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Sep, 2022
从蒙特卡洛到神经网络的边界值问题近似
From Monte Carlo to neural networks approximations of boundary value problems
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Lucian Beznea, Iulian Cimpean, Oana Lupascu-Stamate, Ionel Popescu, Arghir Zarnescu
TL;DR
本文研究用概率方法和神经网络逼近求解Poisson方程,并提出基于球面游走算法轻微改变的蒙特卡洛数值近似方法,其维数无需指定且具有高效性和多项式复杂度。同时,本文证明使用该数值近似方法得出的随机深度神经网络可在多项式时间内对Poisson方程进行有效逼近。
Abstract
In this paper we study probabilistic and
neural network
approximations for solutions to
poisson equation
subject to H\" older or $C^2$ data in general bounded domains of $\mathbb{R}^d$. We aim at two fundamental
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