用于物理感知生成的自增强扩散引导

中文摘要 AI 辅助

扩散模型可用于生成物理现象的时空信号，例如流体动力学的时间序列图像。然而，标准扩散模型的一个主要局限是未纳入从底层物理定律导出的约束，导致生成样本可能在视觉上看似合理，却与真实动力学存在显著偏差。本研究提出一种基于自生成数据增强的扩散引导的简单却有效的物理感知方法，该方法学习以与物理正确动力学的偏差程度为条件的数据分布，并通过显式将偏差条件设为零来生成样本。该方法将控制方程的评估与扩散模型的训练及采样过程解耦，无需在去噪过程的每次迭代中求解控制方程，此设计使其适用于需要计算开销大的数值模拟的问题，并能实现更快的样本生成。实验结果表明，与标准扩散模型相比，所提模型不仅显著降低了偏差，在与现有物理约束扩散方法结合时还能进一步减少偏差。

英文摘要

Diffusion models can be used to generate spatiotemporal signals of physical phenomena, such as time-series images of fluid dynamics. However, a major limitation of standard diffusion models is that they do not incorporate constraints derived from the underlying physical laws. Consequently, generated samples may appear visually plausible while deviating substantially from the true dynamics. In this study, we propose a simple yet effective physics-informed approach based on diffusion guidance with self-generated data augmentation. The proposed method learns the data distribution conditioned on the degree of deviation from the physically correct dynamics and generates samples by explicitly setting the deviation condition to be zero. The method decouples the evaluation of the governing equations from the diffusion model training and sampling processes, avoiding the need to solve the governing equations at every iteration of the denoising process. This design makes the method applicable to problems requiring computationally expensive numerical simulations and enables faster sample generation. Experimental results demonstrate that the proposed model not only significantly reduces the deviations compared with standard diffusion models but also achieves further reductions when combined with existing physics-constrained diffusion methods.

发表机构

• The University of Tokyo（东京大学）
• School of Engineering（工学院）

机构由 AI 辅助整理，请以论文原文为准。