Extending Classical Surrogate Modeling to High Dimensions Through Supervised Dimensionality Reduction: A Data-Driven Approach

Lataniotis, Christos; Marelli, Stefano; Sudret, Bruno

doi:10.1615/int.j.uncertaintyquantification.2020031935

Cited by 75 publications

(46 citation statements)

References 45 publications

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“…Different strategies have been proposed to deal with metamodels for very high-dimensional parameter space see e.g. Bouhlel et al [9] or Lataniotis et al [60]. However this specific problem is out of the scope of this review, so here the dimension of benchmark tests is restricted to a maximum of six dimensions.…”

Section: Higher-dimensional Testsmentioning

confidence: 99%

State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging

Fuhg¹,

Fau²,

Nackenhorst³

2020

Arch Computat Methods Eng

164

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Metamodels aim to approximate characteristics of functions or systems from the knowledge extracted on only a finite number of samples. In recent years kriging has emerged as a widely applied metamodeling technique for resource-intensive computational experiments. However its prediction quality is highly dependent on the size and distribution of the given training points. Hence, in order to build proficient kriging models with as few samples as possible adaptive sampling strategies have gained considerable attention. These techniques aim to find pertinent points in an iterative manner based on information extracted from the current metamodel. A review of adaptive schemes for kriging proposed in the literature is presented in this article. The objective is to provide the reader with an overview of the main principles of adaptive techniques, and insightful details to pertinently employ available tools depending on the application at hand. In this context commonly applied strategies are compared with regards to their characteristics and approximation capabilities. In light of these experiments, it is found that the success of a scheme depends on the features of a specific problem and the goal of the analysis. In order to facilitate the entry into adaptive sampling a guide is provided. All experiments described herein are replicable using a provided open source toolbox.

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Section: Higher-dimensional Testsmentioning

confidence: 99%

State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging

Fuhg¹,

Fau²,

Nackenhorst³

2020

Arch Computat Methods Eng

164

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“…For a full derivation of B-splines and PCA equations, the interested reader may refer to [50] and [52], respectively. Other projection methods such as PLS [53] or kPCA [22] are valid choices as well, and we encourage the inclusion of multiple projection methods in the analysis for comparison. Furthermore, we impose the projection dimension of every functional input to be the same, for simplicity of exposition.…”

Section: Screeningmentioning

confidence: 99%

“…Secondly, active subspaces techniques often rely on the gradient of the output w.r.t the inputs. This information is rarely available and has to be approximated from data [21], a sometimes difficult task when inputs are structured objects such as time series or spatial fields [22]. Finally, techniques relying on stacked models turn out to be quite restrictive regarding the combination of components of the stack; most of the proposals are limited to one specific combination of dimensionality reduction and metamodeling technique.…”

Section: Introductionmentioning

confidence: 99%

“…However, as will be shown in this paper through a set of computer experiments, the ideal metamodel configuration depends on the particular application. Thus, this kind of setting should be optimized each time a metamodel is to be built in order to get the best results from it [22]. Our proposal is a staged exploration strategy which optimizes the set of structural parameters for metamodel predictability.…”

Section: Introductionmentioning

confidence: 99%

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Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

Betancourt

Bachoc

Klein

et al. 2020

Reliability Engineering & System Safety

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et al.. Gaussian process metamodeling of functional-input code for coastal flood hazard assessment. Reliability Engineering and System Safety, Elsevier, 2020, 198, Abstract This paper investigates the construction of a metamodel for coastal flooding early warning at the peninsula of Gâvres, France. The code under study is an hydrodynamic model which receives time-varying maritime conditions as inputs. We concentrate on Gaussian pocess metamodels to emulate the behavior of the code. To model the inputs we make a projection of them onto a space of lower dimension. This setting gives rise to a model selection methodology which we use to calibrate four characteristics of our functional-input metamodel: (i) the family of basis functions to project the inputs; (ii) the projection dimension; (iii) the distance to measure similarity between functional input points; and (iv) the set of functional predictors to keep active. The proposed methodology seeks to optimize these parameters for metamodel predictability, at an affordable computational cost. A comparison to a dimensionality reduction approach based on the projection error of the input functions only showed that the latter may lead to unnecessarily large projection dimensions. We also assessed the adaptability of our methodology to changes in the number of training and validation points. The methodology proved its robustness by finding the optimal solution for most of the instances, while being computationally efficient.

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“…"Big data" may also refer to a system (real or simulated) that has many dimensions. We, however, assume that the number of dimensions has been made manageable through some statistical method; see the discussions including references in Coleman et al (2019), Kleijnen and Van Beers (2018), Lataniotis, Marelli, and Sudret (2018a), and Sangali (2018).…”

Section: Introductionmentioning

confidence: 99%

Prediction for Big Data Through Kriging: Small Sequential and One-Shot Designs

Kleijnen

Beers

2020

American Journal of Mathematical and Management Sciences

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Kriging-or Gaussian process (GP) modeling-is an interpolation method assuming that the outputs (responses) are more correlated, as the inputs (explanatory or independent variables) are closer. Such a GP has unknown (hyper)parameters that are usually estimated through the maximum-likelihood method. Big data, however, make it problematic to compute these estimated parameters, and the corresponding Kriging predictor and its predictor variance. To solve this problem, some authors select a relatively small subset from the big set of previously observed "old" data. These selection methods are sequential, and they depend on the variance of the Kriging predictor; this variance requires a specific Kriging model and the estimation of its parameters. The resulting designs turn out to be "local"; i.e., most selected old input combinations are concentrated around the new combination to be predicted. We develop a simpler oneshot (fixed-sample, non-sequential) design; i.e., from the big data set we select a small subset with the nearest neighbors of the new combination. To compare our designs and the sequential designs empirically, we use the squared prediction errors, in several numerical experiments. These experiments show that our design may yield reasonable performance.

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Extending Classical Surrogate Modeling to High Dimensions Through Supervised Dimensionality Reduction: A Data-Driven Approach

Cited by 75 publications

References 45 publications

State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging

State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging

Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

Prediction for Big Data Through Kriging: Small Sequential and One-Shot Designs

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