High-order network propagation process prediction method, device, equipment, medium and product

Abstract

The present application discloses a method, apparatus, equipment, medium and product for predicting the propagation process of a high-order network, which relates to the technical field of propagation dynamics. Since a high-order network to be predicted is constructed based on data to be processed, the network type of the high-order network to be predicted is determined, and for a first high-order network of cyclic propagation dynamics, a high-order cyclic dynamic message passing equation group is established based on a simple complex structure. The propagation process of the first high-order network is predicted based on the high-order cyclic dynamic message passing equation group, and a prediction result of the propagation process of the first high-order network is obtained. The method can take into account the complex dynamic correlation between nodes of the local structure and the high-order structure, and thus can more accurately predict the propagation process of the high-order network, and can solve the technical problems in related technologies that cannot effectively handle high-order interactions and inaccurate prediction of the propagation process, and achieve the technical effect of being able to effectively handle high-order interactions and improve the prediction accuracy of the propagation process.

Description

Technical Field

[0001] The present application relates to the field of propagation dynamics technology, and in particular to methods, devices, equipment, media and products for predicting high-order network propagation processes. Background Art

[0002] Accurately predicting and analyzing the spread of information or diseases is crucial in fields such as information science, sociology, and epidemiology. Traditional models of communication dynamics are mostly based on the pairwise interaction assumption, assuming that communication occurs only between two individuals, and employ simple graphs as the underlying interaction network. However, many real-world communication phenomena, such as opinion formation on social networks and viral spread in conference rooms, involve group interactions involving multiple individuals. This type of interaction is known as higher-order interaction.

[0003] In order to more realistically portray group interactions, researchers introduced high-order networks, which refer to networks in which multiple nodes interact and communicate with each other. On this basis, they established high-order communication models, which can show rich dynamic phenomena that traditional models cannot describe.

[0004] In related technologies, existing propagation dynamics prediction methods cannot effectively handle high-order interactions, and when local loops and high-order structures exist in high-order networks, these structures will produce echo chamber effects, resulting in inaccurate predictions of the propagation process. Summary of the Invention

[0005] The present application provides a method, apparatus, device, medium and product for predicting high-order network propagation processes, in order to at least solve the problems in related technologies of being unable to effectively handle high-order interactions and inaccurately predicting propagation processes.

[0006] This application provides a high-order network propagation process prediction method, including:

[0007] Acquiring data to be processed, and constructing a high-order network to be predicted based on the data to be processed, wherein the high-order network is a network that represents mutual communication between multiple nodes;

[0008] determining a network type of a high-order network to be predicted, the network type including a first high-order network based on cyclic propagation dynamics;

[0009] For the first high-order network, a high-order cyclic dynamic message passing equation group is established based on the simplicial complex structure, and the propagation process of the first high-order network is predicted based on the high-order cyclic dynamic message passing equation group to obtain a prediction result of the propagation process of the first high-order network.

[0010] The present application also provides a high-order network propagation process prediction device, comprising:

[0011] A construction module is used to obtain data to be processed and construct a high-order network to be predicted based on the data to be processed, wherein the high-order network is a network that represents mutual communication between multiple nodes;

[0012] a determination module, configured to determine a network type of a high-order network to be predicted, the network type comprising a first high-order network based on cyclic propagation dynamics;

[0013] The first prediction module is used to establish a high-order cyclic dynamic message passing equation group for the first high-order network based on the simplicial complex structure, predict the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equation group, and obtain a prediction result of the propagation process of the first high-order network.

[0014] The present application also provides an electronic device, comprising: a memory for storing a computer program; and a processor for implementing the steps of any of the above-mentioned high-order network propagation process prediction methods when executing the computer program.

[0015] The present application also provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, the steps of any of the above-mentioned high-order network propagation process prediction methods are implemented.

[0016] The present application also provides a computer program product, including a computer program, which implements the steps of any of the above-mentioned high-order network propagation process prediction methods when executed by a processor.

[0017] Through the present application, since a high-order network to be predicted is constructed based on the data to be processed, the network type of the high-order network to be predicted is determined, and for the first high-order network of cyclic propagation dynamics, a high-order cyclic dynamic message passing equation group is established based on a simple complex structure, and the propagation process of the first high-order network is predicted based on the said high-order cyclic dynamic message passing equation group, and the prediction result of the propagation process of the first high-order network is obtained. The complex dynamic correlation between the nodes of the local structure and the high-order structure can be taken into account, and the propagation process of the first high-order network can be predicted more accurately. Therefore, the technical problems in the related technology that high-order interactions cannot be effectively handled and the prediction of the propagation process is inaccurate can be solved, and the technical effect of being able to effectively handle high-order interactions and improve the prediction accuracy of the propagation process can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0019] Figure 1 A flow chart of a method for predicting high-order network propagation processes provided in an embodiment of the present application;

[0020] Figure 2 Schematic diagram of neighborhood division and high-order simplex dynamic messages provided in an embodiment of the present application;

[0021] Figure 3 A flow chart of another high-order network propagation process prediction method provided in an embodiment of the present application;

[0022] Figure 4 A flow chart of another method for predicting high-order network propagation process provided in an embodiment of the present application;

[0023] Figure 5 Schematic diagram of the hypergraph and the corresponding acyclic factor graph provided in the embodiment of the present application;

[0024] Figure 6 A schematic diagram of the structure of a high-order network propagation process prediction device provided in an embodiment of the present application;

[0025] Figure 7 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0026] The following will be combined with the accompanying drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0027] It should be noted that, in the description of this application, the terms "comprises," "includes," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. The terms "first," "second," etc., in this application are used to distinguish similar objects, and are not used to describe a particular order or sequence.

[0028] In order to enable those skilled in the art to better understand the present application, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0029] In conjunction with the specific application environment architecture or specific hardware architecture on which the execution of the high-order network propagation process prediction method depends, the specific application environment architecture or specific hardware architecture is described herein.

[0030] The embodiments of the present application provide a method for predicting a high-order network propagation process, and the method is described in detail in conjunction with the execution flow of the method for predicting a high-order network propagation process.

