Efficient Numerical Methods for Solving Nonlinear Filtering Problems in Medium-high Dimensions

Time:Thur., 11:30, Mar. 7, 2024

Venue:Tecent Meeting:792-329-157

Speaker:Zhiwen Zhang 张智文 Hong Kong University


This talk introduces two efficient numerical methods for solving nonlinear filtering (NLF) problems. We propose the utilization of the proper orthogonal decomposition (POD) method and tensor train decomposition method to solve the forward Kolmogorov equation (FKE) associated with NLF problems. Our approach involves offline and online stages. In the offline stage, we discretize the partial differential operators within the FKE using the finite difference method, while extracting low-dimensional structures in the solution through the POD method or tensor train decomposition method. In the online stage, we leverage precomputed POD basis functions or low-rank approximation tensors to rapidly solve the FKE when provided with new observation data. Consequently, real-time solutions to NLF problems can be obtained. Numerical results are also presented to demonstrate the efficiency and accuracy of our proposed method in solving NLF problems of up to six dimensions.

DATEMarch 7, 2024
Related News
    • 0

      Computational methods for the dynamics of the nonlinear Schroedinger/ Gross-Pitaevskii equations

      AbstractIn this talk, I begin wtih the (nonlinear) Schroedinger/Gross-Pitaevskii equations (NLSE/GPE) for modeling Bose-Einstein condensation (BEC), nonlinear optics, quantum physics and chemistry, etc., and review some dynamical properties of NLSE/GPE including conserved quantities, dispersion relation, center-of-mass dynamics, soliton solutions and semiclassical limits. Different numerical me...

    • 1

      Modern Mathematics Lecture Series | BSD in higher dimensions

      Abstract Birch and Swinnerton-Dyer conjecture is one of the most famous and important problem in pure math, which predicts deep relations between several invariants of elliptic curves defined over number fields. In 1980s, Beilinson, Bloch, and Kato proposed a vast generalization of this conjecture to motives over number fields. In this talk, we will survey results in recent years concerning Bei...