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Plausible inference is a growing body of literature that treats stochastic simulation as a gray box when structural properties of the simulation output performance measures as a function of design, decision or contextual variables are known. Plausible inference exploits these properties to allow the outputs from values of decision variables that have been simulated to provide inference about output performance measures at values of decision variables that have not been simulated; statements about the possible optimality or feasibility are examples. Lipschitz continuity is a structural property of many simulation problems. Unfortunately, the all-important—and essential for plausible inference—Lipschitz constant is rarely known. In this paper we show how to obtain plausible inference with an estimated Lipschitz constant that is also derived by plausible inference reasoning, as well as how to create the experiment design to simulate. 

A bottleneck in high-throughput nanomaterials discovery is the pace at which new materials can be structurally characterized. Although current machine learning (ML) methods show promise for the automated processing of electron diffraction patterns (DPs), they fail in high-throughput experiments where DPs are collected from crystals with random orientations. Inspired by the human decision-making process, a framework for automated crystal system classification from DPs with arbitrary orientations was developed. A convolutional neural network was trained using evidential deep learning, and the predictive uncertainties were quantified and leveraged to fuse multiview predictions. Using vector map representations of DPs, the framework achieves a testing accuracy of 0.94 in the examples considered, is robust to noise, and retains remarkable accuracy using experimental data. This work highlights the ability of ML to be used to accelerate experimental high-throughput materials data analytics. 

Abstract Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian optimization (BO) employs uncertainty-aware machine learning models to select promising designs to evaluate, hence reducing the cost. However, BO with mixed numerical and categorical variables, which is of particular interest in materials design, has not been well studied. In this work, we survey frequentist and Bayesian approaches to uncertainty quantification of machine learning with mixed variables. We then conduct a systematic comparative study of their performances in BO using a popular representative model from each group, the random forest-based Lolo model (frequentist) and the latent variable Gaussian process model (Bayesian). We examine the efficacy of the two models in the optimization of mathematical functions, as well as properties of structural and functional materials, where we observe performance differences as related to problem dimensionality and complexity. By investigating the machine learning models’ predictive and uncertainty estimation capabilities, we provide interpretations of the observed performance differences. Our results provide practical guidance on choosing between frequentist and Bayesian uncertainty-aware machine learning models for mixed-variable BO in materials design. 

Many two-level nested simulation applications involve the conditional expectation of some response variable, where the expected response is the quantity of interest, and the expectation is with respect to the inner-level random variables, conditioned on the outer-level random variables. The latter typically represent random risk factors, and risk can be quantified by estimating the probability density function (pdf) or cumulative distribution function (cdf) of the conditional expectation. Much prior work has considered a naïve estimator that uses the empirical distribution of the sample averages across the inner-level replicates. This results in a biased estimator, because the distribution of the sample averages is over-dispersed relative to the distribution of the conditional expectation when the number of inner-level replicates is finite. Whereas most prior work has focused on allocating the numbers of outer- and inner-level replicates to balance the bias/variance tradeoff, we develop a bias-corrected pdf estimator. Our approach is based on the concept of density deconvolution, which is widely used to estimate densities with noisy observations but has not previously been considered for nested simulation problems. For a fixed computational budget, the bias-corrected deconvolution estimator allows more outer-level and fewer inner-level replicates to be used, which substantially improves the efficiency of the nested simulation.