[0031] Figure 1 This is a flowchart of a method for predicting the propagation process of a high-order network, provided in an embodiment of the present application. This method can be applied to electronic devices, including portable mobile devices such as tablets and laptops, as well as stationary devices such as personal computers and servers. The server can be a single server or a server cluster, which can be a distributed cluster or a centralized cluster. This method can be applied to scenarios where the propagation process of a high-order network is predicted, effectively handling high-order interactions and improving the accuracy of propagation predictions.

[0032] It is understandable that the high-order network propagation process prediction method provided in the embodiment of the present application can also be applied in other scenarios.

[0033] Below Figure 1 The method for predicting the propagation process of a high-order network shown in FIG is introduced. The method includes the following steps:

[0034] S101. Obtain data to be processed, and construct a high-order network to be predicted based on the data to be processed. The high-order network is a network that represents mutual communication between multiple nodes.

[0035] In this step, the data to be processed is obtained. This data can be public opinion on a social network or a viral infection in a conference room, without limitation. Furthermore, a high-order network to be predicted can be constructed based on the processed data. A high-order network is a network that represents the intercommunication between multiple nodes.

[0036] S102: Determine the network type of the high-order network to be predicted, where the network type includes a first high-order network based on cyclic propagation dynamics.

[0037] In this step, the electronic device first determines the network type of the high-order network to be predicted, including the first high-order network based on cyclic propagation dynamics. Specifically, the electronic device can obtain configuration information of the high-order network and determine the network type of the high-order network to be predicted based on the configuration information.

[0038] S103. For the first high-order network, establish a high-order cyclic dynamic message passing equation group based on the simplicial complex structure, predict the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equation group, and obtain a prediction result of the propagation process of the first high-order network.

[0039] Optionally, the first high-order network of the cyclic propagation dynamics adopts a simplicial complex structure. In this step, the electronic device establishes a set of high-order cyclic dynamic message passing equations based on the simplicial complex structure for the first high-order network of the cyclic propagation dynamics. Based on the set of high-order cyclic dynamic message passing equations, the propagation process of the first high-order network is predicted, and the predicted results of the propagation process of the first high-order network are obtained. The principle is to predict the propagation process of the first high-order network by transmitting high-order dynamic messages on a simplex of the simplicial complex structure. By transmitting high-order dynamic messages, the echo chamber effect in the high-order structure is suppressed, and the node infection probability and overall infection status of the first high-order network are obtained. In some embodiments, the predicted results of the propagation process of the first high-order network include the node infection probability of the first high-order network and the overall infection status of the first high-order network. Optionally, the node infection probability of the first high-order network refers to the infection probability of each node in the first high-order network at any time, and the overall infection status of the first high-order network refers to the overall infection scale of all nodes in the first high-order network system at any time.

[0040] In some embodiments, the network type includes a second high-order network based on non-cyclic propagation dynamics; the method also includes: for the second high-order network, establishing a high-order dynamic message passing equation group based on a hypergraph structure, predicting the propagation process of the second high-order network based on the high-order dynamic message passing equation group, and obtaining a prediction result of the propagation process of the second high-order network.

[0041] Optionally, the second higher-order network with acyclic propagation dynamics adopts a hypergraph structure. In this step, the electronic device can establish a set of high-order dynamic message passing equations based on the hypergraph structure for the second higher-order network with acyclic propagation dynamics, and predict the propagation process of the second higher-order network based on the high-order dynamic message passing equations to obtain the predicted results of the propagation process of the second higher-order network. The principle is based on the dynamic belief propagation theory on the hypergraph, and the acyclic characteristics of propagation are used to predict the propagation process of the second higher-order network. Through the dynamic belief propagation theory and the acyclic characteristics of propagation, the propagation process of the second higher-order network can be accurately predicted, and then the node infection probability and overall infection status of the second higher-order network can be obtained. In some embodiments, the predicted results of the propagation process of the second higher-order network include the node infection probability of the second higher-order network and the overall infection status of the second higher-order network. Optionally, the node infection probability of the second higher-order network refers to the infection probability of each node in the second higher-order network at any time, and the overall infection status of the second higher-order network refers to the overall infection scale of all nodes in the second higher-order network system at any time. This embodiment can more accurately predict the propagation process of the second high-order network, effectively handle high-order interactions, and improve the prediction accuracy of the propagation process.

[0042] The embodiment of the present application obtains data to be processed, constructs a high-order network to be predicted based on the data to be processed, determines the network type of the high-order network to be predicted, establishes a high-order cyclic dynamic message passing equation group based on a simple complex structure for the first high-order network of cyclic propagation dynamics, predicts the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equation group, and obtains a prediction result of the propagation process of the first high-order network. The complex dynamic correlation between the nodes of the local structure and the high-order structure can be taken into account, and the propagation process of the first high-order network can be predicted more accurately. Therefore, the technical problems in the related technology that high-order interactions cannot be effectively processed and the prediction of the propagation process is inaccurate can be solved, and the technical effect of being able to effectively process high-order interactions and improve the prediction accuracy of the propagation process can be achieved.

[0043] Figure 3 Another high-order network propagation process prediction method flow chart provided in the embodiment of the present application is as follows: Figure 3 As shown, the method includes the following steps:

[0044] S301 , dividing the neighborhood of each node of the simplicial complex structure to determine first-order simplex neighbors and second-order simplex neighbors.

[0045] In this step, for the first high-order network of cyclic propagation dynamics, in order to accurately handle interactions of different orders, the neighborhood of each node of the simplicial complex structure is first divided to determine the first-order simplex neighbors and the second-order simplex neighbors.

[0046] Among them, the first-order simplex neighbors , indicating that only the first-order simplex (edge) and the node Connected neighbors. Second-order simplex neighbors , which means that the second-order simplex (triangle) and the node Connected neighbor pairs. Figure 2 As shown, Figure 2 (a) is a schematic diagram of the neighborhood definition in a simple complex network, where the first-order simplex neighbor Contains all nodes connected neighbor nodes, and through second-order and higher-order simplexes and nodes Connected neighbors are represented by ; Figure 2 (b) is a schematic diagram of the first-order simplex neighbor and the second-order simplex neighbor, and the second-order simplex is defined as the second-order simplex neighbor , and a first-order simplex that is not in any second-order simplex is defined as a first-order simplex neighbor .

[0047] S302 , defining a simplex dynamic message; the simplex dynamic message is used to represent the joint probability distribution of the remaining nodes after removing the target node from the network.

