Network prediction method and device based on graph neural network, electronic device and medium

Abstract

The present disclosure relates to the field of artificial intelligence technology, and in particular to a network prediction method and device, electronic device and medium based on a graph neural network. The method includes obtaining a state prediction task, determining a distribution matrix based on the mapping relationship between each target node and each super node in the target network, renormalizing the target network using the distribution matrix to obtain a network backbone, processing the network backbone using a graph neural network to obtain a dynamic sequence of each super node, performing state prediction based on the dynamic sequence to obtain the node state of each super node in a prediction time period, and performing super-resolution processing based on a historical observation sequence and the node state of each super node in a prediction time period to obtain the node state of each target node in a prediction time period. The network prediction method and device, electronic device and medium according to the present disclosure can achieve long-term accurate prediction of a complex network after effectively reducing the dimensionality of the complex network of the target network to be predicted.

Description

Technical Field

[0001] The present disclosure relates to the field of artificial intelligence technology, and in particular to a network prediction method and device based on a graph neural network, an electronic device, and a medium. Background Art

[0002] The evolutionary behaviors of many complex systems in the real world, such as the brain, social networks, and infectious diseases, can be modeled as dynamic processes on complex networks, where system components are regarded as nodes in the network and the coupling interactions between components are regarded as edges. These complex networks and their dynamic processes have a lot of research and industrial applications, so network prediction is particularly important. The prediction of node states in the network is one of the most important problems in the field of network data mining, which is crucial for analyzing the evolutionary mechanism of such real systems and making decision policies.

[0003] In recent years, in order to achieve network prediction, relevant technologies have proposed the use of graph machine learning methods to perform network prediction, but this method still has many limitations. For example, when faced with complex networks, due to the large scale of network data in complex networks, the time overhead of model calculation and the storage overhead of parameters will be unacceptable. For example, equal-weighted modeling of all network nodes will lead to excessive attention to a large number of unimportant interference nodes when the network scale is large, making it unsuitable for long-term and accurate prediction of future system evolution. Summary of the invention

[0004] In view of this, the present disclosure proposes a network prediction method and device, electronic device and medium based on graph neural network, which can achieve long-term and accurate prediction of the node status of a complex network after effectively reducing the dimension of the complex network to be predicted.

[0005] According to one aspect of the present disclosure, a network prediction method based on a graph neural network is provided, comprising: obtaining a state prediction task for each target node in a target network, wherein the target network comprises a plurality of target nodes and a plurality of edges connected between the target nodes, each edge representing a connection relationship between the connected target nodes, the target network being formed by networked modeling of a real system, the target nodes representing subjects in the real system, wherein the real system is derived from real systems in urban transportation scenarios, ecological environment scenarios, and urban life service scenarios; determining an allocation matrix based on a mapping relationship between each target node in the target network and each preset super node, each super node being a virtual node obtained by performing feature comprehensive simulation on some subjects in the real system; utilizing the The target network is renormalized by the allocation matrix to obtain a network backbone, wherein the network backbone includes each of the super nodes and a plurality of edges connected between the super nodes and representing the connection relationship between the super nodes; the network backbone is processed by a graph neural network to obtain a dynamic sequence of each of the super nodes, wherein each of the dynamic sequences indicates a node state of a corresponding super node that changes with time, and a state prediction is performed based on the dynamic sequence of each of the super nodes to obtain a node state of each of the super nodes in a prediction time period; super-resolution processing is performed based on a historical observation sequence of the target network and a node state of each of the super nodes in the prediction time period to obtain a node state of each of the target nodes in the prediction time period, wherein the historical observation sequence indicates a node state of each of the target nodes in a historical time period.

[0006] In a possible implementation, a distribution matrix is ​​determined based on a mapping relationship between each target node and each preset supernode in the target network, including: determining each first hyperbolic eigenvector representing the node state of the corresponding target node in the hyperbolic space according to the target network and preset prior information, and determining each second hyperbolic eigenvector representing the node state of the corresponding supernode in the hyperbolic space according to each supernode and the prior information; performing a spatial transformation from the hyperbolic space to the Euclidean space on each of the first hyperbolic eigenvectors to obtain each first Euclidean eigenvector representing the node state of the corresponding target node in the Euclidean space, and performing the spatial transformation on each of the second hyperbolic eigenvectors to obtain each second Euclidean eigenvector representing the node state of the corresponding supernode in the Euclidean space; performing a nonlinear operation on each of the first Euclidean eigenvectors using an artificial neural network to obtain a first Euclidean high-order eigenvector, and performing the nonlinear operation on each of the second Euclidean eigenvectors using the artificial neural network to obtain a second Euclidean high-order eigenvector; determining the distribution matrix based on the first Euclidean high-order eigenvector and the second Euclidean high-order eigenvector.

[0007] In a possible implementation, the target network is renormalized using the allocation matrix to obtain a network backbone, including: determining a first adjacency matrix representing a connection relationship between each of the target nodes based on the target network; determining a second adjacency matrix based on the first adjacency matrix and the allocation matrix, the second adjacency matrix representing a connection relationship between each of the super nodes; and obtaining the network backbone based on each of the super nodes and the second adjacency matrix.

[0008] In a possible implementation, state prediction is performed based on the dynamic sequence of each supernode to obtain the node state of each supernode in the prediction time period, including: processing the dynamic sequence of each supernode in the historical time period to obtain the initial state of each supernode; performing state prediction for the prediction time period based on the initial state of each supernode and the second adjacency matrix to determine the node state of each supernode in the prediction time period.

[0009] In a possible implementation, super-resolution processing is performed on the historical observation sequence of the target network and the node state of each super node in the prediction time period to obtain the node state of each target node in the prediction time period, including: clustering the multiple target nodes to obtain a clustering result, the clustering result includes multiple clusters, each cluster includes at least one target node; based on the historical observation sequence of each target node in each cluster and the node state of the super node corresponding to the target node in the prediction time period, the node state of each target node in each cluster in the prediction time period is determined.

[0010] In one possible implementation, clustering the multiple target nodes to obtain a clustering result includes: determining the degree of each target node according to the target network, each degree representing the number of target nodes that have a connection relationship with the corresponding target node; clustering the multiple target nodes based on each degree to obtain the clustering result.

[0011] In a possible implementation, the method also includes a training process for the graph neural network or artificial neural network, the training process includes training based on a sample set and a preset loss function, the loss function includes at least one of a Euclidean loss function, an allocation loss function, a backbone loss function, and an original loss function, the sample set includes multiple sample networks, each of the sample networks includes multiple sample nodes and multiple edges connected between the sample nodes, wherein the Euclidean loss function is determined based on a mapping relationship between each of the sample nodes and corresponding super nodes in the sample network, the allocation loss function is determined based on a connection relationship between each of the sample nodes and a mapping relationship between each of the sample nodes and corresponding super nodes in the sample network, the backbone loss function is determined based on a node state of each super node corresponding to each of the sample nodes in a preset time period, and the original loss function is determined based on a node state of each of the sample nodes in the preset time period.

