A method and system for predicting the resilience of a complex network system

Abstract

The application relates to the technical field of complex network systems, and provides a complex network system resilience prediction method and system, which comprises the following steps: obtaining observation data of a complex network system to be resilience predicted; inputting the observation data into a resilience prediction model to obtain a resilience prediction result output by the resilience prediction model; wherein the training method of the resilience prediction model comprises the following steps: pre-training the resilience prediction model based on labeled data in sample observation data to obtain a pre-trained resilience prediction model; generating labeled enhancement data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model and a preset graph data enhancement algorithm; and retraining the pre-trained resilience prediction model according to the labeled data in the sample observation data and the generated labeled enhancement data to obtain a well-retrained resilience prediction model, so that the accuracy of resilience prediction is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of complex network systems technology, and in particular to a method and system for predicting the resilience of complex network systems. Background Technology

[0002] Complex systems in various real-world fields, such as those in ecology, biochemistry, and physiology, can be modeled using complex systems theory. These complex systems are typically composed of interconnected components. For example, in an ecosystem, different components can represent multiple species, and the relationships of competition, cooperation, and symbiosis among species can be represented by the connections between components. From a graph theory perspective, components can be abstracted as nodes, and the connections between them can be abstracted as edges. Therefore, such complex systems composed of interconnected components can also be called complex network systems. Resilience is one of the important properties of complex network systems; it represents the system's ability to adjust to maintain its normal function in the face of errors, failures, and environmental changes. Understanding and predicting this crucial property of resilience in complex network systems not only enhances the ability to analyze and intervene in natural systems but also provides valuable insights for the design of engineering systems.

[0003] In the field of predicting the resilience of complex networks, several theoretical methods based on nonlinear dynamics have been developed. Studies have shown that the resilience of complex network systems is related to the network's topology and its dynamic mechanisms. However, most existing research is limited to theoretical analysis, aiming to derive complex, high-dimensional analytical solutions to changes in node states. These theoretical methods typically assume a detailed understanding of network evolution dynamics, lacking consideration for real-world realities. Real-world network dynamics are often difficult to measure, and their formulaic forms are often unavailable. Summary of the Invention

[0004] This invention provides a method and system for predicting the resilience of complex network systems, addressing the shortcomings of existing theoretical methods that typically assume a detailed understanding of network evolution dynamics, lack consideration for real-world realities, and where real network dynamics are often difficult to measure and whose formulaic forms are unavailable. This invention significantly improves the accuracy of resilience prediction by pre-training, data augmentation, and retraining the resilience prediction model based on observational data.

[0005] This invention provides a method for predicting the resilience of complex network systems, comprising: acquiring observation data of the complex network system to be resiliently predicted; the observation data including network topology distribution and dynamic state trajectories of network topology nodes; inputting the observation data into a resilience prediction model to obtain a resilience prediction result output by the resilience prediction model; wherein, the training method of the resilience prediction model includes: pre-training the resilience prediction model based on labeled data in the sample observation data to obtain a pre-trained resilience prediction model; generating labeled augmented data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm; retraining the pre-trained resilience prediction model based on the labeled data in the sample observation data and the generated labeled augmented data to obtain a retrained resilience prediction model, and performing resilience prediction based on the retrained resilience prediction model.

[0006] According to the present invention, a method for predicting the resilience of complex network systems includes a resilience prediction model comprising a topology diffusion module, a dynamics learning module, and a resilience prediction module. The method involves pre-training the resilience prediction model based on labeled data from sample observation data to obtain a pre-trained resilience prediction model, comprising: pre-training the topology diffusion module based on a preset generative diffusion algorithm according to the network topology distribution in the sample observation data to obtain a pre-trained topology diffusion module; the topology diffusion module is used to generate the network topology distribution; pre-training the dynamics learning module using neural network constant differential equations according to the dynamics state trajectories in the sample observation data to obtain a pre-trained dynamics learning module; the dynamics learning module is used to generate dynamics state trajectories; and pre-training the resilience prediction module using the Transformer algorithm and graph convolutional networks according to the labeled data in the sample observation data to obtain a pre-trained resilience prediction module; the resilience prediction module is used to predict the resilience of complex network systems.

[0007] According to a method for predicting the resilience of complex network systems provided by the present invention, the step of generating labeled augmented data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm includes: determining a process topology based on the unlabeled data in the sample observation data; the process topology being a network topology distribution generated by the topology diffusion module during the reverse process; determining a process dynamics state trajectory generated by the dynamics learning module based on the process topology; determining a process resilience prediction result generated by the resilience prediction module based on the process topology and the process dynamics state trajectory; and guiding the generation of the labeled augmented data based on the process resilience prediction result; the labeled augmented data including a labeled augmented network topology distribution generated by the topology diffusion module and a labeled augmented dynamics state trajectory generated by the dynamics learning module.

[0008] According to a method for predicting the resilience of complex network systems provided by the present invention, the step of pre-training a topology diffusion module based on a preset generative diffusion algorithm according to the network topology distribution in the sample observation data includes: determining the node set and edge set input to the topology diffusion module according to the network topology distribution in the sample observation data; the forward process of the pre-training of the topology diffusion module is equivalent to sampling the edge type from the classification distribution according to the node set and the edge set to obtain a noisy topology graph; inputting the noisy topology graph into a pre-trained topology prediction network to obtain a predicted topology graph; and performing a reverse process of pre-training the topology diffusion module according to the noisy topology graph and the predicted topology graph to obtain a denoised topology graph.