[0048] In this step, a simple dynamic message will be defined. Order simplex The joint probability of the cavity on for Simplex dynamic messages are used to represent the removal of nodes from the network. After, simplex The joint probability distribution of the rest of the nodes in . Figure 2 As shown, Figure 2 (c) is a schematic diagram of the definition of a simplex dynamic message, a dynamic message on a first-order simplex neighbor Defined as a first-order simplex dynamic message, a dynamic message on a second-order simplex neighbor Defined as a second-order simplex dynamic message.

[0049] S303: Construct a high-order cyclic dynamic message passing equation group based on the first-order simplex neighbors, the second-order simplex neighbors, and the simplex dynamic messages.

[0050] In this step, after defining the simplex dynamic message, the electronic device may construct a higher-order recurrent dynamic message passing (HrDMP) equation group according to the first-order simplex neighbors, the second-order simplex neighbors, and the simplex dynamic message.

[0051] The high-order cyclic dynamic message passing equations are formulated based on the Markov and local sparsity assumptions of the dynamics. The formulation follows these steps:

[0052] The first step is to determine the node Probability of infection The exact master equation P(t) for the time evolution, which depends on the node The joint probability distribution of the states of all its neighbors, node The joint probability distribution of the states of and all its neighbors is expressed as follows:

[0053] .

[0054] The second step is to introduce the key approximate assumption: assuming that the local high-order network is sparse, that is, the nodes Each simplex neighbor (first-order simplex neighbor and second-order simplex neighbors ) are approximately independent. Based on this assumption, the above joint probability distribution can be decomposed into the product of the node's own peripheral probability and each simplex dynamic message, which can be approximately decomposed as follows:

[0055]

[0056] In the third step, this approximate decomposition is substituted into the exact main equation, and marginalization is performed by summing all neighbor states, ultimately establishing a closed set of equations about marginal probabilities and dynamic messages that can be solved iteratively.

[0057] In some embodiments, S303 may include but is not limited to S3031 and S3032:

[0058] S3031. Establish a node infection probability update equation, a first-order simplex dynamic message update equation, and a second-order simplex dynamic message update equation;

[0059] In this embodiment, a node infection probability update equation, a first-order simplex dynamic message update equation, and a second-order simplex dynamic message update equation may be established based on first-order simplex neighbors, second-order simplex neighbors, and simplex dynamic messages.

[0060] (1) The node infection probability update equation is:

[0061]

[0062] in, Representation node exist The probability of being infected at time t is given by node i at The state at the moment and the infection status of its neighbors; represents the probability of recovery, Representation node exist The probability of being in the susceptible state at any moment;

[0063] and Respectively Time Node The probability that both the first-order and second-order simplex neighbors of node i fail to successfully infect node i is expressed as:

[0064]

[0065]

[0066] in, and are the first-order and second-order propagation probabilities, respectively.

[0067] (2) The first-order simplex dynamic message update equation is:

[0068]

[0069] in, Indicates that the node is being dug out In the cavity network, the node The infection probability of the first-order simplex dynamic message update equation is excluded from the calculation of the node , thereby suppressing the echo chamber effect.

[0070] (3) The second-order simplex dynamic message update equation represents the node removal In the cavity network, the node pair The update of the joint probability distribution of . The second-order simplex dynamic message has four configurations , whose update follows the Markov transition rule. Configuration and Taking the configuration as an example, the second-order simplex dynamic message update equation is:

[0071]

[0072]

[0073] The remaining configurations ( , ) is also derived according to this principle, and the sum of the probabilities of all configurations is 1.

[0074] S3032. Based on the node infection probability update equation, the first-order simplex dynamic message update equation, and the second-order simplex dynamic message update equation, a high-order cyclic dynamic message transmission equation group is obtained.

[0075] In this embodiment, a high-order cyclic dynamic message transmission equation group is obtained by combining the node infection probability update equation, the first-order simplex dynamic message update equation, and the second-order simplex dynamic message update equation.

[0076] S304 : Predicting the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equations to obtain the node infection probability and the overall infection status of the first high-order network.

[0077] In this step, the electronic device can predict the propagation process of the first high-order network through a group of high-order cyclic dynamic message passing equations, and obtain the node infection probability and the overall infection status of the first high-order network.

[0078] S305 , calculating the critical propagation probability of the first high-order network based on the high-order cyclic dynamic message passing equations.

[0079] In this step, after obtaining the high-order cyclic dynamic message passing equations, the electronic device can calculate the critical propagation probability of the first high-order network based on the high-order cyclic dynamic message passing equations. Specifically, by calculating the critical propagation probability of the first high-order network in the disease-free steady state ( ) and obtain the critical propagation probability.

[0080] In some embodiments, S305 may include but is not limited to S3051 and S3052:

[0081] S3051. Linearize the simplex dynamic messages in the high-order cyclic dynamic message passing equation system into infinitesimals to obtain a linearized equation system;

[0082] In this step, each simplex dynamic message in the HrDMP equation group (i.e. " " form) is linearized into an infinitesimal quantity , and obtain the linearized system of equations.

[0083] S3052. Convert the linearized equation group into Jacobian matrix form, and determine the critical propagation probability by solving the maximum eigenvalue of the Jacobian matrix.

[0084] In this step, the linearized equations are organized into the Jacobian matrix form, which is expressed as follows:

[0085]

[0086] in, is a state vector consisting of all linearized simplex dynamic messages (infinitesimal quantities), with dimension , and are the number of first-order simplexes (edges) and second-order simplexes (triangles) in the network, respectively. To describe the Jacobian matrix of the linear evolution of the system, it is specifically expressed as:

[0087]

[0088] matrix are non-backtracking matrices that describe the message passing paths between simplexes of different orders. The formal definition of each matrix is ​​as follows, where the rows and columns of the matrix are represented by the index of the message Specify:

[0089] matrix : Characterizes the non-backtracking relationship between first-order simplexes. Its elements ,in Representative Message , Representative Message , if and only if the end point of the message coincides with the starting point ( ) and the message does not backtrack ( )hour, , otherwise 0.

[0090] matrix : Characterizes the non-backtracking relationship from the second-order simplex to the first-order simplex. Its elements ,in Represents a second-order simplex message , Represents a first-order simplex message , if and only if and hour, , otherwise 0.

