An adaptive design approach for defects distribution modeling in materials from first-principle calculations.

Computer experiments are used frequently for the study and improvement of a process under study. Optimizing such process based on a computer model is costly, so an approximation of the computer model, or metamodel, is used. Efficient global optimization (EGO) is a sequential optimization method for computer experiments based on a Gaussian process model approximation to the computer model response. A long‐standing problem in EGO is that it does not consider the uncertainty in the parameter estimates of the Gaussian process. Treating these estimates as if they are the true parameters leads to an improper assessment of the precision of the approximation, a precision that is crucial to assess not only in optimization but in metamodeling in general. One way to account for these uncertainties is to use bootstrapping, studied by previous authors. Alternatively, some other authors have mentioned how a Bayesian approach may be the best way to incorporate the parameter uncertainty in the optimization, but no fully Bayesian approach for EGO has been implemented in practice. In this paper, we present a fully Bayesian implementation of the EGO method. The proposed Bayesian EGO algorithm is validated through simulation of noisy nonlinear functions and compared with the standard EGO method and the bootstrapped EGO. We also apply the Bayesian EGO algorithm to the optimization of a stochastic computer model. It is shown how a Bayesian approach to EGO allows one to optimize any function of the posterior predictive density. Copyright © 2014 John Wiley & Sons, Ltd.

An adaptive Bayesian approach to surrogate-assisted evolutionary multi-objective optimization

Gaussian processes (Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization problems. These optimization problems are nonconvex and global optimization is desired. However, previous literature observed computational burdens limiting deterministic global optimization to Gaussian processes trained on few data points. We propose a reduced-space formulation for deterministic global optimization with trained Gaussian processes embedded. For optimization, the branch-and-bound solver branches only on the free variables and McCormick relaxations are propagated through explicit Gaussian process models. The approach also leads to significantly smaller and computationally cheaper subproblems for lower and upper bounding. To further accelerate convergence, we derive envelopes of common covariance functions for GPs and tight relaxations of acquisition functions used in Bayesian optimization including expected improvement, probability of improvement, and lower confidence bound. In total, we reduce computational time by orders of magnitude compared to state-of-the-art methods, thus overcoming previous computational burdens. We demonstrate the performance and scaling of the proposed method and apply it to Bayesian optimization with global optimization of the acquisition function and chance-constrained programming. The Gaussian process models, acquisition functions, and training scripts are available open-source within the “MeLOn—MachineLearning Models for Optimization” toolbox (https://git.rwth-aachen.de/avt.svt/public/MeLOn).

Rather than optimizing expensive objective functions such as complex engineering simulations directly, Bayesian optimization methodologies fit a surrogate model (typically Kriging or a Gaussian Process) on evaluations of the objective function(s). To determine the next evaluation, an acquisition function is optimized (also referred to as infill criterion or sampling policy) which incorporates the model prediction and uncertainty and balances exploration and exploitation. Therefore, Bayesian optimization methodologies replace a single optimization of the objective function by a sequence of optimization problems: this makes sense as the acquisition function is cheap-to-evaluate whereas the objective is not. Depending on the goal different acquisition functions are available: multi-objective acquisition functions are relatively new and this chapter gives a state-of-the-art overview and illustrates some approaches based on hypervolume improvement. It is shown that the quality of the model is crucial for the performance of Bayesian optimization and illustrate this by using the more flexible Student-t processes as surrogate models.

