BIMSA > 控制理论和非线性滤波讨论班 Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes
Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes
组织者
丘成栋
演讲者
冯敏立
时间
2024年04月17日 15:30 至 16:00
地点
Online
摘要
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.