Double-domain collaborative network dynamic evolution method

Abstract

The invention relates to a double-domain collaborative network dynamic evolution method, and belongs to the field of communication networks. The method comprises the following steps: extracting a node state and a topological structure from cascade propagation data, and respectively constructing a node state matrix and an adjacent matrix; inputting the adjacency matrix into the EvolveGCN to extract spatial features, and regulating and controlling an EvolveGCN updating mechanism through the social behavior factor and the difference quantity of the adjacency matrix; the node state matrix is input into Transform, and time features are extracted; fusing space and time features to obtain propagation dynamic embedding, inputting the propagation dynamic embedding into a multi-layer convolutional network to extract multi-scale features, and performing weighted fusion on outputs of different convolutional layers to obtain propagation structure embedding; and after the spatial feature, the time feature and the propagation structure are embedded and fused, node state prediction and topological structure prediction are respectively performed based on a fusion result, and a prediction result is fed back to a front-end network. According to the invention, the precision of network dynamic evolution prediction and the generalization ability of the model can be improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of communication network and intelligent information processing, and relates to a physical domain-social domain collaborative driving dynamic network structure evolution modeling method. BACKGROUND

[0002] Network evolution is an important research direction for understanding the operation law and propagation mechanism of complex systems, and is widely used in social communication, communication scheduling, energy interconnection and Internet of Things control and the like. With the continuous expansion of the scale of information networks and the sharp rise in the frequency of node interaction, the network structure and node state present the characteristics of high dynamic, heterogeneity and multi-dimensional coupling. The network dynamic evolution method has become the core foundation of intelligent network analysis and prediction. However, the current network modeling method is still mainly concentrated in the static topology or single domain dynamic perspective. The traditional graph neural network (GCN) can only process the relationship of fixed structure nodes, and it is difficult to reflect the law of topology evolution over time; while the simple time series model (such as RNN or LSTM) can capture the change of node state, but cannot perceive the time-varying dependence of network structure. In addition, the node behavior in the actual network is driven by internal and external factors, among which the social behavior characteristics (such as propagation willingness, role function, behavior inertia, etc.) have a significant influence on structure evolution, and the existing method generally ignores the coupling mechanism between this social internal cause and structure evolution.

[0003] With the improvement of the intelligent degree of complex systems, network evolution presents the development trend of “multi-domain driving, time-space interweaving”. Taking the social communication network as an example, the user behavior has obvious time sequence dependence and social interaction characteristics; in the communication network or Internet of Things environment, the node state change depends on the topology dynamics of physical link and is also affected by internal factors such as task, interest and strategy. The existing model often models the physical structure and social behavior separately, which leads to the inability to accurately depict the bidirectional action relationship between structure and state.

[0004] Under this background, it is urgent to need a network evolution method that can establish a dynamic collaborative mechanism between the physical domain and the social domain, so as to realize the synchronous prediction and mutual feedback optimization of node behavior and topology structure. SUMMARY

[0005] Therefore, the purpose of the present application is to provide a network dynamic evolution method with dual-domain collaboration, which can jointly learn the time sequence change of network topology structure and the internal driving force of node behavior by establishing a dynamic collaborative modeling framework between the physical domain and the social domain, realize the synchronous prediction of network evolution in the space, time and propagation dimensions, accurately depict the bidirectional influence relationship between node state evolution and structure evolution, and thus improve the prediction accuracy and interpretability of dynamic network analysis.

[0006] In order to achieve the above purpose, the present application provides the following technical scheme: A dual-domain collaborative network dynamic evolution method, comprising: extracting node state and topology structure from cascading propagation data, dividing time windows, and constructing node state matrix and adjacency matrix in each time window respectively; inputting the adjacency matrix into EvolveGCN to extract spatial features, EvolveGCN dynamically updates graph convolution weights between time steps through a gated recurrent unit, at each time step, a social behavior factor is constructed and injected into the graph convolution update mechanism of EvolveGCN, at the same time, the difference between the adjacency matrices of the last time step and the current time step is introduced and input into the GRU gating update mechanism of EvolveGCN; input the node state matrix into the Transformer to extract time features; fuse spatial features and time features to get propagation dynamic embedding; input the propagation dynamic embedding into a multi-layer convolutional network to extract multi-scale features, and obtain propagation structure embedding by weighting and fusing the outputs of different convolutional layers through channel attention mechanism; fuse spatial features, time features and propagation structure embedding, and based on the fusion result, respectively predict node state and topology structure, and feed the node state prediction result back to the Transformer, and feed the topology structure prediction result back to the EvolveGCN.