[0009] According to the present invention, a method for predicting the resilience of a complex network system includes pre-training a dynamic learning module using a neural network based on the dynamic state trajectory in the sample observation data. This includes: encoding and mapping the node states in the dynamic state trajectory of the sample observation data to a latent space; learning the node states in the latent space using a graph neural network to obtain a latent space representation; and decoding and transforming the latent space representation to obtain a dynamic state trajectory representing the reconstructed node states.

[0010] According to the present invention, a method for predicting the resilience of complex network systems includes pre-training the resilience prediction module using the Transformer algorithm and a graph convolutional network based on labeled data in the sample observation data. This includes: encoding the temporal correlation of node states between time steps using a Transformer layer based on the dynamic state trajectory of nodes at each time step in the labeled data in the sample observation data; and learning the spatial interactions within the network topology distribution in the labeled data using the graph convolutional network.

[0011] This invention also provides a resilience prediction system for complex network systems, comprising: an acquisition module for acquiring observation data of the complex network system to be resilience predicted; the observation data including network topology distribution and dynamic state trajectories of network topology nodes; a resilience prediction module for inputting the observation data into a resilience prediction model to obtain a resilience prediction result output by the resilience prediction model; wherein, the training system of the resilience prediction model includes: a pre-training module for pre-training the resilience prediction model based on labeled data in the sample observation data to obtain a pre-trained resilience prediction model; a data augmentation module for generating labeled augmented data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm; and a retraining module for retraining the pre-trained resilience prediction model based on the labeled data in the sample observation data and the generated labeled augmented data to obtain a retrained resilience prediction model, and performing resilience prediction based on the retrained resilience prediction model.

[0012] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the resilience prediction method for complex network systems as described above.

[0013] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the resilience prediction method for complex network systems as described above.

[0014] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the resilience prediction method for complex network systems as described above.

[0015] This invention provides a method and system for predicting the resilience of complex network systems. The method includes: acquiring observation data of the complex network system to be resiliently predicted; the observation data includes the network topology distribution and the dynamic state trajectories of the network topology nodes; inputting the observation data into a resilience prediction model to obtain the resilience prediction result output by the resilience prediction model; wherein, the training method of the resilience prediction model includes: pre-training the resilience prediction model based on labeled data in the sample observation data to obtain a pre-trained resilience prediction model; generating labeled augmented data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm; and retraining the pre-trained resilience prediction model based on the labeled data in the sample observation data and the generated labeled augmented data to obtain a retrained resilience prediction model, which significantly improves the accuracy of resilience prediction. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating a method for predicting the resilience of complex network systems provided by the present invention.

[0018] Figure 2 This is a schematic diagram illustrating the resilience principle of complex network systems provided by the present invention.

[0019] Figure 3 This is a schematic diagram illustrating the specific process of a resilience prediction method for complex network systems provided by the present invention.

[0020] Figure 4 This is a schematic diagram illustrating the principle of a resilience prediction method for complex network systems provided by the present invention.

[0021] Figure 5 This is a schematic diagram of the topology diffusion module provided by the present invention.

[0022] Figure 6 This is a schematic diagram of the structure of a resilience prediction system for complex network systems provided by the present invention.

[0023] Figure 7 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0025] A complex network is a network that possesses some or all of the following properties: self-organization, self-similarity, attractors, small-world characteristics, and scale-free operation. Key characteristics include: small-world characteristics, the concept of clustering (degree of aggregation), and a power-law degree distribution. From a dynamical system perspective, the evolution of a complex network is driven by its internal nonlinear dynamics. Specifically, if we represent the functional activity of each node by its state value, a resilient complex network system, through its internal nonlinear dynamics, can recover from external perturbations to its node states and evolve to a single stable stage. At this point, all node states are at a relatively high level. A formulaic description of a complex network system is... ,in Represents a set of nodes. This represents the adjacency matrix. Nodes The state can be represented as If over time... Approaching infinity, complex network systems If a complex network system consistently converges only to the desired steady-state node state, then the complex network system is considered to be... It is resilient.

[0026] In the field of predicting the resilience of complex network systems, several theoretical methods based on nonlinear dynamics have been developed. Studies have shown that the resilience of complex network systems is related to the network's topology and its dynamic mechanisms. Existing work typically uses adjacency matrices to abstract the network's topology into a graph structure for further analysis and application. The system's dynamic mechanisms are usually described by a set of nonlinear ordinary differential equations, expressed as:

[0027] in Represents a node The influence of its own state on its state evolution process. The elements of the system network topology adjacency matrix represent nodes. With nodes The weight of the edges between them. If there are no edges connecting them, then . Represents a node For nodes The impact of state evolution. This indicates that the evolution of a node's state in the system is not only related to its own state, but also influenced by the states of its adjacent nodes.

[0028] Existing research has largely been limited to theoretical analysis, aiming to derive complex, high-dimensional analytical solutions to the changes in node states within a network. However, theoretical methods typically assume a detailed understanding of network evolution dynamics and lack consideration for real-world realities. Real-world network dynamics are often difficult to measure, and their formulaic forms are unavailable.

[0029] In contrast, data-driven approaches can directly extract network structure and dynamics information from observational data, enabling resilience prediction without requiring predefined knowledge. Therefore, the task of predicting network resilience can be reinterpreted as a graph classification problem using machine learning techniques. However, collecting large amounts of labeled data from complex real-world systems is both expensive and impractical, often requiring observing the system's evolution to a steady state over extended periods or conducting repeated experiments observing multiple trajectories. Consequently, while most system observational data contains information about network topology and node evolution trajectories, it lacks labels regarding resilience.

