Variational Grey-Box Dynamics Matching

• URL: http://arxiv.org/abs/2602.17477v1
• Date: Thu, 19 Feb 2026 15:43:22 GMT
• Title: Variational Grey-Box Dynamics Matching
• Authors: Gurjeet Sangra Singh, Frantzeska Lavda, Giangiacomo Mercatali, Alexandros Kalousis,
• Abstract summary: We present a novel grey-box method that integrates incomplete physics models directly into generative models.<n>Our approach learns dynamics from observational trajectories alone, without ground-truth physics parameters.<n>Our experiments on representative ODE/PDE problems show that our method performs on par with or superior to fully data-driven approaches.
• Score: 45.595103078998385
• License: http://creativecommons.org/licenses/by/4.0/
• 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 show 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.

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