[0007] Further, in each time window, the node state matrix is constructed as:

[0008] wherein, is the number of nodes, is the state matrix of node i in the time window . is constructed as an adjacency matrix represented as:

[0009] wherein, is the adjacency matrix, represents the propagation from node i to node j, is the time window, is the time window, is the set of all observed propagation events, is the decay term.

[0010] Further, the social behavior factor is constructed, including: after each time window ends, the social behavior factor is constructed based on the social internal factor of the node in the time window, and is injected into the weight update mechanism of EvolveGCN as a regulation signal, so that the social behavior factor guides the EvolveGCN to adjust the parameter evolution direction in the spatial feature extraction process of the next time step by affecting the opening and closing state of the GRU update gate and the forgetting gate, realizes the dynamic learning process driven by the time window, the participation of social dynamics and the evolution of structure representation over time, wherein one time step of EvolveGCN corresponds to one time window; the constructed social behavior factor is represented as:

[0011] In the formula, is the social attribute embedding strength, is the identity embedding of node i, is the result of nonlinear mapping of the statistical characteristics of node structure; The difference between the predicted adjacency matrix of the last time step and the real adjacency matrix of the current time step is introduced , and the difference is input as a regulation signal into the GRU gate update mechanism of EvolveGCN, so as to control the reservation and correction ratio of the graph convolution weight matrix through the update gate and the reset gate, realize the reverse feedback of the structure prediction result to the model update process, and make the convolution kernel adaptively adjust the evolution direction according to the topological change trend; the predicted adjacency matrix is represented as: , represents a convolution operation, is a ReLU function; The spatial feature output by the adjusted EvolveGCN is :

[0012]

[0013]

[0014] In the formula, is the current structure embedding expression, is the predicted structure embedding expression, is a convolution operation, is an individual embedding feature.

[0015] Further, the node state matrix is input into the Transformer to capture the time dependence of node behavior:

[0016] wherein, is the state matrix of the current node, is the node state matrix known at time step is the node state matrix known at time step ~ is the node future state prediction value at each time step in time step ; Then the time position encoding is performed, and the sine-cosine position encoding is added for each time step to maintain the time sequence information; secondly, the long and short term dependency relationships of node behavior are modeled in different subspaces in parallel through the multi-head self-attention mechanism, and the propagation rhythm and behavior inertia features are extracted; finally, the gated mechanism is adopted to weight and fuse the long-term and short-term attention features, and the residual connection and layer normalization are introduced to keep the stable propagation of features; The time feature of the node is represented as:

[0017]

[0018] wherein, is the th row in time step , , , is a learnable parameter. The weight reflects the contribution degree of the th time step to the overall time feature.

[0019] wherein is a time series feature matrix, and is represented as:

[0020] wherein, represents the output of the previous layer, and FFN is a feedforward neural network.

[0021] Further, the spatial feature and the time feature are spliced to form a propagation state vector:

[0022] A propagation strength function is constructed:

[0023] wherein, is the interaction feature of the node and the node at time step ; is a fusion function; It is a multilayer perceptron. The product of Hadamard; Establish the propagation density function:

[0024]

[0025] In the formula, Indicates the event is in Instantaneous trigger strength, , , , All are learnable parameters. It is the probability density function; Performing one-dimensional convolution and nonlinear mapping on the discretized propagation density function yields the propagation dynamic embedding:

[0026]

[0027]

[0028] In the formula, For node pairs i and j, the equally spaced sampling vectors of the propagation density function within a future time window; For time windows The number of sampling points uniformly divided within the area. To characterize the dynamic structure of the propagation potential between node pairs within the current time window as it changes over time, To propagate dynamic embeddings, It is a one-dimensional convolution.

[0029] Furthermore, multi-layer convolutional networks enable the propagation of dynamic embeddings. Perform multi-scale feature extraction; The outputs of different convolutional layers are weighted and fused using a channel attention mechanism:

[0030] In the formula, Out-of-edge feature, For the feature of incoming edges, For the first The convolutional output of the layer; Obtain the propagation structure embedding :

[0031]

[0032] In the formula, It is a multilayer perceptron.