[0030] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating a method for predicting the resilience of complex network systems provided by the present invention.

[0031] Please refer to Figure 2 , Figure 2 A schematic diagram illustrating the resilience principle of complex network systems provided by this invention.

[0032] This invention provides a method for predicting the resilience of complex network systems, comprising: 101: Obtain observational data of complex network systems to be resilience predicted; the observational data includes network topology distribution and dynamic state trajectories of network nodes; 102: Input observation data into the resilience prediction model to obtain the resilience prediction results output by the resilience prediction model; wherein, the training method of the resilience prediction model includes: pre-training the resilience prediction model based on the labeled data in the sample observation data to obtain the pre-trained resilience prediction model; generating labeled augmented data for model retraining based on the unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm; retraining the pre-trained resilience prediction model based on the labeled data in the sample observation data and the generated labeled augmented data to obtain the retrained resilience prediction model, and performing resilience prediction based on the retrained resilience prediction model.

[0033] Considering the challenge of obtaining detailed equations of node state dynamics in real-world scenarios, this work employs a purely data-driven approach to predict network resilience. Complex interactions exist between the topology and dynamics of complex network systems. Constructing practical resilience prediction models enables accurate resilience predictions by modeling these complex interactions based on partial evolutionary trajectories collected from short time windows and observed topology data. In the context of the resilience prediction task, the dataset contains network samples from which topological information and initial conditions before reaching steady state can be extracted. T Step M The dynamic state trajectory of a node. Formally, for a node containing N A network of nodes, the network topology is distributed by an adjacency matrix. The observed dynamic state trajectory of the node is represented as... .

[0034] Accurately determining the resilience of a network requires observing its steady-state characteristics, a requirement often difficult to meet due to high observation costs (e.g., long-term behavior of species population growth). Therefore, only a small fraction of network samples are labeled, denoted as . Most samples are unlabeled, denoted as ,and Relying on a limited amount of labeled data. P Training resilience prediction models may result in suboptimal performance due to limited sample size. Improving prediction accuracy in situations where labeled data is scarce involves utilizing information about system topology and network dynamics from unlabeled data. This invention utilizes unlabeled data based on a pre-defined graph data augmentation algorithm. The information in the model is used to generate diverse, high-quality augmented samples to improve the training of the resilient prediction model, with the goal of achieving better prediction accuracy.

[0035] Specifically, this invention provides a resilience prediction method for complex network systems based on a generative enhanced network resilience prediction framework (TDNetGen) that jointly models topology and nodal state dynamics. TDNetGen addresses the problems of theoretical methods contradicting real-world conditions, lack of applicability to real-world complex network systems, and the limitations of complex network resilience prediction with a limited number of labeled samples by enhancing the generative modeling of network topology and node state dynamics mechanisms. First, observational data of the complex network system to be resilience predicted is acquired. The resilience prediction model can then accurately predict resilience based on the complex interaction relationships between the network topology distribution and the dynamic state trajectories of network nodes within the observational data.

[0036] The training process of the resilience prediction model is as follows: First, the resilience prediction model is pre-trained based on sample observation data. Then, based on the unlabeled data in the sample observation data and the pre-trained resilience prediction model, a pre-defined graph data augmentation algorithm is used to generate labeled augmented data. The training of the resilience prediction model is further enhanced by combining the sample observation data and the newly generated labeled augmented data, thus creating a collaborative feedback loop that significantly improves the resilience prediction accuracy of the model.

[0037] Please refer to Figure 3 , Figure 3 A schematic diagram illustrating the specific process of a resilience prediction method for complex network systems provided by the present invention.

[0038] Please refer to Figure 4 , Figure 4 This is a schematic diagram illustrating the principle of a resilience prediction method for complex network systems provided by the present invention.

[0039] In a preferred embodiment, the resilience prediction model includes a topology diffusion module, a dynamics learning module, and a resilience prediction module. The resilience prediction model is pre-trained based on labeled data from sample observation data to obtain a pre-trained resilience prediction model. This includes: pre-training the topology diffusion module based on a preset generation diffusion algorithm according to the network topology distribution in the sample observation data to obtain a pre-trained topology diffusion module; the topology diffusion module is used to generate the network topology distribution; pre-training the dynamics learning module using neural ordinary differential equations based on the dynamic state trajectories in the sample observation data to obtain a pre-trained dynamics learning module; the dynamics learning module is used to generate dynamic state trajectories; and pre-training the resilience prediction module using the Transformer algorithm and graph convolutional networks according to labeled data from the sample observation data to obtain a pre-trained resilience prediction module; the resilience prediction module is used to predict the resilience of complex network systems.

[0040] In this embodiment, the resilience prediction model includes a topology diffusion module, a dynamics learning module, and a resilience prediction module.

[0041] To improve resilience prediction performance and address the issue of insufficient labeled data, the topology diffusion module is pre-trained using the unlabeled network topology distribution from the sample observation data. This module learns the network topology distribution from the unlabeled data's network topology distribution. Consequently, new network topologies can be sampled from the learned distribution for training the resilience prediction module.

[0042] The dynamics learning module is pre-trained using unlabeled or labeled dynamic state trajectories from the sample observation data. The dynamics learning module uses neural-ODE to learn the node state changes of the network from the dynamic state trajectories in the sample observation data, which can simulate node states for enhanced topology, thereby deriving complete training samples for the resilience prediction module.

