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Data-Driven Filtered Reduced Order Modeling of Fluid Flows

X. Xie, M. Mohebujjaman, L. G. Rebholz, T. Iliescu
2018 SIAM Journal on Scientific Computing  
We propose a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows.  ...  (ii) In the second step, we use data-driven modeling to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved modes.  ...  In this paper, we proposed a novel ROM framework for the numerical simulation of fluid flows. This framework was based on explicit ROM spatial filtering and data-driven modeling.  ... 
doi:10.1137/17m1145136 fatcat:2kiu4dinqreftfsfgsi3q75dbq

Physically-Constrained Data-Driven Correction for Reduced Order Modeling of Fluid Flows

M. Mohebujjaman, L. G. Rebholz, T. Iliescu
2018 International Journal for Numerical Methods in Fluids  
In our earlier work, we proposed a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows, which can be formally written as DDF-ROM = Galerkin-ROM + Correction  ...  The new DDF-ROM was constructed by using ROM spatial filtering and data-driven ROM closure modeling (for the Correction term) and was successfully tested in the numerical simulation of a 2D channel flow  ...  : miñ A, B Physically-Constrained Data-Driven, Filtered Reduced Order Modeling of Fluid Flows  ... 
doi:10.1002/fld.4684 fatcat:mlt457sypfdy3czz6snd4i2mca

From snapshots to modal expansions – bridging low residuals and pure frequencies

Bernd R. Noack
2016 Journal of Fluid Mechanics  
Data-driven low-order modelling has been enjoying rapid advances in fluid mechanics. Arguably, Sirovich (Q. Appl. Maths, vol.  ...  The resulting reduced-order models provide valuable insights into flow physics, allow inexpensive explorations of dynamics and operating conditions, and enable model-based control design.  ...  The discussion of reduced-order modelling approaches could easily be extended.  ... 
doi:10.1017/jfm.2016.416 fatcat:kv7onnfvenepzezsknwztkagtm

Special issue on machine learning and data-driven methods in fluid dynamics

Steven L. Brunton, Maziar S. Hemati, Kunihiko Taira
2020 Theoretical and Computational Fluid Dynamics  
use of data-driven and machine learning tools.  ...  of fluid dynamics.  ...  Acknowledgements We thank Tim Colonius, Kozo Fujii, Koji Fukagata, Petros Koumoutsakos, Nathan Kutz, Jean-Christophe Loiseau, Bernd Noack, and Peter Schmid for stimulating discussions on data-driven methods  ... 
doi:10.1007/s00162-020-00542-y fatcat:xg6u4tnggngo7ewjf7wekejrsu

Data-driven cardiovascular flow modeling: examples and opportunities [article]

Amirhossein Arzani, Scott T. M. Dawson
2021 arXiv   pre-print
In particular, we discuss principal component analysis (PCA), robust PCA, compressed sensing, the Kalman filter for data assimilation, low-rank data recovery, and several additional methods for reduced-order  ...  in the field, looking ultimately towards data-driven patient-specific blood flow modeling.  ...  Data Availability The codes and data used to generate the results in the manuscript will be made publicly available after peer-review. p. 30  ... 
arXiv:2010.00131v2 fatcat:kgjzb4mup5amjdnfipoekthm4q

Evolve Filter Stabilization Reduced-Order Model for Stochastic Burgers Equation

Xuping Xie, Feng Bao, Clayton Webster
2018 Fluids  
The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model  ...  In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems.  ...  Reduced Order Modeling Proper Orthogonal Decomposition POD is one of the most popular data-driven reduced order modeling methods, which we exclusively use to generate the ROM basis in this paper.  ... 
doi:10.3390/fluids3040084 fatcat:3kfd2hynn5eqhfryrjqm66fxqi

On closures for reduced order models - A spectrum of first-principle to machine-learned avenues [article]

Shady E. Ahmed, Suraj Pawar, Omer San, Adil Rasheed, Traian Iliescu, Bernd R. Noack
2021 arXiv   pre-print
Finally, we outline our vision on how state-of-the-art data-driven modeling can continue to reshape the field of reduced order modeling.  ...  For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics.  ...  The main objective of this study is to provide an overview of data-driven reduced order modeling strategies relevant to fluid dynamics applications.  ... 
arXiv:2106.14954v2 fatcat:q6jzbxfjabc3vg3nsn24z4lbyy

Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network

Xuping Xie, Guannan Zhang, Clayton G. Webster
2019 Mathematics  
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics.  ...  Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications.  ...  reduced-order model DDF-ROM Data-driven filtered reduced-order model NSE Naiver-Stokes equations AM Adams-Moulton FOM Full order model ROM Reduced order model LMNet Linear multistep neural network  ... 
doi:10.3390/math7080757 fatcat:mds7igjnsvaehe4tgorkkg33fa