[0012] According to another aspect of the present disclosure, a network prediction device based on a graph neural network is provided, including: a task acquisition module, used to acquire state prediction tasks for each target node in a target network, the target network including multiple target nodes and multiple edges connected between the target nodes, each edge representing a connection relationship between the connected target nodes, the target network being formed by networked modeling of a real system, the target node representing a subject in the real system, wherein the real system comes from a real system in an urban transportation scenario, an ecological environment scenario, and an urban life service scenario; a matrix determination module, used to determine an allocation matrix based on a mapping relationship between each target node in the target network and each preset super node, each super node being a virtual node obtained by performing feature comprehensive simulation on some subjects in the real system; a renormalization group module, A module for performing a renormalization group on the target network using the allocation matrix to obtain a network backbone, wherein the network backbone includes each of the super nodes and a plurality of edges connected between the super nodes and representing the connection relationship between the super nodes; a state prediction module, which is used to process the network backbone using a graph neural network to obtain a dynamic sequence of each of the super nodes, wherein each of the dynamic sequences indicates a node state of a corresponding super node that changes over time, and to perform state prediction based on the dynamic sequence of each of the super nodes to obtain a node state of each of the super nodes in a prediction time period; and a super-resolution module, which is used to perform super-resolution processing based on a historical observation sequence of the target network and a node state of each of the super nodes in the prediction time period to obtain a node state of each of the target nodes in the prediction time period, wherein the historical observation sequence indicates a node state of each of the target nodes in a historical time period.

[0013] In a possible implementation, a distribution matrix is ​​determined based on a mapping relationship between each target node and each preset supernode in the target network, including: determining each first hyperbolic eigenvector representing the node state of the corresponding target node in the hyperbolic space according to the target network and preset prior information, and determining each second hyperbolic eigenvector representing the node state of the corresponding supernode in the hyperbolic space according to each supernode and the prior information; performing a spatial transformation from the hyperbolic space to the Euclidean space on each of the first hyperbolic eigenvectors to obtain each first Euclidean eigenvector representing the node state of the corresponding target node in the Euclidean space, and performing the spatial transformation on each of the second hyperbolic eigenvectors to obtain each second Euclidean eigenvector representing the node state of the corresponding supernode in the Euclidean space; performing a nonlinear operation on each of the first Euclidean eigenvectors using an artificial neural network to obtain a first Euclidean high-order eigenvector, and performing the nonlinear operation on each of the second Euclidean eigenvectors using the artificial neural network to obtain a second Euclidean high-order eigenvector; determining the distribution matrix based on the first Euclidean high-order eigenvector and the second Euclidean high-order eigenvector.

[0014] In a possible implementation, the target network is renormalized using the allocation matrix to obtain a network backbone, including: determining a first adjacency matrix representing a connection relationship between each of the target nodes based on the target network; determining a second adjacency matrix based on the first adjacency matrix and the allocation matrix, the second adjacency matrix representing a connection relationship between each of the super nodes; and obtaining the network backbone based on each of the super nodes and the second adjacency matrix.

[0015] In a possible implementation, state prediction is performed based on the dynamic sequence of each supernode to obtain the node state of each supernode in the prediction time period, including: processing the dynamic sequence of each supernode in the historical time period to obtain the initial state of each supernode; performing state prediction for the prediction time period based on the initial state of each supernode and the second adjacency matrix to determine the node state of each supernode in the prediction time period.

[0016] In a possible implementation, super-resolution processing is performed on the historical observation sequence of the target network and the node state of each super node in the prediction time period to obtain the node state of each target node in the prediction time period, including: clustering the multiple target nodes to obtain a clustering result, the clustering result includes multiple clusters, each cluster includes at least one target node; based on the historical observation sequence of each target node in each cluster and the node state of the super node corresponding to the target node in the prediction time period, the node state of each target node in each cluster in the prediction time period is determined.

[0017] In one possible implementation, clustering the multiple target nodes to obtain a clustering result includes: determining the degree of each target node according to the target network, each degree representing the number of target nodes that have a connection relationship with the corresponding target node; clustering the multiple target nodes based on each degree to obtain the clustering result.

[0018] In a possible implementation, the device also includes a training module for performing a training process for the graph neural network or artificial neural network, the training process including training based on a sample set and a preset loss function, the loss function including at least one of a Euclidean loss function, an allocation loss function, a backbone loss function, and an original loss function, the sample set including a plurality of sample networks, each of the sample networks including a plurality of sample nodes and a plurality of edges connected between the sample nodes, wherein the Euclidean loss function is determined based on a mapping relationship between each of the sample nodes and corresponding super nodes in the sample network, the allocation loss function is determined based on a connection relationship between each of the sample nodes and a mapping relationship between each of the sample nodes and corresponding super nodes in the sample network, the backbone loss function is determined based on a node state of each super node corresponding to each of the sample nodes in a preset time period, and the original loss function is determined based on a node state of each of the sample nodes in the preset time period.

[0019] According to another aspect of the present disclosure, an electronic device is provided, comprising: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0020] According to another aspect of the present disclosure, a non-volatile computer-readable storage medium is provided, on which computer program instructions are stored, wherein the computer program instructions implement the above method when executed by a processor.

[0021] According to another aspect of the present disclosure, a computer program product is provided, including a computer-readable code, or a non-volatile computer-readable storage medium carrying the computer-readable code. When the computer-readable code runs in a processor of an electronic device, the processor in the electronic device executes the above method.

[0022] The network prediction method and device based on graph neural network, electronic device and medium provided by the embodiments of the present disclosure obtain the state prediction task for each target node in the target network, determine the allocation matrix based on the mapping relationship between each target node and each preset super node in the target network, use the allocation matrix to renormalize the target network to obtain the network backbone, use the graph neural network to process the network backbone to obtain the dynamic sequence of each super node, perform state prediction based on the dynamic sequence of each super node to obtain the node state of each super node in the prediction time period, perform super-resolution processing based on the historical observation sequence of the target network and the node state of each super node in the prediction time period to obtain the node state of each target node in the prediction time period, and can perform long-term prediction on the low-dimensional coordinates corresponding to the super node after effectively reducing the dimension of the complex network to be predicted, and then push back to the original target network to obtain the prediction result of the target node, thereby achieving long-term and accurate prediction of the node state of the complex network without huge computing and storage overhead.

[0023] Further features and aspects of the present disclosure will become apparent from the following detailed description of exemplary embodiments with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, and aspects of the disclosure and, together with the description, serve to explain the principles of the disclosure.

[0025] Figures 1 to 3 A schematic diagram of a network prediction method based on a graph neural network provided according to an embodiment of the present disclosure is shown.

[0026] Figures 4 to 5 A block diagram of a network prediction device based on a graph neural network provided according to an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0027] Various exemplary embodiments, features and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.

[0028] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0029] In addition, in order to better illustrate the present disclosure, numerous specific details are given in the following specific embodiments. It should be understood by those skilled in the art that the present disclosure can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the subject matter of the present disclosure.

[0030] In order to facilitate those skilled in the art to understand the technical solution provided by the embodiments of the present disclosure, the technical environment in which the technical solution is implemented is described below.

[0031] The state prediction task for complex networks can be regarded as a node prediction task, which is to infer the possible evolution of the state value of each node at a future time point based on trend analysis and mathematical modeling of historical observation records of the real system of interest. Node state prediction of complex networks has many practical application scenarios, including but not limited to river network runoff prediction, listed company financial network market prediction, urban road network traffic flow prediction, ecological network species abundance prediction and circuit network congestion progress prediction.