[0043] The resilience prediction module is pre-trained using labeled data from the sample observation data. The resilience prediction module is powered by Transformer and Graph Convolutional Networks (GCNs). It simulates the dynamic state of nodes and the interactions between nodes from the observed network topology distribution and the dynamic state trajectories of network nodes, respectively. It predicts the resilience by learning the low-dimensional embedding of the network.

[0044] As a preferred embodiment, based on unlabeled data in the sample observation data, a pre-trained resilience prediction model, and a preset graph data augmentation algorithm, labeled augmented data for model retraining is generated, including: determining the process topology based on the unlabeled data in the sample observation data; the process topology is the network topology distribution generated by the topology diffusion module in the reverse process; determining the process dynamic state trajectory generated by the dynamics learning module based on the process topology; determining the process resilience prediction result generated by the resilience prediction module based on the process topology and the process dynamic state trajectory; and guiding the generation of labeled augmented data based on the process resilience prediction result; the labeled augmented data includes the labeled augmented network topology distribution generated by the topology diffusion module and the labeled augmented dynamic state trajectory generated by the dynamics learning module.

[0045] The topology diffusion module and the dynamics learning module can generate network samples with topological structures and node state trajectories. However, the simulated node states are limited to an initial time period, corresponding to the maximum duration present in the training dataset. This forces the dynamics learning module to simulate time steps beyond its training range, resulting in questionable reliability. Therefore, the main challenge stems from the inability to determine the steady-state conditions of the generated network. This limitation hinders the possibility of directly obtaining resilience labels, posing a significant obstacle to data augmentation. To overcome this problem, this embodiment proposes a strategy to guide the topology diffusion module, enabling it to generate networks with predefined resilience characteristics. Specifically, classifier guidance is integrated into the topology diffusion model to determine the process topology (the network topology distribution generated by the topology diffusion module during the reverse process). G t Based on the process topology, the process dynamics state trajectory generated by the dynamics learning module is determined; the resilience prediction results obtained from the resilience prediction module trained on the labeled dataset (process topology and process dynamics state trajectory) are utilized. The conceptual basis of the guidance mechanism is that the resilience prediction module provides the resilience conditions of clean samples of intermediate samples generated by the topology diffusion model, thereby guiding the generation process to exhibit the desired resilience characteristics.

[0046] Therefore, by setting the desired final sample label to resilience ( y G =1) and the expected final sample label is non-resilient ( y G (=0) can generate new labeled network topologies guided by the resilience prediction module. These topologies are then used as input to simulate their respective node dynamic state trajectories through the dynamics learning module, which facilitates the augmentation of the dataset with additional fully labeled data. This allows for the retraining of the resilience prediction module, significantly improving its prediction accuracy and ensuring more reliable assessment of the resilience of complex network systems under conditions of scarce labeled data.

[0047] The principles of the topology diffusion module, dynamics learning module, and resilience prediction module are introduced below, taking the pre-training stage as an example. The principles of each module in the data augmentation stage and retraining stage are the same as those in the pre-training stage, and will not be elaborated here.

[0048] In a preferred embodiment, the topology diffusion module is pre-trained based on a preset generation diffusion algorithm according to the network topology distribution in the sample observation data. This includes: determining the node set and edge set to be input into the topology diffusion module based on the network topology distribution in the sample observation data; the forward process of the topology diffusion module pre-training is equivalent to sampling the edge type from the classification distribution based on the node set and edge set, resulting in a noisy topology graph; inputting the noisy topology graph into a pre-trained topology prediction network to obtain a predicted topology graph; and performing a reverse process of pre-training the topology diffusion module based on the noisy topology graph and the predicted topology graph to obtain a denoised topology graph.

[0049] Please refer to Figure 5 , Figure 5 This is a schematic diagram of the topology diffusion module provided by the present invention.

[0050] In this embodiment, the topology diffusion module uses a discrete diffusion model to model the network topology distribution of the unlabeled dataset. During training, the topology diffusion module is trained using the unlabeled networks in the dataset. Consider a dataset containing... Input topology of nodes ,in For a set of nodes, Let be an edge set, in which Represents a node and nodes There exists a connecting edge between them. A discrete type of noise is applied to each edge, meaning the type of noise can change during the diffusion process. Define each edge. At time step The transition probabilities are matrix ,in Representing an edge At time step From type Transform into type Directed graph structure Adding noise to the forward pass is equivalent to sampling the edge type from the classification distribution to obtain a noisy topological graph;

[0051] The reverse process aims to gradually transform a noisy graph. The original image was recovered from the image. That is, its output is a prediction graph. To this end, a parameterized neural network was trained. (Topology prediction network), which uses a noisy graph As input and predict the original graph The structure, i.e., nodes and The probability that an edge exists between them. The predicted topology is obtained. Binary cross-entropy loss is used to optimize the parameters. The formula is as follows:

[0052] BinaryCrossEntropy is the cross-entropy loss function, and its definition is:

[0053] for The parameterization employs a multi-layer graph transformer backbone structure. Intuitively, node features are updated at each layer via a self-attention mechanism, while edge features are updated from information about their head and tail nodes. Once the neural network is trained... This can be used to generate new network topologies. Specifically, the validation process after training first involves sampling a number of nodes based on the node distribution in the training set. This generates a node with a number of nodes. random graph The probability of each edge in the graph is the same as the probability of each edge in the training set. The total number of noise-adding steps in the diffusion model at the th step in the reverse process Step, needs to be estimated It can be broken down as follows:

