论文标题
闭环地热系统的深度学习盖尔金方法
A Deep Learning Galerkin Method for the Closed-Loop Geothermal System
论文作者
论文摘要
采用深度学习方法来研究部分微分方程（PDE）一直存在一种趋势。本文将为闭环地热系统提出一种深度学习的Galerkin方法（DGM），该方法是一种新的耦合多物理PDE，主要由地下热交换管道的框架组成，以从地热储层中提取地热热量。该方法是Galerkin方法和机器学习与神经网络近似的解决方案的自然组合，而不是基础函数的线性组合。我们通过随机采样时空点并最大程度地减少损失功能来训练神经网络，以满足差分运算符，初始条件，边界和界面条件。此外，神经网络的近似能力是通过在某些条件下的损失函数的收敛以及神经网络与精确解决方案的收敛证明的。最后，进行了一些数值示例，以证明神经网络的近似能力。
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). This article is to propose a Deep Learning Galerkin Method (DGM) for the closed-loop geothermal system, which is a new coupled multi-physics PDEs and mainly consists of a framework of underground heat exchange pipelines to extract the geothermal heat from the geothermal reservoir. This method is a natural combination of Galerkin Method and machine learning with the solution approximated by a neural network instead of a linear combination of basis functions. We train the neural network by randomly sampling the spatiotemporal points and minimize loss function to satisfy the differential operators, initial condition, boundary and interface conditions. Moreover, the approximate ability of the neural network is proved by the convergence of the loss function and the convergence of the neural network to the exact solution in L^2 norm under certain conditions. Finally, some numerical examples are carried out to demonstrate the approximation ability of the neural networks intuitively.