PurposeThe purpose of this paper is to investigate the mechanical properties’ behaviors of woven composite cut-out structures with specific parameters. Because of the complexity of micro-scale and meso-scale structure, it is difficult to accurately predict the mechanical material behavior of woven composites. Numerical simulations are increasingly necessary for the design and optimization of test procedures for composite structures made by the woven composite. The results of the proposed method are well satisfied with the results obtained from the experiment and other studies. Moreover, parametric studies on different plates based on the stacking sequences are investigated.Design/methodology/approachA multi-scale modeling approach is suggested. Back-propagation neural networks (BPNN), radial basis function (RBF) and least square support vector regression are integrated with efficient global optimization (EGO) to reduce the weight of assigned structure. Optimization results are verified by finite element analysis.FindingsCompared with other similar studies, the advantage of the suggested strategy uses homogenized properties behaviors with more complex analysis of woven composite structures. According to investigation results, it can be found that 450/−450 ply-orientation is the best buckling load value for all the cut-out shape requirements. According to the optimal results, the BPNN-EGO is the best candidate for the EGO to optimize the woven composite structures.Originality/valueA multi-scale approach is used to investigate the mechanical properties of a complex woven composite material architecture. Buckling of different cut-out shapes with the same area is surveyed. According to investigation, 45°/−45° ply-orientation is the best for all cut-out shapes. Different surrogate models are integrated in EGO for optimization. The BPNN surrogate model is the best choice for EGO to optimization difficult problems of woven composite materials.

Modern performance earthquake engineering practices frequently require a large number of time‐consuming non‐linear time‐history simulations to appropriately address excitation and structural uncertainties when estimating engineering demand parameter (EDP) distributions. Surrogate modeling techniques have emerged as an attractive tool for alleviating such high computational burden in similar engineering problems. A key challenge for the application of surrogate models in earthquake engineering context relates to the aleatoric variability associated with the seismic hazard. This variability is typically expressed as high‐dimensional or non‐parametric uncertainty, and so cannot be easily incorporated within standard surrogate modeling frameworks. Rather, a surrogate modeling approach that can directly approximate the full distribution of the response output is warranted for this application. This approach needs to additionally address the fact that the response variability may change as input parameter changes, yielding a heteroscedastic behavior. Stochastic emulation techniques have emerged as a viable solution to accurately capture aleatoric uncertainties in similar contexts, and recent work by the second author has established a framework to accommodate this for earthquake engineering applications, using Gaussian Process (GP) regression to predict the EDP response distribution. The established formulation requires for a portion of the training samples the replication of simulations for different descriptions of the aleatoric uncertainty. In particular, the replicated samples are used to build a secondary GP model to predict the heteroscedastic characteristics, and these predictions are then used to formulate the primary GP that produces the full EDP distribution. This practice, however, has two downsides: it always requires minimum replications when training the secondary GP, and the information from the non‐replicated samples is utilized only for the primary GP. This research adopts an alternative stochastic GP formulation that can address both limitations. To this end, the secondary GP is trained by measuring the square of sample deviations from the mean instead of the crude sample variances. To establish the primitive mean estimates, another auxiliary GP is introduced. This way, information from all replicated and non‐replicated samples is fully leveraged for estimating both the EDP distribution and the underlying heteroscedastic behavior, while formulation accommodates an implementation using no replications. The case study examples using three different stochastic ground motion models demonstrate that the proposed approach can address both aforementioned challenges.

Ultrasonic testing (UT) is used to detect internal flaws in materials and to characterize material properties. In many applications, computational simulations are an important part of the inspection-design and analysis processes. Having fast surrogate models for UT simulations is key for enabling efficient inverse analysis and model-assisted probability of detection (MAPOD). In many cases, it is impractical to perform the aforementioned tasks in a timely manner using current simulation models directly. Fast surrogate models can make these processes computationally tractable. This paper presents investigations of using surrogate modeling techniques to create fast approximate models of UT simulator responses. In particular, we propose to integrate data-driven methods (here, kriging interpolation with variable-fidelity models to construct an accurate and fast surrogate model. These techniques are investigated using test cases involving UT simulations of solid components immersed in a water bath during the inspection process. We will apply the full ultrasonic solver and the surrogate model to the detection and characterization of the flaw. The methods will be compared in terms of quality of the responses.