[0032] How to realize the state prediction task is the basic tool for solving the prediction task in specific application scenarios. To solve this problem, the traditional method generally uses the autoregressive moving average (ARMA) model and the autoregressive integrated moving average (ARIMA) model in traditional statistical methods to stabilize the non-stationary time series data, and then calculate the relevant parameters of the series for subsequent regression analysis. However, this type of method only uses simple time series information and cannot capture the interactive dynamic mechanism between the original nodes in the complex network, especially when dealing with large-scale, high-dimensional system prediction tasks, resulting in unacceptable prediction accuracy, inability to generalize or predict for a long time, and unacceptable computational and time overheads. With the development of artificial intelligence technology, graph machine learning methods represented by graph neural networks (GNN) can avoid the assumptions of traditional domain models on data mechanisms and directly use graph machine learning models to characterize the inherent mechanisms in the original observation data. However, the scale of complex networks in real-world problems is often very large, resulting in extremely high dimensions of prediction problems. This means that when the scale of network data increases, the time overhead of model calculation and the storage overhead of parameters will be unacceptable. In addition, when making network predictions, current graph machine learning methods only retain the static features of complex networks, such as the category attributes of nodes, and perform equal weight modeling on all network nodes, which results in excessive attention to a large number of unimportant interference nodes when the network scale is large, making it unsuitable for long-term accurate prediction of future system evolution. Therefore, there is an urgent need for a network prediction method for complex networks.

[0033] In order to solve the above technical problems, the embodiment of the present disclosure provides a network prediction method based on a graph neural network, which obtains a state prediction task for each target node in a target network, wherein the target network includes multiple target nodes and multiple edges connected between the target nodes, each edge represents a connection relationship between the connected target nodes, and the target network is formed by network modeling of a real system, and the target node represents a subject in the real system, wherein the real system comes from a real system in an urban transportation scenario, an ecological environment scenario, and an urban life service scenario; an allocation matrix is ​​determined based on a mapping relationship between each target node in the target network and each preset super node, and each super node is a virtual node obtained by performing a feature comprehensive simulation on a part of the subjects in the real system; the target network is renormalized into a group using the allocation matrix, A network backbone is obtained, which includes each supernode and multiple edges connected between the supernodes and representing the connection relationship between the supernodes; the network backbone is processed by using a graph neural network to obtain a dynamic sequence of each supernode, each dynamic sequence indicates the node state of the corresponding supernode that changes with time, and a state prediction is performed based on the dynamic sequence of each supernode to obtain the node state of each supernode in the prediction time period; super-resolution processing is performed based on the historical observation sequence of the target network and the node state of each supernode in the prediction time period to obtain the node state of each target node in the prediction time period, and the historical observation sequence indicates the node state of each target node in the historical time period. After the complex network of the target network to be predicted is effectively reduced in dimensionality, long-term accurate prediction of the node state of the complex network can be achieved.

[0034] Figures 1 to 3 A schematic diagram of a network prediction method based on a graph neural network provided according to an embodiment of the present disclosure is shown. Figures 1 to 3 The network prediction method provided by the embodiment of the present disclosure is schematically illustrated.

[0035] like Figure 1 As shown, the network prediction method may include the following steps S101 to S105.

[0036] Step S101: Obtain a state prediction task for each target node in a target network.

[0037] The target network is formed by network modeling of the real system in the actual application scenario. The actual application scenario can be any one of the urban transportation scenario, ecological environment scenario, and urban life service scenario. The real system comes from the objective real system in the actual application scenario. The real system is generally a large-scale complex network, such as a railway network, a power transmission network, etc. The target network includes multiple target nodes and multiple edges connected between the target nodes. The target node represents the subject in the real system. For example, if the target network represents a railway network, the target node in the target network can represent a station. For another example, if the target network represents a power transmission network, the target node in the target network can represent a network point. Each edge represents the connection relationship between the connected target nodes. For example, if the target network represents a railway network, the target node 1 representing station 1 and the target node 2 representing station 2 in the target network are connected by an edge, then the edge indicates that station 1 can be connected to station 2. It should be noted that the subject represented by the target node and the connection relationship represented by the edge can be determined according to the specific situation of the complex network in the actual application scenario.

[0038] The state prediction task is to predict the node state of each target node in the target network. Similarly to the target nodes and edges, the node state can be determined according to the specific situation of the complex network in the actual application scenario. For example, if the target network represents a railway network, the node state of each target node in the target network can represent the passenger flow of the station.

[0039] Based on the target network, a graph G = (V, A) can be modeled, which can also be called the original connection topology graph. V represents the target node set, which includes multiple target nodes. The first adjacency matrix A represents the connection relationship between the target nodes, A∈{0,1} N×N , can be obtained by element a in the first adjacency matrix A ij =1 indicates that there is a connection relationship between the target node i and the target node j, and N is the number of target nodes. In this way, the topological structure of the complex network can be represented by the first adjacency matrix A and the target node set V.

[0040] The dynamics of the target network can describe the evolution of the node state of each target node on the graph G. Considering the dynamics of each node and its interaction with its neighboring nodes, the dynamics of the target network can follow the following formula (1):

[0041]

[0042] In formula (1), f represents the target node’s own dynamics, g represents the coupled dynamics between target nodes, and the specific representations of f and g can be set according to actual needs. i and x jFrom the node state matrix, the node state matrix represents the observed values ​​of the d-dimensional node states of N target nodes in the target network in consecutive time steps, x i represents the observed value of the d-dimensional node state of the i-th target node in consecutive time steps, x j Represents the observed value of the d-dimensional node state of the j-th target node in consecutive time steps. The element a in the first adjacency matrix A ij Represents the connection relationship between target node i and target node j in the first adjacency matrix.

[0043] This network prediction method effectively reduces the dimensionality of complex networks and the dynamics thereon by integrating statistical physics and artificial intelligence. The dimensionality reduction process may include the setting of each supernode, the determination of the connection relationship between each supernode, and the determination of the dynamic sequence of each supernode.

[0044] Each supernode is a virtual node that simulates the characteristics of some entities in the real system. For example, the number of supernodes can be set to 100 based on the number of target nodes being 1000. It should be noted that although the number of supernodes is introduced as 100 as an example, those skilled in the art can understand that users can flexibly set the number of supernodes according to actual application scenarios, as long as the final prediction results meet expectations.

[0045] Before determining the connection relationship between each supernode, the mapping relationship between each target node and each supernode is determined first. In other words, it is determined to which supernode the target node belongs.

[0046] Step S102: determining a distribution matrix based on a mapping relationship between each target node in the target network and each preset super node.

[0047] In a possible implementation, step S102 may include: first, determining each first hyperbolic eigenvector representing the node state of the corresponding target node in the hyperbolic space according to the target network and preset prior information, and determining each second hyperbolic eigenvector representing the node state of the corresponding supernode in the hyperbolic space according to each supernode and prior information. Among them, the prior information may include prior physical knowledge related to physical rules, statistical rules, etc., which is specifically set according to actual conditions, and the embodiments of the present disclosure do not limit this. The first hyperbolic eigenvectors and the second hyperbolic eigenvectors initialized based on the target network, each supernode, and prior physical knowledge only have initial values, and need to be subjected to subsequent nonlinear operations to obtain a distribution matrix, so as to predict the node state. Setting corresponding hyperbolic eigenvectors for each target node and each supernode has higher efficiency when dealing with complex networks with hierarchical structures or network characteristics.

[0048] Then, each first hyperbolic eigenvector is spatially transformed from the hyperbolic space to the Euclidean space to obtain each first Euclidean eigenvector representing the node state of the corresponding target node in the Euclidean space, and each second hyperbolic eigenvector is spatially transformed to obtain each second Euclidean eigenvector representing the node state of the corresponding supernode in the Euclidean space. In order to perform Euclidean space operations on the hyperbolic eigenvectors (each first hyperbolic eigenvector, each second hyperbolic eigenvector), before calculating the allocation matrix, the hyperbolic eigenvector is first mapped to the Euclidean space corresponding to the tangent space of the origin of the Poincare disk with a curvature of -1, wherein the mapping process can be implemented by the following formula (2):

[0049]

[0050] In formula (2), θ H is the hyperbolic eigenvector, θ E is the Euclidean eigenvector, and arctanh represents the inverse hyperbolic tangent function. Taking the first hyperbolic eigenvector corresponding to the target node as an example, substituting the first hyperbolic eigenvector into the above formula (2) can obtain the first Euclidean eigenvector corresponding to the target node. The method for determining the second Euclidean eigenvector of the supernode is similar to this and will not be repeated here.

