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GenCP: Towards Generative Modeling Paradigm of Coupled Physics

Tianrun Gao, Haoren Zheng, Wenhao Deng, Haodong Feng, Tao Zhang, Ruiqi Feng, Qianyi Chen, Tailin Wu

TL;DR

GenCP tackles the challenge of simulating coupled multiphysics with decoupled training data by reframing coupling as probability-density evolution in function spaces. It combines flow matching with operator splitting to perform conditional-to-joint sampling, supported by a theoretical error bound under Lipschitz and growth conditions. Empirical results across synthetic 2D distributions, fluid-structure interaction benchmarks, and nuclear-thermal coupling show notable gains in accuracy (often doubling the fidelity) and efficiency (few sampling steps) over surrogate and diffusion-based baselines. This approach offers a scalable, principled path toward high-fidelity, data-efficient multiphysics simulation with broad potential impact in engineering and science.

Abstract

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.

GenCP: Towards Generative Modeling Paradigm of Coupled Physics

TL;DR

GenCP tackles the challenge of simulating coupled multiphysics with decoupled training data by reframing coupling as probability-density evolution in function spaces. It combines flow matching with operator splitting to perform conditional-to-joint sampling, supported by a theoretical error bound under Lipschitz and growth conditions. Empirical results across synthetic 2D distributions, fluid-structure interaction benchmarks, and nuclear-thermal coupling show notable gains in accuracy (often doubling the fidelity) and efficiency (few sampling steps) over surrogate and diffusion-based baselines. This approach offers a scalable, principled path toward high-fidelity, data-efficient multiphysics simulation with broad potential impact in engineering and science.

Abstract

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.
Paper Structure (66 sections, 2 theorems, 73 equations, 8 figures, 10 tables, 4 algorithms)

This paper contains 66 sections, 2 theorems, 73 equations, 8 figures, 10 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Numerical simulation.
  4. Learning-based simulation.
  5. Method
  6. Problem reformulation
  7. Weak continuity equation.
  8. Decomposing the weak equation.
  9. Lie--Trotter splitting.
  10. Time-parameterized linear interpolation and training
  11. Reference distributions.
  12. Learning the velocity for the field.
  13. Learning objectives.
  14. Coupled inference via operator splitting
  15. Coupled inference.
  16. ...and 51 more sections

Key Result

Theorem 3.1

Let $\mu_1$ denote the true terminal measure at $t=1$ generated by the unknown joint velocity $v$. Let $\mu^{(\tau,\mathrm{learn})}_1$ denote the terminal measure obtained by applying the learned Lie--Trotter composition with step size $\tau$ using $\hat{v}_f,\hat{v}_g$. If the learned fields unifor where $W_1$ is the Wasserstein-1 distance and $C_{\mathrm{stab}}$ depends on Lipschitz and growth c

Figures (8)

  • Figure 1: The schematic of GenCP. With a pretrained model with decoupled physics, GenCP could manage to achieve coupled physics during flow steps. Note that here we only use Lie-Trotter Splitting as a demonstration.
  • Figure 2: Visualization of sampling results on complex distribution with different paradigms in the synthetic setting. In order to examine behavior except outlier sampling, the visualized results of M2PDE also include a zoomed-in view on the same coordinate region as the other views.
  • Figure 3: The visualization of results from different paradigms using FNO* as backbone on Turek-Hron setting. (Note that the structural boundary shown in the fluid field visualization is masked from the ground truth and does not represent actual structural deformation.)
  • Figure 4: The visualization of the final frame of predicted results from different paradigms on NT Coupling setting. (Here we only represent $T_f$ as fluid field visualization.)
  • Figure 5: The geometric configuration and coupling mechanism of NT Coupling setting.
  • ...and 3 more figures

Theorems & Definitions (5)

  • Theorem 3.1: Informal error bound
  • proof
  • proof
  • Theorem C.1: Equivalence under bijective coordinate reparametrization.
  • proof