Variational Grey-Box Dynamics Matching

Gurjeet Sangra Singh, Frantzeska Lavda, Giangiacomo Mercatali, Alexandros Kalousis
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2782-2790, 2026.

Abstract

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 \url{https://github.com/DMML-Geneva/VGB-DM}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-singh26a, title = { Variational Grey-Box Dynamics Matching }, author = {Singh, Gurjeet Sangra and Lavda, Frantzeska and Mercatali, Giangiacomo and Kalousis, Alexandros}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2782--2790}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/singh26a/singh26a.pdf}, url = {https://proceedings.mlr.press/v300/singh26a.html}, abstract = { 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 \url{https://github.com/DMML-Geneva/VGB-DM}. } }
Endnote
%0 Conference Paper %T Variational Grey-Box Dynamics Matching %A Gurjeet Sangra Singh %A Frantzeska Lavda %A Giangiacomo Mercatali %A Alexandros Kalousis %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-singh26a %I PMLR %P 2782--2790 %U https://proceedings.mlr.press/v300/singh26a.html %V 300 %X 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 \url{https://github.com/DMML-Geneva/VGB-DM}.
APA
Singh, G.S., Lavda, F., Mercatali, G. & Kalousis, A.. (2026). Variational Grey-Box Dynamics Matching . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2782-2790 Available from https://proceedings.mlr.press/v300/singh26a.html.

Related Material