[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120725-en":3,"doc-seo-120725-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120725,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Multi-Fidelity Data Assimilation For Physics Inspired Machine Learning In Uncertainty Quantification Of Fluid Turbulence Simulations","Reliable prediction of turbulent flows is essential across science and engineering. In Computational Fluid Dynamics, eddy viscosity models are efficient but introduce significant epistemic and model-form uncertainty. The Eigenspace Perturbation Method quantifies this uncertainty using physics-based perturbations in the spectral space, but it does not determine how much or where to perturb. A physics-inspired machine learning framework is introduced to learn spatially varying perturbation corrections with a CNN, improving estimates of turbulence model errors while preserving computational economy.","arXiv :2307 . 12453v1 [physics .flu-dyn] 23 Jul 2023  \nMulti-Fidelity Data Assimilation For Physics Inspired Machine Learning In Uncertainty Quantification Of Fluid Turbulence Simulations  \nMinghan Chu * 1 Weicheng Qian * 2  \nDepartment of Mechanical and Materials Engineering 1 Department of Computer Science 2 Queen's University 1 University of Saskatchewwan 2  \n[17MC93@queensu.ca](17MC93@queensu.ca1 weicheng.qian@usask.ca2)[1](17MC93@queensu.ca1 weicheng.qian@usask.ca2)[ weicheng.qian@usask.ca](17MC93@queensu.ca1 weicheng.qian@usask.ca2)[2](17MC93@queensu.ca1 weicheng.qian@usask.ca2)  \nAbstract  \nReliable prediction of turbulent flows is an important necessity across different fields of science and engineering. In Computational Fluid Dynamics (CFD) simulations, the most common type of models are eddy viscosity models that are computationally inexpensive but introduce a high degree of epistemic error. The Eigenspace Perturbation Method (EPM) attempts to quantify this predictive uncertainty via physics based perturbation in the spectral representation of the predictions.  \nWhile the EPM outlines how to perturb, it does not address how much or even where to perturb. We address this need by introducing machine learning models to predict the details of the perturbation, thus creating a physics inspired machine learning (ML) based perturbation framework. In our choice of ML models, we focus on incorporating physics based inductive biases while retaining computational economy. Specifically we use a Convolutional Neural Network (CNN) to learn the correction between turbulence model predictions and true results. This physics inspired machine learning based perturbation approach is able to modulate the intensity and location of perturbations and leads to improved estimates of turbulence model errors.  \n1. Introduction  \nTurbulent fluid flows are common across different fields of science and engineering. The most commonly used models are Eddy Viscosity Models (EVMs) that are computationally inexpensive but introduce a high degree of epistemic error or model-form uncertainty, due to simplifications like the Boussinesq Turbulent Viscosity Hypothesis (TVH) . The quantification of these model-form uncertainty (Duraisamy et al., 2017) ensures reliable designs and analysis. The Eigenspace Perturbation Method (EPM) (Emory et al., 2013 ; Iaccarino et al., 2017) is a physics based framework  \nto quantify model-form uncertainty introduced in EVMs. This method has shown reliable uncertainty quantification with low computational cost, and has been applied to a variety of engineering problems including virtual certification of aircraft designs (Mukhopadhaya et al., 2020 ; Nigamet al., 2021), design of urban structures(Gorlé et al., 2019), aerospace design and analysis(Mishra et al., 2019b ; Mishra & Iaccarino, 2017a ; Mishra et al., 2019a ; Mishra & Iaccarino, 2017b), application to design under uncertainty (DUU) (Demir et al., 2023 ; Cook et al., 2019 ; Mishra et al., 2020 ; Righi, 2023), etc .  \nThe EPM only outlines how to perturb, while it does not address how much to perturb. As an illustration the EPMuses the maximal physics permissible perturbation all over the flow domain. The strength of perturbation should reflect the degree of discrepancy between EVMs and the truth, asthe discrepancy actually varies spatially in the flow domain. We address this need by developing a function to predict the degree of perturbation at different locations. While there aren't physics based precepts to completely determine this function to predict the spatial variation of perturbations, it can be estimated reliably from data. Machine Learning based approaches are becoming more used in fluid mechanics applications (Duraisamy et al., 2019 ; Chung et al., 2021 ; Brunton et al., 2020) . Some prior investigators have tried to use ML to improve turbulence model UQ (Xiao et al., 2016 ; Wu et al., 2018 ; Heyse et al., 2021b ;a; Zeng et al., 2022) . These studies have focused on more c","cbCaitnO65gxiu2l","https://ap.wps.com/l/cbCaitnO65gxiu2l","pdf",292359,1,6,"English","en",105,"# Abstract\n# Introduction\n# Methodology","[{\"question\":\"Why are eddy viscosity models widely used in CFD despite uncertainty?\",\"answer\":\"They are computationally inexpensive, but their simplified turbulence modeling introduces substantial epistemic and model-form uncertainty.\"},{\"question\":\"What limitation does the Eigenspace Perturbation Method have?\",\"answer\":\"It specifies how to perturb within the spectral representation, but it does not indicate how much to perturb or where in the flow domain to apply the perturbations.\"},{\"question\":\"How does the proposed physics-inspired machine learning approach improve EPM?\",\"answer\":\"It uses a CNN to learn a correction function that predicts the intensity and location of perturbations, enabling improved estimates of turbulence model errors while keeping computation efficient.\"}]","Multi-Fidelity Data Assimilation For Physics Inspired Machine Learning In Uncertainty Quantification Of Fluid Turbulence Simulations | 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are eddy viscosity models widely used in CFD despite uncertainty?","Question",{"text":76,"@type":77},"They are computationally inexpensive, but their simplified turbulence modeling introduces substantial epistemic and model-form uncertainty.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What limitation does the Eigenspace Perturbation Method have?",{"text":81,"@type":77},"It specifies how to perturb within the spectral representation, but it does not indicate how much to perturb or where in the flow domain to apply the perturbations.",{"name":83,"@type":74,"acceptedAnswer":84},"How does the proposed physics-inspired machine learning approach improve EPM?",{"text":85,"@type":77},"It uses a CNN to learn a correction function that predicts the intensity and location of perturbations, enabling improved estimates of turbulence model errors while keeping computation 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