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

arXiv: https://arxiv.org/abs/2506.22204 · HTML: https://mlsanity.com/paper/2506.22204/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 28 references that are in the map.
- First posted on arXiv 27 Jun 2025.

## Builds on (most cited first, 17 of 17)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Kernel Neural Optimal Transport](https://mlsanity.com/paper/2205.15269/) (2022)
- [Existence, Duality, and Cyclical monotonicity for weak transport costs](https://mlsanity.com/paper/1809.05893/) (2018)
- [Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Prediction](https://mlsanity.com/paper/2006.12682/) (2020)
- [Robust Hybrid Learning With Expert Augmentation](https://mlsanity.com/paper/2202.03881/) (2022)
- [Deep Grey-Box Modeling With Adaptive Data-Driven Models Toward Trustworthy Estimation of Theory-Driven Models](https://mlsanity.com/paper/2210.13103/) (2022)
- [Unifying Model-Based and Neural Network Feedforward: Physics-Guided Neural Networks with Linear Autoregressive Dynamics](https://mlsanity.com/paper/2209.12489/) (2022)
- [A Hybrid Simulation of DNN-based Gray Box Models](https://mlsanity.com/paper/2410.17103/) (2024)

## Built on by (most cited first, 1 of 1)

- [Variational Grey-Box Dynamics Matching](https://mlsanity.com/paper/2602.17477/) (2026)

## Abstract (arXiv)

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.