[0054] in

[0055] in, For a given Under the condition that the model parameters are What I learned at that time The probability distribution, For a given Under the condition that the model parameters are What I learned at that time (i.e., node) and nodes The edge between them in the reverse process The probability distribution of the presence or absence of a step. for (Topology prediction network) with noisy graph As input and predict the original graph Middle node and There is a probability that an edge exists between them. For a given and the original image Middle node and The case where there are edges is At that time, node and nodes The edge between them in the reverse process The presence or absence of steps probability distribution For a given node, the calculation is based on Bayesian rules. and nodes The edge between them in the reverse process The existence state of step and the original image Middle node and The case where there are edges is At that time, node and nodes The edge between them in the reverse process The presence or absence of steps The probability distribution can be calculated using Bayes' rule. In the preset... After sampling, a new network topology (denoised topology graph) that follows the distribution of the unlabeled dataset can be generated.

[0056] As a preferred embodiment, the dynamic learning module is pre-trained using neural network ordinary differential equations based on the dynamic state trajectory in the sample observation data, including: encoding and mapping the node state in the dynamic state trajectory in the sample observation data to the latent space; learning the node state in the latent space using a graph neural network to obtain the latent space representation; and decoding and transforming the latent space representation to obtain the dynamic state trajectory representing the reconstructed node state.

[0057] In this embodiment, the topology diffusion module can generate new network topologies for training the resilience prediction module. However, it is also necessary to obtain their node dynamic state trajectories to predict their resilience. The node state dynamics in complex network systems typically have a generalized form of ordinary differential equations (ODEs):

[0058] in Indicates time step t time NNode network G state, Let W represent the dynamic function, and W represent all dynamic parameters. Therefore, the dynamics learning module aims to infer changes in node states solely from the data. This module learns node state dynamics in the expressive hidden space based on neural-ODE. Given the initial states of all network nodes... For each time step t The process first involves the encoder. The states of nodes in the dynamic state trajectory are mapped to a latent space. Then, graph neural networks (GNNs) are used as a parameterization technique to facilitate the dynamic learning of node states within this latent space, resulting in a latent space representation. This is achieved by using a decoder function. The latent space representation is decoded and transformed back to the node state at each time step. The decoder function then decodes the latent space embedding to reconstruct the dynamic state trajectory of the node state. This process can be represented as follows:

[0059] in, for The embedding of each node in the latent space of a complex network at a given time. for Given the model's predicted values ​​for the states of each node in a complex network at any given time, This is the integration step size.

[0060] GNNs can be implemented as graph convolutional layers of any design type. Without loss of generality, we choose to use multilayer perceptrons (MLPs) to implement the encoder. and decoder Functions. Furthermore, GNNs are instantiated through graph convolutional networks, thus leveraging their powerful ability to capture and process the inherent topological features of graphs. Using - The loss is used to train the dynamics learning module, as shown in the following formula:

[0061] in, for The state of each node in a complex network given at time t. for The model prediction of the state of each node in a complex network at a given time.

[0062] In unlabeled datasets and labeled datasets The dynamics learning module is trained to achieve better performance, and its input is... Step-by-step node state sequence After training is complete, given the initial states of all network nodes... The dynamics learning module can recover any node. exist State within a step .

[0063] As a preferred embodiment, the resilience prediction module is pre-trained using the Transformer algorithm and a graph convolutional network based on the labeled data in the sample observation data. This includes: encoding the temporal correlation of node states between time steps using the Transformer layer based on the dynamic state trajectory of nodes at each time step in the labeled data in the sample observation data; and learning the spatial interactions within the network topology distribution in the labeled data using a graph convolutional network.

[0064] In this embodiment, a resilience prediction module predicts the resilience of a complex network system based on labeled data. The input to the resilience prediction module is the network topology. and before Step-by-step node state evolution trajectory The resilience prediction module utilizes stacked Transformer layers to encode the temporal correlations of node states between time steps and uses a graph convolutional network to learn spatial interactions within the network topology distribution in labeled data. Specifically, for a dataset with... N A network of nodes, using d Observation steps and nodes u of M The trajectory represents the sequence of node states. For the first k Trajectory The state at each time step is input into a feedforward layer, and a Transformer layer is further used to encode the temporal correlation between time steps, as shown in the formula:

[0065] in and These are trainable parameters. Then, the embeddings of all nodes in the network at the terminal time step are integrated, represented as... As their first k Trajectory embedding.

[0066] To simulate the interactions between nodes within the topology, a graph convolutional network (GCN) powered by multi-layer message passing was designed. Given the adjacency matrix A of the network topology, the Laplace operator is first computed. ,in and The diagonal of the node represents its in-degree and out-degree. The node's first degree is... k The trajectory is embedded into the graph convolutional network, and its trace is... l Message passing at a layer can be represented as:

[0067] in and g (·) is implemented as a multilayer perceptron (MLP). For the node's Trajectory Embedded Through Embedding after message passing in layered graph convolutional networks. For the node's Trajectory Embedded Through Embedding after message passing in layered graph convolutional networks. This message passing design aims to more accurately simulate the effects from a specific node itself and its neighborhood.

[0068] It is worth noting that in the above process, different trajectories are processed in parallel. A trajectory attention module is further introduced to integrate information from different trajectories to obtain a better representation. Specifically, it will... L After layer message passing, the node embedding matrices of different trajectories are considered as combinations of feature maps. Mean pooling and max pooling are then performed on them, and the results are expressed as follows: and They are then fed into a shared multilayer perceptron and fused to derive trajectory attention weights, as shown in the following formula:

[0069] in ,and (·) denotes the Sigmoid activation function. Therefore, the fused node embedding matrix can be derived from the following formula:

[0070] in, For the first Attention weights for each trajectory For the node's Trajectory Embedded Through Embedding after message passing in layered graph convolutional networks.