Bayesian optimization (BO) based on the Gaussian process (GP) surrogate model has attracted extensive attention in the field of optimization and design of experiments (DoE). It usually faces two problems: the unstable GP prediction due to the ill-conditioned Gram matrix of the kernel and the difficulty of determining the trade-off parameter between exploitation and exploration. To solve these problems, we investigate the K-optimality, aiming at minimizing the condition number. Firstly, the Sequentially Bayesian K-optimal design (SBKO) is proposed to ensure the stability of the GP prediction, where the K-optimality is given as the acquisition function. We show that the SBKO reduces the integrated posterior variance and maximizes the hyper-parameters’ information gain simultaneously. Secondly, a K-optimal enhanced Bayesian Optimization (KO-BO) approach is given for the optimization problems, where the K-optimality is used to define the trade-off balance parameters which can be output automatically. Specifically, we focus our study on the K-optimal enhanced Expected Improvement algorithm (KO-EI). Numerical examples show that the SBKO generally outperforms the Monte Carlo, Latin hypercube sampling, and sequential DoE approaches by maximizing the posterior variance with the highest precision of prediction. Furthermore, the study of the optimization problem shows that the KO-EI method beats the classical EI method due to its higher convergence rate and smaller variance.

Design of systems based on computer simulations is prevalent. An important idea to improve design quality, called robust parameter design (RPD), is to optimize control factors based on the expectation of a loss function so that the design is robust to noise factor variations. When computer simulations are time consuming, optimizing the simulator based on a Gaussian process (GP) emulator for the response is a computationally efficient approach. For this purpose, acquisition functions (AFs) are used to sequentially determine the next design point so that the GP emulator can more accurately locate the optimal setting. Despite this, few articles consider AFs for positive definite quadratic forms such as the expected quadratic loss (EQL) function, which is the standard expected loss function for RPD with nominally-the-best responses. This paper proposes new AFs for optimizing the EQL, analyzes their convergence, and develops quick and accurate methods based on the characteristic function of the EQL to compute them. We apply the AFs to RPD problems with internal noise factors based on a GP model and an initial design tailored for such problems. Numerical results indicate that all four AFs considered have similar performance, and they outperform an optimization approach based on modeling the quadratic loss as a GP and maximin Latin hypercube designs. MATLAB codes for reproducing reported results are given in the online supplement.

Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional ($\mathrm{DFT}+U$, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials.

This paper explores the adaptive optimal design of Active Thermally Insulated (ATI) windows to significantly improve energy efficiency. The ATI window design uses thermostats to actively control thermoelectric (TE) units and fans to regulate the overall thermodynamic properties of the windows. The windows are used to maintain a comfortable indoor temperature. Since weather conditions vary with different geographical locations and with time, the thermodynamic properties of the windows should adapt accordingly. The electric power supplied to the TE units and the fans are dynamically controlled so as to provide an optimal operation under varying weather conditions. Optimization of the ATI window design is a multiobjective problem. The problem minimizes both the heat transferred through the window and electric power consumption. The heat transfer through the ATI windows is analyzed using FLUENT; and the optimization is performed using MATLAB. Since the computational expense of optimization for numerous weather conditions is excessive, the power supplies are optimized under a reasonably small number of weather conditions. Based on the optimal results obtained for these conditions, a surrogate model is developed to represent the optimal results in a wide range of weather conditions. The surrogate model is used to evaluate optimal power supplies with respect to different values of outside temperature, wind speed, and intensity of solar radiation. Thermometers, anemometers, and solar radiation sensors are used to sense these weather conditions. With the inputs from the sensors, the thermostats determine the operating conditions and calculate the corresponding optimal power supplies using the surrogate model. Since the ATI windows are operated with optimal power supplies, high energy efficiency is achieved.

The properties of defects in materials are crucial in order to determine their performance and behavior, especially at extreme conditions (at high temperature, under irradiation or with other types of constraints). Formation and migration energies of defects are studied routinely using first-principles calculations. However, most of the time, they are studied by static zero-temperature calculations, and the entropic contributions to the free energies are completely neglected. In this paper we address the first-principles calculation of the vibrational part of the free energies of formation and migration of silicon and carbon interstitials in silicon carbide. The latter is an important material for high-temperature applications. We find that formation free enthalpies can vary by up to 1 eV, in the range from 0 to 2000 K, while migration free energies vary by only a few tenth of an electron volt. Our results give us not only the activation energies for diffusion but also diffusion prefactors. The comparison with experimental results shows good agreement for carbon self-diffusion while for silicon self-diffusion our results underestimate by three orders of magnitude the experimental values, suggesting that defects other than the interstitials are the dominant diffusing species. As a last point, in the light of our results, we discuss empirical models concerning diffusion coefficients and entropy-energy relations.

