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A framework for reliable modeling of high-frequency structures by nested kriging with an improved sampling procedure is developed and extensively validated. A comprehensive benchmarking including conventional kriging and previously reported design of experiments technique is provided. The proposed technique is also demonstrated in solving parameter optimization task.

The keystone of the proposed approach is to focus the modeling process on a small region of the parameter space (constrained domain containing high-quality designs with respect to the selected performance figures) instead of adopting traditional, hyper-cube-like domain defined by the lower and upper parameter bounds. A specific geometry of the domain is explored to improve a uniformity of the training data set. In consequence, the predictive power of the model is improved.

Building the model in a constrained domain allows for a considerable reduction of a training data set size without a necessity to either narrow down the parameter ranges or to reduce the parameter space dimensionality. Improving uniformity of training data set allocation permits further reduction of the computational cost of setting up the model. The proposed technique can be used to expedite the parameter optimization and enables locating good initial designs in a straightforward manner.

The developed framework opens new possibilities inaccurate surrogate modeling of high-frequency structures described by a large number of geometry and/or material parameters. Further extensions can be investigated such as the inclusion of the sensitivity data into the model or exploration of the particular geometry of the model domain to further reduce the computational overhead of training data acquisition.

The efficiency of the proposed method has been demonstrated for modeling and parameter optimization of high-frequency structures. It has also been shown to outperform conventional kriging and previous constrained modeling approaches. To the authors’ knowledge, this approach to formulate and handle the modeling process is novel and permits the establishment of accurate surrogates in highly dimensional spaces and covering wide ranges of parameters.

This study seeks to explore the nature of a data‐generating process for four dollar exchange rates.

Using a discrete parametric modeling approach, an efficient test statistic was computed for nonlinearity in terms of variance of the residuals of the linear and nonlinear autoregressive models by Akaike Information Criterion, and a surrogate data analysis was conducted.

It shows that a nonlinear autoregressive model outperforms a linear stochastic model in certain subsamples of baht, pound, ringgit, and yen dollar exchange rates. However, when the test statistics using different model orders and the data for the entire samples are estimated, it appears that the nonlinear model has a better performance than the linear model in fitting Thai and Malaysian currencies. The nonlinear model performs better than the linear model in the case of the UK pound in two thirds of the models, but the linear models completely outperform the nonlinear models for the yen data.

More financial and economic time series will be explored to employ the methodology used in the study, and tests for possible presence of nonlinear deterministic dynamics (chaos) in the exchange rates series will be conducted based on the present findings in further study.

These findings suggest that the assumption of linear stochastic process as the underlying dynamics for all currencies examined in this study may not be justifiable.

To the best of the authors' knowledge, this study is the first attempt to use the test statistic based on the information‐theoretical method in testing nonlinearity in financial and economic time series.

The purpose of this paper is to propose physically based varying fidelity surrogates to be used in structural design optimization of space trusses. The main aim is to demonstrate its efficiency in reducing the number of high fidelity (HF) runs in the optimization process.

In this work, surrogate models are built for space truss structures. This study uses functional as well as physical surrogates. In the latter, a grid analogy of the space truss is used thereby reducing drastically the analysis cost. Global and local approaches are considered. The latter will require a globalization scheme (sequential approximate optimization (SAO)) to ensure convergence.

Physically based surrogates were proposed. Classical techniques, namely Taylor series and kriging, are also implemented for comparison purposes. A parameter study in kriging is necessary to select the best kriging model to be used as surrogate. A test case was considered for optimization and several surrogates were built. The CPU time is reduced when compared with the HF solution, for all surrogate‐based optimization performed. The best result was achieved combining the proposed physical model with additive corrections in a SAO strategy in which C1 continuity was imposed at each trust region center. Some guidance for other engineering applications was given.

This is the first time that physical‐based surrogates for optimum design of space truss systems are used in the SAO framework. Physical surrogates typically exhibit better generalization properties than other surrogates forms, produce faster solutions, and do not suffer from dimensionality curse when used in approximate optimization strategies.

