In this paper, we explore the finite difference approximation of the fractional Laplace operator in conjunction with a neural network method for solving it. We discretized the fractional Laplace operator using the Riemann-Liouville formula relevant to fractional equations. A shallow neural network was constructed to address the discrete fractional operator, coupled with the OGA algorithm. To validate the feasibility of our approach, we conducted numerical experiments, testing both the Laplace operator and the fractional Laplace operator, yielding favorable convergence results.

翻译：本文探讨了分数阶拉普拉斯算子的有限差分近似，并结合神经网络方法对其进行求解。我们采用与分数阶方程相关的Riemann-Liouville公式对分数阶拉普拉斯算子进行离散化处理。构建了一个浅层神经网络来处理离散分数阶算子，并与OGA算法相结合。为验证所提方法的可行性，我们进行了数值实验，分别测试了拉普拉斯算子和分数阶拉普拉斯算子，均获得了良好的收敛结果。