论文标题
用神经网络在数字上模拟Krusell-Smith模型
Simulating numerically the Krusell-Smith model with neural networks
论文作者
论文摘要
著名的Krusel-Smith增长模型是具有共同噪音的平均野外游戏的重要例子。平均现场游戏是在主方程中编码的，这是一个依赖于整个状态分布的游戏值满足的部分微分方程。因此，后一个方程在无限的尺寸空间中构成。这使数值模拟既具有挑战性又具有挑战性。但是，克鲁塞尔（Krusell）和史密斯（Smith）猜想游戏的价值函数主要取决于状态分布，这是通过低维数量的。在本文中，我们希望提出一种数值方法，用于近似Krusell-Smith模型中产生的主方程的解决方案，并用于自适应地识别保留信息的重要部分的低维变量。这个新的数值框架基于半拉格朗日方法，并将神经网络用作重要成分。
The celebrated Krusel-Smith growth model is an important example of a Mean Field Game with a common noise. The Mean Field Game is encoded in the master equation, a partial differential equation satisfied by the value of the game which depends on the whole distribution of states. The latter equation is therefore posed in an infinite dimensional space. This makes the numerical simulations quite challenging. However, Krusell and Smith conjectured that the value function of the game mostly depends on the state distribution through low dimensional quantities. In this paper, we wish to propose a numerical method for approximating the solutions of the master equation arising in Krusell-Smith model, and for adaptively identifying low-dimensional variables which retain an important part of the information. This new numerical framework is based on a semi-Lagrangian method and uses neural networks as an important ingredient.