[0033] Furthermore, spatial features Time characteristics and propagation structure embedding The vectors are fused to form a propagation state vector. :

[0034] In the formula, It is a multilayer perceptron; Predicting node states based on propagating state vectors:

[0035] In the formula, For learnable state prediction weight vectors, For learnable bias terms; Predicting topology based on propagation state vectors:

[0036]

[0037] In the formula, It is a learnable structure-interaction mapping matrix. Let be the adjacency matrix between predicted nodes i and j.

[0038] The beneficial effects of this invention are as follows: Addressing the problem of the separation between topological evolution and node behavior in existing dynamic network modeling, this invention proposes a cross-domain collaborative modeling framework that integrates the dynamic characteristics of physical domain topology and the behavioral mechanisms of nodes in the social domain. It describes the network structure reconstruction rules through the link establishment and failure processes in the physical domain, and combines the behavioral intentions, functional roles, and endogenous driving forces of nodes in the social domain to achieve multi-level expression and evolutionary prediction of network states. This invention uses an evolutionary graph convolutional network to obtain structural dependencies between nodes through a spatial feature extraction module; captures the temporal features of node behavior based on a time-series Transformer through a behavior modeling module; characterizes the event triggering mechanism and propagation rhythm through a neural temporal point process module; dynamically adjusts the adjacency matrix to reflect the structural evolution trend through an adaptive graph convolutional module; and feeds the prediction results back to the front-end module through a closed-loop prediction module, achieving bidirectional interaction and cross-domain collaboration between structure and state.

[0039] This invention enables joint evolution modeling of communication network structure and node states in complex topology and asynchronous behavior scenarios, significantly improving the accuracy of network dynamic evolution prediction and the generalization ability of the model. It is applicable to various application scenarios such as intelligent networks, social propagation analysis, and dynamic prediction of network traffic.

[0040] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a schematic diagram of a dual-domain collaborative network dynamic evolution method provided in an embodiment of the present invention. Detailed Implementation

[0042] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0043] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0044] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0045] To address the shortcomings of existing network evolution modeling methods, such as reliance on single-domain features, difficulty in simultaneously capturing topological evolution and behavior-driven relationships, and lack of structure-state interaction feedback, this invention provides a network dynamic evolution method based on a dual-domain collaborative mechanism. This method, based on a dual-domain collaborative mechanism, integrates EvolveGCN, Transformer, neural temporal point processes, and multi-layer convolutional modules to achieve dynamic network evolution modeling. Specifically: EvolveGCN is used to extract spatial features of the network topology, and social behavior factors are introduced into graph convolution to characterize structural evolution patterns; Transformer is used to extract temporal dependency features of node behavior; neural temporal point processes are introduced to describe the triggering rhythm of propagation events; structural evolution features are extracted from the propagation tensor through multi-layer convolutional modules, node pair embeddings are mapped to node-level representations, and multi-order adjacency relationships are fused to output unified structural evolution features; finally, a joint prediction and dual-domain feedback mechanism is used to achieve synchronous prediction and adaptive optimization of node states and topology structure, constructing a structure-state collaborative dynamic network evolution model.

[0046] Please see Figure 1 An embodiment of the present invention provides a method for dynamic evolution of networks with dual-domain cooperation, which is described in detail below: 1. Dynamic data extraction and input construction: Extract node states and topology from cascaded propagation data to construct a time-series dynamic graph input.

[0047] (1) Cascaded data parsing. Extract node IDs, propagation paths and timestamp information from the original cascaded propagation files to form a time-seriesd set of propagation events.

[0048] (2) Construction of the node state matrix. Based on the time window division results, the active state of the nodes at each time point is recorded as the node state matrix. The propagation state of a node at time t can be represented by the following formula:

[0049] in, For the number of nodes, Let T be the state matrix of a node within the time window T.

[0050] (3) Topology extraction. An adjacency matrix is ​​constructed within each time window based on the propagation relationship. Describe the physical topology of the network and its dynamic changes:

[0051] in, For the contiguous matrix, This indicates propagation from node i to node j. For time window, For time window, For the set of all observed propagation events, This is the attenuation term.

[0052] (4) Input tensor generation. Using... This provides a set of snapshot-style inputs to subsequent modeling modules, offering a unified input for spatial and temporal feature extraction.

