Robust principal component analysis for modal decomposition of corrupt fluid flows

Scherl, Isabel; Strom, Benjamin; Shang, Jessica; Williams, Owen; Polagye, Brian; Brunton, Steven L.

doi:10.1103/physrevfluids.5.054401

Cited by 97 publications

(55 citation statements)

References 73 publications

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“…statistics yielded by bicubic interpolation and CNN were rather similar to those of low-resolution input data. Such non-physical results, which are present in many previous works (Fukami et al 2019a,b;Kim & Lee 2020b;Liu et al 2020;Scherl et al 2020), might be inevitable consequences of minimizing the pointwise error against the target data because the given information is insufficient to determine the solution uniquely and the target is only one of the possible solutions. On the other hand, GAN-based models focus on more sophisticated errors related to spatial correlation and significant features in the turbulence.…”

Section: Resultsmentioning

confidence: 94%

“…2020; Scherl et al. 2020), might be inevitable consequences of minimizing the pointwise error against the target data because the given information is insufficient to determine the solution uniquely and the target is only one of the possible solutions. On the other hand, GAN-based models focus on more sophisticated errors related to spatial correlation and significant features in the turbulence.…”

Section: Resultsmentioning

confidence: 99%

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Unsupervised deep learning for super-resolution reconstruction of turbulence

et al. 2021

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Section: Resultsmentioning

confidence: 94%

Section: Resultsmentioning

confidence: 99%

Unsupervised deep learning for super-resolution reconstruction of turbulence

et al. 2021

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“…Section 3 will discuss an extension of PCA that is explicitly designed to remove random noise from data. In general, convergence of PCA can be evaluated by testing the extent to which adding or removing data influences the [56], and recently applied to fluids data in [57] has been proposed to overcome these limitations by separating the noisy data from the rest of the data using an optimization framework.…”

Section: Opportunities and Challengesmentioning

confidence: 99%

“…RPCA is an excellent method to detect low-dimensionality and coherent patterns in experimental haemodynamics data where noise is inevitable. Recently, RPCA has been successfully applied to experimental PIV data of complex fluid flow [57]. Experimental cardiovascular fluid mechanics techniques such as 4D flow MRI often carry a significant amount of noisy and corrupted data.…”

Section: Opportunities and Challengesmentioning

confidence: 99%

“…In general, convergence of PCA can be evaluated by testing the extent to which adding or removing data influences the results, with convergence obtained if adding additional data does not have a tangible effect on the results of the analysis. [56], and recently applied to fluids data in [57] has been proposed to overcome these limitations by separating the noisy data from the rest of the data using an optimization framework.…”

Section: Opportunities and Challengesmentioning

confidence: 99%

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Data-driven cardiovascular flow modelling: examples and opportunities

Arzani

Dawson

2021

J. R. Soc. Interface.

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High-fidelity blood flow modelling is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from such investigations remains limited by the presence of uncertainty in parameters, low resolution, and measurement noise. Additionally, extracting useful information from these datasets is challenging. Data-driven modelling techniques have the potential to overcome these challenges and transform cardiovascular flow modelling. Here, we review several data-driven modelling techniques, highlight the common ideas and principles that emerge across numerous such techniques, and provide illustrative examples of how they could be used in the context of cardiovascular fluid mechanics. 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 modelling of cardiovascular flows, including the dynamic mode decomposition and the sparse identification of nonlinear dynamics. All techniques are presented in the context of cardiovascular flows with simple examples. These data-driven modelling techniques have the potential to transform computational and experimental cardiovascular research, and we discuss challenges and opportunities in applying these techniques in the field, looking ultimately towards data-driven patient-specific blood flow modelling.

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A comparison of machine learning methods for recovering noisy and missing 4D flow MRI data

Csala,

Amili,

D'Souza

et al. 2024

Numer Methods Biomed Eng

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Experimental blood flow measurement techniques are invaluable for a better understanding of cardiovascular disease formation, progression, and treatment. One of the emerging methods is time‐resolved three‐dimensional phase‐contrast magnetic resonance imaging (4D flow MRI), which enables noninvasive time‐dependent velocity measurements within large vessels. However, several limitations hinder the usability of 4D flow MRI and other experimental methods for quantitative hemodynamics analysis. These mainly include measurement noise, corrupt or missing data, low spatiotemporal resolution, and other artifacts. Traditional filtering is routinely applied for denoising experimental blood flow data without any detailed discussion on why it is preferred over other methods. In this study, filtering is compared to different singular value decomposition (SVD)‐based machine learning and autoencoder‐type deep learning methods for denoising and filling in missing data (imputation). An artificially corrupted and voxelized computational fluid dynamics (CFD) simulation as well as in vitro 4D flow MRI data are used to test the methods. SVD‐based algorithms achieve excellent results for the idealized case but severely struggle when applied to in vitro data. The autoencoders are shown to be versatile and applicable to all investigated cases. For denoising, the in vitro 4D flow MRI data, the denoising autoencoder (DAE), and the Noise2Noise (N2N) autoencoder produced better reconstructions than filtering both qualitatively and quantitatively. Deep learning methods such as N2N can result in noise‐free velocity fields even though they did not use clean data during training. This work presents one of the first comprehensive assessments and comparisons of various classical and modern machine‐learning methods for enhancing corrupt cardiovascular flow data in diseased arteries for both synthetic and experimental test cases.

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Robust principal component analysis for modal decomposition of corrupt fluid flows

Cited by 97 publications

References 73 publications

Unsupervised deep learning for super-resolution reconstruction of turbulence

Unsupervised deep learning for super-resolution reconstruction of turbulence

Data-driven cardiovascular flow modelling: examples and opportunities

A comparison of machine learning methods for recovering noisy and missing 4D flow MRI data

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