戴万阳

教授 (博导、重要学科岗)
单位:南京大学数学系
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量子计算区块链国际工业革命论坛 理事长
江苏大数据区块链与智能信息专委会 主任
江苏省概率 统计学会    理事长
江苏金融科技研究中心 特邀专家
国际《应用数学进展》 主编



卷积神经网络算法与归一化倒向随机偏微分方程


  • 论文发表信息


  • 英文摘要

      We develop a generic convolutional neural network (CNN) based 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 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.
  • 中文简介

      人工智能卷积神经网络在现代科技中有重要应用并产生重大影响,但其背后的数学机制与理论是什么?这个问题 一直是国际上关注的热点,也是各个国家科学基金资助的焦点。该文在国际上作有关特邀大会嘉宾主旨报告及学 术交流时,也是各国科学家重点提问与关注的问题。本质上,人工智能卷积神经网络是如何确定数据集及如何基 于该数据集构造各种线性或非线性模型而产生的,这在数学上的本质表现就是我们文中介绍的条件数学期望在给 定条件空间上的投影及相应的线性或非线性基的构造问题。当然,具体算法会与倒向随机偏微分方程交互。

  • 关键词

      AI based Monte Carlo simulation, convolution neural network modeling, mean-square and almost sure convergence, backward stochastic partial differential equation, Cauchy terminal value problem, random field Malliavin calculus

  • 国际会议特邀大会嘉宾主旨报告(Keynote Speeches)

    • 该文中的主要学术成就曾作为特邀大会嘉宾主旨报告在国际会议上报告。
    • The main results in the paper are presented as invited keynote talks in international conferences.




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