English(EN) From Monte Carlo to neural networks approximations of boundary value problems

新方法结合蒙特卡洛和神经网络求解边值问题

作者 PulseAugur 编辑部 · [1 个来源] · 2026-08-18 04:00

本文探讨了近似泊松方程解的新方法，泊松方程是数学物理中的一个基本问题。研究人员证明，蒙特卡洛方法，特别是加速球面行走算法，可以有效地为该方程的解提供数值近似。此外，研究表明，这些蒙特卡洛求解器如何用于构建也近似解的深度神经网络（DNN），这些网络的规模在多项式上取决于问题的维度和所需的精度。 AI

影响引入了解决复杂数学问题的新颖计算方法，可能影响科学模拟和建模。

排序理由该项目是一篇详细介绍新研究方法的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.AI TIER_1 English(EN) · Lucian Beznea, Iulian Cimpean, Oana Lupascu-Stamate, Ionel Popescu, Arghir Zarnescu · 2026-08-18 04:00

从蒙特卡洛到神经网络求解边值问题

arXiv:2209.01432v4 Announce Type: replace-cross Abstract: In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to Holder data in general bounded domains of $\mathbb{R}^d$. We aim at two fundamental goals. The first, and …