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

Ahmed, Shady E.; Pawar, Suraj; San, Omer; Rasheed, Adil; Iliescu, Traian; Noack, Bernd R.

doi:10.1063/5.0061577

Cited by 114 publications

(55 citation statements)

References 402 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Specifically, we aim at constructing a two-dimensional ROM that is as accurate as possible (preferably, as accurate as the three-dimensional G-ROM (2)). For our toy problem (1), this amounts to constructing a dynamical system for 𝑎 1 and 𝑎 2 (assuming that the first two ROM basis functions dominate the third, as is often the case; see Section 3).…”

Section: Closure Errormentioning

confidence: 99%

“…(iii) Data-driven, which use available data. The three types of ROM closure models are surveyed in [1]. In this tutorial, we take a different approach and, for clarity of presentation, focus on data-driven approaches, which have experienced a tremendous development over the last few years.…”

Section: • > A5mentioning

confidence: 99%

“…The answer A6 is elaborated in the survey in [1], which presents a plethora of examples of under-resolved ROM simulations of complex dynamics (e.g., turbulent flows) in which ROM closures significantly increase the accuracy at a modest computational overhead. In this section, for clarity of presentation, we illustrate how a specific ROM closure model (i.e., the D2-VMS-ROM outlined in Section 5) increases the ROM accuracy for the 2D flow past a circular cylinder [37], which is a simple test problem commonly used in the ROM community.…”

Section: Do Rom Closures Work In Practice?mentioning

confidence: 99%

“…To our knowledge, the first (and only) survey of ROM closure models was performed in [1], where the authors discuss dozens of ROM closures for fluids that have been developed over the last four decades. We are not aware, however, of a tutorial on ROM closures.…”

Section: Introductionmentioning

confidence: 99%

“…We also emphasize that our goal in this tutorial is not to explain the "how," but the "why." That is, we carefully explain the principles used to develop ROM closures, without focusing on particular approaches (which are carefully discussed in [1]).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Reduced Order Model Closures: A Brief Tutorial

Snyder¹,

Mou²,

Liu³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Section: Closure Errormentioning

confidence: 99%

Section: • > A5mentioning

confidence: 99%

Section: Do Rom Closures Work In Practice?mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Reduced Order Model Closures: A Brief Tutorial

Snyder¹,

Mou²,

Liu³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Data‐driven variational multiscale reduced order modeling of vaginal tissue inflation

Snyder

McGuire

Mou

et al. 2022

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

The vagina undergoes large finite deformations and has complex geometry and microstructure, resulting in material and geometric nonlinearities, complicated boundary conditions, and nonhomogeneities within finite element (FE) simulations. These nonlinearities pose a significant challenge for numerical solvers, increasing the computational time by several orders of magnitude.Simplifying assumptions can reduce the computational time significantly, but this usually comes at the expense of simulation accuracy. This study proposed the use of reduced order modeling (ROM) techniques to capture experimentally measured displacement fields of rat vaginal tissue during inflation testing in order to attain both the accuracy of higher-fidelity models and the speed of simpler simulations. The proper orthogonal decomposition (POD) method was used to extract the significant information from FE simulations generated by varying the luminal pressure and the parameters that introduce the anisotropy in the selected constitutive model. A new data-driven (DD) variational multiscale (VMS) ROM framework was extended to obtain the displacement fields of rat vaginal tissue under pressure. For comparison purposes, we also investigated the classical Galerkin ROM (G-ROM). In our numerical study, both the G-ROM and the DD-VMS-ROM decreased the FE computational cost by orders of magnitude without a significant decrease in numerical accuracy. Furthermore, the DD-VMS-ROM improved the G-ROM accuracy at a modest computational overhead. Our numerical investigation showed that ROM has the potential to provide efficient and accurate computational tools to describe vaginal deformations, with the ultimate goal of improving maternal health.

show abstract

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

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 114 publications

References 402 publications

Reduced Order Model Closures: A Brief Tutorial

Reduced Order Model Closures: A Brief Tutorial

Data‐driven variational multiscale reduced order modeling of vaginal tissue inflation

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

Contact Info

Product

Resources

About