Bayesian Optimisation for Sequential Experimental Design with Applications in Additive Manufacturing

Engineering designs are usually performed under strict budget constraints. Collecting a single datum from computer experiments such as computational fluid dynamics can potentially take weeks or months. Each datum obtained, whether from a simulation or a physical experiment, needs to be maximally informative of the goals we are trying to accomplish. It is thus crucial to decide where and how to collect the necessary data to learn most about the subject of study. Data-driven experimental design appears in many different contexts in chemistry and physics (e.g. Lam et al., 2018) where the design is an iterative process and the outcomes of previous experiments are exploited to make an informed selection of the next design to evaluate. Mathematically, it is often formulated as an optimization problem of a black-box function (that is, the input-output relation is complex and not analytically available). Bayesian optimization (BO) is a well-established technique for blackbox optimization and is primarily used in situations where (1) the objective function is complex and does not have a closed form, (2) no gradient information is available, and (3) function evaluations are expensive (see Frazier, 2018, for a tutorial). BO has been shown to be sample-efficient in many domains (e.g.