###### Abstract
However, the main problem with this method is that the network structure and the number of nodes need to be determined by users' experience, and there is no clear mathematical analysis guidance. For example, the number of nodes in the input layer and output layer requires users' experience. If the number of nodes is too small, it will affect the effectiveness of the prediction, and too many nodes will affect the training time and efficiency. In addition, there are some problems such as over fitting, especially the poor generalization ability of extrapolation. Based on the Markov prediction model: [PERSON] et al. established the Markov model to predict the quantity of recovered products in different states at the end of a certain period [31]. The Markov chain organically combines the prediction of product state quantity and time, which proves the validity of the Markov model in theory. [PERSON] and [PERSON] (2011) established a Markov prediction model considering the two states of recycled products after treatment [32]. The prediction model of reverse logistics return based on the Markov process can be expressed in Figure 1, where \(S\) is the different state of the product, and \(P\) is the probability. The Markov process in Figure 1 is described by the probability matrix of product state transition, and the return amount of waste products is predicted. The Markov method makes full use of the correlation between product states, and the example results show that the [PERSON] method has advantages in predicting the return amount based on the correlation of time series. Prediction model based on Grey Theory: [PERSON] et al. established grey theory prediction of plastic product return of enterprises [33]. The grey model method is a dynamic model of difference equation of discrete time series. [PERSON] and [PERSON] proposed an improved  
Figure 1: Prediction model of remanufacturing systems return based on Markov method. grey transfer function noise two-stage prediction model [34]. Prediction model based on fuzzy intelligence: [PERSON] et al. put forward a method to establish the prediction model of recycling quantity by using a fuzzy model reasoning system based on analyzing the main factors affecting the reverse logistics [35]. The fuzzy intelligence model uses fuzzy theory to express fuzzy information and fuzzy knowledge in digital way, which realizes the organic combination of symbolic intelligence and computational intelligence. The Mamdani fuzzy inference system is used to predict the recycling of waste machine tools, and good prediction results are obtained. However, the model makes important assumptions about business return and incentive mechanism, which needs to be modified according to the actual situation, otherwise it has certain limitations. Prediction model based on Bayes method: [PERSON] assumes that in the reverse logistics volume of products follows binomial probability distribution, and Bayesian inference and expectation maximization algorithm are used to solve the total probability and backward logistics lag probability parameters of a product, so as to determine the quantity and time of product return [36]. In the above study, the amount of waste products recovered from each recycling site in the reverse logistics network is predicted as the time series data, mainly considering the time correlation of the data. These methods have achieved good prediction results under certain applicable conditions. However, in WEEE reverse logistics, the return amount of each recycling network is not only related in the time sequence, but also has spatial correlation between different recycling sites. Assuming that an electronic company owns \(q\) recycling sites in a limited two-dimensional area \(\mathbf{D}\) (see Figure 2), the recycling sites can be denoted by \(s_{i}(x,y)\) (\(i=1,2,\ldots,q\)), where \(x\) and \(y\) represent the abscissa and ordinate of the geographical location of the recycling site in \(\mathbf{D}\) respectively. The distance between any two recycling sites is denoted by \(h\).