Scalable Adaptive Batch Sampling in Simulation-Based Design With Heteroscedastic Noise

Abstract

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.