Method for predicting complex network public opinion evolution based on high-order interaction and multi-theme coupling

Abstract

This invention discloses a method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling, belonging to the field of online public opinion data processing technology. The method includes the following steps: constructing a multi-layer network topology based on a simple complex structure, and dynamically determining core input data based on the multi-layer network topology; using dynamic core control parameters as weight coefficients, and based on the core input data, dynamically controlling the interaction intensity between individuals and the correlation degree between topic layers through dynamic equations, iteratively calculating each interaction term of all individual nodes in the multi-layer network topology until the system reaches a steady state, obtaining the global order parameters of each topic layer; dynamically detecting whether a bistable region exists in the evolution of complex online public opinion based on the global order parameters; if it exists, dynamically destabilizing the high-order interaction intensity; if it does not exist, using the global order parameters as the objective function, dynamically optimizing the high-order interaction intensity.

Description

Technical Field

[0001] This invention relates to the field of online public opinion data processing technology, and in particular to a method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling. Background Technology

[0002] In today's digital society, social media platforms have formed a highly connected and dynamically evolving complex public opinion system. Information within this system exhibits multi-center, non-linear, and abrupt diffusion characteristics, making it difficult to predict the evolution of public opinion using traditional monitoring methods. Therefore, complex network public opinion evolution prediction—a method based on complex network theory, system dynamics, and information propagation models to simulate and infer the diffusion path, group interaction, and trend development of public opinion—has become crucial. This method has significant application value in areas such as public emergency management, brand reputation risk prevention and control, policy feedback evaluation, and social stability early warning. Its core significance lies in providing decision-makers with a critical time window and scientific basis by identifying risks in advance and grasping public opinion fluctuations, thereby achieving a shift from passive response to proactive guidance and improving the accuracy and foresight of social governance.

[0003] However, current mainstream technical models supporting this prediction (such as the classic Kuramoto model and Deffuant model) have significant limitations and are difficult to match the complexity of the aforementioned real-world public opinion systems. Their shortcomings are mainly reflected in three aspects: First, the interaction models are overly simplified, mostly based on binary interaction assumptions, ignoring the nonlinear impact of high-order interactions among multiple people on the evolution of viewpoints in scenarios such as group pressure and echo chamber effects; second, the topic settings are too isolated, usually only simulating the evolution of a single topic, failing to consider the cognitive coupling and viewpoint transfer that exist between real individuals on multiple related topics; third, there are biases in the regulation of cognition, generally employing linear intervention strategies (such as simple connection enhancement), failing to reveal the possible non-monotonic relationship between the intensity of high-order interactions and group consensus, leading to the possibility that inappropriate intervention may exacerbate viewpoint fragmentation in practical applications. Therefore, in order to more accurately predict real public opinion and achieve effective guidance, it is urgent to break through the traditional framework and develop a new modeling method that can integrate multi-topic coupling and high-order network interactions. Summary of the Invention

[0004] To overcome the shortcomings of existing public opinion analysis and opinion dynamics models, which only consider binary interactions, ignore multi-topic coupling, and have a single control strategy, this invention provides a method for predicting the evolution of complex network public opinion based on high-order interactions and multi-topic coupling. This method includes: constructing a multi-layer network topology based on a simple complex structure, and dynamically determining core input data based on the multi-layer network topology. The simple complex structure includes points, edges, and triangles. Using dynamic core control parameters as weight coefficients, based on the core input data, the interaction strength between individuals and the correlation degree between topic layers are dynamically controlled through dynamic equations. Iterative calculations are performed on each interaction term of all individual nodes in the multi-layer network topology until the system reaches a steady state, obtaining the global data for each topic layer. The order parameters, the core dynamic control parameters, include pairwise interaction strength, higher-order interaction strength, and interlayer coupling strength. Interaction terms include pairwise interaction terms, higher-order interaction terms, and multi-topic coupling terms. The core input data serve as the computational input and structural basis for the corresponding interaction terms, driving and quantifying the dynamic processes simulated by the interaction terms. Based on the global order parameters, the system dynamically detects whether there is a bistable region in the evolution of public opinion in complex networks. If it exists, the higher-order interaction strength is dynamically destabilized to eliminate bistable risks and restore the system to monostable state. If it does not exist, the higher-order interaction strength is dynamically optimized using the global order parameters as the objective function. The global order parameters include forward-evolution steady-state order parameters and backward-evolution steady-state order parameters.

