Uncertainty-aware mixed-variable machine learning for materials design

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.

Accelerating the design of lattice structures using machine learning

“…To explore whether greater acceleration can be achieved by employing a mixed-search space BO strategy, we designed a set of simulated learning campaigns that combine our BO approach with one-hot encoding. One-hot encoding is an approach that assigns an integer representation for each category where no ordinal relationship exists between them and the similarity between any two categories is assumed to be equal 38,39 . Given these considerations and keeping the independence and similarity between the lattice design families, we selected one-hot encoding as a method to reparametrize our feature space (Figure S5).…”

Data‐Driven Design for Metamaterials and Multiscale Systems: A Review

“…In general, uncertainty-based acquisition can be conducted based on either frequentist approaches, e.g., random forests and deep neural networks, or Bayesian approaches, e.g., GPs and generalized linear models. For practical guidance on which to employ, readers are referred to Zhang et al [141] Meanwhile, diversity is frequently modeled as a pair-wise, model-agnostic metric that involves a mapping from a pair of instances to a scalar similarity. [135] By harnessing the pair-wise kernel trick, the diversity-based acquisition is capable of handling high-dimensional input instances.…”

“…Sequential Acquisition for Generic Use: Uncertainty vs Diversity: Sequential acquisition can be thought of as designing the rules with which to query an existing pool of unlabeled data, which, in our review, is typically a large number of unit cells with unknown properties. Here, we discuss and compare two key approaches to acquisition for DMD: uncertainty-based sampling, [140,141] and diversity-based sampling. [65,85,86,132] Uncertainty-based sampling is centered on improving the prediction confidence of a model, typically resulting in a distributional imbalance that poorly represents the distribution of unlabeled data.…”

Using machine learning to increase efficiency in design of experiments for cyclic characterization of fibre-reinforced plastics

“…The basic procedure of the new method is shown in Figure 3. It is based upon the adaptive sampling method proposed in [8], but modified for the usage with FRPs. This new type of DOE -in this respect similar to the pearl-string method -adaptively selects the next design point based on the experiments already performed [3,5].…”

“…Figure3: Usage of Gaussian process regression for increasing efficiency in design of experiments (based on[8]). …”