Fei Lu awarded an NSF CAREER grant

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Congratulation to Professor Fei Lu on being awarded a CAREER grant from the NSF. Prof. Lu’s award project, titled “Learning kernels in operators from high-dimensional data: scalable algorithms, theory, and applications”, aims to develop a unified computational approach for the nonparametric learning of kernels/functions in operators from high- or infinite-dimensional data, and introduce scalable algorithms with performance guarantees in a variational framework. It will study four groups of applications where the goals are to recover the kernels/functions in PDE operators, non-Markovian processes, state-space models, and weighted convolution operators. A systematic learning theory, covering identifiability and convergence of regularized estimators, will address the challenges from nonlocal dependence and high-dimensional data. This theory builds the mathematical foundations for a large class of machines learning and inverse problems.