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Bayesian optimization has emerged at the forefront of expensive black-box optimization due to its data efficiency. Recent years have witnessed a proliferation of studies on the development of new Bayesian optimization algorithms and their applications. Hence, this article attempts to provide a comprehensive and updated survey of recent advances in Bayesian optimization that are mainly based on Gaussian processes and identify challenging open problems. We categorize the existing work on Bayesian optimization into nine main groups according to the motivations and focus of the proposed algorithms. For each category, we present the main advances with respect to the construction of surrogate models and adaptation of the acquisition functions. Finally, we discuss the open questions and suggest promising future research directions, in particular with regard to heterogeneity, privacy preservation, and fairness in distributed and federated optimization systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider a mathematical model which describes the quasistatic frictionless contact between a viscoplastic body and a foundation. The contact is modeled with normal compliance and unilateral constraint. We present the variational-hemivariational formulation of the model and prove its unique solvability. Then we introduce a fully discrete scheme to solve the problem and derive an error estimate. Under appropriate regularity assumptions of the exact solution, we obtain the optimal order error estimate. Finally, numerical results are reported to show the performance of the numerical method. [ABSTRACT FROM AUTHOR]

A Milky Way Type Ia supernova (SNIa) could be unidentified or even initially unnoticed, being dim in radio, X-rays, and neutrinos, and suffering large optical/IR extinction in the Galactic plane. But SNIa emit nuclear gamma-ray lines from 56Ni → 56Co → 56Fe radioactive decays. These lines fall within the Fermi /GBM energy range, and the 56Ni 158 keV line is detectable by Swift /BAT. Both instruments frequently monitor the Galactic plane, which is transparent to gamma rays. Thus GBM and BAT are ideal Galactic SNIa early warning systems. We simulate SNIa MeV light curves and spectra to show that GBM and BAT could confirm a Galactic SNIa explosion, followed by Swift localization and observation in X-rays and UVOIR band. The time of detection depends sensitively on the 56Ni distribution, and can be as early as a few days if |${\gtrsim } 10{{\ \rm per\ cent}}$| of the 56Ni is present in the surface as suggested by SN2014J gamma data. [ABSTRACT FROM AUTHOR]

Several starburst galaxies have been observed in the GeV and TeV bands. In these dense environments, gamma-ray emission should be dominated by cosmic ray (CR) interactions with the interstellar medium (pcrpism → π0 → γγ). Indeed, starbursts may act as proton 'calorimeters' where a substantial fraction of CR energy input is emitted in gamma-rays. Here, we build a one-zone, 'thick-target' model implementing calorimetry and placing a firm upper bound on gamma-ray emission from CR interactions. The model assumes that CRs are accelerated by supernovae (SNe), and all suffer nuclear interactions rather than escape. Our model has only two free parameters: the CR proton acceleration energy per SN ϵcr, and the proton injection spectral index s. We calculate the pionic gamma-ray emission from 10 MeV to 10 TeV, and derive thick-target parameters for six galaxies with Fermi, H.E.S.S., and/or VERITAS data. Our model provides good fits for the M82 and NGC 253, and yields ϵcr and s values suggesting that SN CR acceleration is similar in starbursts and in our Galaxy. We find that these starbursts are indeed nearly if not fully proton calorimeters. For NGC 4945 and NGC 1068, the models are consistent with calorimetry but are less well-constrained due to the lack of TeV data. However, the Circinus galaxy and the ultra-luminous infrared galaxy Arp 220 exceed our pionic upper-limit; possible explanations are discussed. [ABSTRACT FROM AUTHOR]

Rapid advancement of sensor technologies and computing power has led to wide availability of massive population-based shape data. In this paper, we present a Taylor expansion-based method for computing structural performance variation over its shape population. The proposed method consists of four steps: (1) learning the shape parameters and their probabilistic distributions through the statistical shape modeling (SSM), (2) deriving analytical sensitivity of structural performance over shape parameter, (3) approximating the explicit function relationship between the finite element (FE) solution and the shape parameters through Taylor expansion, and (4) computing the performance variation by the explicit function relationship. To overcome the potential inaccuracy of Taylor expansion for highly nonlinear problems, a multipoint Taylor expansion technique is proposed, where the parameter space is partitioned into different regions and multiple Taylor expansions are locally conducted. It works especially well when combined with the dimensional reduction of the principal component analysis (PCA) in the statistical shape modeling. Numerical studies illustrate the accuracy and efficiency of this method. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with an optimal control problem of a quasistatic frictional contact model with history-dependent operators. The contact boundary of the model is divided into two parts where different contact conditions are specified. For the contact problem, we first derive its weak formulation and prove the existence and uniqueness of the solution to the weak formulation. Then we give a priori estimate of the unique solution and prove a continuous dependence result for the solution map. Finally, an optimal control problem that contains boundary and initial condition controls is proposed, and the existence of optimal solutions to the control problem is established. [ABSTRACT FROM AUTHOR]