Deep Convolutional Recurrent Autoencoders for Flow Field Prediction [article]

Sandeep Reddy Bukka, Allan Ross Magee, Rajeev Kumar Jaiman
2020 arXiv   pre-print
The methodology is developed in the context of the overall data-driven reduced-order model framework proposed in the paper.  ...  Specifically, the multiscale nature and the gap flow dynamics of the side-by-side cylinders are captured by the proposed data-driven model reduction methodology.  ...  CONCLUSION An overall framework for the data-driven reduced order model is presented in this work. The current work can be considered as a extension of our previous work on POD-RNN [2] .  ... 
arXiv:2003.12147v1 fatcat:sl73fh6inregvhxkj5m2kcemce

A hybrid partitioned deep learning methodology for moving interface and fluid-structure interaction [article]

Rachit Gupta, Rajeev Kumar Jaiman
2021 arXiv   pre-print
The hybrid operation of this methodology comes by combining two data-driven models for fluid and solid subdomains via deep learning-based reduced-order models (DL-ROMs).  ...  We present a hybrid partitioned deep learning framework for the reduced-order modeling of fluid-structure interaction.  ...  Acknowledgement The authors would like to acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) for the funding.  ... 
arXiv:2102.09095v2 fatcat:r5s5r4mskzcvrawb42gidu2wmy

The Potential of Machine Learning to Enhance Computational Fluid Dynamics [article]

Ricardo Vinuesa, Steven L. Brunton
2021 arXiv   pre-print
This paper highlights some of the areas of highest potential impact, including to accelerate direct numerical simulations, to improve turbulence closure modelling, and to develop enhanced reduced-order  ...  models.  ...  Reduced-order models Machine-learning is also being used to develop reduced-order models (ROMs) in fluid dynamics.  ... 
arXiv:2110.02085v1 fatcat:fu4b2dym6bd53ihnpqprdpwefu

Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems [article]

Francisco J. Gonzalez, Maciej Balajewicz
2018 arXiv   pre-print
The deep convolutional autoencoder returns a low-dimensional representation in terms of coordinates on some expressive nonlinear data-supporting manifold.  ...  We demonstrate our model on three illustrative examples each highlighting the model's performance in prediction tasks for fluid systems with large parameter-variations and its stability in long-term prediction  ...  Simulations and model training were also made possible in part by an exploratory award from the Blue Waters sustainedpetascale computing project, which is supported by the National Science Foundation (  ... 
arXiv:1808.01346v2 fatcat:g46ttwgcdbfj5prd2l7f6lbzma

A Hybrid Reduced Order Model for nonlinear LES filtering [article]

Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
2021 arXiv   pre-print
We develop a Reduced Order Model (ROM) for a Large Eddy Simulation (LES) approach that combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method  ...  a data-driven reduction method to approximate the indicator function used by the nonlinear differential filter.  ...  Acknowledgements We acknowledge the support provided by the European Research Council Executive Agency by the Consolidator Grant project AROMA-CFD "Advanced Reduced Order Methods with Applications in Computational  ... 
arXiv:2107.12933v1 fatcat:mubmmhwhcreivofzycc7iy6qr4

On linking the filter width to the boundary layer thickness in explicitly filtered large eddy simulations of wall bounded flows

Mahfuz Sarwar, M.J. Cleary, K.A.M. Moinuddin, G.R. Thorpe
2017 International Journal of Heat and Fluid Flow  
However, the value of this model coefficient also depends on the types of filter and fluid flow.  ...  data which demonstrates the adequacy of the second-order numerical scheme.  ... 
doi:10.1016/j.ijheatfluidflow.2017.04.004 fatcat:auq5xstg6nfh5b542wafecvukm

Charge density enhancement due to recirculatory flow

A.P. Washabaugh, M. Zahn
1994 IEEE transactions on dielectrics and electrical insulation  
This paper develops a system model for electrification in a flow loop and investigates volume charge accumulation due t o recirculatory flow between a charge source and several charge relaxation regions  ...  On the other hand, when the reservoir is bypassed, the volume of the pipes for recirculating the flow (region 5 of the model) is on the order of V~=2.6 1, giving a reduced residence time of about 2.1 s  ...  Ideally, a single set of model parameters, such as pd, the volumes, fluid properties, and filter paper permittivity, would describe all of the data.  ... 
doi:10.1109/94.300231 fatcat:a3c2nk2iojgwzp56wxaujc52ju
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