题目：Low-Rank Methods for Bayesian Inverse Problems
报告人：邱越 助理教授 （上海科大）
摘要：In this talk, I will introduce our recent work on low-rank methods for Bayesian inverse problems. For linear problems with Gaussian noise and Gaussian prior, the posterior is also Gaussian and characterized by the posterior mean and covariance. We propose a low-rank Arnoldi method to approximate the large dense posterior covariance matrix by making use of tensor computations. For nonlinear systems, the posterior is not Gaussian anymore, however, can often be approximated by a Gaussian distribution using the ensemble Kalman filter (EnKF) or the extended Kalman filter (ExKF). We propose a randomized low-rank method to reduce the computational complexity of the EnKF. We use numerical experiments to show the efficiency of our low-rank methods.
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