This $250,000 National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) project grant, awarded to the Regents of the University of Michigan, aims to develop new theoretical tools and algorithm design techniques for the emerging area of operator learning. The key research themes include: 1) developing a deep understanding of learning linear operators, 2) exploring specific classes of nonlinear operators like operator-valued kernels and neural operators, 3) analyzing empirical risk minimization and regularized estimators, and 4) extending the results to more general adversarial online learning models. The project will offer training and mentoring opportunities for future statisticians. This award reflects NSF's mission to advance scientific knowledge and address national research priorities in mathematical and physical sciences.
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