Surrogate modeling of high-dimensional problems via data-driven polynomial chaos expansions and sparse partial least square

Zhou, Yicheng; Hu, Jing‐Han; Hu, Yingshi

doi:10.1016/j.cma.2020.112906

Cited by 31 publications

(8 citation statements)

References 53 publications

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“…Methods such as non-intrusive Polynomial Chaos Expansions (niPCEs), while effective for low-dimensional uncertain spaces [59], suffer from the curse of dimensionality, where the minimum number of simulations required to determine the coefficients of the expansion grows rapidly with n u . While there is current research targeted at mitigating this aspect of niPCEs (see, e.g., [60,61]), at present, niPCEs are generally infeasible for the high-dimensional problems faced by industry. On the other hand, intrusive Polynomial Chaos Expansions, which require alterations to the CFD code, are criticised for being difficult to implement in an industrial context, although again academics working to mitigate this critique (see, e.g., [62,63]).…”

Section: Quantifying Aleatoric Uncertaintymentioning

confidence: 99%

Machine Learning Methods in CFD for Turbomachinery: A Review

Hammond

Pepper

Montomoli

et al. 2022

IJTPP

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Computational Fluid Dynamics is one of the most relied upon tools in the design and analysis of components in turbomachines. From the propulsion fan at the inlet, through the compressor and combustion sections, to the turbines at the outlet, CFD is used to perform fluid flow and heat transfer analyses to help designers extract the highest performance out of each component. In some cases, such as the design point performance of the axial compressor, current methods are capable of delivering good predictive accuracy. However, many areas require improved methods to give reliable predictions in order for the relevant design spaces to be further explored with confidence. This paper illustrates recent developments in CFD for turbomachinery which make use of machine learning techniques to augment prediction accuracy, speed up prediction times, analyse and manage uncertainty and reconcile simulations with available data. Such techniques facilitate faster and more robust searches of the design space, with or without the help of optimization methods, and enable innovative designs which keep pace with the demand for improved efficiency and sustainability as well as parts and asset operation cost reduction.

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Section: Quantifying Aleatoric Uncertaintymentioning

confidence: 99%

Machine Learning Methods in CFD for Turbomachinery: A Review

Hammond

Pepper

Montomoli

et al. 2022

IJTPP

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“…PCE was introduced first by Wiener [105] to project the output on an orthogonal stochastic polynomial basis function in the random inputs. The general form of the PCE can be defined as Equation ( 9) [106]:…”

Section: Polynomial Chaos Expansion (Pce)mentioning

confidence: 99%

A Review of Proxy Modeling Highlighting Applications for Reservoir Engineering

2022

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Numerical models can be used for many purposes in oil and gas engineering, such as production optimization and forecasting, uncertainty analysis, history matching, and risk assessment. However, subsurface problems are complex and non-linear, and making reliable decisions in reservoir management requires substantial computational effort. Proxy models have gained much attention in recent years. They are advanced non-linear interpolation tables that can approximate complex models and alleviate computational effort. Proxy models are constructed by running high-fidelity models to gather the necessary data to create the proxy model. Once constructed, they can be a great choice for different tasks such as uncertainty analysis, optimization, forecasting, etc. The application of proxy modeling in oil and gas has had an increasing trend in recent years, and there is no consensus rule on the correct choice of proxy model. As a result, it is crucial to better understand the advantages and disadvantages of various proxy models. The existing work in the literature does not comprehensively cover all proxy model types, and there is a considerable requirement for fulfilling the existing gaps in summarizing the classification techniques with their applications. We propose a novel categorization method covering all proxy model types. This review paper provides a more comprehensive guideline on comparing and developing a proxy model compared to the existing literature. Furthermore, we point out the advantages of smart proxy models (SPM) compared to traditional proxy models (TPM) and suggest how we may further improve SPM accuracy where the literature is limited. This review paper first introduces proxy models and shows how they are classified in the literature. Then, it explains that the current classifications cannot cover all types of proxy models and proposes a novel categorization based on various development strategies. This new categorization includes four groups multi-fidelity models (MFM), reduced-order models (ROM), TPM, and SPM. MFMs are constructed based on simplifying physics assumptions (e.g., coarser discretization), and ROMs are based on dimensional reduction (i.e., neglecting irrelevant parameters). Developing these two models requires an in-depth knowledge of the problem. In contrast, TPMs and novel SPMs require less effort. In other words, they do not solve the complex underlying mathematical equations of the problem; instead, they decouple the mathematical equations into a numeric dataset and train statistical/AI-driven models on the dataset. Nevertheless, SPMs implement feature engineering techniques (i.e., generating new parameters) for its development and can capture the complexities within the reservoir, such as the constraints and characteristics of the grids. The newly introduced parameters can help find the hidden patterns within the parameters, which eventually increase the accuracy of SPMs compared to the TPMs. This review highlights the superiority of SPM over traditional statistical/AI-based proxy models. Finally, the application of various proxy models in the oil and gas industry, especially in subsurface modeling with a set of real examples, is presented. The introduced guideline in this review aids the researchers in obtaining valuable information on the current state of PM problems in the oil and gas industry.

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“…This phenomenon is known as the "curse of dimension." 17 To address the problem of "curse of dimension," researchers have developed several dimension reduction methods.…”

Section: Introductionmentioning

confidence: 99%

“…However, when constructing a surrogate model for high-dimension reliability problems, the number of training points grows exponentially with the dimensions of input variables. 17 For the Kriging model, the order of correlation function matrix increases with the amount of training points, which may result in low computational efficiency, low-precision fitting, and even a wrong conclusion. This phenomenon is known as the “curse of dimension.” 17 To address the problem of “curse of dimension,” researchers have developed several dimension reduction methods.…”

Section: Introductionmentioning

confidence: 99%

A high-dimension structural reliability method based on active learning Kriging and dimension reduction technique

Zhao

Zhou

Shi

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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For efficiently and accurately estimating the failure probability and the further sensitivity index of the high-dimension structures, a novel AS-AK-MCS method is proposed in this work. This method fully employs the merits of the active subspace-based dimension reduction technique, the active learning (AL) Kriging surrogate model, and the Monte Carlo simulation. In the proposed method, the intractable gradient information needed by the active subspace method is obtained by a crude Kriging model with initial training sample points. In the construction of the crude Kriging model, the proposed trend model selection criterion reduces the man-made error. Then the active subspace method converts the reliability analysis from the original high-dimension space into the low-dimension subspace, which facilities constructing an AL-Kriging model and also avoids the tricky “curse of dimension” problem. The state-of-the-art U learning function is applied as the points adding criterion in the active subspace. In order to demonstrate the effectivity and versatility of the proposed method, three representative examples including the linear/nonlinear and the explicit/implicit performance functions are studied for estimating the failure probability and the failure probability-based sensitivity index. Finally, the proposed method is applied to the reliability and sensitivity analysis of a composite radome structure.

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Surrogate modeling of high-dimensional problems via data-driven polynomial chaos expansions and sparse partial least square

Cited by 31 publications

References 53 publications

Machine Learning Methods in CFD for Turbomachinery: A Review

Machine Learning Methods in CFD for Turbomachinery: A Review

A Review of Proxy Modeling Highlighting Applications for Reservoir Engineering

A high-dimension structural reliability method based on active learning Kriging and dimension reduction technique

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