[0051] Next, an artificial neural network such as a multilayer perceptron (MLP) is used to perform nonlinear operations on each first Euclidean eigenvector to obtain a first Euclidean high-order eigenvector representing higher-order information of the target node, and an artificial neural network is used to perform nonlinear operations on each second Euclidean eigenvector to obtain a second Euclidean high-order eigenvector representing higher-order information of the supernode. The process of nonlinear operations can be determined according to actual needs and the actual structure of the MLP, and the disclosed embodiment is not limited to this. The artificial neural network can be obtained by training based on a sample set, wherein the sample network in the sample set is preferably the target network, and the data in the sample set is preferably a historical observation sequence indicating the node state of each target node in the target network within a historical time period, so that the artificial neural network can better learn based on the topological structure of the original connection topology graph from the target network and the dynamic characteristics of each target node determined from the historical observation sequence, so that in the actual prediction process, the first Euclidean high-order eigenvector and the second Euclidean high-order eigenvector that are conducive to accurate prediction can be obtained.

[0052] Finally, the allocation matrix is ​​determined based on the first Euclidean high-order eigenvector and the second Euclidean high-order eigenvector. For example, the allocation matrix P = softmax (C s C T ), where softmax represents the normalized exponential function, C srepresents the second Euclidean high-order eigenvector, C represents the first Euclidean high-order eigenvector, and T represents the transposition operation. The correspondence between each supernode and each target node is calculated by the assignment matrix P∈{0,1} γN×N Definition, assign element p in the matrix ij =1 means that the target node j is aggregated to the supernode i, γ represents the dimensionality reduction rate, which can be preset according to actual needs. The dimensionality reduction rate represents the degree of simplification of the network backbone (see below for details) relative to the target network topology, and N is the number of target nodes.

[0053] The allocation matrix thus determined can indicate to which supernode each target node should be mapped. Based on this, each target node in the target network can be mapped to the corresponding supernode, so that each target node similar to the supernode can be mapped to the supernode respectively, and the prediction of the target node can be converted into the prediction of the supernode, which greatly reduces the computational overhead.

[0054] Step S103: Renormalize the target network using the allocation matrix to obtain a network backbone.

[0055] Through the above step S102, an allocation matrix indicating the mapping relationship between each target node and each super node can be determined, and then based on the allocation matrix, the connection relationship between each super node can be determined, thereby obtaining a network backbone. In a possible implementation, step S103 may include: determining a first adjacency matrix representing the connection relationship between each target node according to the target network; determining a second adjacency matrix according to the first adjacency matrix and the allocation matrix, for example, according to A s =PAP T Determine the second adjacency matrix A representing the connection relationship between each supernode s , P represents the allocation matrix, A represents the first adjacency matrix, and T represents the transposition operation; a network backbone is obtained based on each supernode and the second adjacency matrix. The network backbone includes each supernode and multiple edges connected between the supernodes representing the connection relationship between the supernodes.

[0056] Similarly to the target network, the network backbone can be represented as graph G s =(V s ,A s ), which can also be called a backbone topology diagram. s represents a supernode set, which includes multiple supernodes. These supernodes are aggregates of target nodes in the target network, and each supernode is an aggregate of at least one target node. The second adjacency matrix A s Represents the connection relationship between super nodes, A s ∈{0,1} γN×γN , γ represents the dimensionality reduction rate, γ is detailed in the previous article and will not be repeated here, N is the number of target nodes.

[0057] In this way, the target network can be renormalized by using the distribution matrix, which can effectively simplify the complex target network including many target nodes into a network backbone including a relatively small number of super nodes (see Figure 2 ), which significantly improves the efficiency of subsequent network analysis and prediction based on the network backbone, helps to reduce computing costs and speed up processing.

[0058] like Figure 3 As shown, when the original nodes are aggregated into super nodes through the above steps, the problem of solving the future evolution trajectory of the original nodes is converted into the problem of solving the future evolution trajectory of the super nodes. In other words, the prediction task for the target network is converted into a prediction task for the network backbone, which can be achieved through the following step S104.

[0059] Step S104: Use the graph neural network to process the network backbone to obtain the dynamic sequence of each super node, perform state prediction based on the dynamic sequence of each super node, and obtain the node state of each super node in the prediction time period.

[0060] The graph neural network can select models such as the graph convolution network (GCN) model and the graph attention (GAT) model. The processing of the network backbone by the graph neural network can also be determined according to actual needs and the actual structure of the graph neural network, and the embodiments of the present disclosure do not limit this. Similarly to the artificial neural network, the graph neural network can also be obtained by training based on a sample set. Please refer to the above text for details, which will not be repeated here. It should be noted that the artificial neural network and the graph neural network can be jointly trained, and the specific training process can be set according to actual needs, which is not limited in the embodiments of the present disclosure.

[0061] In a possible implementation, the use of a graph neural network to process the network backbone in step S104 to obtain the dynamic sequence of each supernode may include: capturing the dynamic propagation of each target node from the input historical observation sequence of each target node through a graph convolutional neural network, and aggregating the dynamic propagation of each target node into a dynamic representation of the supernode in combination with the network backbone, that is, the dynamic sequence of each supernode. Among them, the historical observation sequence can be determined together when acquiring the state prediction task, and the time corresponding to the input historical observation sequence of each target node can be determined based on the expected prediction time period. For example, if it is expected to predict the passenger flow of the station in the next 7 days, the historical observation sequence of the past 28 days can be input. It should be noted that the 7 days and 28 days here are only examples, and the specific time can be set according to actual needs. The embodiment of the present disclosure does not limit this. Each dynamic sequence indicates the node state of the corresponding supernode that changes with time. The node state is similar to the node state of the target node, and is also determined according to the specific situation of the complex network in the actual application scenario. For example, if the target network represents a railway network, the node state of the supernode can also represent the passenger flow of the station. For example, the dynamic sequence of each supernode can be represented by the following formula (3):

[0062]

[0063] In formula (3), X s represents the dynamic sequence of the supernode, P represents the allocation matrix, represents the domain, γ represents the dimensionality reduction rate, N represents the number of target nodes, d represents the dimension of H, and H represents the nonlinear transformation result of the node state of each target node corresponding to the supernode. For example, H can be expressed by the following formula (4):

[0064]

[0065] In formula (4), σ represents the preset activation function, represents the self-connected adjacency matrix, A represents the first adjacency matrix, I represents the identity matrix, represents the degree matrix of the self-connected adjacency matrix, Right now The diagonal elements of yes The row sum of the corresponding rows, The off-diagonal elements of are all 0. express The element in the i-th row and j-th column, Θ1 represents the learnable parameter, and the other parameters are the same as before and will not be repeated here.

[0066] When the dynamic sequence of each supernode is obtained, state prediction can be performed. In a possible implementation, the state prediction based on the dynamic sequence of each supernode in step S104 to obtain the node state of each supernode in the prediction time period may include: processing the dynamic sequence of each supernode in the historical time period to obtain the initial state of each supernode; performing state prediction for the prediction time period based on the initial state of each supernode and the second adjacency matrix to determine the node state of each supernode in the prediction time period.

