Beijing Institute of Mathematical Sciences and Applications

Stephen S-T. Yau

Xiaopei Jiao

Monday, May 8, 2023 4:30 PM - 5:00 PM

Online

Schrodinger equation plays an important role in quantum physics and many other fields in applied mathematics such as control theory. In nonlinear filtering, under the framework of Yau-Yau algorithm, Schrodinger equation at a short time interval plays a crucial role for state estimation problem. In this paper, Schrodinger equation with polynomial potential has been investigated and explicit fundamental solution has been written down. By applying Euler operator theory developed in estimation algebra theory, uniqueness and existence of fundamental solution are verified. We propose two numerical algorithms for Schrodinger equation including the first order approximation and PINN based solver. We compare our algorithms with classical spectrum method. Numerical results demonstrate that our two new algorithms are superior to the traditional filtering algorithms in effectiveness and accuracy.

Jiao Xiaopei graduated with a bachelor's degree from the Zhi Yuan College of Shanghai Jiao Tong University (Physics Department) in 2017 and obtained his PhD from the Department of Mathematical Sciences at Tsinghua University in 2022, under the guidance of Professor Stephen Shing-Toung Yau (IEEE Fellow, former tenured professor at the University of Illinois at Chicago). He has conducted postdoctoral research at the Beijing Institute of Mathematica Science and Application and at the University of Twente in the Netherlands (under the guidance of Professor Johannes Schmidt-Hieber, Fellow of the Institute of Mathematical Statistics). His current research interests include control theory, numerical partial differential equations, and bioinformatics.