Title: Diffusion-based Models for Unpaired Super-resolution in Fluid Dynamics Show Chinese title

Title: 基于扩散模型的流体力学非配对超分辨率研究

Abstract: High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are computationally prohibitive. As an alternative, super-resolution techniques enable the enhancement of low-fidelity, low-resolution simulations. However, traditional super-resolution approaches rely on paired low-fidelity, low-resolution and high-fidelity, high-resolution datasets for training, which are often impossible to acquire in complex flow systems. To address this challenge, we propose a novel two-step approach that eliminates the need for paired datasets. First, we perform unpaired domain translation at the low-resolution level using an Enhanced Denoising Diffusion Implicit Bridge. This process transforms low-fidelity, low-resolution inputs into high-fidelity, low-resolution outputs, and we provide a theoretical analysis to highlight the advantages of this enhanced diffusion-based approach. Second, we employ the cascaded Super-Resolution via Repeated Refinement model to upscale the high-fidelity, low-resolution prediction to the high-resolution result. We demonstrate the effectiveness of our approach across three fluid dynamics problems. Moreover, by incorporating a neural operator to learn system dynamics, our method can be extended to improve evolutionary simulations of low-fidelity, low-resolution data. Show Chinese abstract

Abstract: 高保真、高分辨率的数值模拟对于研究流体力学中的复杂多尺度现象（如湍流和海洋波浪）至关重要。 然而，使用高分辨率求解器进行直接数值模拟在计算上是不可行的。 作为替代方案，超分辨率技术能够增强低保真、低分辨率的模拟。 然而，传统的超分辨率方法依赖于配对的低保真、低分辨率和高保真、高分辨率数据集进行训练，在复杂的流动系统中通常无法获取此类配对数据集。 为了解决这一挑战，我们提出了一种新颖的两步法，无需配对数据集。 首先，我们在低分辨率水平上使用增强去噪扩散隐式桥进行非配对域转换。 此过程将低保真、低分辨率的输入转换为高保真、低分辨率的输出，并提供理论分析以突出这种基于增强扩散的方法的优势。 其次，我们采用级联的通过重复细化实现超分辨率模型来将高保真、低分辨率的预测放大到高分辨率结果。 我们在三个流体力学问题中展示了我们的方法的有效性。 此外，通过结合神经算子学习系统动态，我们的方法可以扩展到改进低保真、低分辨率数据的演化模拟。