[0091] matrix : Characterizes the non-backtracking relationship from the first-order simplex to the second-order simplex, which is opposite to the direction of matrix C. Its elements ,in represent represent , if and only if and hour, , otherwise 0.

[0092] matrix : Characterizes the non-backtracking relationship between second-order simplexes. Its elements ,in represent , represent , if and only if and hour, , otherwise 0.

[0093] Furthermore, by solving the maximum eigenvalue of the Jacobian matrix, the critical propagation probability can be determined. Specifically, the critical propagation probability The Jacobian matrix The maximum eigenvalue of The critical condition for the propagation phenomenon to occur is By solving the equation , can be given and The critical propagation probability under , as shown below:

[0094] .

[0095] S306 , using a factor graph conversion method, converting nodes in the hypergraph structure into factor nodes, and converting hyperedges in the hypergraph structure into variable nodes, to obtain an acyclic factor graph.

[0096] In this step, for the second high-order network of acyclic propagation dynamics, the factor graph transformation method can be used to transform the nodes in the original hypergraph structure into Considered as factor nodes, and hyperedges Treated as variable nodes. Through this transformation, a linear hypertree (i.e., a hypertree in which any two hyperedges share at most one node) can be accurately mapped into an acyclic factor graph. This lays the theoretical foundation for the subsequent application of the dynamic belief propagation algorithm. Since the second-order network is mapped into an acyclic factor graph, there are no local cycles, which can effectively suppress the echo chamber effect. Figure 5 As shown, Figure 5 (a) is a 3rd order linear hypergraph; Figure 5 (b) By treating hyperedges as variable nodes and nodes as factor nodes, a linear hypergraph can be transformed into a tree-like acyclic factor graph.

[0097] On the basis of this acyclic factor graph, we further utilize the characteristics of acyclic dynamics, that is, the node state can only change in one direction. ,node The entire history of dissemination The time of first infection can be used This greatly simplifies the variables in the HDBP framework and makes the originally complex derivation possible.

[0098] S307 . Introduce two groups of intermediate variables, where the two groups of intermediate variables include a first intermediate variable and a second intermediate variable.

[0099] In this step, two sets of intermediate variables are introduced. The first intermediate variable and the second intermediate variable The complex high-order dynamic message passing operation that originally required integration or summation over the entire time trajectory is transformed into an efficient recursive relationship that is only related to the state at the previous moment. Can be understood as from the neighbors Infection message sent to Until time t, node i is still "alive" (i.e., not successfully infected) ). It represents Moment, Neighbor Just got infected and The probability of generating a new infection "flux". This transformation greatly reduces the computational complexity, making it computationally possible to accurately infer the acyclic transmission process in large-scale networks.

[0100] S308. Construct a high-order dynamic message passing equation group based on the first intermediate variable, the second intermediate variable, and the acyclic factor graph.

[0101] In this step, after introducing two sets of intermediate variables, the electronic device may construct a higher-order dynamic message passing (HDMP) equation group according to the first intermediate variable, the second intermediate variable, and the acyclic factor graph.

[0102] In some embodiments, S308 may include but is not limited to S3081 and S3082:

[0103] S3081. Establish a simplex dynamic message update equation, a first intermediate variable update equation, a second intermediate variable update equation, and a node infection probability calculation equation;

[0104] In this step, a simplex dynamic message update equation, a first intermediate variable update equation, a second intermediate variable update equation, and a node infection probability calculation equation can be established based on the first intermediate variable, the second intermediate variable, and the acyclic factor graph.

[0105] (1) The simplex dynamic message update equation is expressed as follows:

[0106]

[0107] (2) The first intermediate variable update equation is expressed as follows:

[0108]

[0109] (3) The second intermediate variable update equation is expressed as follows:

[0110]

[0111] (IV) The equation for calculating the node infection probability is as follows:

[0112]

[0113] S3082. Based on the simplex dynamic message update equation, the first intermediate variable update equation, the second intermediate variable update equation, and the node infection probability calculation equation, a high-order dynamic message transmission equation group is obtained.

[0114] Furthermore, the electronic device may jointly establish a simplex dynamic message update equation, a first intermediate variable update equation, a second intermediate variable update equation, and a node infection probability calculation equation to establish a high-order dynamic message transmission equation group.

[0115] S309: Predicting the propagation process of the second high-order network based on the high-order dynamic message passing equations to obtain the node infection probability and overall infection status of the second high-order network.

[0116] In this step, the electronic device can predict the propagation process of the second high-order network through a group of high-order dynamic message passing equations, and obtain the node infection probability and the overall infection situation of the second high-order network.

[0117] The embodiment of the present application divides the neighborhood of each node of the simple complex structure, determines the first-order simplex neighbors and the second-order simplex neighbors, defines the simplex dynamic message, and constructs a high-order cyclic dynamic message transmission equation group based on the first-order simplex neighbors, the second-order simplex neighbors and the simplex dynamic message. Further, based on the high-order cyclic dynamic message transmission equation group, the propagation process of the first high-order network is predicted, and the node infection probability and the overall infection situation of the first high-order network are obtained. The critical propagation probability of the first high-order network is calculated based on the high-order cyclic dynamic message transmission equation group. And by adopting the factor graph conversion method, the nodes in the hypergraph structure are converted into factor nodes, and the hyperedges in the hypergraph structure are converted into variable nodes to obtain an acyclic factor graph, and two groups of intermediate variables are introduced. The two groups of intermediate variables include a first intermediate variable and a second intermediate variable. Based on the first intermediate variable, the second intermediate variable and the acyclic factor graph, a high-order dynamic message transmission equation group is constructed. Then, based on the high-order dynamic message transmission equation group, the propagation process of the second high-order network is predicted, and the node infection probability and the overall infection situation of the second high-order network are obtained. Through this method, the embodiment of the present application expands the scope of application of message passing theory by dividing the neighborhood and defining simplex dynamic messages. The introduction of simplex dynamic messages effectively suppresses the echo chamber effect in high-order structures, avoids overestimation of the propagation scale, improves the prediction accuracy of the propagation process, and provides an accurate inference framework for non-cyclic propagation processes. Based on the belief propagation theory, a high-order dynamic message passing equation group is constructed for prediction, which can provide more accurate prediction results than the existing mean field method. The introduction of two sets of intermediate dynamic variables can simplify calculations and reduce computing power requirements. The complex dynamic correlations between nodes of local structures and high-order structures can be taken into account, further improving the accuracy of the prediction of the propagation process of high-order networks.