[0053] 2. Spatial structure feature extraction: EvolveGCN is used to extract the spatial structure features of nodes, and social behavior factors are injected into graph convolution to achieve structural evolution modeling.

[0054] (1) EvolveGCN feature update. The EvolveGCN network structure is adopted, and the graph convolution weights are dynamically updated between time steps through gated recurrent units (GRU), so that the model has the ability to adapt to the evolution of the structure over time.

[0055] (2) Neighborhood information aggregation. At each time step, nodes aggregate feature information from their first-order and second-order neighborhoods and capture local and mid-range structural dependencies through graph convolution operations.

[0056]

[0057] in, This is the node feature matrix after convolution of the Kth layer graph. For attention weights, In the current time window t The dynamic adjacency matrix, The initial input feature matrix, Let be the trainable weight matrix for the Kth layer.

[0058] (3) Social behavior factor modeling: After each time window ends (corresponding to a time step of the model), social behavior factors are constructed based on the node's willingness to spread, behavioral inertia and functional role within the time window. These factors are then injected into the weight update mechanism of EvolveGCN as a regulatory signal. This allows social behavior factors to influence the opening and closing states of the GRU update gate and forget gate, thereby guiding EvolveGCN to adjust the parameter evolution direction during the spatial feature extraction process in the next time step. This achieves a dynamic learning process driven by time windows, with social dynamics participating and structural representation evolving over time.

[0059]

[0060] in, The intensity of the embedding is used to represent social attributes. To represent the identity embedding of node i, This represents the result of nonlinear mapping to represent the structural statistical characteristics of nodes (such as degree, clustering coefficient, centrality, etc.).

[0061] (4) Structural feedback fusion: in the first In each time step, the predicted adjacency matrix generated by the model in the previous time step is introduced. The true adjacency matrix obtained with the current time window The difference between The difference is then used as a control signal to be input into the GRU gated update mechanism of EvolveGCN. By controlling the retention and correction ratio of the graph convolution weight matrix by the update gate and reset gate, the structural prediction results are fed back to the model update process, so that the convolution kernel (i.e. the dynamic graph convolution weights used for spatial feature extraction in EvolveGCN) can adaptively adjust its evolution direction according to the topological change trend.

[0062]

[0063] in," " indicates a convolution operation. This is the ReLU function.

[0064] (5) Spatial feature output. The output node at time step Spatial feature representation , as input for neural temporal point process modeling.

[0065]

[0066]

[0067]

[0068] in, Embedding the expression for the current structure, To predict structural embedding expressions, For convolution operations, These are individual embedded features.

[0069] 3. Temporal Feature Extraction. The Transformer model is used to extract the temporal dependency features of node behavior, capturing the temporal variation patterns during the propagation process.

[0070] (1) Time series input. The node state matrix... Input the Transformer encoder to capture the time dependency of node behavior:

[0071] In the formula, This is the state matrix of the current node. For time step Given the known node state matrix, ~ For time step The predicted future state of nodes at each time step.

[0072] (2) Time position coding. Add sine-cosine position coding to each time step to preserve time sequence information.

[0073] (3) Multi-head attention mechanism. The multi-head self-attention mechanism is used to model the long-term and short-term dependencies of node behavior in parallel in different subspaces, and to extract the propagation rhythm and behavioral inertia features. Each attention head independently learns different attention weights, which enables the model to understand the input sequence from multiple perspectives, thereby obtaining a richer and finer-grained temporal representation.

[0074] (4) Gated fusion and residual update. A gating mechanism is used to perform weighted fusion between long-term and short-term attention features, and residual connections and layer normalization are introduced to maintain stable feature propagation.

[0075] (5) Time Feature Output. Output the time features of the node. As input to the neural timeline process module:

[0076]

[0077] in, for The Middle OK, , , These are learnable parameters. Weights Reflects the first The contribution of each time step to the overall temporal characteristics. Among them Let be the time series feature matrix, where each row corresponds to a high-dimensional context representation of a time step in the sequence.

[0078]

[0079] in, This represents the output of the previous layer; FFN stands for Feedforward Neural Network.

[0080] 4. Neural temporal point process modeling: Integrating spatial and temporal features, establishing an intensity function for propagation events, and characterizing the dynamic rhythm of propagation triggering.

