GTApprox: Surrogate modeling for industrial design

Abstract

We describe GTApprox -a new tool for medium-scale surrogate modeling in industrial design. Compared to existing software, GTApprox brings several innovations: a few novel approximation algorithms, several advanced methods of automated model selection, novel options in the form of hints. We demonstrate the efficiency of GTApprox on a large collection of test problems. In addition, we describe several applications of GTApprox to real engineering problems.

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

“…A total of 890807 data points were randomly selected for training and the remaining 46885 data points are used for testing. For this construction, the smart selection routine of Datadvance chose the high dimensional approximation [25], which is essentially a two-layer neural network. The relative mean distance measure (RDM) is 0.2102 and the natural logarithm of the magnification factor (ln(MAG)) is −0.0208.…”

“…It is noted that pSeven has a smart selection option for scanning through a set of algorithms to select the best model amongst the set. 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]).…”

“…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.…”

Large scale variable fidelity surrogate modeling

“…Constructed model can be used to speed-up evaluations [57,2,36], for surrogate-based optimization [31,46], uncertainty quantification [42], sensitivity analysis [16,17,18] and adaptive design of experiments [19]. Maturity of this approach is further confirmed not only by numerous applications but also by availability of software packages that are dedicated to surrogate modeling and include Gaussian process regression-based approaches [8,35,1,10].…”

“…As the Cholesky factor for the updated model differs only in the last row we calculate (8) and (9) in O(n 2 ) operations. The total computational complexity is the sum of computational complexities of the Cholesky decomposition update and the posterior mean and variance recalculation, so for a Variable fidelity Gaussian process regression with a blackbox, representing the low fidelity function, the following theorem holds true.…”