[0118] Figure 4 A flow chart of a method for predicting high-order network propagation process provided by another embodiment of the present application is shown in FIG. Figure 4 As shown, the method includes the following steps:

[0119] S401 , dividing the neighborhood of each node of the simplicial complex structure to determine first-order simplex neighbors and second-order simplex neighbors.

[0120] Specifically, the implementation process and principle of S401 and S301 are the same and will not be described in detail here.

[0121] S402. Define a simplex dynamic message. The simplex dynamic message is used to represent the joint probability distribution of the remaining nodes after removing the target node from the network.

[0122] Specifically, the implementation process and principle of S402 and S302 are the same and will not be repeated here.

[0123] S403: Construct a high-order cyclic dynamic message passing equation group based on the first-order simplex neighbors, the second-order simplex neighbors, and the simplex dynamic messages.

[0124] Specifically, the implementation process and principle of S403 and S103 are the same and will not be described in detail here.

[0125] S404: Iteratively solve the high-order cyclic dynamic message passing equations to obtain the infection probability of each node of the first high-order network at each moment.

[0126] In this step, after constructing the high-order cyclic dynamic message passing equation group, the high-order cyclic dynamic message passing equation group is iteratively solved to obtain the infection probability of each node of the first high-order network at each moment.

[0127] In some embodiments, S404 may include but is not limited to S4041, S4042, S4043, and S4044:

[0128] S4041. Determine the structure and dynamic parameters of the first high-order network and the initial infection probability of each node;

[0129] In this step, the structure of the first high-order network is determined to be a simple complex SC, and the dynamic parameters are determined. The dynamic parameters include the first-order propagation probability , second-order propagation probability , probability of recovery , and determine the initial infection probability of all nodes .

[0130] S4042, initializing the simplex dynamic message in the high-order cyclic dynamic message passing equation group;

[0131] In this step, the infected part of the simplex dynamic message is initialized to 0, for example , Etc. The susceptible part of the simplex dynamic message is initialized to 1, e.g. .

[0132] S4043. For each moment, iterate the high-order cyclic dynamic message passing equations to obtain the infection probability of each node at each moment and the overall infection status at each moment;

[0133] In this step, the iteration At each time step ,use Known at all times and The value of is taken as input, and according to the second-order simplex dynamic message update equation, all second-order simplex dynamic messages are calculated in The value of the moment According to the first-order simplex dynamic message update equation, calculate all first-order simplex dynamic messages in The value of the moment . Update the equation according to the node infection probability, using First-order and second-order simplex dynamic messages at time , calculate the infection probability of all nodes .

[0134] S4044. If the current iteration time reaches the preset time threshold or the overall infection situation tends to converge, the iteration is completed, and the infection probability of each node of the first high-order network at each time is output.

[0135] In this step, the iteration process continues until the current iteration time reaches the preset time threshold. or overall infection status It tends to converge, and the iteration is completed at this time, and the infection probability of each node of the first high-order network at each moment is output.

[0136] S405: Calculate the overall infection situation at each moment based on the infection probability of each node at each moment.

[0137] In this step, the electronic device can calculate the overall infection situation at each moment based on the infection probability of each node at each moment. Specifically, the infection probability of each node at each moment is added up to obtain the overall infection situation at each moment.

[0138] In some embodiments, the method further includes: outputting the infection probability time series of each node at each moment , and output the overall infection time series .

[0139] S406 , using a factor graph conversion method, converting nodes in the hypergraph structure into factor nodes, and converting hyperedges in the hypergraph structure into variable nodes, to obtain an acyclic factor graph.

[0140] Specifically, the implementation process and principle of S406 and S306 are the same, and will not be repeated here.

[0141] S407 . Introduce two groups of intermediate variables, where the two groups of intermediate variables include a first intermediate variable and a second intermediate variable.

[0142] Specifically, the implementation process and principle of S407 and S307 are the same and will not be repeated here.

[0143] S408. Construct a high-order dynamic message passing equation group based on the first intermediate variable, the second intermediate variable, and the acyclic factor graph.

[0144] Specifically, the implementation process and principle of S408 and S308 are the same and will not be repeated here.

[0145] S409: Iteratively solve the high-order dynamic message passing equations to obtain the infection probability of each factor node of the second high-order network at each moment.

[0146] In this step, after constructing the high-order dynamic message passing equations, the high-order dynamic message passing equations are iteratively solved to obtain the infection probability of each factor node of the second high-order network at each moment.

[0147] In some embodiments, S409 may include but is not limited to S4091, S4092, S4093, and S4094:

[0148] S4091. Determine the structure and dynamic parameters of the second high-order network and the initial infection probability of each factor node;

[0149] In this step, the structure of the second high-order network is determined to be a hypergraph H, and the dynamic parameters are determined. The dynamic parameters include the first-order propagation probability , second-order propagation probability , and determine the initial infection probability of each factor node .

[0150] S4092, initializing the simplex dynamic message, the first intermediate variable, and the second intermediate variable in the high-order dynamic message passing equation group;

[0151] In this step, the single dynamic message All use Initialize all first intermediate variables Initialized to 1: , All second intermediate variables Initialized according to the initial infection probability: ; .

[0152] S4093. For each moment, iterate the high-order dynamic message passing equations to obtain the infection probability of each factor node at each moment;

[0153] In this step, the iteration At each time step , calculated in the following order:

[0154] 1) Utilize Moment and The value of , according to the second intermediate variable update equation calculates all Variables in The value at the moment.

[0155] 2) Utilize Moment and Moment , calculate all the values ​​according to the first intermediate variable update equation Variables in The value at the moment.

[0156] 3) Utilize Moment , all cavity probabilities are calculated according to the simplex dynamic message update equation exist The value at the moment.

[0157] 4) Utilize Moment , calculate the infection probability of all nodes according to the node infection probability calculation equation .

[0158] S4094: If the current iteration time reaches the preset time threshold, the iteration is completed, and the infection probability of each factor node of the second high-order network at each time is output.

[0159] In this step, the iteration process continues until the current iteration time reaches the preset time threshold. , at this time the iteration is completed, and the infection probability of each factor node of the second high-order network at each moment is output.