[0067] For example, after determining the network backbone and the dynamic sequence of each supernode, the neural ordinary differential equations (NODEs) can be used to model it by combining the combined effects of the supernode's own dynamics and the coupled dynamics of neighbor interactions. Now define the potential dynamics dZ of the network backbone s / dt is the forward ordinary differential function. Considering that the evolution of each supernode is affected by its own dynamics and coupled dynamics, the parameterized time derivative consists of two terms, one of which is the dynamic function f(Z s ), and the other comes from the coupled dynamics function g(Z s ,A s ), the dynamic equation of each supernode can be expressed by the following formula (5):

[0068]

[0069] In formula (5), Z s Indicates the node state of the supernode, A s represents the second adjacency matrix, f can be determined based on MLP, g can be determined based on GNN and used for information propagation, for example, g(Z s , A s )=σ(Aσ(Z s Θ3)Θ2), σ represents the preset activation function, A represents the first adjacency matrix, and Θ3 and Θ2 represent learnable parameters. In this way, given the ordinary differential equation (ODE) function, the prediction task of the network backbone (i.e., the problem of solving the future evolution trajectory of the supernode) can be solved as the initial value problem of the ODE, thereby obtaining the node state of each supernode at any time point in the prediction time period, for example, the node state Z of the supernode at time point T s,T It can be expressed by the following formula (6):

[0070]

[0071] In formula (6), Z s,T represents the node state of the supernode at time point T, Zs,0 represents the initial state of the supernode and Z s,0 =MLP(X s )∈R γN×1 , MLP represents multi-layer perceptron, X s represents the dynamic sequence of the supernode, Z s,0 =MLP(X s ) indicates that the multilayer perceptron processes the dynamic sequence of the supernode to obtain the initial state of the supernode, R indicates the domain, T indicates the time point, t indicates a time point between 0 and T, and Z s,t Represents the node state of the supernode at a certain time point t. The other parameters are detailed in the previous text and will not be repeated here. The node state of each supernode in the prediction time period includes the node state of each supernode at each time point in the prediction time period, and each preset time period includes at least one time point. The number and division criteria of the time points in the prediction time period are set according to the actual prediction requirements, and the embodiments of the present disclosure do not limit this.

[0072] After determining the node status of each supernode in the prediction time period through the above process, that is, obtaining the predicted trajectory of each supernode in the network backbone, the target node is inferred from the supernode (refer to Figure 3 ), that is, the prediction results of each target node in the target network are determined based on the prediction results of each super node.

[0073] Step S105 : performing super-resolution processing based on the historical observation sequence of the target network and the node state of each super node in the prediction time period to obtain the node state of each target node in the prediction time period.

[0074] The historical observation sequence indicates the node status of each target node within the historical time period, where the historical time period can be determined based on the predicted time period. For example, if the predicted time period is the next 7 days, the past 28 days can be selected as the historical time period. The historical time period and the predicted time period can be set completely according to actual needs.

[0075] Since information loss is inevitable in the process of aggregating target nodes into supernodes, such as the heterogeneity of the states of subnodes, i.e., target nodes, within the same supernode, this network prediction method does not simply copy the prediction result of the supernode, i.e., the node state of the supernode in the prediction time period, to the target node corresponding to the supernode. Instead, a super-resolution processing method based on degree clustering is selected to obtain the node state of each target node in the prediction time period.

[0076] In a possible implementation, step S105 may include: clustering multiple target nodes to obtain clustering results, the clustering results include multiple clusters, each cluster includes at least one target node; based on the historical observation sequence of each target node in each cluster and the node state of the super node corresponding to the target node in the prediction time period, determining the node state of each target node in each cluster in the prediction time period. For example, the node set in the cth cluster is represented as N c , N c The number of target nodes in is at least one, and N c The historical observation sequence corresponding to the target node in is represented as X c , N c The prediction result of the super node corresponding to the target node in (i.e., Z in the above text) s,T )Use Z c and T, where the super node corresponding to the target node is determined according to the mapping relationship between each target node and each super node in the previous text, so that super-resolution processing can be performed according to the following formula (7) to determine the node state of the target node in the cth cluster in the prediction time period:

[0077] X c，T =σ((h0||h1)Θ4) Formula (7)

[0078] In formula (7), X c,T represents the node state of the target node in the cth cluster in the prediction time period T, σ represents the preset activation function, h0=MLP(X c ), X c represents the historical observation sequence of the target node in the cth cluster in the historical time period, h1=MLP(Z c ,T),Z c and T come from the prediction result Z of the super node corresponding to the target node in the cth cluster s,T , due to N c The target node in Z may correspond to different super nodes, so c The prediction results can come from different super nodes, || represents the serial operation, and Θ4 represents the learnable parameters. Based on formula (7), the prediction results of the prediction task for the target network can be obtained, thereby realizing the state prediction task.

[0079] Among them, clustering multiple target nodes to obtain clustering results may include: determining the degree of each target node according to the target network, each degree represents the number of target nodes that have a connection relationship with the corresponding target node; clustering multiple target nodes based on each degree to obtain clustering results. Considering that the network in the real world usually follows a power law distribution, this network prediction method chooses to use the logarithm of the degree of each target node as a feature, clustering each target node through the K-means algorithm, and performing super-resolution processing within each cluster. In fact, in the Poincare disk, the degree of the node directly corresponds to its radius, so nodes with similar radial coordinates should be identified as belonging to the same supernode.

[0080] In this way, the collective dynamics of the target nodes show homogeneity in degree. First, the target nodes are clustered to obtain multiple clusters, and then super-resolution processing is performed within each cluster, which can obtain more accurate prediction results for the state prediction task.

[0081] The network prediction method includes a training process for a graph neural network or an artificial neural network, and the training process may include training based on a sample set and a preset loss function. The sample set includes multiple sample networks, each sample network includes multiple sample nodes and multiple edges connected between the sample nodes. In order to obtain a better prediction effect, the sample network is preferably a target network, but may also include other networks, which are selected according to actual needs.

[0082] The loss function includes at least one of a Euclidean loss function, an allocation loss function, a backbone loss function, and an original loss function. The Euclidean loss function is determined based on the mapping relationship between each sample node and the corresponding supernodes in the sample network, the allocation loss function is determined based on the connection relationship between each sample node and the mapping relationship between each sample node and the corresponding supernodes in the sample network, the backbone loss function is determined based on the node state of each supernode corresponding to each sample node in a preset time period, and the original loss function is determined based on the node state of each sample node in a preset time period. In one example, the model can be trained based on the sum of the hyperbolic loss function, the Euclidean loss function, the backbone loss function, and the original loss function, and the model is determined based on a graph neural network and an artificial neural network.

