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

2025-06-27

AI Summary

Physical models with unknown terms deviate from the true data-generating process (DGP), leading to distributional mismatch. Method: We propose a deep gray-box–optimal transport (OT) fusion framework that aligns distributions and completes imperfect physics-based models using limited, unpaired real observations and model-simulated data. A gray-box generative model is constructed by embedding physical priors into a deep neural network, while OT theory establishes an interpretable, minimal-perturbation mapping between source (simulated) and target (observed) distributions for unpaired alignment. Contribution/Results: This work is the first to jointly leverage OT and gray-box modeling for dynamic correction of partial differential equation systems. Experiments demonstrate that our method significantly outperforms purely black-box approaches under low-data regimes, achieving high generation fidelity, strong robustness to model imperfections, and intrinsic physical interpretability.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Completing incomplete physics models with hybrid generative modeling
• Resolving unpaired data issues between observations and simulations
• Enhancing model accuracy while preserving interpretability and physics parameters

Innovation

• Hybrid generative model combines grey-box and OT
• Optimal Transport maps data with minimal distortion
• Leverages physics biases for interpretable dynamics