CAREER: Goal-Oriented Variable Transformations for Efficient Reduced-Order and Data-Driven Modeling

University Of California-San Diego, La Jolla CA

Investigators

Abstract

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). This Faculty Early Career Development Program (CAREER) grant will fund research that enables efficient data-driven modeling of complex natural and engineering processes, including climate dynamics and rocket combustion, thereby promoting the progress of science, and advancing the national prosperity and welfare. Fast and accurate computer simulation of such processes is required for real-time prediction, control intervention, or engineering design. Current techniques for developing simulation models from measurements rely on approximations that may complicate analysis and certification, without a reduction in computational cost or guarantees that underlying physical laws are respected. This project overcomes these challenges by developing a new theoretical approach for systematically uncovering optimal formulations of the system dynamics that are computationally tractable and rigorously certifiable, and that preserve key properties of the physical processes. Such formulations may enable computationally efficient and reliable modeling of chemical and thermal processes or be used to predict long-term ocean flow dynamics that can then be integrated with coupled climate models. In collaboration with industry, this research will advance the design and control of air-conditioning systems by allowing them to use more accurate and faster models of air flow in buildings. Through close integration of research and education, this project will support and engage with first-generation and low-income students from local high schools, community colleges, and universities through outreach, mentoring, and undergraduate research. Free educational material aimed at an undergraduate audience will be disseminated widely to promote training of new generations of engineers with strong computational skills. This research aims to develop the foundations of a new theoretical and computational paradigm that leverages variable transformations to uncover low-dimensional structures in nonlinear dynamical systems and achieve efficient and accurate model reduction that may be certified with respect to stability and structure-preservation. It accomplishes this aim in model- and data-driven settings by exploiting symbolic computing algorithms for systematically identifying transformations and subsequent order-reduction projections that result in optimal quadratic or polynomial models that also preserve symplectic structure for Hamiltonian systems. In the data-driven case, transformations are sought that lead to long-term predictive reduced-order models that are physically interpretable and have favorable numerical properties. Through this effort, new low-dimensional models of the physics of medium-scale applications of chemical reaction dynamics and additive manufacturing will be discovered. The methodological contributions will be assessed on large-scale models of reactive flows and ocean dynamics. 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.