60:, that mimic the behavior of the simulation model as closely as possible while being computationally cheaper to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), relying solely on the input-output behavior. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points. This approach is also known as behavioral modeling or
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170:, and therefore it is not clear which surrogate model will be the most accurate one. In addition, there is no consensus on how to obtain the most reliable estimates of the accuracy of a given surrogate. Many other problems have known physics properties. In these cases, physics-based surrogates such as
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In design space approximation, one is not interested in finding the optimal parameter vector, but rather in the global behavior of the system. Here the surrogate is tuned to mimic the underlying model as closely as needed over the complete design space. Such surrogates are a useful, cheap way to gain
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In surrogate model-based optimization, an initial surrogate is constructed using some of the available budgets of expensive experiments and/or simulations. The remaining experiments/simulations are run for designs which the surrogate model predicts may have promising performance. The process usually
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shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (e.g., length, curvature, material, etc.). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as
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package that contains a collection of surrogate modeling methods, sampling techniques, and benchmarking functions. This package provides a library of surrogate models that is simple to use and facilitates the implementation of additional methods. SMT is different from existing surrogate modeling
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The scientific challenge of surrogate modeling is the generation of a surrogate that is as accurate as possible, using as few simulation evaluations as possible. The process comprises three major steps which may be interleaved iteratively:
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Though using surrogate models in lieu of experiments and simulations in engineering design is more common, surrogate modeling may be used in many other areas of science where there are expensive experiments and/or function evaluations.
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of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal
284:-enhanced modeling, prediction derivatives, and derivatives with respect to the training data. It also includes new surrogate models that are not available elsewhere: kriging by partial-least squares reduction and energy-minimizing
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Bliek, L.; Verstraete, H. R.; Verhaegen, M.; Wahls, S. Online optimization with costly and noisy measurements using random
Fourier expansions. IEEE transactions on neural networks and learning systems 2016, 29(1),
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Manzoni, L.; Papetti, D. M.; Cazzaniga, P.; Spolaor, S.; Mauri, G.; Besozzi, D.; Nobile, M. S. Surfing on
Fitness Landscapes: A Boost on Optimization by Fourier Surrogate Modeling. Entropy 2020, 22, 285.
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insight into the global behavior of the system. Optimization can still occur as a post-processing step, although with no update procedure (see above), the optimum found cannot be validated.
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An important distinction can be made between two different applications of surrogate models: design optimization and design space approximation (also known as emulation).
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111:(DOE) techniques cater to different sources of errors, in particular, errors due to noise in the data or errors due to an improper surrogate model.
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An improved approach for estimating the hyperparameters of the kriging model for high-dimensional problems through the partial least squares method
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The accuracy of the surrogate depends on the number and location of samples (expensive experiments or simulations) in the design space. Various
552:"Power in simplicity with ASM: tracing the aggressive space mapping algorithm over two decades of development and engineering applications"
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Cardenas, IC (2019). "On the use of
Bayesian networks as a meta-modeling approach to analyse uncertainties in slope stability analysis".
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modeling, though the terminology is not always consistent. When only a single design variable is involved, the process is known as
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is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate
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and "what-if" analysis become impossible since they require thousands or even millions of simulation evaluations.
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Improving kriging surrogates of high-dimensional design models by
Partial Least Squares dimension reduction
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Depending on the type of surrogate used and the complexity of the problem, the process may converge on a
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Bouhlel, M.A.; Hwang, J.H.; Bartoli, Nathalie; Lafage, R.; Morlier, J.; Martins, J.R.R.A. (2019).
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527:"Random Forest Surrogate Models to Support Design Space Exploration in Aerospace Use-Case"
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Run and update experiment/simulation at new location(s) found by search and add to sample
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One way of alleviating this burden is by constructing approximation models, known as
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packages which offers tools like random forests, radial basis methods and kriging.
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Auto-Extraction of
Modelica Code from Finite Element Analysis or Measurement Data
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Georisk: Assessment and
Management of Risk for Engineered Systems and Geohazards
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Construction of the surrogate model and optimizing the model parameters (i.e.,
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Search surrogate model (the model can be searched extensively, e.g., using a
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A Surrogate
Modeling and Adaptive Sampling Toolbox for Computer Based Design
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D. Gorissen, I. Couckuyt, P. Demeester, T. Dhaene, K. Crombecq, (2010), “
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Bouhlel, M. A. and
Bartoli, N. and Otsmane, A. and Morlier, J. (2016) "
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Bouhlel, M. A. and
Bartoli, N. and Otsmane, A. and Morlier, J. (2016) "
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Initial sample selection (the experiments and/or simulations to be run)
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A taxonomy of global optimization methods based on response surfaces
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Recently proposed comparison-based surrogate models (e.g., ranking
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554:, IEEE Microwave Magazine, vol. 17, no. 4, pp. 64-76, April 2016.
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Iterate steps 2 to 4 until out of time or design is "good enough"
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Artificial
Intelligence Applications and Innovations (AIAI 2019)
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For some problems, the nature of the true function is not known
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Engineering design via surrogate modelling: a practical guide
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395:"Bayesian Surrogate Analysis and Uncertainty Propagation"
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takes the form of the following search/update procedure.
601:"A Python surrogate modeling framework with derivatives"
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Forrester, Alexander, Andras Sobester, and Andy Keane,
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Ranftl, Sascha; von der Linden, Wolfgang (2021-11-13).
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Popular surrogate modeling approaches are: polynomial
701:, Goel, T., Vaidyanathan, R., Tucker, P.K. (2005), “
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85:Sample selection (also known as sequential design,
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564:Loshchilov, I.; M. Schoenauer; M. Sebag (2010).
525:Dasari, S.K.; P. Andersson; A. Cheddad (2019).
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573:Parallel Problem Solving from Nature (PPSN XI)
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103:Appraisal of the accuracy of the surrogate.
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742:", Mathematical Problems in Engineering
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715:T-Q. Pham, A. Kamusella, H. Neubert, “
276:libraries because of its emphasis on
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605:Advances in Engineering Software
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269:https://github.com/SMTorg/smt
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314:Response surface methodology
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262:Surrogate modeling software
205:Invariance with respect to
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207:orthogonal transformations
149:artificial neural networks
329:Gradient-enhanced kriging
229:Construct surrogate model
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115:Types of surrogate models
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159:surrogate modeling and
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39:design space exploration
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188:evolutionary algorithms
184:support vector machines
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324:Radial basis functions
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801:Mathematical modeling
786:Design of experiments
422:10.3390/psf2021003006
355:Fitness approximation
178:Invariance properties
137:radial basis function
109:design of experiments
585:Jones, D.R (2001), "
309:Linear approximation
286:spline interpolation
43:sensitivity analysis
550:J.E. Rayas-Sanchez,
477:2019GAMRE..13...53C
370:Bayesian regression
360:Computer experiment
127:; more generalized
35:design optimization
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345:Surrogate endpoint
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135:(GEK);
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