[0083] The four loss functions designed for this network prediction method are briefly described. Other training details can be determined according to the specific composition of the model. They are determined according to the actual situation and will not be described in detail in this article. Before starting end-to-end training, the hyperbolic feature vectors corresponding to the target node and supernode are initialized. Subsequently, in each iteration, the model is calculated by the following Euclidean loss function L E And the distribution loss function L R Update and optimize, L E and L RBoth represent the constraint loss on the allocation matrix:

[0084]

[0085] In formula (8), H represents the entropy function, N represents the number of sample nodes, and P i represents the mapping relationship between each sample node i and the corresponding super nodes in the sample network, A represents the connection relationship between each sample node in the sample network, P represents the allocation matrix of the mapping relationship between each sample node and the corresponding super nodes in the sample network, F represents the norm, and T represents the transpose. L R The representative heuristic guides the network backbone to retain the information in the original connection topology as much as possible. Then, in the process of predicting the network backbone, the backbone loss function Ls is used to update the model, Ls = MSE (Z s,T ,Z ～ s,T ), where MSE stands for mean square error, Z s,T Represents the prediction result of the supernode, i.e., the node status of the supernode in the prediction time period T, Z ～ s,T It is based on P i Finally, the original loss function Lp representing the error of the prediction result of the sample node can be used to update the super-resolution module for super-resolution processing, Lp = MSE (X T ,X ～ T ), where MSE stands for mean square error, X T represents the prediction result of the sample node, that is, the node status of the sample node in the prediction time period T, X ～ T Based on P i and the true value of the prediction result of the sample node obtained by the state encoder. Since the Poincare disk is a conformal mapping of the Euclidean space, when updating the node embedding with the gradient, the gradient needs to be scaled according to the Riemann metric tensor, such as the following equation (9):

[0086]

[0087] In formula (9), and They are the Euclidean gradient and hyperbolic gradient of the feature vector θ respectively. After completing the end-to-end training, the super-resolution module can be fine-tuned to enhance its prediction performance.

[0088] The network prediction method provided by the embodiment of the present disclosure is to effectively reduce the dimension of complex networks and the dynamics on them by integrating statistical physics and artificial intelligence, so as to identify the backbone of large-scale network data, and then realize long-term node status prediction based on the network backbone. The effect is obvious. Figure 3 . This network prediction method is based on the end-to-end graph deep learning model in the field of statistical physics in the renormalization group and artificial intelligence. It can improve the modeling ability of complex networks while ensuring the interpretability of the model, and model the nonlinear dynamics of the interaction between the nodes themselves and their neighbors in the complex network by fitting the historical observation data, so as to achieve effective node state prediction. This network prediction method only needs to input the historical observation sequence and connection relationship of each target node representing the original node after the system is modeled, and it can automatically analyze the network backbone that retains the node dynamics, and can achieve accurate long-term prediction of the node state. The process of the network prediction method may include first obtaining the hyperbolic eigenvector corresponding to the target network based on all the original nodes and the preset initial super nodes in the complex network, automatically identifying and calculating a distribution matrix, and then using this distribution matrix to perform the renormalization group of the target network, that is, compressing the original connection topology map into a trunk topology map, and then aggregating the historical observation sequences of all target nodes to obtain the dynamic sequence of each super node, and then using a deep learning model to perform long-term prediction of the dynamics of the super node, and returning the prediction result to the corresponding target node as a rough prediction result, and the rough prediction result is processed by a super-resolution to obtain the long-term prediction output of the node state of each original node of the complex system. In the whole process, the calculation of the distribution matrix can be pre-trained using prior physical knowledge, and the results of the dynamics prediction can be used to update the hyperbolic eigenvector of the super node.

[0089] The prediction task of the power transmission network is now used as an example to illustrate the network prediction method. The user now has a network point map of a city's power transmission network and has obtained the power consumption of each network point in the past 12 days. Due to the large number of network points, it is difficult to recognize the main distribution of the city's power consumption. It is necessary to first identify the coarsened main components of the city's power consumption. First, a model can be built based on the network point map of the city's power transmission network to form a graph G = (V, A) of the target network corresponding to the city's power transmission network, where the element a in the adjacency matrix A is ij=1 indicates that there is an electric connection between network point i and network point j, and V represents the set of all network points, thus obtaining the original connection topology graph G representing the urban power transmission network. Then, the dimension reduction rate is specified, and the power consumption data of each network point in the past 12 days is used to construct the historical observation sequence of each target node representing the network point. The historical observation sequence is split into a training set and a test set to complete the training of the model determined by the graph neural network and the artificial neural network. The trained model can automatically generate the most appropriate allocation matrix containing the internal dynamics of this urban power transmission network based on the target network and the preset super nodes. The element p in the allocation matrix ij =1 indicates that the target node j is aggregated to the supernode i. Thus, the original connection topology corresponding to the target network is compressed into the backbone topology G using the allocation matrix. s =(V s ,A s ), where V s represents a supernode set, A s Indicates the connection relationship between supernodes. Thus, the main components of the expected power grid data can be obtained. In this way, users can effectively identify the main components of power consumption from the complex urban power transmission network, and predict future power demand based on this, thereby providing more accurate decision support for power grid planning and power dispatching.

[0090] The network prediction method is now explained by taking the prediction task of the airport or railway network as an example. The user now has a connectivity topology map of thousands of stations such as airports or railways in a certain country, and has obtained the historical passenger flow observations of each station in the past 12 days. He wants to use the change patterns of the past 12 days to predict the changes of these thousands of stations in the next 120 days, so as to guide the scheduling of flights or trains. First, modeling can be carried out based on the connectivity topology map of the provided airport or railway network, which is the urban transportation network, to form a target network graph G = (V, A) corresponding to the urban transportation network, where the element a in the adjacency matrix A ij =1 indicates that there is a direct connection between site i and site j, and V represents the set of all sites, thus obtaining the original connection topology G representing the urban transportation network. Then, the dimensionality reduction rate is specified, and the historical observation sequence of the target node representing each site is constructed using the passenger flow observation data of each site in the past 12 days. The historical observation sequence will provide the dynamic behavior of the urban transportation network and the interaction information between each target node. Then, the training method is applied to complete the model training based on the historical observation sequence. The trained model can automatically calculate the allocation matrix based on the target network and the preset super nodes, so as to use the allocation matrix to compress the original connection topology corresponding to the target network into a more simplified backbone topology G. s =(V s ,A s ) represents the network backbone, where Vs represents a supernode set, A s Represents the connection relationship between supernodes in the network backbone, which not only reduces the complexity of data processing, but also retains the most important structure and dynamic characteristics of the network. Next, the network backbone is processed to obtain the dynamic sequence of each supernode. Through the graph convolutional neural network, the connection relationship between supernodes, that is, the interaction, and the historical flow pattern inside the node reflected by the dynamic sequence of the supernode can be used to capture and predict the dynamics of the flow of people in the entire network backbone. This step uses the topological structure of the network and the historical observation sequence to predict the future state of the supernode, thereby predicting the future flow distribution of the entire network. Finally, the prediction results of the supernode are mapped from the supernode of the network backbone back to each target node of the original target network. In this process, considering that information may be lost in the aggregation process, super-resolution technology is used to refine and optimize the prediction results of each target node (see the super-resolution processing above for details) to improve the accuracy of the prediction. Through this series of steps, users can eventually predict the flow changes of thousands of stations in the next 120 days based on the historical observation sequence indicating the flow data, which is helpful for traffic planning and management.

[0091] Compared with the existing methods, the network prediction method proposed in the embodiment of the present disclosure can be used for large-scale complex networks through the above steps. First, the original complex system is effectively reduced in dimension, and long-term prediction is performed on the low-dimensional coordinates corresponding to the super node. Finally, it is lifted back to the original space to obtain the prediction result of the target node, thereby achieving long-term and accurate prediction of the node status while avoiding huge computing and storage overhead.

[0092] The disclosed embodiment also provides a network prediction device based on a graph neural network. Figure 4 A block diagram of a network prediction device based on a graph neural network provided according to an embodiment of the present disclosure is shown. Figure 4 As shown, the network prediction device 400 may include the following task acquisition module 401, matrix determination module 402, renormalization group module 403, state prediction module 404, and super-resolution module 405.

