By analyzing the background of land leasing in Shanghai, the hypotheses of the mathematical models of industrial land leasing in Shanghai are proposed, and then, the mathematical models of the land price and land area are presented for analyzing the factors of industrial land leasing. Based on the mathematical models and the district data of Shanghai from 2007 to 2015, the factors influencing industrial land leasing by the district government are studied. It is shown that the influencing factors, such as the land area, GDP, tenure of district mayor, and the distance between the land and the nearest subway station, affect the government behavior on industrial land leasing.

This paper uses the physical information neural network (PINN) model to solve a 3D anisotropic steady-state heat conduction problem based on deep learning techniques. The model embeds the problem’s governing equations and boundary conditions into the neural network and treats the neural network’s output as the numerical solution of the partial differential equation. Then, the network is trained using the Adam optimizer on the training set. The output progressively converges toward the accurate solution of the equation. In the first numerical example, we demonstrate the convergence of the PINN by discussing the effect of the neural network’s number of layers, each hidden layer’s number of neurons, the initial learning rate and decay rate, the size of the training set, the mini-batch size, the amount of training points on the boundary, and the training steps on the relative error of the numerical solution, respectively. The numerical solutions are presented for three different examples. Thus, the effectiveness of the method is verified.