Kalani Rubasinghe
will speak on
Localized Radial Basis Function Collocation Methods for Data Interpolation and for Solving Partial Differential Equations
Abstract: A radial basis Function (RBF) is a real-valued function whose value depends only on the distance between the input and some fixed point, called a center. Widely used applications of RBFs include function approximation in machine learning, classification, and numerical solutions of partial differential equations (PDEs). In this presentation, we first focus on interpolation and approximation of scattered data in 2D and 3D using polyharmonic splines RBF and low-order polynomial basis. This combination overcomes the instability of high degree polynomial interpolations and achieves high numerical accuracy. Localized versions of such techniques allow large scale interpolation and approximation of functions in high dimensional spaces. Next, we develop a localized RBF collocation method, the localized method of approximated particular solutions. This is successfully used for numerical solutions of nonlinear elliptic PDEs and time-dependent PDEs. Furthermore, one of the most important concepts in modern financial theory, the Black Scholes equations are investigated using four RBF collocation methods. Work on such financial models using deep learning algorithms in high dimensional spaces such as 100 dimensions is also in progress.
Committee Members: Dr. Guangming Yao (advisor)
Dr. Kathleen Kavanagh
Dr. Emmanuel Asante-Asamani
Dr. Olaniyi Samuel Iyiola
Dr. Zhilu Lin
Tuesday, March 08, 2022
11 AM – SC 346
