## 2 Methods  
### Back Propagation Neural Network  
#### 2.1.1 Back Propagation Neural Network Structure  
Artificial neural network (ANN) is an up-and-coming network algorithm tool hinging on self-learning, which means it does not require a human to set the weights and automatically adjust the weights through deep learning. ANN is related to a signal processing system and information composed of a massive number of called neurons that stimulate the biological nervous system in a program. These neurons connect to each other through direct connections called synapses, allowing distributed parallel processing. The main characteristic of ANN is its adaptability, which could learn and establish accurate and complex relationships among various numerical variables without the need for any pre-defined models [27]. ANN is often used in systems where no mathematical model exists or is precise enough to represent the phenomenon [28; 29; 30; 31]. BP neural network is the foremost representative artificial neural network with three or more layers, including the input layer, the hidden layer, and the output layer. Neurons connect fully on the same layer and are not connected between the different layers. The signal starts from the input layer nodes and transmits to the output layer nodes after passing the hidden layer nodes [32]. BP neural network, with its self-organizing ability, can automatically find patterns in the input information without any a priori knowledge, adjust the connection weights between the processing units according to the back propagation of errors, and after a period of self-learning training or perception, form a nonlinear model suitable for expressing the patterns and produce reasonable output values based on the given input information. In the process of processing information, it is adaptive and fault-tolerant, allowing a certain amount of inaccurate or even wrong information, and it can approximate any function, which makes comprehensive, dynamic, and fuzzy evaluations with large amounts of data have a scientific basis. Compared with traditional scoring and evaluation methods, BP neural network overcomes the deficiency of subjectivity in the initial evaluation process. It only requires a small number of training samples to determine the weights and thresholds with a high degree of accuracy, and could achieve any complex nonlinear function fitting with any accuracy, truthfully reflecting and approaching the reality, with scientific, objective, and reliable characteristics [33; 34; 35]. A typical structure of three layers in the BP neural network model is shown in Figure 1.  
This paper uses a three-layer BP network to realize an arbitrary function approximation to evaluate the agricultural investment climate of CEE countries. The number of input layer nodes is set for \(n\). The number of hidden layer nodes is set for \(m\). The number of output layer nodes is set for \(p\). Figure 1: BP neural network topology structure. [PERSON] theorem proves that for a given arbitrary continuous function \(\phi\): \(E^{n}\to R^{m}\), \(\phi(\mathrm{x})=y_{i}\)\(\phi\) could be precisely realized by a three-layer neural network. In other words, a neural network with only one nonlinear hidden layer can approximate a function of arbitrary complexity with arbitrary accuracy [36; 37]. The selection of hidden nodes is a challenging issue. If the number of hidden nodes is relatively small, it may lead to poor training effect of the BP neural network. If the number of hidden nodes is large, although it could reduce the training error of the system, the training efficiency of the BP neural network would be reduced, since the network training will be stuck in the local minima and will not be optimized, which will eventually lead to the phenomenon of overfitting. The basic principle for determining the number of hidden layer nodes is to achieve a structure as compact as possible while meeting the accuracy requirements, i.e., to have as few hidden layer nodes as possible.