A deep learning method for solving Fokker-Planck equations
A deep learning method for solving Fokker-Planck equations
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发表时间：
2020-12
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通讯作者：
Jiayu Zhai;M. Dobson;Yao Li-
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作者：
Jiayu Zhai;M. Dobson;Yao Li-
随机微分方程的概率分布的时间演化遵循福克-普朗克方程，其通常具有无界的高维区域。受我们在\cite{li 2018 data}中早期研究的启发，我们提出了一种无网格的Fokker-Planck求解器，其中Fokker-Planck方程的解现在由神经网络表示。损失函数中微分算子的引入提高了神经网络表示的准确性，减少了训练过程中对数据的需求。几个高维数值例子进行了演示。
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.