PiRD：用于流场重构的物理信息残差扩散模型
PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction
AI总结：
针对CNN流场重构依赖训练分布且缺乏物理解释的问题，本文提出Physics-informed Residual Diffusion，通过扩散残差建模与物理约束目标函数，在含噪、稀疏等多种低保真输入下无需重训即可重构二维湍流。
摘要：
机器学习在流体动力学中的应用正变得越来越普遍，以加快求解偏微分方程正问题和反问题时的计算速度。然而，现有用于提升数据保真度的基于卷积神经网络（CNN）的方法面临一个显著挑战，即它们在训练阶段依赖特定的低保真数据模式和分布。此外，基于CNN的方法本质上将流场重构任务视为一项计算机视觉任务，优先考虑逐元素精度，缺乏物理和数学层面的解释。这种依赖性会显著影响模型在真实场景中的有效性，尤其是当低保真输入偏离训练数据或包含训练期间未考虑的噪声时。在此背景下，扩散模型的引入为提升性能和泛化能力带来了希望。与从特定低保真分布到高保真分布的直接映射不同，扩散模型学习从任意低保真分布向高保真分布转换。我们提出的模型——Physics-informed Residual Diffusion（物理信息残差扩散）——展示了将数据质量从标准低保真输入提升到注入高斯噪声的低保真输入以及随机采集样本的能力。通过将基于物理的洞察整合到目标函数中，该模型进一步提高了推断高质量数据的准确性和保真度。实验结果表明，我们的方法能够在无需重新训练的情况下，从一系列低保真输入条件中有效重构二维湍流的高质量结果。
英文摘要：
The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural network (CNN)-based methods for data fidelity enhancement is their reliance on specific low-fidelity data patterns and distributions during the training phase. In addition, the CNN-based method essentially treats the flow reconstruction task as a computer vision task that prioritizes the element-wise precision which lacks a physical and mathematical explanation. This dependence can dramatically affect the models' effectiveness in real-world scenarios, especially when the low-fidelity input deviates from the training data or contains noise not accounted for during training. The introduction of diffusion models in this context shows promise for improving performance and generalizability. Unlike direct mapping from a specific low-fidelity to a high-fidelity distribution, diffusion models learn to transition from any low-fidelity distribution towards a high-fidelity one. Our proposed model - Physics-informed Residual Diffusion, demonstrates the capability to elevate the quality of data from both standard low-fidelity inputs, to low-fidelity inputs with injected Gaussian noise, and randomly collected samples. By integrating physics-based insights into the objective function, it further refines the accuracy and the fidelity of the inferred high-quality data. Experimental results have shown that our approach can effectively reconstruct high-quality outcomes for two-dimensional turbulent flows from a range of low-fidelity input conditions without requiring retraining.
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