BIMSA > Seminar on Control Theory and Nonlinear Filtering Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes
Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes
Organizer
Shing Toung Yau
Speaker
Minli Feng
Time
Wednesday, April 10, 2024 2:30 PM - 3:00 PM
Venue
理科楼A-304
Abstract
In this presentation, we will present a sparse Cholesky factorization algorithm for dense kernel matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We will then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute epsilon-approximate inverse Cholesky factors of the kernel matrices with complexity O(N*log^d(N/epsilon)) in space and O(N*log^{2d}(N/epsilon)) in time.