[0081] (1) Propagation state fusion. Integrating spatial features With time characteristics Concatenate to form the propagation state vector:

[0082] (2) Definition of the intensity function. A propagation intensity function is constructed using a neural network to describe the dynamic rate at which a node triggers propagation events in the future. The propagation intensity function is expressed as follows:

[0083] in, For nodes and nodes At time step Interactive features; This is a fusion function used to merge nodes. and Feature vector fusion; It is a multilayer perceptron. It is the product of Hadamard.

[0084] (3) Calculation of propagation probability density. Derive the propagation density function to characterize the temporal distribution of propagation events:

[0085]

[0086] in, To indicate the event in Instantaneous trigger strength, , , , All are learnable parameters. Let be the probability density function.

[0087] (4) Generation of propagation rhythm embedding. One-dimensional convolution and nonlinear mapping are performed on the discretized propagation density function to extract the high-order dynamic features of the propagation rhythm, resulting in the propagation dynamic embedding:

[0088]

[0089]

[0090] in, This is the equally spaced sampling vector of the propagation density function for node pair (i, j) within a future time window. For time windows The number of sampling points uniformly divided within the area. To characterize the dynamic structure of the propagation potential between node pairs within the current time window as it changes over time, For propagation of dynamic embeddings. It is a one-dimensional convolution.

[0091] 5. Multi-layer convolutional module fusion of propagation dynamic features: Multi-layer convolutional aggregation is performed on the propagation dynamic embedding to extract multi-scale propagation patterns and spatial diffusion features.

[0092] (1) Construction of multi-layer convolutional modules. Constructing multi-layer convolutional networks to propagate dynamic embeddings. Perform multi-scale feature extraction.

[0093] (2) Cross-layer feature aggregation. The outputs of different convolutional layers are weighted and fused through the channel attention mechanism to achieve adaptive integration of cross-layer propagation features.

[0094]

[0095] in, Out-of-edge feature, For the feature of incoming edges, For the first The convolutional output of the layer.

[0096] (3) Propagation structure embedded in the output. The propagation structure embedded in the output after fusion is represented. As input to the joint prediction module:

[0097]

[0098] in, It is a multilayer perceptron.

[0099] 6. Joint prediction and dual-domain feedback optimization: Jointly predict future topology and node states, and achieve closed-loop evolution optimization of structure and behavior through a dual-domain feedback mechanism.

[0100] (1) Feature fusion. Fusion of spatial features. Time characteristics and propagation structure embedding , forming a propagation state vector :

[0101] in, It is a multilayer perceptron.

[0102] (2) Node state prediction. The activation state of nodes at future times is predicted using the fully connected layer:

[0103] in, For learnable state prediction weight vectors, This is a learnable bias term.

[0104] (3) Topology prediction. Future adjacency matrices are generated through inner product mapping sampling to predict network topology evolution trends.

[0105]

[0106] in, It is a learnable structure-interaction mapping matrix. Let be the adjacency matrix between predicted nodes i and j.

[0107] (4) Dual-domain feedback mechanism. The node states in the prediction results are fed back to the Transformer module, and the predicted topology is fed back to the EvolveGCN module, forming a closed-loop interaction mechanism between the physical domain and the social domain.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for dynamic network evolution through dual-domain cooperation, characterized in that, The method includes: Extract node states and topology from cascaded propagation data, divide time windows, and construct node state matrix and adjacency matrix in each time window; Spatial features are extracted by inputting the adjacency matrix into EvolveGCN. EvolveGCN dynamically updates the graph convolution weights between time steps through gated recurrent units. In each time step, social behavior factors are constructed and injected into the graph convolution update mechanism of EvolveGCN. At the same time, the difference between the adjacency matrix of the previous time step and the current time step is introduced and input into the GRU gated update mechanism of EvolveGCN. Temporal features are extracted by inputting the node state matrix into the Transformer. By integrating spatial and temporal features, a dynamic embedding of propagation is obtained; The propagation dynamics are embedded into a multi-layer convolutional network to extract multi-scale features. The outputs of different convolutional layers are weighted and fused through a channel attention mechanism to obtain the propagation structure embedding. After embedding and fusing spatial features, temporal features, and propagation structure, node state prediction and topology prediction are performed based on the fusion results. The node state prediction results are fed back to the Transformer, and the topology prediction results are fed back to EvolveGCN.