[0160] S410: Calculate the overall infection situation at each moment based on the infection probability of each factor node at each moment.

[0161] In this step, the electronic device can calculate the overall infection situation at each moment based on the infection probability of each factor node at each moment. Specifically, the infection probability of each factor node at each moment is added up to obtain the overall infection situation at each moment.

[0162] In some embodiments, the method further includes: outputting the infection probability time series of all factor nodes at each moment , and output the overall infection time series .

[0163] The embodiment of the present application divides the neighborhood of each node of the simple complex structure, determines the first-order simplex neighbors and the second-order simplex neighbors, and defines the simplex dynamic message; the simplex dynamic message is used to characterize the joint probability distribution of the remaining nodes after the target node is removed from the network, and based on the first-order simplex neighbors, the second-order simplex neighbors and the simplex dynamic message, a high-order cyclic dynamic message transmission equation group is constructed. Further, the high-order cyclic dynamic message transmission equation group is iteratively solved to obtain the infection probability of each node of the first high-order network at each moment, and based on the infection probability of each node at each moment, the overall infection situation at each moment is calculated. In addition, a factor graph conversion method is adopted to convert the nodes in the hypergraph structure into factor nodes, and the hyperedges in the hypergraph structure into variable nodes to obtain an acyclic factor graph, introduce two groups of intermediate variables, and the two groups of intermediate variables include a first intermediate variable and a second intermediate variable. Based on the first intermediate variable, the second intermediate variable and the acyclic factor graph, a high-order dynamic message transmission equation group is constructed. Then, the high-order dynamic message passing equations are iteratively solved to obtain the infection probability of each factor node of the second high-order network at each moment, and based on the infection probability of each factor node at each moment, the overall infection situation at each moment is calculated. Through this method, the embodiment of the present application constructs a high-order cyclic dynamic message passing equation group and a high-order dynamic message passing equation group, and then iteratively solves the high-order cyclic dynamic message passing equation group to obtain the infection probability of each node of the first high-order network at each moment, and iteratively solves the high-order dynamic message passing equation group to obtain the infection probability of each factor node of the second high-order network at each moment. The complex dynamic correlation between the nodes of the local structure and the high-order structure can be taken into account, effectively suppressing the echo chamber effect in the high-order structure, avoiding overestimation of the propagation scale, and further improving the accuracy of the prediction of the propagation process of the high-order network. It can be extended to higher-order simplicial complexes and hypergraph structures, as well as more complex non-cyclic dynamic models, and has strong scalability.

[0164] Through the description of the above implementation methods, those skilled in the art can clearly understand that the method according to the above embodiment can be implemented by means of software plus the necessary general hardware platform, and of course it can also be implemented by hardware, but in many cases the former is a better implementation method.

[0165] Figure 6 The embodiment of the present application provides a high-order network propagation process prediction device, which can be an electronic device as described in the above embodiment, or a component or assembly in the electronic device. The high-order network propagation process prediction device provided by the embodiment of the present disclosure can execute the processing flow provided by the embodiment of the high-order network propagation process prediction method, such as Figure 6As shown, the high-order network propagation process prediction device 50 includes: a construction module 51, a determination module 52, and a first prediction module 53; wherein the construction module 51 is used to obtain data to be processed, and construct a high-order network to be predicted based on the data to be processed, and the high-order network is a network that characterizes mutual propagation between multiple nodes; the determination module 52 is used to determine the network type of the high-order network to be predicted, and the network type includes a first high-order network based on cyclic propagation dynamics; the first prediction module 53 is used to establish a high-order cyclic dynamic message passing equation group based on a simple complex structure for the first high-order network, and predict the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equation group to obtain a prediction result of the propagation process of the first high-order network.

[0166] Optionally, the prediction result of the propagation process of the first high-order network includes the node infection probability of the first high-order network and the overall infection situation of the first high-order network; the first prediction module 53 establishes a high-order cyclic dynamic message passing equation group based on the simplicial complex structure, predicts the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equation group, and obtains the prediction result of the propagation process of the first high-order network, which is specifically used for: dividing the neighborhood of each node of the simplicial complex structure, determining the first-order simplex neighbors and the second-order simplex neighbors; defining the simplex dynamic message; the simplex dynamic message is used to characterize the joint probability distribution of the remaining nodes after the target node is removed from the network; constructing a high-order cyclic dynamic message passing equation group based on the first-order simplex neighbors, the second-order simplex neighbors and the simplex dynamic message; predicting the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equation group, and obtaining the node infection probability and the overall infection situation of the first high-order network.

[0167] Optionally, when the first prediction module 53 constructs a group of high-order cyclic dynamic message transmission equations based on first-order simplex neighbors, second-order simplex neighbors and simplex dynamic messages, it is specifically used to: establish a node infection probability update equation, a first-order simplex dynamic message update equation and a second-order simplex dynamic message update equation; based on the node infection probability update equation, the first-order simplex dynamic message update equation and the second-order simplex dynamic message update equation, obtain a group of high-order cyclic dynamic message transmission equations.

[0168] Optionally, the first prediction module 53 predicts the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equation group to obtain the node infection probability and the overall infection situation of the first high-order network. It is specifically used to: iteratively solve the high-order cyclic dynamic message passing equation group to obtain the infection probability of each node of the first high-order network at each moment; based on the infection probability of each node at each moment, calculate the overall infection situation at each moment.

[0169] Optionally, when the first prediction module 53 iteratively solves the high-order cyclic dynamic message passing equation group to obtain the infection probability of each node of the first high-order network at each moment, it is specifically used to: determine the structure, dynamic parameters and initial infection probability of each node of the first high-order network; initialize the simplex dynamic message in the high-order cyclic dynamic message passing equation group; for each moment, iterate the high-order cyclic dynamic message passing equation group to obtain the infection probability of each node at each moment and the overall infection situation at each moment; if the current iteration moment reaches the preset moment threshold or the overall infection situation tends to converge, the iteration is completed, and the infection probability of each node of the first high-order network at each moment is output.

[0170] Optionally, the high-order network propagation process prediction device 50 further includes: a calculation module 55, which is used to calculate the critical propagation probability of the first high-order network based on the high-order cyclic dynamic message passing equation group.