[0071] in And ⊙ represents the Hadhamed product. A readout function is used to obtain the embedding of the entire network, i.e. The readout function is implemented as mean pooling among nodes. Then, the resilience of complex network systems is predicted as follows:

[0072] The resilience prediction module was trained using a labeled dataset and binary cross-entropy (BCE) loss.

[0073]

[0074] in For the network The true label, For the network predicted by the model, The number of networks used for training is [number]. However, the predictive performance of the resilience prediction module is generally below optimal, mainly due to the scarcity of data. Notably, after the training phase on labeled data, the resilience prediction module is further fine-tuned on the same topology, where node state trajectories are generated via the neural-ODE of the dynamics learning module. This allows the resilience prediction module to accurately adapt to the small differences observed between real trajectories and those generated through simulation, thus ensuring robust predictive performance.

[0075] To construct the dataset, three typical complex network systems from physics and life sciences were synthesized. Indicating time steps t Time node i The states of various complex network systems are described as follows: Reciprocal complex network systems. The dynamic processes governing these network systems. Describes the migration items B Environmental capacity K Logical growth terms, with threshold C Allee effect term and interactive network A Changes in species populations caused by mutually beneficial interactions among species. For species and species The interaction situation, For species The population size is denoted by D, E, and H, which are network system parameters.

[0076] Gene regulation is a complex network system. The dynamic processes governing this network system are called gene regulatory dynamics, also known as Michellis-Menten dynamics. describe. f Indicates degradation or dimerization Furthermore, the second term in the equation aims to capture gene activation with a Hill coefficient ℎ, used to quantify the degree of gene regulatory cooperation. Among these, For genes j The activity.

[0077] Neural complex network systems. The dynamic processes governing this network system are called neuronal dynamics, also known as Wilson-Cowen dynamics, and are governed by equations... Description. For each node in the network, it receives cumulative input from its neighbors. The second term of the equation represents the activation signal jointly contributed by all neighboring nodes. Wherein, These are system parameters.

[0078] For each dynamic, this embodiment synthesizes a dynamic with fewer than 60 nodes and an edge creation probability of less than 0.15. Random networks were used, and their node state trajectories were simulated using a fourth-order Runge-Kutta stepper. This embodiment created 2000 network samples for training, 200 samples for validation, and another 200 samples for testing. In the training dataset, 100 (5%) samples were randomly selected as labeled data, and the remaining 1900 samples were used as unlabeled data.

[0079] A resilient prediction model was implemented in PyTorch, and all training and testing tasks were completed on a single NVIDIA RTX 4090 GPU. This example generated 1000 new networks, evenly distributed among 500 resilient networks and 500 non-resilient networks. Half of these networks were then randomly selected as augmentation data. The guidance strength was set. =2000. The parameters of the resilience prediction model were optimized using the Adam optimizer and combined with Xavier initialization to ensure a robust starting point for learning. At least five experiments with different random seeds were performed for each experiment, and the average value was reported. Experimental results show that: This invention effectively improves prediction performance by generating complex network data containing topology and node states for retraining. Results show that the predictive performance of the resilient predictor is significantly enhanced with the data augmentation framework proposed in this invention. For example, on a reciprocal complex network system, the F1 score of the resilient prediction model, originally trained on 100 labeled datasets, increased from 0.838 to 0.929 (+10.86%), and its accuracy (ACC) increased from 0.848 to 0.934 (+10.14%). Furthermore, this invention also improves the F1 score by 4.26%, 4.89%, and 3.30% and the accuracy by 5.18%, 5.23%, and 4.80% respectively on the reciprocal, gene regulation, and neural complex network system datasets. All these results demonstrate the superior performance of this invention. It was found that the best baseline methods on the three datasets all belong to the graph data augmentation category. Compared to TRY and G-mixup, this invention enables fine-grained co-modeling of network topology and node state dynamics.

[0080] TDNetGen maintains robust performance even when node state trajectories in unlabeled datasets are available. Since even capturing the initial stages of node state evolution proves difficult or expensive in some cases, this invention analyzes scenarios where node state trajectories in unlabeled datasets are inaccessible—that is, scenarios where the invention can only train its dynamics learning module on node state trajectories in a limited set of labeled datasets. The experimental results in Table 1 demonstrate that even under these constrained conditions, the invention maintains excellent performance and surpasses the best baseline in most cases. This highlights the versatility of the invention and its effectiveness in situations with limited real-world data observations.

[0081] Data augmentation based on pseudo-labels cannot guarantee improved performance of resilience prediction models. Results show that, compared to TDNetGen, pseudo-label-based data augmentation has a relatively small positive impact on prediction performance across the three datasets. For example, on the Gene Regulation Complex Network System dataset, the F1 score of the resilience prediction model improved by 0.051, and the accuracy improved by 0.079. This is because the labels assigned to the augmented data during pseudo-label-based data augmentation originate from the resilience prediction model itself, which has suboptimal prediction performance. This method inherently carries the risk of assigning labels inconsistent with reality and potentially introducing contradictory information into the training data. The presence of these inaccurately labeled data may confuse the resilience prediction model, leading to a decline in its predictive ability.