The purpose of this paper is to propose a novel contribution to adaptive sampling strategies for non‐intrusive reduced order models based on Proper Orthogonal Decomposition (POD). These strategies aim at reducing the cost of optimization by improving the efficiency and accuracy of POD data‐fitting surrogate models to be used in an online surrogate‐assisted optimization framework for industrial design.

The effect of the strategies on the model accuracy is investigated considering the snapshot scaling, the design of experiment size and the truncation level of the POD basis and compared to a state‐of‐the‐art radial basis function network surrogate model on objectives and constraints. The selected test case is a Mach number and angle of attack domain exploration of the well‐known RAE2822 airfoil. Preliminary airfoil shape optimization results are also shown.

The numerical results demonstrate the potential of the capture/recapture schemes proposed for adequately filling the parametric space and maximizing the surrogates relevance at minimum computational cost.

The proposed approaches help in building POD‐based surrogate models more efficiently.

This paper aims to investigates several design strategies to solve multi-objective aerodynamic optimization problems using high-fidelity simulations. The purpose is to find strategies which reduce the overall optimization time while still maintaining accuracy at the high-fidelity level.

Design strategies are proposed that use an algorithmic framework composed of search space reduction, fast surrogate models constructed using a combination of physics-based surrogates and kriging and global refinement of the Pareto front with co-kriging. The strategies either search the full or reduced design space with a low-fidelity model or a physics-based surrogate.

Numerical investigations of airfoil shapes in two-dimensional transonic flow are used to characterize and compare the strategies. The results show that searching a reduced design space produces the same Pareto front as when searching the full space. Moreover, as the reduced space is two orders of magnitude smaller (volume-wise), the number of required samples to setup the surrogates can be reduced by an order of magnitude. Consequently, the computational time is reduced from over three days to less than half a day.

The proposed design strategies are novel and holistic. The strategies render multi-objective design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search spaces computationally tractable.

To improve the speed and accuracy of turbine blade film cooling design process, the most advanced deep learning models were introduced into this study to investigate the most suitable define for prediction work. This paper aims to create a generative surrogate model that can be applied on multi-objective optimization problems.

The latest backbone in the field of computer vision (Swin-Transformer, 2021) was introduced and improved as the surrogate function for prediction of the multi-physics field distribution (film cooling effectiveness, pressure, density and velocity). The basic samples were generated by Latin hypercube sampling method and the numerical method adopt for the calculation was validated experimentally at first. The training and testing samples were calculated at experimental conditions. At last, the surrogate model predicted results were verified by experiment in a linear cascade.

The results indicated that comparing with the Multi-Scale Pix2Pix Model, the Swin-Transformer U-Net model presented higher accuracy and computing speed on the prediction of contour results. The computation time for each step of the Swin-Transformer U-Net model is one-third of the original model, especially in the case of multi-physics field prediction. The correlation index reached more than 99.2% and the first-order error was lower than 0.3% for multi-physics field. The predictions of the data-driven surrogate model are consistent with the predictions of the computational fluid dynamics results, and both are very close to the experimental results. The application of the Swin-Transformer model on enlarging the different structure samples will reduce the cost of numerical calculations as well as experiments.

The number of U-Net layers and sample scales has a proper relationship according to equation (8). Too many layers of U-Net will lead to unnecessary nonlinear variation, whereas too few layers will lead to insufficient feature extraction. In the case of Swin-Transformer U-Net model, incorrect number of U-Net layer will reduce the prediction accuracy. The multi-scale Pix2Pix model owns higher accuracy in predicting a single physical field, but the calculation speed is too slow. The Swin-Transformer model is fast in prediction and training (nearly three times faster than multi Pix2Pix model), but the predicted contours have more noise. The neural network predicted results and numerical calculations are consistent with the experimental distribution.

