{"title":"利用神经网络移位增广流形变换对平流控制的双曲型问题进行非侵入式模型约简","authors":"Harshith Gowrachari , Nicola Demo , Giovanni Stabile , Gianluigi Rozza","doi":"10.1016/j.compfluid.2025.106758","DOIUrl":null,"url":null,"abstract":"<div><div>Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods are ill-suited for these problems, due to slow Kolmogorov <em>n</em>-width decay. This results in inefficient and inaccurate reduced order models (ROMs). There are few non-linear approaches to accelerate the Kolmogorov <em>n</em>-width decay. In this work, we use a neural network shift augmented transformation technique that employs automatic shift detection. This approach leverages a deep-learning framework to derive a parameter-dependent mapping between the original manifold <span><math><mi>M</mi></math></span> and the transformed manifold <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>. We apply a linear compression method to obtain a low-dimensional linear approximation subspace of the transformed manifold <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>. Furthermore, we construct non-intrusive reduced order models on the resulting transformed linear approximation subspace and employ automatic shift detection for predictions in the online stage. We propose a complete framework, the neural network shift-augmented proper orthogonal decomposition-based reduced order model (NNsPOD-ROM) algorithm, comprising both offline and online stages for model reduction of advection-dominated problems. We test our proposed methodology on numerous experiments to evaluate its performance on the 1D linear advection equation, a higher order method benchmark case - the 2D isentropic convective vortex, and 2D two-phase flow.</div></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"300 ","pages":"Article 106758"},"PeriodicalIF":3.0000,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-intrusive model reduction of advection-dominated hyperbolic problems using neural network shift augmented manifold transformation\",\"authors\":\"Harshith Gowrachari , Nicola Demo , Giovanni Stabile , Gianluigi Rozza\",\"doi\":\"10.1016/j.compfluid.2025.106758\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods are ill-suited for these problems, due to slow Kolmogorov <em>n</em>-width decay. This results in inefficient and inaccurate reduced order models (ROMs). There are few non-linear approaches to accelerate the Kolmogorov <em>n</em>-width decay. In this work, we use a neural network shift augmented transformation technique that employs automatic shift detection. This approach leverages a deep-learning framework to derive a parameter-dependent mapping between the original manifold <span><math><mi>M</mi></math></span> and the transformed manifold <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>. We apply a linear compression method to obtain a low-dimensional linear approximation subspace of the transformed manifold <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>. Furthermore, we construct non-intrusive reduced order models on the resulting transformed linear approximation subspace and employ automatic shift detection for predictions in the online stage. We propose a complete framework, the neural network shift-augmented proper orthogonal decomposition-based reduced order model (NNsPOD-ROM) algorithm, comprising both offline and online stages for model reduction of advection-dominated problems. We test our proposed methodology on numerous experiments to evaluate its performance on the 1D linear advection equation, a higher order method benchmark case - the 2D isentropic convective vortex, and 2D two-phase flow.</div></div>\",\"PeriodicalId\":287,\"journal\":{\"name\":\"Computers & Fluids\",\"volume\":\"300 \",\"pages\":\"Article 106758\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2025-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Fluids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S004579302500218X\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Fluids","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S004579302500218X","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Non-intrusive model reduction of advection-dominated hyperbolic problems using neural network shift augmented manifold transformation
Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods are ill-suited for these problems, due to slow Kolmogorov n-width decay. This results in inefficient and inaccurate reduced order models (ROMs). There are few non-linear approaches to accelerate the Kolmogorov n-width decay. In this work, we use a neural network shift augmented transformation technique that employs automatic shift detection. This approach leverages a deep-learning framework to derive a parameter-dependent mapping between the original manifold and the transformed manifold . We apply a linear compression method to obtain a low-dimensional linear approximation subspace of the transformed manifold . Furthermore, we construct non-intrusive reduced order models on the resulting transformed linear approximation subspace and employ automatic shift detection for predictions in the online stage. We propose a complete framework, the neural network shift-augmented proper orthogonal decomposition-based reduced order model (NNsPOD-ROM) algorithm, comprising both offline and online stages for model reduction of advection-dominated problems. We test our proposed methodology on numerous experiments to evaluate its performance on the 1D linear advection equation, a higher order method benchmark case - the 2D isentropic convective vortex, and 2D two-phase flow.
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.