Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transport

TL;DR

This paper introduces a hybrid generative modeling approach combining deep grey-box models with optimal transport to improve incomplete physics models, especially with limited and unpaired data, ensuring interpretability and better system dynamics learning.

Contribution

The paper presents a novel method integrating deep grey-box modeling with optimal transport to complete and enhance physics models using limited, unpaired data, maintaining interpretability.

Findings

Superior performance in unpaired data scenarios

Enhanced physics parameter usage accuracy

Improved model transparency and interpretability

Abstract

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.