Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transport
This work addresses the challenge of improving physics-based models for real-world systems where equations are incomplete, offering a solution that enhances accuracy and interpretability for researchers and practitioners in fields like engineering and science, though it is incremental as it builds on existing grey-box and OT methods.
The paper tackles the problem of incomplete physics models with missing or unknown terms, which cause a mismatch between model simulations and true data distributions, by proposing a hybrid generative model that combines deep grey-box modeling with Optimal Transport methods to complete the physics using limited, unpaired data. The method demonstrates superior performance in resolving unpaired data issues and ensuring correct physics parameter usage, validated through experiments on generation tasks and model transparency.
Physics phenomena are often described by ordinary and/or partial differential equations (ODEs/PDEs), and solved analytically or numerically. Unfortunately, many real-world systems are described only approximately with missing or unknown terms in the equations. This makes the distribution of the physics model differ from the true data-generating process (DGP). Using limited and unpaired data between DGP observations and the imperfect model simulations, we investigate this particular setting by completing the known-physics model, combining theory-driven models and data-driven to describe the shifted distribution involved in the DGP. We present a novel hybrid generative model approach combining deep grey-box modelling with Optimal Transport (OT) methods to enhance incomplete physics models. Our method implements OT maps in data space while maintaining minimal source distribution distortion, demonstrating superior performance in resolving the unpaired problem and ensuring correct usage of physics parameters. Unlike black-box alternatives, our approach leverages physics-based inductive biases to accurately learn system dynamics while preserving interpretability through its domain knowledge foundation. Experimental results validate our method's effectiveness in both generation tasks and model transparency, offering detailed insights into learned physics dynamics.