Reliable data-driven optimization with complex physics-based systems

Simulation models have greatly enhanced our understanding of various phenomena, such as climate change impacts, weather patterns, the spread of pathogens, and nuclear fusion. These models are essential for advancing clean energy and reaching goals like reducing emissions to net zero. Modern computing environments allow scientists to leverage these models for decision-making. Despite today's advanced computational capabilities, optimizing computational processes with physics-based simulation models involves trade-offs between model fidelity, data utilization, and computational resources. This project aims to analyze the computational resources needed for reliable, data-driven decision-making with physics-based models, focusing on enhancing the design of renewable tidal energy farms. Open-source computer code and simulation output will be created and archived. Through outreach activities, students will learn about the importance of computer-aided decision-making. The project will establish informative estimates of the computational resources required for optimizing physics-based systems, which are challenging infinite-dimensional optimization problems. Specifically, the complexity of deterministic and stochastic optimization problems governed by complex physics-based systems will be analyzed, focusing on those given by partial differential equations. A key aspect is analyzing the accuracy and reliability of low-fidelity and sample-based approximations of deterministic, risk-averse, and chance-constrained optimization problems. The focus is on objective and constraint functions with nonsmooth, nonconvex, and nonconvex dependence on decision variables and uncertain parameters. The project employs tools from high-dimensional statistics and nonsmooth analysis to quantify the generalization properties of sample-based and data-driven solutions. Theoretical findings will be empirically validated through simulations, with computer code and simulation outputs published open-source and archived. The results will be disseminated through research publications in scientific journals and presentations at workshops and conferences. Additionally, one Ph.D. student will be integrated into the research of this project. 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.