[0093] The task acquisition module 401 is used to obtain the state prediction task for each target node in the target network, wherein the target network includes multiple target nodes and multiple edges connected between the target nodes, each edge represents the connection relationship between the connected target nodes, and the target network is formed by networked modeling of the real system, and the target node represents the subject in the real system, wherein the real system comes from the real system in the urban transportation scenario, the ecological environment scenario, and the urban life service scenario.

[0094] The matrix determination module 402 is used to determine the allocation matrix based on the mapping relationship between each target node in the target network and each preset super node, each super node is a virtual node simulated by comprehensive feature of some entities in the real system.

[0095] The renormalization group module 403 is used to renormalize the target network using the allocation matrix to obtain a network backbone, wherein the network backbone includes each of the super nodes and a plurality of edges connected between the super nodes and representing the connection relationship between the super nodes.

[0096] The state prediction module 404 is used to process the network backbone using a graph neural network to obtain a dynamic sequence of each super node, each of which indicates a node state of a corresponding super node that changes over time, and perform state prediction based on the dynamic sequence of each super node to obtain a node state of each super node in a predicted time period.

[0097] The super-resolution module 405 is used to perform super-resolution processing based on the historical observation sequence of the target network and the node state of each super node in the prediction time period to obtain the node state of each target node in the prediction time period, and the historical observation sequence indicates the node state of each target node in the historical time period.

[0098] In a possible implementation, a distribution matrix is ​​determined based on a mapping relationship between each target node and each preset supernode in the target network, including: determining each first hyperbolic eigenvector representing the node state of the corresponding target node in the hyperbolic space according to the target network and preset prior information, and determining each second hyperbolic eigenvector representing the node state of the corresponding supernode in the hyperbolic space according to each supernode and the prior information; performing a spatial transformation from the hyperbolic space to the Euclidean space on each of the first hyperbolic eigenvectors to obtain each first Euclidean eigenvector representing the node state of the corresponding target node in the Euclidean space, and performing the spatial transformation on each of the second hyperbolic eigenvectors to obtain each second Euclidean eigenvector representing the node state of the corresponding supernode in the Euclidean space; performing a nonlinear operation on each of the first Euclidean eigenvectors using an artificial neural network to obtain a first Euclidean high-order eigenvector, and performing the nonlinear operation on each of the second Euclidean eigenvectors using the artificial neural network to obtain a second Euclidean high-order eigenvector; determining the distribution matrix based on the first Euclidean high-order eigenvector and the second Euclidean high-order eigenvector.

[0099] In a possible implementation, the target network is renormalized using the allocation matrix to obtain a network backbone, including: determining a first adjacency matrix representing a connection relationship between each of the target nodes based on the target network; determining a second adjacency matrix based on the first adjacency matrix and the allocation matrix, the second adjacency matrix representing a connection relationship between each of the super nodes; and obtaining the network backbone based on each of the super nodes and the second adjacency matrix.

[0100] In a possible implementation, state prediction is performed based on the dynamic sequence of each supernode to obtain the node state of each supernode in the prediction time period, including: processing the dynamic sequence of each supernode in the historical time period to obtain the initial state of each supernode; performing state prediction for the prediction time period based on the initial state of each supernode and the second adjacency matrix to determine the node state of each supernode in the prediction time period.

[0101] In a possible implementation, super-resolution processing is performed on the historical observation sequence of the target network and the node state of each super node in the prediction time period to obtain the node state of each target node in the prediction time period, including: clustering the multiple target nodes to obtain a clustering result, the clustering result includes multiple clusters, each cluster includes at least one target node; based on the historical observation sequence of each target node in each cluster and the node state of the super node corresponding to the target node in the prediction time period, the node state of each target node in each cluster in the prediction time period is determined.

[0102] In one possible implementation, clustering the multiple target nodes to obtain a clustering result includes: determining the degree of each target node according to the target network, each degree representing the number of target nodes that have a connection relationship with the corresponding target node; clustering the multiple target nodes based on each degree to obtain the clustering result.

[0103] In a possible implementation, the device also includes a training module for performing a training process for the graph neural network or artificial neural network, the training process including training based on a sample set and a preset loss function, the loss function including at least one of a Euclidean loss function, an allocation loss function, a backbone loss function, and an original loss function, the sample set including a plurality of sample networks, each of the sample networks including a plurality of sample nodes and a plurality of edges connected between the sample nodes, wherein the Euclidean loss function is determined based on a mapping relationship between each of the sample nodes and corresponding super nodes in the sample network, the allocation loss function is determined based on a connection relationship between each of the sample nodes and a mapping relationship between each of the sample nodes and corresponding super nodes in the sample network, the backbone loss function is determined based on a node state of each super node corresponding to each of the sample nodes in a preset time period, and the original loss function is determined based on a node state of each of the sample nodes in the preset time period.

[0104] In some embodiments, the functions or modules included in the network prediction device provided in the embodiments of the present disclosure can be used to execute the method described in the above method embodiment. Its specific implementation can refer to the description of the above network prediction method embodiment, and for the sake of brevity, it will not be repeated here.

[0105] The embodiment of the present disclosure also provides a computer-readable storage medium on which computer program instructions are stored, and when the computer program instructions are executed by a processor, the above network prediction method is implemented. The computer-readable storage medium can be a volatile or non-volatile computer-readable storage medium.

[0106] The disclosed embodiment further proposes an electronic device, comprising: a processor; a memory for storing instructions executable by the processor; wherein the processor is configured to implement the above-mentioned network prediction method when executing the instructions stored in the memory.

[0107] The embodiment of the present disclosure also provides a computer program product, including a computer-readable code, or a non-volatile computer-readable storage medium carrying the computer-readable code. When the computer-readable code runs in a processor of an electronic device, the processor in the electronic device executes the above-mentioned network prediction method.

[0108] Figure 5 1900 is a block diagram of a network prediction device based on a graph neural network according to an embodiment of the present disclosure. For example, the device 1900 may be provided as a server or a terminal device. Figure 5, the apparatus 1900 includes a processing component 1922, which further includes one or more processors, and a memory resource represented by a memory 1932 for storing instructions, such as an application, that can be executed by the processing component 1922. The application stored in the memory 1932 may include one or more modules, each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute instructions to perform the above method.

[0109] The device 1900 may also include a power supply component 1926 configured to perform power management of the device 1900, a wired or wireless network interface 1950 configured to connect the device 1900 to a network, and an input / output interface 1958 (I / O interface). The device 1900 may operate based on an operating system stored in the memory 1932, such as Windows Server 2000. TM , MacOS X TM , Unix TM ,Linux TM , FreeBSD TM or similar.

[0110] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions, which can be executed by the processing component 1922 of the device 1900 to perform the above method.

[0111] The present disclosure may be a system, a method and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.

[0112] A computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples of computer-readable storage media (a non-exhaustive list) include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a raised structure in a groove on which instructions are stored, and any suitable combination of the foregoing. As used herein, a computer-readable storage medium is not to be interpreted as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through a wire.

[0113] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0114] The computer program instructions for performing the operation of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, etc., and conventional procedural programming languages, such as "C" language or similar programming languages. Computer-readable program instructions may be executed completely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be customized by utilizing the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.

[0115] Various aspects of the present disclosure are described herein with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present disclosure. It should be understood that each box in the flowchart and / or block diagram and the combination of each box in the flowchart and / or block diagram can be implemented by computer-readable program instructions.