[0171] Optionally, when the calculation module 55 calculates the critical propagation probability of the first high-order network based on the high-order cyclic dynamic message passing equation group, it is specifically used to: linearize the simplex dynamic messages in the high-order cyclic dynamic message passing equation group into infinitesimals to obtain the linearized equation group; convert the linearized equation group into Jacobian matrix form, and determine the critical propagation probability by solving the maximum eigenvalue of the Jacobian matrix.

[0172] Optionally, the network type includes a second high-order network based on non-cyclic propagation dynamics; the high-order network propagation process prediction device 50 also includes: a second prediction module 54, which is used to establish a high-order dynamic message passing equation group for the second high-order network based on the hypergraph structure, and predict the propagation process of the second high-order network based on the high-order dynamic message passing equation group to obtain a prediction result of the propagation process of the second high-order network.

[0173] Optionally, the prediction result of the propagation process of the second high-order network includes the node infection probability of the second high-order network and the overall infection situation of the second high-order network; the second prediction module 54 establishes a high-order dynamic message passing equation group based on the hypergraph structure, and predicts the propagation process of the second high-order network based on the high-order dynamic message passing equation group. When obtaining the prediction result of the propagation process of the second high-order network, it is specifically used to: adopt a factor graph conversion method to convert the nodes in the hypergraph structure into factor nodes, and convert the hyperedges in the hypergraph structure into variable nodes to obtain an acyclic factor graph; introduce two groups of intermediate variables, the two groups of intermediate variables include a first intermediate variable and a second intermediate variable; based on the first intermediate variable, the second intermediate variable and the acyclic factor graph, construct a high-order dynamic message passing equation group; predict the propagation process of the second high-order network based on the high-order dynamic message passing equation group to obtain the node infection probability and the overall infection situation of the second high-order network.

[0174] Optionally, when the second prediction module 54 constructs a high-order dynamic message passing equation group based on the first intermediate variable, the second intermediate variable and the acyclic factor graph, it is specifically used to: establish a simplex dynamic message update equation, a first intermediate variable update equation, a second intermediate variable update equation and a node infection probability calculation equation; based on the simplex dynamic message update equation, the first intermediate variable update equation, the second intermediate variable update equation and the node infection probability calculation equation, obtain a high-order dynamic message passing equation group.

[0175] Optionally, the second prediction module 54 predicts the propagation process of the second high-order network based on the high-order dynamic message passing equations to obtain the node infection probability and the overall infection situation of the second high-order network. It is specifically used to: iteratively solve the high-order dynamic message passing equations to obtain the infection probability of each factor node of the second high-order network at each moment; based on the infection probability of each factor node at each moment, calculate the overall infection situation at each moment.

[0176] Optionally, when the second prediction module 54 iteratively solves the high-order dynamic message passing equation group to obtain the infection probability of each factor node of the second high-order network at each moment, it is specifically used to: determine the structure, dynamic parameters and initial infection probability of each factor node of the second high-order network; initialize the simplex dynamic message, the first intermediate variable and the second intermediate variable in the high-order dynamic message passing equation group; for each moment, iterate the high-order dynamic message passing equation group to obtain the infection probability of each factor node at each moment; if the moment of the current iteration reaches the preset moment threshold, the iteration is completed, and the infection probability of each factor node of the second high-order network at each moment is output.

[0177] For the description of the features in the embodiment corresponding to the high-order network propagation process prediction device, please refer to the relevant description of the embodiment corresponding to the high-order network propagation process prediction method, and no further details will be given here.

[0178] An embodiment of the present application also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor is configured to run the computer program to execute the steps in any of the above-mentioned high-order network propagation process prediction method embodiments.

[0179] An embodiment of the present application further provides a computer-readable storage medium, which stores a computer program, wherein the computer program is configured to execute the steps of any of the above-mentioned high-order network propagation process prediction method embodiments when running.

[0180] In an exemplary embodiment, the computer-readable storage medium may include, but is not limited to, various media that can store computer programs, such as a USB flash drive, a read-only memory (ROM), a random access memory (RAM), a mobile hard disk, a magnetic disk, or an optical disk.

[0181] An embodiment of the present application further provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the steps in any of the above-mentioned high-order network propagation process prediction method embodiments are implemented.

[0182] An embodiment of the present application also provides another computer program product, including a non-volatile computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps in any of the above-mentioned high-order network propagation process prediction method embodiments.

[0183] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the components and steps of each example according to their functions. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0184] The above is a detailed introduction to the high-order network propagation process prediction method, device, equipment, medium and product provided by this application. Specific examples are used herein to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of this application, several improvements and modifications can be made to this application, and these improvements and modifications also fall within the scope of protection of the claims of this application.

Claims

1. A method for predicting high-order network propagation process, characterized in that: The method comprises: Acquiring data to be processed, and constructing a high-order network to be predicted based on the data to be processed, wherein the high-order network is a network that represents mutual communication between multiple nodes; determining a network type of a high-order network to be predicted, the network type comprising a first high-order network based on cyclic propagation dynamics; For the first high-order network, establishing a high-order cyclic dynamic message passing equation system based on a simplicial complex structure, and predicting a propagation process of the first high-order network based on the high-order cyclic dynamic message passing equation system to obtain a prediction result of the propagation process of the first high-order network; The method of establishing a high-order cyclic dynamic message passing equation system based on a simple complex structure includes: The neighborhood of each node of the simplicial complex structure is divided to determine the first-order simplex neighbors and the second-order simplex neighbors; A simplex dynamic message is defined; the simplex dynamic message is used to represent the joint probability distribution of the remaining nodes after removing the target node from the network; A high-order cyclic dynamic message passing equation system is constructed based on the first-order simplex neighbors, the second-order simplex neighbors, and the simplex dynamic messages.

2. The method according to claim 1, characterized in that The prediction result of the propagation process of the first high-order network includes the infection probability of the nodes in the first high-order network and the overall infection status of the first high-order network; The predicting of the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equations to obtain a prediction result of the propagation process of the first high-order network includes: The propagation process of the first high-order network is predicted based on the high-order cyclic dynamic message passing equations to obtain the node infection probability and the overall infection situation of the first high-order network.

