Surrogate modeling of multifidelity data for large samples

Burnaev, Evgeny; Zaytsev, Alexey

doi:10.1134/s1064226915120037

Cited by 20 publications

(16 citation statements)

References 9 publications

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“…It performs for each training set a numerical optimization of the technique as well as its parameters [27,28] by minimizing the cross-validation error, see [25]. Among the algorithms scanned by pSeven are the following: ridge regression [29], stepwise regression [30], elastic net [31], Gaussian processes [32], sparse Gaussian processes [33,34], High Dimensional Approximation (HDA) [25,35], and High dimensional approximation combined with Gaussian processes (HDAGP) (this technique is related to artificial neural networks and, more specifically, to the two-layer perceptron with a non-linear activation function [35]). Two desirable features of pSeven are: (i) all data manipulation is done via graphical user interface (GUI) and (ii) it can export the constructed surrogate model as a stand alone function in a number of scientific computing languages, including Matlab, C source for MEX, C source for stand alone program, C header for library, C source for library, functional mock-up interface (FMU) for Co-simulation 1.0 and executable.…”

Section: Regression Model Of U S (R τ τ ) For a Realistic Head Modelmentioning

confidence: 99%

A hybrid analytical–numerical algorithm for determining the neuronal current via electroencephalography

Hashemzadeh

Fokas

Schönlieb

2020

J. R. Soc. Interface.

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In this study, the neuronal current in the brain is represented using Helmholtz decomposition. It was shown in earlier work that data obtained via electroencephalography (EEG) are affected only by the irrotational component of the current. The irrotational component is denoted by Ψ and has support in the cerebrum. This inverse problem is severely ill-posed and requires that additional constraints are imposed. Here, we impose the requirement of the minimization of the L 2 norm of the current (energy). The function Ψ is expanded in terms of inverse multiquadric radial basis functions (RBF) on a uniform Cartesian grid inside the cerebrum. The minimal energy constraint in conjunction with the RBF parametrization of Ψ results in a Tikhonov regularized solution of Ψ. The RBF shape parameter (regularization parameter), is computed by solving a 1-D non-linear maximization problem. Reconstructions are presented using synthetic data with a signal to noise ratio (SNR) of 20 dB. The root mean square error (RMSE) between the exact and the reconstructed Ψ is RMSE=0.1122. The proposed reconstruction algorithm is computationally efficient and can be vectorized in MATLAB.

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Section: Regression Model Of U S (R τ τ ) For a Realistic Head Modelmentioning

confidence: 99%

A hybrid analytical–numerical algorithm for determining the neuronal current via electroencephalography

Hashemzadeh

Fokas

Schönlieb

2020

J. R. Soc. Interface.

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“…Maximum likelihood estimation of a Gaussian process regression model sometimes provides degenerate results -a phenomenon closely connected to overfitting [65,68,48,51]. To regularize the problem and avoid inversion of large ill-conditioned matrices, one can impose a prior distribution on a Gaussian process regression model and then use Bayesian MAP (Maximum A Posteriory) estimates [20,23,11]. In particular in this paper we adopted the approach described in [20]: we impose prior distributions on all parameters of the covariance function and additional hyperprior distributions on parameters of the prior distributions.…”

Section: Gaussian Process Regression For Single Fidelity Datamentioning

confidence: 99%

“…Nice property of Gaussian process regression is an ability to treat variable fidelity data [30,43,52,37,26,23]: one can construct a surrogate model of a high fidelity function using data both from high and low fidelity sources (e.g., high fidelity evaluations can be obtained using a computational code with a fine mesh, and low fidelity evaluations can be obtained using the same computational code with a coarser mesh). Recent results provide theoretical analysis of obtained models [67,69] and of parameters estimates [24].…”

Section: Introductionmentioning

confidence: 99%

Large scale variable fidelity surrogate modeling

Zaytsev

Burnaev

2017

Ann Math Artif Intell

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Engineers widely use Gaussian process regression framework to construct surrogate models aimed to replace computationally expensive physical models while exploring design space. Thanks to Gaussian process properties we can use both samples generated by a high fidelity function (an expensive and accurate representation of a physical phenomenon) and a low fidelity function (a cheap and coarse approximation of the same physical phenomenon) while constructing a surrogate model. However, if samples sizes are more than few thousands of points, computational costs of the Gaussian process regression become prohibitive both in case of learning and in case of prediction calculation. We propose two approaches to circumvent this computational burden: one approach is based on the Nyström approximation of sample covariance matrices and another is based on an intelligent usage of a blackbox that can evaluate a low fidelity function on the fly at any point of a design space. We examine performance of the proposed approaches using a number of artificial and real problems, including engineering optimization of a rotating disk shape.

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“…Yet, GPs have found success on various applications. They are in use on a wide range of fields and use cases ranging from surrogate modeling, experiment design, mining and geo-spatial data to battery health [3], [71], [87], [11], [33], [32], [8], [10], [5], [6], [9]. On techniques for demand forecasting in the FMCG sector, there has been little academic research and not enough efforts to expose practitioners to them.…”

Section: Introductionmentioning

confidence: 99%

Forecasting of Commercial Sales with Large Scale Gaussian Processes

Rivera¹,

Burnaev

2017

2017 IEEE International Conference on Data Mining Workshops (ICDMW)

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This paper argues that there has not been enough discussion in the field of applications of Gaussian Process for the fast moving consumer goods industry. Yet, this technique can be important as it e.g., can provide automatic feature relevance determination and the posterior mean can unlock insights on the data. Significant challenges are the large size and high dimensionality of commercial data at a point of sale. The study reviews approaches in the Gaussian Processes modeling for large data sets, evaluates their performance on commercial sales and shows value of this type of models as a decision-making tool for management.

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Surrogate modeling of multifidelity data for large samples

Cited by 20 publications

References 9 publications

A hybrid analytical–numerical algorithm for determining the neuronal current via electroencephalography

A hybrid analytical–numerical algorithm for determining the neuronal current via electroencephalography

Large scale variable fidelity surrogate modeling

Forecasting of Commercial Sales with Large Scale Gaussian Processes

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