[0116] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine, so that when these instructions are executed by the processor of the computer or other programmable data processing device, a device that implements the functions / actions specified in one or more boxes in the flowchart and / or block diagram is generated. These computer-readable program instructions can also be stored in a computer-readable storage medium, and these instructions cause the computer, programmable data processing device, and / or other equipment to work in a specific manner, so that the computer-readable medium storing the instructions includes a manufactured product, which includes instructions for implementing various aspects of the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0117] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operating steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0118] The flow chart and block diagram in the accompanying drawings show the possible architecture, function and operation of the system, method and computer program product according to multiple embodiments of the present disclosure. In this regard, each square box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and a part of the module, program segment or instruction includes one or more executable instructions for realizing the specified logical function. In some alternative implementations, the function marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two continuous square boxes can actually be executed substantially in parallel, and they can sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or action, or can be implemented with a combination of special hardware and computer instructions.

[0119] The embodiments of the present disclosure have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A network prediction method based on graph neural network, characterized in that: include: Obtaining a state prediction task for each target node in a target network, wherein the target network includes a plurality of target nodes and a plurality of edges connected between the target nodes, wherein each edge represents a connection relationship between the connected target nodes, wherein the target network is formed by network modeling of a real system, and the target node represents a subject in the real system, wherein the real system comes from a real system in an urban transportation scenario, an ecological environment scenario, and an urban life service scenario; Determine a distribution matrix based on a mapping relationship between each target node and each preset super node in the target network, each super node is a virtual node simulated by comprehensive feature of some subjects in the real system; Renormalize the target network using the allocation matrix to obtain a network backbone, wherein the network backbone includes each of the super nodes and a plurality of edges connected between the super nodes and representing connection relationships between the super nodes; The network backbone is processed by using a graph neural network to obtain a dynamic sequence of each supernode, each of which indicates a node state of a corresponding supernode that changes over time, and a state prediction is performed based on the dynamic sequence of each supernode to obtain a node state of each supernode in a predicted time period; Performing super-resolution processing on the target network and the node state of each super node in the prediction time period to obtain the node state of each target node in the prediction time period, wherein the historical observation sequence indicates the node state of each target node in the historical time period; Among them, if the target network is formed based on the railway network modeling in the urban transportation scenario, the target node in the target network represents the station, the edge represents the route between two stations, and the node state of the target node represents the passenger flow.

2. The method according to claim 1, characterized in that Determining a distribution matrix based on a mapping relationship between each of the target nodes and each of the preset super nodes in the target network includes: Determine, according to the target network and preset prior information, each first hyperbolic eigenvector representing the node state of the corresponding target node in the hyperbolic space, and Determine, according to each of the supernodes and the prior information, each second hyperbolic eigenvector representing a node state of the corresponding supernode in the hyperbolic space; Performing a spatial transformation from the hyperbolic space to the Euclidean space on each of the first hyperbolic eigenvectors to obtain each first Euclidean eigenvector representing the node state of the corresponding target node in the Euclidean space, and Performing the spatial transformation on each of the second hyperbolic eigenvectors to obtain each second Euclidean eigenvector representing a node state of a corresponding supernode in the Euclidean space; Using an artificial neural network to perform a nonlinear operation on each of the first Euclidean eigenvectors to obtain a first Euclidean high-order eigenvector, and using the artificial neural network to perform the nonlinear operation on each of the second Euclidean eigenvectors to obtain a second Euclidean high-order eigenvector; The allocation matrix is ​​determined based on the first Euclidean high-order eigenvector and the second Euclidean high-order eigenvector.

3. The method according to claim 1 or 2, characterized in that: The target network is renormalized using the allocation matrix to obtain a network backbone, including: Determine a first adjacency matrix representing a connection relationship between each of the target nodes according to the target network; Determine a second adjacency matrix according to the first adjacency matrix and the allocation matrix, wherein the second adjacency matrix represents the connection relationship between each of the super nodes; The network backbone is obtained based on each of the super nodes and the second adjacency matrix.

4. The method according to claim 3, characterized in that The state prediction is performed based on the dynamic sequence of each super node to obtain the node state of each super node in the prediction time period, including: Processing the dynamic sequences of each supernode in the historical time period to obtain the initial state of each supernode; The state of the prediction time period is predicted based on the initial state of each super node and the second adjacency matrix, and the node state of each super node in the prediction time period is determined.

5. The method according to claim 1, characterized in that The node state of each of the target nodes in the prediction time period is obtained by performing super-resolution processing based on the historical observation sequence of the target network and the node state of each of the super nodes in the prediction time period, including: Clustering the multiple target nodes to obtain a clustering result, wherein the clustering result includes multiple clusters, each of which includes at least one target node; Based on the historical observation sequence of each target node in each of the clusters and the node state of the super node corresponding to the target node in the prediction time period, the node state of each target node in each of the clusters in the prediction time period is determined.

6. The method according to claim 5, characterized in that Clustering the multiple target nodes to obtain a clustering result includes: Determining the degree of each target node according to the target network, each degree representing the number of target nodes that have a connection relationship with the corresponding target node; The multiple target nodes are clustered based on the degrees to obtain the clustering result.

7. The method according to any one of claims 1 to 2, 5 to 6, characterized in that: The method also includes a training process for the graph neural network or artificial neural network, the training process includes training based on a sample set and a preset loss function, the loss function includes at least one of a Euclidean loss function, a distribution loss function, a backbone loss function, and an original loss function, the sample set includes a plurality of sample networks, each of the sample networks includes a plurality of sample nodes and a plurality of edges connected between the sample nodes, wherein, The Euclidean loss function is determined based on the mapping relationship between each of the sample nodes and the corresponding super nodes in the sample network. The allocation loss function is determined based on the connection relationship between the sample nodes in the sample network and the mapping relationship between the sample nodes and the corresponding super nodes. The backbone loss function is determined based on the node status of each supernode corresponding to each sample node in a preset time period. The original loss function is determined based on the node status of each of the sample nodes in the preset time period.

8. A network prediction device based on graph neural network, characterized in that: include: A task acquisition module, used to acquire a state prediction task for each target node in a target network, wherein the target network includes a plurality of target nodes and a plurality of edges connected between the target nodes, each edge representing a connection relationship between the connected target nodes, and the target network is formed by network modeling of a real system, and the target node represents a subject in the real system, wherein the real system comes from a real system in an urban transportation scenario, an ecological environment scenario, and an urban life service scenario; A matrix determination module, used to determine a distribution matrix based on a mapping relationship between each of the target nodes in the target network and each of the preset super nodes, each of which is a virtual node simulated by comprehensive feature analysis of some entities in the real system; A renormalization group module, used to renormalize the target network by using the allocation matrix to obtain a network backbone, wherein the network backbone includes each of the super nodes and a plurality of edges connected between the super nodes and representing connection relationships between the super nodes; A state prediction module, used to process the network backbone using a graph neural network to obtain a dynamic sequence of each supernode, each of which indicates a node state of a corresponding supernode that changes over time, and to perform state prediction based on the dynamic sequence of each supernode to obtain a node state of each supernode in a prediction time period; A super-resolution module, configured to perform super-resolution processing based on a historical observation sequence of the target network and a node state of each super node in the prediction time period to obtain a node state of each target node in the prediction time period, wherein the historical observation sequence indicates a node state of each target node in the historical time period; Among them, if the target network is formed based on the railway network modeling in the urban transportation scenario, the target node in the target network represents the station, the edge represents the route between two stations, and the node state of the target node represents the passenger flow.

9. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to implement the method described in any one of claims 1 to 7 when executing the instructions stored in the memory.

10. A non-volatile computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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