用简单扩散模型预测流体动力学，精度远超传统方法
DiffFluid: Plain Diffusion Models are Effective Predictors of Flow Dynamics
- 将流体预测转为图像转换问题，用纯扩散模型建模
- 解纳维-斯托克斯方程相对精度提升44.8%，在多个基准上领先
- 适合需要高精度物理模拟的工程与科研场景
我们展示了基于Transformer的纯扩散模型在多种工况下（如达西流和高雷诺数流动）有效预测流体动力学。不同于依赖复杂架构提取复杂相关性和学习物理状态的传统求解器，本方法将流体动力学预测建模为图像翻译问题，利用纯扩散模型求解。这种简化模型设计的方法并未削弱其捕捉复杂物理状态与几何特征的能力，实现了高精度求解。初步测试表明，DiffFluid在多个流体相关基准上均达到一致的最先进性能，尤其在求解纳维-斯托克斯方程时相对精度提升44.8%；在达西流方程和欧拉方程下的机翼问题中分别实现14.0%和11.3%的相对提升。代码将在论文录用后公开于https://github.com/DongyuLUO/DiffFluid。
原文摘要 · Abstract (English)
We showcase the plain diffusion models with Transformers are effective predictors of fluid dynamics under various working conditions, e.g., Darcy flow and high Reynolds number. Unlike traditional fluid dynamical solvers that depend on complex architectures to extract intricate correlations and learn underlying physical states, our approach formulates the prediction of flow dynamics as the image translation problem and accordingly leverage the plain diffusion model to tackle the problem. This reduction in model design complexity does not compromise its ability to capture complex physical states and geometric features of fluid dynamical equations, leading to high-precision solutions. In preliminary tests on various fluid-related benchmarks, our DiffFluid achieves consistent state-of-the-art performance, particularly in solving the Navier-Stokes equations in fluid dynamics, with a relative precision improvement of +44.8%. In addition, we achieved relative improvements of +14.0% and +11.3% in the Darcy flow equation and the airfoil problem with Euler's equation, respectively. Code will be released at https://github.com/DongyuLUO/DiffFluid upon acceptance.
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