey-Box Dynamics Matching
Feb 19, 2026Gurjeet Sangra Singh, Frantzeska Lavda, Giangiacomo Mercatali +1Physics-Informed Generative Modeling System Identification
Evaluating Dynamical Fidelity through Predictive Structure in Physical Representations
Sep 28, 2026Oskar Bohn Lassen, Joao Paulo de Souza Boger, Simon Driscoll +4Spatiotemporal Forecasting Weather Forecasting
Department of Technology, Management, and Economics Technical University of Denmark · Department of Applied Mathematics and Theoretical Physics University of Cambridge · Department of Mathematics and Statistics University of Exeter
PhysMetrics.Weather: An Evaluation Framework for Physical Consistency in ML Weather Models
Jun 9, 2026Emma Kasteleyn, Timo Maier, Axel Lauer +3Forecasting Benchmarks Physics-Informed ML
University of Amsterdam, Amsterdam, The Netherlands · Deutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany · University of Bremen, Institute of Environmental Physics (IUP), Bremen, Germany +1

Feb 19, 2026J/K move · Enter open · S save

Variational Grey-Box Dynamics Matching

Gurjeet Sangra Singh, Frantzeska Lavda, Giangiacomo Mercatali, Alexandros Kalousis

Physics-Informed Generative Modeling System Identification Flow Matching

Open paper AskPDF arXiv

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based simulation models described by ODEs/PDEs remain interpretable, but may have missing or unknown terms, unable to fully describe real-world observations. We bridge this gap with a novel grey-box method that integrates incomplete physics models directly into generative models. Our approach learns dynamics from observational trajectories alone, without ground-truth physics parameters, in a simulation-free manner that avoids scalability and stability issues of Neural ODEs. The core of our method lies in modelling a structured variational distribution within the flow matching framework, by using two latent encodings: one to model the missing stochasticity and multi-modal velocity, and a second to encode physics parameters as a latent variable with a physics-informed prior. Furthermore, we present an adaptation of the framework to handle second-order dynamics. Our experiments on representative ODE/PDE problems and real-world weather forecasting demonstrate that our method performs on par with or superior to fully data-driven approaches and previous grey-box baselines, while preserving the interpretability of the physics model. Our code is available at https://github.com/DMML-Geneva/VGB-DM.

Abstract

Weather Forecasting

Explore similar work

Variational Grey-Box Dynamics Matching

Evaluating Dynamical Fidelity through Predictive Structure in Physical Representations

PhysMetrics.Weather: An Evaluation Framework for Physical Consistency in ML Weather Models