论文标题
解决fokker-planck方程的深度学习方法
A deep learning method for solving Fokker-Planck equations
论文作者
论文摘要
随机微分方程的概率分布的时间演变遵循Fokker-Planck方程，该方程通常具有无界的高维域。受到我们在\ cite {li2018data}的早期研究的启发，我们提出了一个无网状的fokker-planck求解器，其中fokker-planck方程的解决方案现在由神经网络表示。损失函数中差分运算符的存在提高了神经网络表示的准确性，并减少了训练过程中数据的需求。证明了几个高维数值示例。
The time evolution of the probability distribution of a stochastic differential equation follows the Fokker-Planck equation, which usually has an unbounded, high-dimensional domain. Inspired by our early study in \cite{li2018data}, we propose a mesh-free Fokker-Planck solver, in which the solution to the Fokker-Planck equation is now represented by a neural network. The presence of the differential operator in the loss function improves the accuracy of the neural network representation and reduces the the demand of data in the training process. Several high dimensional numerical examples are demonstrated.
