Collaborative Research: Experimental Design, Surrogate Modeling, and Sensitivity Analysis for Complex Computer Experiments

Computer experiments evaluate computer models at carefully chosen input settings to investigate systems that are too costly, risky, time-consuming, or impractical to examine solely through physical experiments. These models may be implemented as numerical simulators, digital twins, or related computational tools used in environmental prediction, aerospace and materials design, biomedical modeling, drug development, manufacturing, and uncertainty analysis. A primary statistical goal in computer experiments is to use selected input settings and their corresponding outputs to build surrogate models, which are fast statistical approximations of complex computer models. Because each model evaluation can require substantial computing resources, careful selection of input settings is essential to efficiently use the resulting data. This task becomes even harder in high-dimensional computer experiments, where many uncertain inputs must be studied, and standard analyses can become too slow or memory-intensive. Many standard designs in computer experiments cover the input space broadly but lack the closely spaced, structured input settings needed to learn how individual inputs affect the output. Without this local information, surrogate models can become unstable, leading to less dependable predictions, weaker uncertainty assessments, and less reliable conclusions. This project develops statistical tools for planning and analyzing computer experiments, enabling limited computational resources to be used more effectively. The methods can support better decisions in areas important to national health, prosperity, welfare, and security, including environmental risk assessment, aerospace engineering, biomedical research, materials discovery, and industrial innovation. The project also advances education and workforce development through training graduate students, incorporating research into teaching materials, and developing open-source software. This project develops a geometry-driven framework that integrates experimental design, Gaussian process surrogate modeling, scalable computation, and variance-based sensitivity analysis. The first goal examines how local design geometry improves Gaussian process inference by connecting closely spaced axis-neighbor pairs to Fisher information for correlation length scales. This connection guides strong orthogonal array-based designs and structured level expansions that preserve global space-filling coverage while improving local identifiability, and it also supports design-based Sobol sensitivity estimation with fewer additional model evaluations. The second goal extends the framework to multifidelity computer experiments through nested low-fidelity and high-fidelity designs and fidelity-aware Sobol indices that attribute high-fidelity variation to the low-fidelity contribution, the discrepancy between fidelities, and their interaction. The third goal develops Cartesian-product designs for large and high-dimensional computer experiments, using Kronecker-structured Gaussian process computation, group total-effect sensitivity measures, data-driven factor grouping, and sequential sparse-grid refinement to improve scalability. The methods will be evaluated through theory, simulation studies, benchmark functions, and public scientific and engineering applications, and will be disseminated through an open-source R package. 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.