[0082] Self-supervised learning models can only extract limited knowledge from unlabeled datasets to assist in resilience prediction tasks. The results show that, compared to this invention, the improvements of self-supervised learning models (ContextPred and Infomax) to the original models are still relatively small. The main reason for this observed difference lies in the significant difference between hand-designed self-supervised learning tasks and resilience prediction tasks. Hand-designed self-supervised learning tasks only focus on topological modeling, while resilience prediction tasks also need to consider the dynamic information of node states in complex networks.

[0083] Table 1 Comparison of Experimental Results

[0084] The resilience prediction system for complex network systems provided by this invention is described below. The resilience prediction system for complex network systems described below can be referred to in correspondence with the resilience prediction method for complex network systems described above.

[0085] Please refer to Figure 6 , Figure 6 This is a schematic diagram of the structure of a resilience prediction system for complex network systems provided by the present invention.

[0086] This invention also provides a resilience prediction system for complex network systems, comprising: an acquisition module 1, used to acquire observation data of the complex network system to be resilience predicted; the observation data includes network topology distribution and dynamic state trajectories of network topology nodes; a resilience prediction module 2, used to input the observation data into a resilience prediction model and obtain the resilience prediction result output by the resilience prediction model; wherein, the training system of the resilience prediction model includes: a pre-training module, used to pre-train the resilience prediction model based on labeled data in the sample observation data to obtain a pre-trained resilience prediction model; a data augmentation module, used to generate labeled augmented data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm; and a retraining module, used to retrain the pre-trained resilience prediction model based on the labeled data in the sample observation data and the generated labeled augmented data to obtain a retrained resilience prediction model, and to perform resilience prediction based on the retrained resilience prediction model.

[0087] Figure 7 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 7As shown, the electronic device may include: a processor 710, a communications interface 720, a memory 730, and a communications bus 740, wherein the processor 710, the communications interface 720, and the memory 730 communicate with each other through the communications bus 740. The processor 710 can call logic instructions in the memory 730 to execute a resilience prediction method for complex network systems. This method includes: acquiring observation data of the complex network system to be resiliently predicted; the observation data includes the network topology distribution and the dynamic state trajectories of the network topology nodes; inputting the observation data into a resilience prediction model to obtain the resilience prediction result output by the resilience prediction model; wherein the training method of the resilience prediction model includes: pre-training the resilience prediction model based on labeled data in the sample observation data to obtain a pre-trained resilience prediction model; generating labeled augmented data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm; retraining the pre-trained resilience prediction model based on the labeled data in the sample observation data and the generated labeled augmented data to obtain a retrained resilience prediction model, and performing resilience prediction based on the retrained resilience prediction model.

[0088] Furthermore, the logical instructions in the aforementioned memory 730 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0089] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the resilience prediction method for complex network systems provided by the above methods. The method includes: acquiring observation data of the complex network system to be resilience predicted; the observation data includes network topology distribution and dynamic state trajectories of network topology nodes; inputting the observation data into a resilience prediction model to obtain the resilience prediction result output by the resilience prediction model; wherein, the training method of the resilience prediction model includes: pre-training the resilience prediction model based on labeled data in the sample observation data to obtain a pre-trained resilience prediction model; generating labeled augmented data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm; retraining the pre-trained resilience prediction model based on the labeled data in the sample observation data and the generated labeled augmented data to obtain a retrained resilience prediction model, and performing resilience prediction based on the retrained resilience prediction model.

[0090] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements a method for predicting the resilience of complex network systems provided by the methods described above. This method includes: acquiring observation data of the complex network system to be resiliently predicted; the observation data includes network topology distribution and dynamic state trajectories of network topology nodes; inputting the observation data into a resilience prediction model to obtain a resilience prediction result output by the resilience prediction model; wherein the training method of the resilience prediction model includes: pre-training the resilience prediction model based on labeled data in the sample observation data to obtain a pre-trained resilience prediction model; generating labeled augmented data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm; retraining the pre-trained resilience prediction model based on the labeled data in the sample observation data and the generated labeled augmented data to obtain a retrained resilience prediction model, and performing resilience prediction based on the retrained resilience prediction model.

[0091] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0092] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the resilience of complex network systems, characterized in that, include: Acquire observational data of a complex network system whose resilience needs to be predicted; the observational data includes the network topology distribution and the dynamic state trajectories of the network topology nodes; the complex network system is an ecosystem, where different components represent multiple species, and the relationships between species are represented by the connections between components; components are abstracted as nodes, and the connections between nodes are abstracted as edges; Input the observed data into the resilience prediction model to obtain the resilience prediction results output by the resilience prediction model; The training method for the resilience prediction model includes: The resilience prediction model is pre-trained based on the labeled data in the sample observation data to obtain the pre-trained resilience prediction model. Based on the unlabeled data in the sample observation data, the pre-trained resilience prediction model, and the preset graph data augmentation algorithm, labeled augmented data for model retraining is generated. Based on the labeled data in the sample observation data and the generated labeled augmented data, the pre-trained resilience prediction model is retrained to obtain the retrained resilience prediction model, and resilience prediction is performed based on the retrained resilience prediction model. The resilience prediction model includes a topology diffusion module, a dynamics learning module, and a resilience prediction module. The process of pre-training the resilience prediction model based on labeled data from sample observation data to obtain a pre-trained resilience prediction model includes: Based on the network topology distribution in the sample observation data, the topology diffusion module is pre-trained using a preset generation diffusion algorithm to obtain a pre-trained topology diffusion module; the topology diffusion module is used to generate network topology distribution. Based on the dynamic state trajectory in the sample observation data, the dynamic learning module is pre-trained using a neural ordinary differential equation to obtain a pre-trained dynamic learning module; the dynamic learning module is used to generate dynamic state trajectories. Based on the labeled data in the sample observation data, the resilience prediction module is pre-trained using the Transformer algorithm and graph convolutional network to obtain the pre-trained resilience prediction module; the resilience prediction module is used to predict the resilience of complex network systems. The process of generating labeled augmented data for model retraining based on unlabeled data from the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm includes: The process topology is determined based on the unlabeled data in the sample observation data; the process topology is the network topology distribution generated by the topology diffusion module during the reverse process. Based on the process topology, the process dynamics state trajectory generated by the dynamics learning module is determined; Based on the process topology and the process dynamics state trajectory, the process toughness prediction result generated by the toughness prediction module is determined; The labeled augmented data is generated based on the process resilience prediction results; the labeled augmented data includes the labeled augmented network topology distribution generated by the topology diffusion module and the labeled augmented dynamic state trajectory generated by the dynamics learning module.

