Polynomial-Chaos–Kriging with Gradient Information for Surrogate Modeling in Aerodynamic Design

AIAA Journal ◽  
2021 ◽  
pp. 1-18
Author(s):  
Lavi R. Zuhal ◽  
Kemas Zakaria ◽  
Pramudita Satria Palar ◽  
Koji Shimoyama ◽  
Rhea Patricia Liem
Keyword(s):  
Polynomial Chaos ◽  
Surrogate Modeling ◽  
Aerodynamic Design ◽  
Gradient Information

A review of the artificial neural network surrogate modeling in aerodynamic design

2019 ◽  
Vol 233 (16) ◽  
pp. 5863-5872 ◽  
Author(s):  
Gang Sun ◽  
Shuyue Wang
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Design Space ◽  
Optimal Solution ◽  
Surrogate Modeling ◽  
Aerodynamic Design ◽  
Hidden Information ◽  
Data Manipulation ◽  
Artificial Neural ◽  
Selection Of

Artificial neural network surrogate modeling with its economic computational consumption and accurate generalization capabilities offers a feasible approach to aerodynamic design in the field of rapid investigation of design space and optimal solution searching. This paper reviews the basic principle of artificial neural network surrogate modeling in terms of data treatment and configuration setup. A discussion of artificial neural network surrogate modeling is held on different objectives in aerodynamic design applications, various patterns of realization via cutting-edge data technique in numerous optimizations, selection of network topology and types, and other measures for improving modeling. Then, new frontiers of modern artificial neural network surrogate modeling are reviewed with regard to exploiting the hidden information for bringing new perspectives to optimization by exploring new data form and patterns, e.g. quick provision of candidates of better aerodynamic performance via accumulated database instead of random seeding, and envisions of more physical understanding being injected to the data manipulation.

scholarly journals A Comparison of Surrogate Modeling Techniques for Global Sensitivity Analysis in Hybrid Simulation

2021 ◽  
Vol 4 (1) ◽  
pp. 1-21
Author(s):  
Nikolaos Tsokanas ◽  
Roland Pastorino ◽  
Božidar Stojadinović
Keyword(s):  
Sensitivity Analysis ◽  
Hybrid Model ◽  
Polynomial Chaos ◽  
Global Sensitivity Analysis ◽  
Hybrid Simulation ◽  
Surrogate Modeling ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Model Response ◽  
Modeling Techniques

Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario. The system under consideration is divided into multiple individual substructures, out of which one or more are tested physically, whereas the remaining are simulated numerically. The coupling of all substructures forms the so-called hybrid model. Although hybrid simulation is extensively used across various engineering disciplines, it is often the case that the hybrid model and related excitation are conceived as being deterministic. However, associated uncertainties are present, whilst simulation deviation, due to their presence, could be significant. In this regard, global sensitivity analysis based on Sobol’ indices can be used to determine the sensitivity of the hybrid model response due to the presence of the associated uncertainties. Nonetheless, estimation of the Sobol’ sensitivity indices requires an unaffordable amount of hybrid simulation evaluations. Therefore, surrogate modeling techniques using machine learning data-driven regression are utilized to alleviate this burden. This study extends the current global sensitivity analysis practices in hybrid simulation by employing various different surrogate modeling methodologies as well as providing comparative results. In particular, polynomial chaos expansion, Kriging and polynomial chaos Kriging are used. A case study encompassing a virtual hybrid model is employed, and hybrid model response quantities of interest are selected. Their respective surrogates are developed, using all three aforementioned techniques. The Sobol’ indices obtained utilizing each examined surrogate are compared with each other, and the results highlight potential deviations when different surrogates are used.

scholarly journals Deep Active Subspaces: A Scalable Method for High-Dimensional Uncertainty Propagation

2019 ◽  
Author(s):  
Rohit Tripathy ◽  
Ilias Bilionis
Keyword(s):  
Dimensionality Reduction ◽  
Stochastic Systems ◽  
Uncertainty Propagation ◽  
Gaussian Process Regression ◽  
Surrogate Modeling ◽  
Forward Model ◽  
High Dimensional ◽  
Great Promise ◽  
Gradient Information ◽  
Active Subspaces

Abstract A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. The difficulty of accurate surrogate modeling in such systems, is further compounded by data scarcity brought about by the large cost of forward model evaluations. Traditional response surface techniques, such as Gaussian process regression (or Kriging) and polynomial chaos are difficult to scale to high dimensions. To make surrogate modeling tractable in expensive high-dimensional systems, one must resort to dimensionality reduction of the stochastic parameter space. A recent dimensionality reduction technique that has shown great promise is the method of ‘active subspaces’. The classical formulation of active subspaces, unfortunately, requires gradient information from the forward model — often impossible to obtain. In this work, we present a simple, scalable method for recovering active subspaces in high-dimensional stochastic systems, without gradient-information that relies on a reparameterization of the orthogonal active subspace projection matrix, and couple this formulation with deep neural networks. We demonstrate our approach on challenging synthetic datasets and show favorable predictive comparison to classical active subspaces.

scholarly journals Surrogate modeling based on resampled polynomial chaos expansions

2020 ◽  
Vol 202 ◽  
pp. 107008 ◽  
Author(s):  
Zicheng Liu ◽  
Dominique Lesselier ◽  
Bruno Sudret ◽  
Joe Wiart
Keyword(s):  
Polynomial Chaos ◽  
Surrogate Modeling ◽  
Polynomial Chaos Expansions
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