Work

Diffusion-Based Models for Unpaired Superresolution in Fluid Dynamics

Year: 2026

Type: article

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, superresolution techniques enable the enhancement of low-fidelity, low-resolution simulations. However, traditional superresolution 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 Superresolution 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. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/woodssss/Unpaired_SR_demo_code and in the supplementary materials ( M175142_Supplementary_Materials_1.pdf [342KB], Unpaired_SR_demo_code-main.zip [122MB]). [Formula: see text]

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/25m1751426

Authors: Wuzhe Xu, Yulong Lu, Lian Shen, Anqing Xuan, Ali Barzegari

Institutions: Purdue University West Lafayette, University of Minnesota

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of Minnesota, Office of Naval Research

Award: CAREER: Mathematical Foundations of Generative Scientific Deep Learning