3. The method according to claim 2, characterized in that The constructing of a high-order cyclic dynamic message passing equation group based on the first-order simplex neighbors, the second-order simplex neighbors, and the simplex dynamic messages includes: Establish node infection probability update equation, first-order simplex dynamic message update equation and second-order simplex dynamic message update equation; Based on the node infection probability update equation, the first-order simplex dynamic message update equation and the second-order simplex dynamic message update equation, a high-order cyclic dynamic message passing equation group is obtained.

4. The method according to claim 2, characterized in that The method predicts the propagation process of the first high-order network based on the high-order cyclic dynamic message passing equations to obtain the node infection probability and the overall infection status of the first high-order network, including: Iteratively solving the high-order cyclic dynamic message passing equations to obtain the infection probability of each node of the first high-order network at each moment; Based on the infection probability of each node at each moment, the overall infection situation at each moment is calculated.

5. The method according to claim 4, characterized in that The iteratively solving the high-order cyclic dynamic message passing equations to obtain the infection probability of each node of the first high-order network at each moment includes: Determine the structure and dynamic parameters of the first high-order network and the initial infection probability of each node; Initializing a simplex dynamic message in the high-order cyclic dynamic message passing equation system; At each moment, the high-order cyclic dynamic message passing equations are iterated to obtain the infection probability of each node at each moment and the overall infection situation at each moment; If the current iteration time reaches the preset time threshold or the overall infection situation tends to converge, the iteration is completed and the infection probability of each node of the first high-order network at each time is output.

6. The method according to claim 1, characterized in that The method further comprises: Calculating a critical propagation probability of the first high-order network based on the high-order cyclic dynamic message passing equations; The calculating the critical propagation probability of the first high-order network based on the high-order cyclic dynamic message passing equations includes: Linearizing the simplex dynamic messages in the high-order cyclic dynamic message passing equations into infinitesimals to obtain a linearized equation system; The linearized equation group is converted into a Jacobian matrix form, and the critical propagation probability is determined by solving the maximum eigenvalue of the Jacobian matrix.

7. The method according to claim 1, characterized in that The network type comprises a second higher-order network based on acyclic propagation dynamics; and the method further comprises: For the second high-order network, a high-order dynamic message passing equation group is established based on the hypergraph structure, and the propagation process of the second high-order network is predicted based on the high-order dynamic message passing equation group to obtain a prediction result of the propagation process of the second high-order network.

8. The method according to claim 7, characterized in that The prediction result of the propagation process of the second high-order network includes the infection probability of the nodes in the second high-order network and the overall infection status of the second high-order network; The step of establishing a high-order dynamic message passing equation group based on the hypergraph structure, and predicting the propagation process of the second high-order network based on the high-order dynamic message passing equation group to obtain a prediction result of the propagation process of the second high-order network includes: Using a factor graph conversion method, the nodes in the hypergraph structure are converted into factor nodes, and the hyperedges in the hypergraph structure are converted into variable nodes, so as to obtain an acyclic factor graph; Introducing two groups of intermediate variables, the two groups of intermediate variables including a first intermediate variable and a second intermediate variable; Constructing a high-order dynamic message passing equation system based on the first intermediate variable, the second intermediate variable, and the acyclic factor graph; The propagation process of the second high-order network is predicted based on the high-order dynamic message passing equations to obtain the node infection probability and the overall infection situation of the second high-order network.

9. The method according to claim 8, characterized in that The constructing of a high-order dynamic message passing equation system based on the first intermediate variable, the second intermediate variable, and the acyclic factor graph includes: Establish a simplex dynamic message update equation, a first intermediate variable update equation, a second intermediate variable update equation, and a node infection probability calculation equation; Based on the simplex dynamic message update equation, the first intermediate variable update equation, the second intermediate variable update equation and the node infection probability calculation equation, a high-order dynamic message transmission equation group is obtained.

10. The method according to claim 8, characterized in that The method predicts the propagation process of the second high-order network based on the high-order dynamic message passing equations to obtain the node infection probability and the overall infection status of the second high-order network, including: Iteratively solving the high-order dynamic message passing equations to obtain the infection probability of each factor node of the second high-order network at each moment; Based on the infection probability of each factor node at each moment, the overall infection situation at each moment is calculated.

11. The method according to claim 10, characterized in that The iterative solution of the high-order dynamic message passing equations to obtain the infection probability of each factor node of the second high-order network at each moment includes: Determine the structure and dynamic parameters of the second higher-order network and the initial infection probability of each factor node; Initializing a simplex dynamic message, a first intermediate variable, and a second intermediate variable in the high-order dynamic message passing equation group; At each moment, the high-order dynamic message passing equations are iterated to obtain the infection probability of each factor node at each moment; If the current iteration time reaches the preset time threshold, the iteration is completed, and the infection probability of each factor node of the second high-order network at each time is output.

12. A high-order network propagation process prediction device, characterized in that: include: A construction module is used to obtain data to be processed and construct a high-order network to be predicted based on the data to be processed, wherein the high-order network is a network that represents mutual communication between multiple nodes; a determination module, configured to determine a network type of a high-order network to be predicted, wherein the network type comprises a first high-order network based on cyclic propagation dynamics; a first prediction module, configured to establish, for the first high-order network, a set of high-order cyclic dynamic message passing equations based on a simplicial complex structure, and predict a propagation process of the first high-order network based on the set of high-order cyclic dynamic message passing equations to obtain a prediction result of the propagation process of the first high-order network; When the first prediction module establishes a high-order cyclic dynamic message passing equation system based on a simple complex structure, it is specifically used to: The neighborhood of each node of the simplicial complex structure is divided to determine the first-order simplex neighbors and the second-order simplex neighbors; A simplex dynamic message is defined; the simplex dynamic message is used to represent the joint probability distribution of the remaining nodes after removing the target node from the network; A high-order cyclic dynamic message passing equation system is constructed based on the first-order simplex neighbors, the second-order simplex neighbors, and the simplex dynamic messages.

13. An electronic device, characterized in that: include: memory for storing computer programs; A processor, configured to implement the steps of the high-order network propagation process prediction method as claimed in any one of claims 1 to 11 when executing the computer program.

14. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, wherein when the computer program is executed by a processor, the steps of the high-order network propagation process prediction method according to any one of claims 1 to 11 are implemented.

15. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the high-order network propagation process prediction method according to any one of claims 1 to 11 are implemented.

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