# GenCP: Towards Generative Modeling Paradigm of Coupled Physics

arXiv: https://arxiv.org/abs/2601.19541 · HTML: https://mlsanity.com/paper/2601.19541/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 54 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Functional Flow Matching](https://mlsanity.com/paper/2305.17209/) (2023)
- [Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs](https://mlsanity.com/paper/2403.12553/) (2024)
- [Differentiable hybrid neural modeling for fluid-structure interaction](https://mlsanity.com/paper/2303.12971/) (2023)
- [Parallel Multi-Block ADMM with o(1/k) Convergence](https://mlsanity.com/paper/1312.3040/) (2013)
- [Predicting fluid-structure interaction with graph neural networks](https://mlsanity.com/paper/2210.04193/) (2022)
- [Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs](https://mlsanity.com/paper/2505.17575/) (2025)
- [Machine-Learning Enhanced Predictors for Accelerated Convergence of Partitioned Fluid-Structure Interaction Simulations](https://mlsanity.com/paper/2405.09941/) (2024)
- [M2M: Learning controllable Multi of experts and multi-scale operators are the Partial Differential Equations need](https://mlsanity.com/paper/2410.11617/) (2024)
- [Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems](https://mlsanity.com/paper/2507.03660/) (2025)
- [Solid-Fluid Interaction with Surface-Tension-Dominant Contact](https://mlsanity.com/paper/2105.08471/) (2021)

## Built on by (most cited first, 2 of 2)

- [PCGD: Physics-Guided Conditional Graph Diffusion for TCAD Device Simulation](https://mlsanity.com/paper/2606.29272/) (2026)
- [Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains](https://mlsanity.com/paper/2609.00297/) (2026)

## Abstract (arXiv)

Real-world physical systems are inherently complex, often involving the coupling of multiple physics, making their simulation both highly valuable and challenging. Many mainstream approaches face challenges when dealing with decoupled data. Besides, they also suffer from low efficiency and fidelity in strongly coupled spatio-temporal physical systems. Here we propose GenCP, a novel and elegant generative paradigm for coupled multiphysics simulation. By formulating coupled-physics modeling as a probability modeling problem, our key innovation is to integrate probability density evolution in generative modeling with iterative multiphysics coupling, thereby enabling training on data from decoupled simulation and inferring coupled physics during sampling. We also utilize operator-splitting theory in the space of probability evolution to establish error controllability guarantees for this "conditional-to-joint" sampling scheme. We evaluate our paradigm on a synthetic setting and three challenging multi-physics scenarios to demonstrate both principled insight and superior application performance of GenCP. Code is available at this repo: github.com/AI4Science-WestlakeU/GenCP.