A Bayesian Optimal Experimental Design for High-dimenstional Physics based Models

James Oreluk is a postdoctoral researcher at Sandia National Laboratories in Livermore, CA. He earned his Ph.D. in Mechanical Engineering from UC Berkeley with research on developing optimization methods for validating physics-based models. His current research focuses on advancing uncertainty quantification and machine learning methods to efficiently solve complex problems, with recent work on utilizing low-dimensional representation for optimal decision making.
Many scientific and engineering experiments are developed to study specific questions of interest. Unfortunately, time and budget constraints make operating these controlled experiments over wide ranges of conditions intractable, thus limiting the amount of data collected. In this presentation, we discuss a Bayesian approach to identify the most informative conditions, based on the expected information gain. We will present a framework for finding optimal experimental designs that can be applied to physics-based models with high-dimensional inputs and outputs. We will study a real-world example where we aim to infer the parameters of a chemically reacting system, but there are uncertainties in both the model and the parameters. A physics-based model was developed to simulate the gas-phase chemical reactions occurring between highly reactive intermediate species in a high-pressure photolysis reactor coupled to a vacuum-ultraviolet (VUV) photoionization mass spectrometer. This time-of-flight mass spectrum evolves in both kinetic time and VUV energy producing a high-dimensional output at each design condition. The high-dimensional nature of the model output poses a significant challenge for optimal experimental design, as a surrogate model is built for each output. We discuss how accurate low-dimensional representations of the high-dimensional mass spectrum are necessary for computing the expected information gain. Bayesian optimization is employed to maximize the expected information gain by efficiently exploring a constrained design space, taking into account any constraint on the operating range of the experiment. Our results highlight the trade-offs involved in the optimization, the advantage of using optimal designs, and provide a workflow for computing optimal experimental designs for high-dimensional physics-based models.