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Recent advances and applications of surrogate models for finite element method computations: a review

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Jakub Kůdela at Brno University of Technology
Jakub Kůdela
Radomil Matousek
Radomil Matousek
Radomil Matousek
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Abstract

The utilization of surrogate models to approximate complex systems has recently gained increased popularity. Because of their capability to deal with black-box problems and lower computational requirements, surrogates were successfully utilized by researchers in various engineering and scientific fields. An efficient use of surrogates can bring considerable savings in computational resources and time. Since literature on surrogate modelling encompasses a large variety of approaches, the appropriate choice of a surrogate remains a challenging task. This review discusses significant publications where surrogate modelling for finite element method-based computations was utilized. We familiarize the reader with the subject, explain the function of surrogate modelling, sampling and model validation procedures, and give a description of the different surrogate types. We then discuss main categories where surrogate models are used: prediction, sensitivity analysis, uncertainty quantification, and surrogate-assisted optimization, and give detailed account of recent advances and applications. We review the most widely used and recently developed software tools that are used to apply the discussed techniques with ease. Based on a literature review of 180 papers related to surrogate modelling, we discuss major research trends, gaps, and practical recommendations. As the utilization of surrogate models grows in popularity, this review can function as a guide that makes surrogate modelling more accessible.
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Soft Computing (2022) 26:13709–13733
https://doi.org/10.1007/s00500-022-07362-8
APPLICATION OF SOFT COMPUTING
Recent advances and applications of surrogate models for finite
element method computations: a review
Jakub Kudela1
·Radomil Matousek1
Accepted: 7 June 2022 / Published online: 17 July 2022
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022
Abstract
The utilization of surrogate models to approximate complex systems has recently gained increased popularity. Because of
their capability to deal with black-box problems and lower computational requirements, surrogates were successfully utilized
by researchers in various engineering and scientific fields. An efficient use of surrogates can bring considerable savings in
computational resources and time. Since literature on surrogate modelling encompasses a large variety of approaches, the
appropriate choice of a surrogate remains a challenging task. This review discusses significant publications where surrogate
modelling for finite element method-based computations was utilized. We familiarize the reader with the subject, explain
the function of surrogate modelling, sampling and model validation procedures, and give a description of the different
surrogate types. We then discuss main categories where surrogate models are used: prediction, sensitivity analysis, uncertainty
quantification, and surrogate-assisted optimization, and give detailed account of recent advances and applications. We review
the most widely used and recently developed software tools that are used to apply the discussed techniques with ease. Based
on a literature review of 180 papers related to surrogate modelling, we discuss major research trends, gaps, and practical
recommendations. As the utilization of surrogate models grows in popularity, this review can function as a guide that makes
surrogate modelling more accessible.
Keywords Surrogate model ·Surrogate-assisted optimization ·Sensitivity analysis ·Uncertainty quantification ·Finite
element method
1 Introduction
The methods of numerical analysis, such as the finite-element
method (FEM), computational fluid dynamics (CFD), or
structural finite-element analysis (FEA), are routinely
employed to perform analysis of complex systems and
structures where obtaining an analytical solution may be
either difficult or impossible. Such analyses are becoming
ubiquitous in evaluating and optimizing design, reliabil-
ity, and maintenance of complex systems and structures
in a broad range of various industrial applications includ-
ing aerospace (Yan et al. 2020), automotive (Berthelson
et al. 2021), architecture (Westermann and Evins 2019),
biomedical engineering (Putra et al. 2018), chemical engi-
neering (Bhosekar and Ierapetritou 2018), and many others.
BJakub Kudela
Jakub.Kudela@vutbr.cz
1Institute of Automation and Computer Science, Brno
University of Technology, Technicka 2, Brno 616 00, Czech
Republic
However, these computer simulations tend to be very compu-
tationally demanding because of their intrinsically detailed
description of the studied systems. These engineering prob-
lems based on computer models also require the computation
of thousands of simulations in order to construct a suitable
solution, requiring a large computational budget (Alizadeh
et al. 2020). Additionally, because of their high fidelity, var-
ious issues in performing computer simulations can occur
regardless of how much computer power can be used. Even
the recent advance of parallel and pooling (Kudela and Popela
2020) computing methods, that carry out many calculations
or executions of processes simultaneously, do not seem to be
very helpful (Grama et al. 2003).
The principle purpose of using surrogate models (or
metamodels) is to approximately emulate the expensive-to-
evaluate high-fidelity models, such as a FEM-based model,
employing computationally less costly statistical models.
These surrogates are constructed based on a relatively low
number of simulation input and output data, that are com-
puted employing the high-fidelity expensive computations.
123
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