2. The method for predicting the resilience of complex network systems according to claim 1, characterized in that, The step of pre-training the topology diffusion module based on a preset generation and diffusion algorithm according to the network topology distribution in the sample observation data includes: Based on the network topology distribution in the sample observation data, determine the node set and edge set to be input to the topology diffusion module; Based on the node set and the edge set, the forward process of the topology diffusion module pre-training is equivalent to sampling the edge type from the classification distribution to obtain a noisy topology graph; The noisy topology graph is input into a pre-trained topology prediction network to obtain a predicted topology graph. Based on the noisy topology graph and the predicted topology graph, the topology diffusion module is pre-trained in reverse to obtain the denoised topology graph.

3. The method for predicting the resilience of complex network systems according to claim 1, characterized in that, The step of pre-training the dynamics learning module using neural ordinary differential equations based on the dynamic state trajectories in the sample observation data includes: The node state encodings in the dynamic state trajectories of the sample observation data are mapped to the latent space; In the latent space, the node states are learned using a graph neural network to obtain the latent space representation; The latent space representation is decoded and transformed to obtain the dynamic state trajectory that represents the state of the reconstructed node.

4. The method for predicting the resilience of complex network systems according to any one of claims 1 to 3, characterized in that, The step of pre-training the resilience prediction module using the Transformer algorithm and graph convolutional network based on the labeled data in the sample observation data includes: Based on the dynamic state trajectory of the node at each time step in the labeled data of the sample observation data, the temporal correlation of the node state between time steps is encoded using the Transformer layer. The graph convolutional network is used to learn the spatial interactions within the network topology distribution of the labeled data.

5. A resilience prediction system for complex network systems, characterized in that, include: The acquisition module is used to acquire observation data of the complex network system to be resilience predicted; the observation data includes the network topology distribution and the dynamic state trajectory of the network topology nodes; the complex network system is an ecosystem, different components represent multiple species, and the relationship between species is represented by the connection relationship between components; components are abstracted as nodes, and the connection relationship between nodes is abstracted as edges; The resilience prediction module is used to input the observed data into the resilience prediction model and obtain the resilience prediction results output by the resilience prediction model. The training system for the resilience prediction model includes: The pre-training module is used to pre-train the resilience prediction model based on the labeled data in the sample observation data to obtain the pre-trained resilience prediction model. The data augmentation module is used to generate labeled augmented data for model retraining based on unlabeled data in the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm. The retraining module is used to retrain the pre-trained resilience prediction model based on the labeled data in the sample observation data and the generated labeled augmented data to obtain the retrained resilience prediction model, so as to perform resilience prediction based on the retrained resilience prediction model. The resilience prediction model includes a topology diffusion module, a dynamics learning module, and a resilience prediction module. The process of pre-training the resilience prediction model based on labeled data from sample observation data to obtain a pre-trained resilience prediction model includes: Based on the network topology distribution in the sample observation data, the topology diffusion module is pre-trained using a preset generation diffusion algorithm to obtain a pre-trained topology diffusion module; the topology diffusion module is used to generate network topology distribution. Based on the dynamic state trajectory in the sample observation data, the dynamic learning module is pre-trained using a neural ordinary differential equation to obtain a pre-trained dynamic learning module; the dynamic learning module is used to generate dynamic state trajectories. Based on the labeled data in the sample observation data, the resilience prediction module is pre-trained using the Transformer algorithm and graph convolutional network to obtain the pre-trained resilience prediction module; the resilience prediction module is used to predict the resilience of complex network systems. The process of generating labeled augmented data for model retraining based on unlabeled data from the sample observation data, the pre-trained resilience prediction model, and a preset graph data augmentation algorithm includes: The process topology is determined based on the unlabeled data in the sample observation data; the process topology is the network topology distribution generated by the topology diffusion module during the reverse process. Based on the process topology, the process dynamics state trajectory generated by the dynamics learning module is determined; Based on the process topology and the process dynamics state trajectory, the process toughness prediction result generated by the toughness prediction module is determined; The labeled augmented data is generated based on the process resilience prediction results; the labeled augmented data includes the labeled augmented network topology distribution generated by the topology diffusion module and the labeled augmented dynamic state trajectory generated by the dynamics learning module.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the resilience prediction method for complex network systems as described in any one of claims 1 to 4.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the resilience prediction method for complex network systems as described in any one of claims 1 to 4.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the resilience prediction method for complex network systems as described in any one of claims 1 to 4.

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