北京雁栖湖应用数学研究院

丘成栋

焦小沛

2023年05月08日 16:30 至 17:00

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.

焦小沛，本科毕业于上海交通大学致远学院，博士毕业于清华大学数学科学系。先后在北京雁栖湖应用数学研究院，荷兰特文特大学从事博士后工作。现研究方向包括有限维滤波理论，丘-丘滤波方法，物理信息神经网络以及生物信息学。研究兴趣主要集中于（1）利用李代数等几何工具进行偏微分方程求解与有限维滤波系统的分类；（2）设计基于物理信息神经网络的新型数值算法。