Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids Pub Date : 2025-09-19 DOI:10.1016/j.compfluid.2025.106841

Lorenzo Tomada, Moaad Khamlich, Federico Pichi, Gianluigi Rozza

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引用次数: 0

Abstract

This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced Order Models (ROMs) capable of capturing dynamics associated with bifurcations by identifying a minimal set of coordinates.

Our methodology combines the Sparse Identification of Nonlinear Dynamics (SINDy) method with a deep learning framework based on Autoencoder (AE) architectures. To enhance dimensionality reduction, we integrate a nested Proper Orthogonal Decomposition (POD) with the SINDy-AE architecture, enabling a sparse discovery of system dynamics while maintaining efficiency of the reduced model.

We demonstrate our approach via two challenging test cases defined on sudden-expansion channel geometries: a symmetry-breaking bifurcation and a Hopf bifurcation. Starting from a comprehensive analysis of their high-fidelity behavior, i.e. symmetry-breaking phenomena and the rise of unsteady periodic solutions, we validate the accuracy and computational efficiency of our ROMs.

The results show successful reconstruction of the bifurcations, accurate prediction of system evolution for unseen parameter values, and significant speed-up compared to full-order methods.

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计算流体力学中分岔现象的稀疏识别

本文研究了非线性参数化和时变偏微分方程的模型简化技术，特别关注计算流体动力学（CFD）中的分岔现象。我们开发了可解释和非侵入性的降阶模型（rom），能够通过识别最小坐标集来捕获与分岔相关的动态。我们的方法结合了非线性动力学的稀疏识别（SINDy）方法和基于自编码器（AE）架构的深度学习框架。为了增强降维，我们将嵌套的适当正交分解（POD）与SINDy-AE体系结构相结合，在保持降维模型效率的同时，实现了系统动力学的稀疏发现。我们通过定义在突然扩展通道几何上的两个具有挑战性的测试用例来演示我们的方法：对称破坏分岔和Hopf分岔。从全面分析它们的高保真行为，即对称性破坏现象和非定常周期解的兴起开始，我们验证了我们的rom的准确性和计算效率。结果表明，与全阶方法相比，该方法可以成功地重建分岔，准确地预测未知参数值下的系统演化，并且具有显著的加速效果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computers & Fluids 物理-计算机：跨学科应用

CiteScore

5.30

自引率

7.10%

发文量

242

审稿时长

10.8 months

期刊介绍： Computers & Fluids is multidisciplinary. The term ''fluid'' is interpreted in the broadest sense. Hydro- and aerodynamics, high-speed and physical gas dynamics, turbulence and flow stability, multiphase flow, rheology, tribology and fluid-structure interaction are all of interest, provided that computer technique plays a significant role in the associated studies or design methodology.