Collaborative Research: Gaussian Process Frameworks for Modeling and Control of Stochastic Systems

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Quantitative models for decision making under uncertainty continue to attract intense effort across natural sciences and engineering. With the advent of ever more sophisticated models in applications, computational demands continue to outpace what is feasible and the premium on efficient numerical approaches remains high. The investigators will explore synergies between the latest machine learning techniques and control paradigms, arising in applications as diverse as finance, energy storage and security, and the epidemiological modeling of infectious diseases. The developed "smart" algorithms will deliver performance upgrades essential for using simulations in tackling large-scale/complex settings. The project will also contribute to inter-disciplinary training in mathematical sciences across undergraduate, graduate and post-doctoral levels. The investigators will investigate statistical learning techniques for modeling, analysis and control of nonlinear dynamic stochastic systems. Through developing algorithms and statistical models for complex stochastic simulators, and active learning strategies for autonomous data acquisition, the project will achieve enhanced capabilities and efficiency in mathematical analysis of dynamic random phenomena. The approach hinges on the use of high fidelity approximate Gaussian Process surrogates to adaptively allocate computing resources in order to maximize the learning rate of the input-output relationship for modeling objectives or of the input-control map for dynamic programming. By connecting stochastic simulation with machine learning and non-parametric statistics, and integrating with the computational implementation, the project will enhance knowledge discovery in large-scale simulation and optimization settings.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.