Collaborative Research: Design, Modeling and Active Learning of Quantitative-Sequence Experiments

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A new type of experiment concerning both quantitative and sequence (QS) factors has recently drawn great attention in science and engineering applications. In chemotherapy, to develop efficient drug combinations involving several drug components, researchers need to conduct experiments optimizing both the doses and the sequence orders of drug components. Such a problem raises new challenges for statisticians since the input space is semi-discrete and grows exponentially with the number of drugs. Researchers rely more than ever on statistical modeling and active learning to identify optimal settings given limited experimental resources. Additionally, QS experiments often have specific requirements. In the computer experiment for metal additive manufacturing processes, the output response is binary (success/failure), and it requires both interpolation and uncertainty quantification, which is an unsolved problem in the current literature. In this project, the investigators will provide systematic solutions to QS experiments, addressing challenges in design, modeling, uncertainty quantification, and active learning. The outcome of this project will help save experimental costs in applications involving QS factors. The applications to chemotherapy will help advance cancer research in the U.S., while the applications to manufacturing processes will enhance the industrial competitiveness of the U.S. Also, this project provides research training opportunities for graduate students. Active learning in experiments, aka reinforcement learning under the broad context of machine learning, allocates runs in an adaptive manner, which is generally more efficient than one-shot experiments for optimizing the experimental settings. This project will establish new Gaussian process-based models for physical experiments with QS factors, based on which new active learning procedures will be developed. For analyzing computer experiments, a novel Hopfield process (HP) framework will be established as an accurate surrogate for interpolating binary (and categorical) outputs, which will facilitate uncertainty quantification and active learning. Optimal QS experimental designs will also be constructed by combing several Williams-transformed good lattice point sets, which possess desirable properties including space-filling, orthogonality, and paired balance. This research project will provide systematic solutions for various types of QS experiments that are of interest in scientific research and industrial applications.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.