BIMSA > Seminar on Control Theory and Nonlinear Filtering A Uniform Framework of Yau-Yau Algorithm Based on Deep Learning with the Capability of Overcoming the Curse of Dimensionality
A Uniform Framework of Yau-Yau Algorithm Based on Deep Learning with the Capability of Overcoming the Curse of Dimensionality
Organizer
Shing Toung Yau
Speaker
Zeju Sun
Time
Monday, April 24, 2023 2:30 PM - 3:00 PM
Venue
Online
Abstract
In numerous application areas, high-dimensional nonlinear filtering is still a challenging problem. The introduction of deep learning and neural network has improved the efficiency of classical algorithms and performs well in many tasks in practice. However, there is still a lack of theoretical interpretation of its feasibility. In this paper, we leverage on the representation ability of recurrent neural network and provide a computationally efficient and optimal framework for nonlinear filter design based on Yau-Yau algorithm and recurrent neural network. Theoretically, it can be proved that the size of the neural network required in this algorithm only increases polynomially (rather than exponentially) with respect to the dimension, which implies that the Yau-Yau algorithm based on recurrent neural network has the capability to overcome the curse of dimensionality. Numerical results also show that our method is more competitive than classical algorithms in high-dimensional problems.