[0005] Beneficial effects Numerical simulations of this invention were performed in a Python environment. The simulation results show that this invention has the following beneficial effects: 1. Compared to traditional simple network models built solely with points and edges, this invention introduces a simple complex structure including points, edges, and triangles. It quantifies the interaction effects of groups of three or more (such as WeChat groups or meeting discussions) through high-order interaction intensity, accurately capturing the nonlinear effects of group pressure in real-world social networks, such as the "three men make a tiger" phenomenon and the echo chamber effect. Simultaneously, it combines a cognitive coupling matrix of multiple topic layers within individual nodes to fully reproduce the cognitive dependencies between related topics. Numerical simulation results show that this topology modeling method improves the fit between the speed and pattern of public opinion dissemination and real-world social network data by approximately 15%-20% compared to traditional models, significantly enhancing the fidelity of public opinion evolution scenarios.

[0006] 2. This invention successfully plots a bistable hysteresis loop by systematically scanning the parameter space of high-order interaction intensity and combining the calculation and analysis of global order parameters. Simulation results show that when the simple complex interaction intensity is too large, the system will exhibit a significant bistable region. At this time, by comparing the forward-evolving steady-state order parameters with the backward-evolving steady-state order parameters, if the absolute deviation between the two exceeds a preset judgment threshold, the bistable risk interval can be accurately located. Once public opinion falls into a disordered state within this interval, even if the initial external environment is restored, consensus is difficult to re-establish. The early warning mechanism of this invention can identify this risk in advance, providing a precise basis for the timing and scope of intervention for public opinion management.

[0007] 3. This invention verifies through simulation the non-monotonic relationship (camel hump effect) between the intensity of higher-order interactions and the system synchronization level (order parameter), contrary to the traditional strategy's assumption that enhanced interaction equates to improved consensus. Simulation results show that there exists an optimal higher-order interaction intensity of approximately 0.58. When the higher-order interaction intensity is adjusted to this optimal value, the system can fully utilize the accelerated consensus advantage of higher-order interactions while avoiding the fragmentation of viewpoints and bistable risks caused by excessive higher-order interaction intensity. Compared to the traditional linear adjustment strategy of blindly enhancing node connections, the non-monotonic optimization strategy of this invention significantly improves the final consensus level (order parameter amplitude) of the system, and the distribution of viewpoints at each topic level exhibits a single-peak concentration, effectively verifying the scientific validity and efficiency of using higher-order nonlinear effects to assist in consensus achievement. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 A flowchart of a complex online public opinion evolution prediction method based on high-order interaction and multi-topic coupling provided in an embodiment of this application; Figure 2 A flowchart illustrating the high-order dynamics evolution and risk assessment of a complex online public opinion evolution prediction method based on high-order interaction and multi-topic coupling, provided for embodiments of this application; Figure 3 A multi-layer network topology diagram based on a simple complex structure is provided in the embodiments of this application; Figure 4 The evolution diagram of the order parameters over time for different network structures provided in the embodiments of this application.

[0010] Figure 5 The evolution diagram of the order parameters for different pairwise interaction intensities under different higher-order interaction intensities is provided in the embodiments of this application.

[0011] Figure 6 The diagram illustrates the impact of high-order interaction intensity on viewpoint fragmentation, as provided in the embodiments of this application.

[0012] Figure 7 The non-monotonic effect curve of high-order interaction intensity provided in the embodiments of this application. Detailed Implementation

[0013] Embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of the present disclosure are shown in the drawings, it should be understood that embodiments of the present disclosure may be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present disclosure.

[0014] It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure. In the description of the embodiments of this disclosure, the terms "including" and similar expressions should be understood as open-ended, i.e., including but not limited to. The term "based on" should be understood as at least partially based on. The term "an embodiment" or "this embodiment" should be understood as at least one embodiment.

