The spatial Solow model can take into account the geographical interdependence and the spatial organization of economic activities, and offers a better understanding of economic growth. In this work, governing equations of the spatial Solow model were solved by using the Physics Informed Neural Networks (PINNs) method, and both the forward and inverse problems were considered. For the forward problems, the conditions with and without considering the technology progress were solved, and the results were validated against the existing ones and good agreement can be found. For the inverse problems, the parameter identification of the production function was conducted by using very sparse data points. For the data without noise, two parameters of the production function can be estimated by using only 2 data points, where the errors can be below 3 %. For the low level noisy data, the parameters can also be inversed with 30 data points, and the errors for the two parameters were both less than 1 %.

中文翻译：

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一种使用物理信息神经网络 （PINN） 求解空间 Solow 模型的正向和逆向问题的新方法


空间 Solow 模型可以考虑地理上的相互依存关系和经济活动的空间组织，并提供更好的对经济增长的理解。在这项工作中，使用物理信息神经网络 （PINN） 方法求解空间 Solow 模型的控制方程，并考虑了正向和逆向问题。对于前向问题，解决了考虑和不考虑技术进步的条件，并针对现有结果进行了验证，可以找到良好的一致性。对于逆问题，通过使用非常稀疏的数据点来进行生产函数的参数识别。对于无噪声的数据，仅使用 2 个数据点即可估计生产函数的两个参数，其中误差可以低于 3 %。对于低级别噪声数据，参数也可以与 30 个数据点进行反转，并且两个参数的误差都小于 1 %。