CAREER: Advancing Efficient Global Optimization of Extremely Expensive Functions under Uncertainty using Structure-Exploiting Bayesian Methods

Ohio State University, The, Columbus OH

Investigators

Abstract

Mathematical optimization is the process of finding the best option from many possible choices in order to improve performance or quality. These types of problems appear in many fields where people need to make decisions, including engineering, economics, healthcare, manufacturing, and environmental sustainability. Some optimization problems are very difficult to solve because testing each option can require expensive computer simulations or experiments, and the results may contain random errors. One modern method used to solve these problems is called Bayesian optimization, which uses machine learning to search for good solutions more efficiently. This approach has been successful in areas such as training deep learning models, testing complex simulations, and designing new materials or medicines. However, many current Bayesian optimization methods treat the system they study like a “black box,” meaning they do not use information about how the system actually works. Because of this, their efficiency is limited. This research project aims to develop new algorithms that improve Bayesian optimization by using known information about the structure of a problem. These improved methods will be applied to important real-world challenges, including understanding how cells make decisions in biomanufacturing, discovering more sustainable materials for lithium-ion batteries, and reducing energy use in heating, ventilation, and air conditioning systems. The project will also create workshops and educational activities to help students learn about decision science. The proposed optimization methodology is inspired by the principle of grey-box modeling, which states that one should avoid learning what is already known when applying machine learning methods. The investigator conjectures a significant reduction in experimental and/or computational effort can be obtained in practice over traditional Bayesian optimization (BO) methods by properly leveraging prior (or domain) knowledge, which is almost always available in practice. Since prior knowledge can come in many diverse forms, the proposed research will focus on some of the most common and important examples. The three specific research aims are: (1) optimizing with hybrid physics-based and data-driven models given noisy and incomplete datasets; (2) optimizing with constrained multi-fidelity models that fuse data from a collection of heterogeneous sources of variable accuracy and cost; and (3) scaling to high-dimensional and sparse data problems through the incorporation of non-myopic and graph-structured formulations. The proposed research aims to promote convergence of statistics, machine learning, optimization, and process systems engineering. More broadly, the improved methods developed as a part of this research project will allow practitioners to solve a wide range of grey-box optimization problems with greater speed and accuracy. Planned outreach activities include educating K-12 students about decision-making under uncertainty via interactive workshops and games, incorporating new data-driven optimization material into the chemical engineering curriculum, and organizing cross-disciplinary professional workshops on the potential significance and impacts of cutting-edge BO technology. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.