An Efficient Surrogate Model for Emulation and Physics Extraction of Large Eddy Simulations

Mak, Simon; Sung, Chih-Li; Wang, Xingjian; Yeh, Shiang-Ting; Chang, Yung-Chung; Joseph, V. Roshan; Yang, Vigor; Wu, Congjun

doi:10.1080/01621459.2017.1409123

Cited by 99 publications

(50 citation statements)

References 53 publications

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“…The cost is dominated by a truncated SVD of the n-by-m snapshot matrix, which takes O(nmk) time. To compare the costs, take the rocket injector example in [27], where n ≈ 10 5 , m = 10 3 , k = 45, l = 30. We have (nmk)/(k 3 l 3 ) ≈ 1.83.…”

Section: Algorithm 42 Gps: Predictionmentioning

confidence: 99%

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Gaussian Process Subspace Regression for Parametric Reduced-Order Modeling

Zhang¹,

Mak²,

Dunson³

2021

Preprint

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Subspace-valued functions arise in a wide range of problems, including parametric reduced order modeling (PROM). In PROM, each parameter point can be associated with a subspace, which is used for Petrov-Galerkin projections of large system matrices. Previous efforts to approximate such functions use interpolations on manifolds, which can be inaccurate and slow. To tackle this, we propose a novel Bayesian nonparametric model for subspace prediction: the Gaussian Process Subspace regression (GPS) model. This method is extrinsic and intrinsic at the same time: with multivariate Gaussian distributions on the Euclidean space, it induces a joint probability model on the Grassmann manifold, the set of fixed-dimensional subspaces. The GPS adopts a simple yet general correlation structure, and a principled approach for model selection. Its predictive distribution admits an analytical form, which allows for efficient subspace prediction over the parameter space. For PROM, the GPS provides a probabilistic prediction at a new parameter point that retains the accuracy of local reduced models, at a computational complexity that does not depend on system dimension, and thus is suitable for online computation. We give four numerical examples to compare our method to subspace interpolation, as well as two methods that interpolate local reduced models. Overall, GPS is the most data efficient, more computationally efficient than subspace interpolation, and gives smooth predictions with uncertainty quantification.

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Section: Algorithm 42 Gps: Predictionmentioning

confidence: 99%

“…For accurate analysis and prediction, these mathematical models usually need to be discretized and simulated numerically. This has lead to the development of computational science and engineering, with wide-ranging applications such as aeroelastic systems [3], structural systems [33,4], turbomachinery [27], ocean modeling [46], and biomedicine [10].…”

mentioning

confidence: 99%

Gaussian Process Subspace Regression for Parametric Reduced-Order Modeling

Zhang¹,

Mak²,

Dunson³

2021

Preprint

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“…the high-fidelity simulation in Mak et al (2018)). Therefore, it is not practical to have (2014); Gramacy et al (2015).…”

Section: A New Calibration Frameworkmentioning

confidence: 99%

Calibration for Computer Experiments With Binary Responses and Application to Cell Adhesion Study

Sung

Hung

Rittase

et al. 2020

Journal of the American Statistical Association

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Calibration refers to the estimation of unknown parameters which are present in computer experiments but not available in physical experiments. An accurate estimation of these parameters is important because it provides a scientific understanding of the underlying system which is not available in physical experiments. Most of the work in the literature is limited to the analysis of continuous responses. Motivated by a study of cell adhesion experiments, we propose a new calibration framework for binary responses. Its application to the T cell adhesion data provides insight into the unknown values of the kinetic parameters which are difficult to determine by physical experiments due to the limitation of the existing experimental techniques.

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“…Simulation data that typically takes a week, or around 30,000 CPU hours to simulate, can be predicted by the model with an associated uncertainty in a manner of tens of minutes. The full emulator model and algorithm are provided in the complementary statistical paper [23], which considers the statistical properties of a broader class of models. The current paper focuses on applying new machine-learning techniques and investigates the practical performance of the emulator with respect to flow physics.…”

Section: Kriging Surrogate Model (Emulator)mentioning

confidence: 99%

“…Similar results are obtained for the Benchmark F, which are not shown here. To reiterate the importance of the decision tree, a comparison is made with predictions from the emulator without dataset classification [23]. Although Benchmark E experiences marginal improvement, Benchmark F's prediction is visibly enhanced.…”

Section: Root Mean Square Relative Errormentioning

confidence: 99%

Common Proper Orthogonal Decomposition-Based Spatiotemporal Emulator for Design Exploration

et al. 2018

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The present study proposes a data-driven framework trained with high-fidelity simulation results to facilitate decision making for combustor designs. At its core is a surrogate model employing a machine-learning technique called kriging, which is combined with data-driven basis functions to extract and model the underlying coherent structures. This emulation framework encompasses key design parameter sensitivity analysis, physics-guided classification of design parameter sets, and flow evolution modeling for efficient design survey. To better inform the model of quantifiable physical knowledge, a sensitivity analysis using Sobol' indices and a decision tree are incorporated into the framework. This information improves the surrogate model training process, which employs basis functions as regression functions over the design space for the kriging model. The novelty of the proposed approach is the construction of the model through Common Proper Orthogonal Decomposition, which allows for data-reduction and extraction of common coherent structures. The accuracy of prediction of mean flow features for new swirl injector designs is assessed and the dynamic flowfield is captured in the form of power spectrum densities. This data-driven framework also demonstrates the uncertainty quantification of predictions, 2 providing a metric for model fit. The significantly reduced computation time required for evaluating new design points enables efficient survey of the design space.

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An Efficient Surrogate Model for Emulation and Physics Extraction of Large Eddy Simulations

Cited by 99 publications

References 53 publications

Gaussian Process Subspace Regression for Parametric Reduced-Order Modeling

Gaussian Process Subspace Regression for Parametric Reduced-Order Modeling

Calibration for Computer Experiments With Binary Responses and Application to Cell Adhesion Study

Common Proper Orthogonal Decomposition-Based Spatiotemporal Emulator for Design Exploration

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