This paper creates a generative surrogate model that can be applied on multi-objective optimization problems. The generative adversarial networks using new backbone is chosen to adjust the output from single contour to multi-physics fields, which will generate more results simultaneously than traditional surrogate models and reduce the time-cost. And it is more applicable to multi-objective spatial optimization algorithms. The Swin-Transformer surrogate model is three times faster to computation speed than the Multi Pix2Pix model. In the prediction results of multi-physics fields, the prediction results of the Swin-Transformer model are more accurate.

The purpose of this work is to apply and compare surrogate-assisted and multi-fidelity, multi-objective optimization (MOO) algorithms to simulation-based aerodynamic design exploration.

The three algorithms for multi-objective aerodynamic optimization compared in this work are the combination of evolutionary algorithms, design space reduction and surrogate models, the multi-fidelity point-by-point Pareto set identification and the multi-fidelity sequential domain patching (SDP) Pareto set identification. The algorithms are applied to three cases, namely, an analytical test case, the design of transonic airfoil shapes and the design of subsonic wing shapes, and are evaluated based on the resulting best possible trade-offs and the computational overhead.

The results show that all three algorithms yield comparable best possible trade-offs for all the test cases. For the aerodynamic test cases, the multi-fidelity Pareto set identification algorithms outperform the surrogate-assisted evolutionary algorithm by up to 50 per cent in terms of cost. Furthermore, the point-by-point algorithm is around 27 per cent more efficient than the SDP algorithm.

The novelty of this work includes the first applications of the SDP algorithm to multi-fidelity aerodynamic design exploration, the first comparison of these multi-fidelity MOO algorithms and new results of a complex simulation-based multi-objective aerodynamic design of subsonic wing shapes involving two conflicting criteria, several nonlinear constraints and over ten design variables.

This study aimed to examine the efficient market hypothesis (EMH) for the stock markets of 12 member countries of the Organization of Islamic Cooperation (OIC), such as Egypt, Indonesia, Jordan, Kuwait, Malaysia, Morocco, Pakistan, Saudi Arabia, Tunisia, Turkey and the United Arab Emirates (UAE), during the global financial crisis (GFC) and the COVID-19 (CV-19) epidemic. The objective was to classify the effects on individual indices.

The study employed the multifractal detrended fluctuation analysis (MF-DFA) on daily returns. After calculation and analysis, the data were then divided into two significant events: the GFC and the CV-19 pandemic. Additionally, the market deficiency measure (MDM) was utilized to assess and rank market efficiency.

The findings indicate that the average returns series exhibited persistent and non-persistent patterns during the GFC and the CV-19 pandemic, respectively. The study employed MF-DFA to analyze the sequence of normal returns. The results suggest that the average returns series displayed persistent and non-persistent patterns during the GFC and the CV-19 pandemic, respectively. Furthermore, all markets demonstrated efficiency during the two crisis periods, with Turkey and Tunisia exhibiting the highest and deepest levels of efficiency, respectively. The multifractal properties were influenced by long-range correlations and fat-tailed distributions, with the latter being the primary contributor. Moreover, the impact of the fat-tailed distribution on multifractality was found to be more pronounced for indices with lower market efficiency. In conclusion, this study categorizes indices with low market efficiency during both crisis periods, which subsequently affect the distribution of assets among shareholders in the stock markets of OIC member countries.

Multifractal patterns, especially the long memory property observed in stock markets, can assist investors in formulating profitable investment strategies. Additionally, this study will contribute to a better understanding of market trends during similar events should they occur in the future.

This research marks the initial effort to assess the impact of the GFC and the CV19 pandemic on the efficiency of stock markets in OIC countries. This undertaking is of paramount importance due to the potential destabilizing and harmful effects of these events on global financial markets and societal well-being. Furthermore, to the best of the authors’ knowledge, this study represents the first investigation utilizing the MFDFA method to analyze the primary stock markets of OIC countries, encompassing both the GFC and CV19 crises.