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Abstract In this study, we propose a scalable batch sampling scheme for optimization of simulation models with spatially varying noise. The proposed scheme has two primary advantages: (i) reduced simulation cost by recommending batches of samples at carefully selected spatial locations and (ii) improved scalability by actively considering replicating at previously observed sampling locations. Replication improves the scalability of the proposed sampling scheme as the computational cost of adaptive sampling schemes grow cubicly with the number of unique sampling locations. Our main consideration for the allocation of computational resources is the minimization of the uncertainty in the optimal design. We analytically derive the relationship between the “exploration versus replication decision” and the posterior variance of the spatial random process used to approximate the simulation model’s mean response. Leveraging this reformulation in a novel objective-driven adaptive sampling scheme, we show that we can identify batches of samples that minimize the prediction uncertainty only in the regions of the design space expected to contain the global optimum. Finally, the proposed sampling scheme adopts a modified preposterior analysis that uses a zeroth-order interpolation of the spatially varying simulation noise to identify sampling batches. Through the optimization of three numerical test functions and one engineering problem, we demonstrate (i) the efficacy and of the proposed sampling scheme to deal with a wide array of stochastic functions, (ii) the superior performance of the proposed method on all test functions compared to existing methods, (iii) the empirical validity of using a zeroth-order approximation for the allocation of sampling batches, and (iv) its applicability to molecular dynamics simulations by optimizing the performance of an organic photovoltaic cell as a function of its processing settings. 

CrBr 3 is a layered van der Waals material with magnetic ordering down to the 2D limit. For decades, based on optical measurements, it is believed that the energy gap of CrBr 3 is in the range of 1.68–2.1 eV. However, controversial results have indicated that the band gap of CrBr 3 is possibly smaller than that. An unambiguous determination of the energy gap is critical to the correct interpretations of the experimental results of CrBr 3 . Here, we present the scanning tunneling microscopy and spectroscopy (STM/S) results of CrBr 3 thin and thick flakes exfoliated onto highly ordered pyrolytic graphite (HOPG) surfaces and density functional theory (DFT) calculations to reveal the small energy gap (peak-to-peak energy gap to be 0.57 ± 0.04 eV; or the onset signal energy gap to be 0.29 ± 0.05 eV from d I /d V spectra). Atomic resolution topography images show the defect-free crystal structure and the d I /d V spectra exhibit multiple peak features measured at 77 K. The conduction band – valence band peak pairs in the multi-peak d I /d V spectrum agree very well with all reported optical transitions. STM topography images of mono- and bi-layer CrBr 3 flakes exhibit edge degradation due to short air exposure (∼15 min) during sample transfer. The unambiguously determined small energy gap settles the controversy and is the key in better understanding CrBr 3 and similar materials. 

Objective-driven adaptive sampling is a widely used tool for the optimization of deterministic black-box functions. However, the optimization of stochastic simulation models as found in the engineering, biological, and social sciences is still an elusive task. In this work, we propose a scalable adaptive batch sampling scheme for the optimization of stochastic simulation models with input-dependent noise. The developed algorithm has two primary advantages: (i) by recommending sampling batches, the designer can benefit from parallel computing capabilities, and (ii) by replicating of previously observed sampling locations the method can be scaled to higher-dimensional and more noisy functions. Replication improves numerical tractability as the computational cost of Bayesian optimization methods is known to grow cubicly with the number of unique sampling locations. Deciding when to replicate and when to explore depends on what alternative minimizes the posterior prediction accuracy at and around the spatial locations expected to contain the global optimum. The algorithm explores a new sampling location to reduce the interpolation uncertainty and replicates to improve the accuracy of the mean prediction at a single sampling location. Through the application of the proposed sampling scheme to two numerical test functions and one real engineering problem, we show that we can reliably and efficiently find the global optimum of stochastic simulation models with input-dependent noise.