The microscopic mechanism for H and He trapping by vacancy defects and bubble formation in a Be host lattice is investigated using first-principles calculations. A single He atom prefers to occupy a vacancy centre while H does not. He can segregate towards the vacancy from the interstitial site much more easily than H. Both H and He exhibit lower diffusion barriers from a remote interstitial to a vacancy with regard to their diffusion barriers inside a perfect Be solid. Up to five H or 12 He atoms can be accommodated into the monovacancy space, and the Be–He interaction is much weaker than Be–H. The physical origin for aggregation of multiple H or He atoms in a vacancy is further discussed. The strong tendency of H and He trapping at vacancies provides an explanation for why H and He bubbles were experimentally observed at vacancy defects in materials. We therefore argue that vacancies provide a primary nucleation site for bubbles of H and He gases inside Be materials.

View Video Presentation: https://doi.org/10.2514/6.2023-3313.vid In this study, an optimization approach based solely on open-source libraries is employed to optimize a centrifugal blower (both impeller and housing). Salome, OpenFoam, and Dakota are used for geometry and mesh generation, Computational Fluid Dynamics (CFD) simulation, and optimization, respectively. For the numerical analysis, Reynolds-averaged Navier-Stokes equations with the k-�� SST turbulence model are used. The Latin Hypercube Sampling (LHS) method is used to determine the design points while eleven design variables related to both the impeller and housing are chosen. Then different metamodels, including Artificial Neural Networks (ANN), Efficient Global Optimization (EGO), Gaussian Process (GP), and Multivariate Adaptive Regression Spline (MARS) are built to obtain optimal design. The findings show that GP proposes the best design among metamodels, with maximum efficiency (57.62%) and negligible error (0.12%) when compared to CFD calculation. In order to validate the optimal design from GP, a centrifugal blower is finally fabricated, demonstrating an acceptable agreement between experimental and numerical results

Pfizer Global Virtual Library (PGVL) of 10(13) readily synthesizable molecules offers a tremendous opportunity for lead optimization and scaffold hopping in drug discovery projects. However, mining into a chemical space of this size presents a challenge for the concomitant design informatics due to the fact that standard molecular similarity searches against a collection of explicit molecules cannot be utilized, since no chemical information system could create and manage more than 10(8) explicit molecules. Nevertheless, by accepting a tolerable level of false negatives in search results, we were able to bypass the need for full 10(13) enumeration and enabled the efficient similarity search and retrieval into this huge chemical space for practical usage by medicinal chemists. In this report, two search methods (LEAP1 and LEAP2) are presented. The first method uses PGVL reaction knowledge to disassemble the incoming search query molecule into a set of reactants and then uses reactant-level similarities into actual available starting materials to focus on a much smaller sub-region of the full virtual library compound space. This sub-region is then explicitly enumerated and searched via a standard similarity method using the original query molecule. The second method uses a fuzzy mapping onto candidate reactions and does not require exact disassembly of the incoming query molecule. Instead Basis Products (or capped reactants) are mapped into the query molecule and the resultant asymmetric similarity scores are used to prioritize the corresponding reactions and reactant sets. All sets of Basis Products are inherently indexed to specific reactions and specific starting materials. This again allows focusing on a much smaller sub-region for explicit enumeration and subsequent standard product-level similarity search. A set of validation studies were conducted. The results have shown that the level of false negatives for the disassembly-based method is acceptable when the query molecule can be recognized for exact disassembly, and the fuzzy reaction mapping method based on Basis Products has an even better performance in terms of lower false-negative rate because it is not limited by the requirement that the query molecule needs to be recognized by any disassembly algorithm. Both search methods have been implemented and accessed through a powerful desktop molecular design tool (see ref. (33) for details). The chapter will end with a comparison of published search methods against large virtual chemical space.