2. The method according to claim 1, characterized in that, Within each time window, construct the node state matrix: In the formula, For the number of nodes, For node i in the time window The state matrix within; Constructing it as an adjacency matrix is ​​represented as follows: In the formula, For the contiguous matrix, This indicates propagation from node i to node j. For time window, For time window, For the set of all observed propagation events, This is the attenuation term.

3. The method according to claim 2, characterized in that, The construction of social behavior factors includes: after each time window ends, constructing social behavior factors based on the node's intrinsic social factors within that time window, and injecting them as regulatory signals into the weight update mechanism of EvolveGCN. This allows the social behavior factors to influence the opening and closing states of the GRU update and forget gates, guiding EvolveGCN to adjust its parameter evolution direction during the spatial feature extraction process in the next time step. This achieves a dynamic learning process driven by time windows, involving social dynamics, and involving the evolution of structural representation over time. One time step in EvolveGCN corresponds to one time window. The constructed social behavior factors are represented as follows: In the formula, The intensity of the embedding is used to represent social attributes. To represent the identity embedding of node i, This represents the result of nonlinear mapping of the structural statistical characteristics of nodes; Introducing the predicted adjacency matrix from the previous time step The true adjacency matrix at the current time step The difference between The difference is then used as a control signal input to the GRU-gated update mechanism of EvolveGCN. By controlling the retention and correction ratio of the graph convolution weight matrix by the update gate and reset gate, the structure prediction results are fed back to the model update process, enabling the convolution kernel to adaptively adjust its evolution direction according to the topological change trend; the adjacency matrix is ​​predicted. Represented as: , This represents the convolution operation. For ReLU functions; By adjusting the output spatial characteristics of EvolveGCN : In the formula, Embedding the expression for the current structure, To predict structural embedding expressions, For convolution operations, These are individual embedded features.

4. The method according to claim 3, characterized in that, Input the node state matrix into the Transformer to capture the time dependency of node behavior: In the formula, This is the state matrix of the current node. For time step Given the known node state matrix, ~ For time step Predicted future states of nodes at each time step; Then, temporal position encoding is performed, adding sine-cosine position codes to each time step to preserve temporal order information. Next, a multi-head self-attention mechanism is used to model the long-term and short-term dependencies of node behavior in parallel across different subspaces, extracting propagation rhythm and behavioral inertia features. Finally, a gating mechanism is used to weightedly fuse long-term and short-term attention features, introducing residual connections and layer normalization to maintain stable feature propagation. The temporal features of the nodes... Represented as: In the formula, for The Middle OK, , , For learnable parameters; weights Reflects the first The contribution of each time step to the overall temporal characteristics; among which The time series feature matrix is ​​represented as follows: In the formula, This represents the output of the previous layer; FFN stands for Feedforward Neural Network.

5. The method according to claim 4, characterized in that, Spatial and temporal features are concatenated to form a propagation state vector: Construct the propagation strength function: In the formula, For nodes and nodes At time step Interactive features; This is the fusion function; It is a multilayer perceptron. The product of Hadamard; Establish the propagation density function: In the formula, Indicates the event is in Instantaneous trigger strength, , , , All are learnable parameters. It is the probability density function; Performing one-dimensional convolution and nonlinear mapping on the discretized propagation density function yields the propagation dynamic embedding: In the formula, For node pairs i and j, the equally spaced sampling vectors of the propagation density function within a future time window; For time windows The number of sampling points uniformly divided within the area. To characterize the dynamic structure of the propagation potential between node pairs within the current time window as it changes over time, To propagate dynamic embeddings, It is a one-dimensional convolution.

6. The method according to claim 5, characterized in that, Multilayer convolutional networks for propagating dynamic embeddings Perform multi-scale feature extraction; The outputs of different convolutional layers are weighted and fused using a channel attention mechanism: In the formula, Out-of-edge feature, For the feature of incoming edges, For the first The convolutional output of the layer; Obtain the propagation structure embedding : In the formula, It is a multilayer perceptron.

7. The method according to claim 6, characterized in that, spatial features Time characteristics and propagation structure embedding The vectors are fused to form a propagation state vector. : In the formula, It is a multilayer perceptron; Predicting node states based on propagated state vectors: In the formula, For learnable state prediction weight vectors, For learnable bias terms; Predicting topology based on propagation state vectors: In the formula, It is a learnable structure-interaction mapping matrix. Let be the adjacency matrix between predicted nodes i and j.

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