| 个人简介 | |
|---|---|
 Prof. Wanyang Dai Nanjing University, China |
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| 标题： Simulation and Scheme Modeling via CNN with Convergence Analysis for Backward Stochastic Partial Differential Equations | |
| 摘要： We develop a generic numerical scheme to simulate the 2-tuple adapted strong solution to a unified system of backward stochastic partial differential equations (B-SPDEs) driven by Brownian motions, which can be used to model many real-world system dynamics such as optimal control and differential game problems. The dynamics of the scheme is modeled by a convolutional neural network (CNN) through conditional expectation projection. It consists of two convolution parts: W layers of backward networks and L layers of reinforcement iterations. Furthermore, it is a completely discrete and iterative algorithm in terms of both time and space with mean-square error estimation and almost sure (a.s.) convergence supported by both theoretical proof and numerical examples. In doing so, we need to prove the unique existence of the 2-tuple adapted strong solution to the system under both conventional and Malliavin derivatives with general local Lipschitz and linear growth conditions. | |
| 简介： Wanyang Dai is a Distinguished Professor in Nanjing University and Chief Scientist in DepthsData Digital Economic Research Institute. He is the current President & CEO of U.S. based (Blockchain & Quantum-Computing) SIR Forum (Industrial 6.0 Forum), President of Jiangsu Probability & Statistical Society in China, Chairman of Jiangsu BigData-Blockchain and Smart Information Special Committee in China. He received his Ph.D. from Georgia Institute of Technology in USA. He was an MTS and principal investigator in U.S. based AT&T Bell Labs (currently Nokia Bell Labs) with some project won “Technology Transfer” now called cloud system. He published numerous influential papers in big name journals and received various academic awards. He has presented around 40 keynote/plenary speeches in IEEE/ACM, mathematics & statistics, and other international conferences. He has been serving as IEEE/ACM conference chairs, editor-in-chiefs and editorial board members for various international journals ranging from pure mathematics & statistics to their applications. | |