[0015] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0016] like Figure 1 The diagram shows a flowchart of a complex network public opinion evolution prediction method based on high-order interaction and multi-topic coupling provided in this application embodiment. It clearly presents the core pre-process of public opinion evolution modeling, divided into three key steps: Step S1 is multi-layer high-order network construction, the core of which is to build a simple complex structure containing points, edges, and triangles, define the network adjacency matrix of binary connections between nodes and the cognitive coupling matrix between topic layers, and complete the network topology initialization; Step S2 is dynamic initialization, establishing multi-topic high-order dynamic equations containing paired interaction terms, high-order interaction terms, and multi-topic coupling terms, clarifying the boundary of action of each core control parameter; Step S3 is critical point and early warning, calculating the steady-state order parameters of forward evolution and backward evolution through mean-field dynamic evolution, detecting whether the system has bistable states based on the order parameter characteristics, and then branching to bistable risk handling (continued). Figure 2 ) or monostable range optimization (connected to) Figure 2 This provides a basis for subsequent control strategies. The method includes the following steps: constructing a multi-layer network topology of a complex network based on a simple complex structure, and dynamically determining the core input data based on the multi-layer network topology. The simple complex structure contains points, edges, and triangles, where the network adjacency matrix is ​​determined by the edges representing the binary connections between individual nodes in the topology, and its elements... The model directly corresponds to whether there is a one-to-one connection between nodes i and j; the higher-order correlation tensor is derived from the triangle representing the interaction of groups of three or more people in the topology, and is used to quantify the higher-order interaction correlation at the group level; the initial phase distribution is based on the setting of multiple topic layers within individual nodes in the topology, and the initial viewpoint state of each topic layer is assigned in the form of phase. Combined with the cognitive coupling relationship between topic layers within the node, the initial state data of each node in different topic dimensions are formed. The three together constitute the core input for public opinion evolution modeling; using the core dynamic control parameters as weight coefficients, based on the core input data, the interaction strength between individuals and the correlation degree between topic layers are dynamically controlled through dynamic equations. The interaction terms of all individual nodes in the multi-layer network topology are iteratively calculated until the system reaches a steady state, simulating the dynamic evolution process of public opinion over time, and thus obtaining a system reflecting the evolution of public opinion. The system uses global order parameters for each topic layer in a synchronized state to achieve a balance between public opinion evolution, consensus level, and risk control. The core dynamic control parameters include pairwise interaction strength, higher-order interaction strength, and inter-layer coupling strength. Interaction terms include pairwise interaction terms, higher-order interaction terms, and multi-topic coupling terms. Core input data serve as the computational input and structural basis for the corresponding interaction terms, driving and quantifying the dynamic process simulated by the interaction terms. Based on the global order parameters, the system dynamically detects whether there is a bistable region in the evolution of public opinion in the complex network. If it exists, the higher-order interaction strength is dynamically destabilized to eliminate bistable risks and restore the system to monostable state, so that the system returns to the monostable range. If it does not exist, the higher-order interaction strength is dynamically optimized using the global order parameters as the objective function. The global order parameters include forward-evolution steady-state order parameters and backward-evolution steady-state order parameters.

[0017] like Figure 2 The diagram shown is a flowchart of the high-order dynamics evolution and risk assessment of a complex network public opinion evolution prediction method based on high-order interaction and multi-topic coupling provided in this application embodiment. Figure 1 The bistable detection results are divided into two main branches: For the monostable interval (B branch), the process enters the S4 non-monotonic consensus optimization stage. By scanning the high-order interaction strength parameter space, a synchronization level-high-order strength curve is plotted to determine whether there is a non-monotonic peak (camel hump effect). If it exists, the optimal high-order strength is located, and strategy B (adjusting to the optimal high-order strength to improve consensus using stochastic resonance) is executed. If it does not exist, a conventional linear enhancement strategy is adopted. For the bistable risk (A branch), the process directly enters the S5 regulation and intervention stage, and strategy A (reducing the high-order interaction strength to break the echo chamber and eliminate bistableness) is executed. Finally, the optimal regulation instruction adapted to the current network state is output to achieve a balance between consensus level and risk control.

[0018] like Figure 3The diagram shown is a multi-layer network topology diagram based on a simple complex structure provided in this application embodiment, which visualizes the model structure from two dimensions: macroscopic network and microscopic individual. The left diagram shows the macroscopic multi-layer network topology, where dots represent individual nodes and thin solid lines represent binary connections between nodes (corresponding to...). (representing paired interactions), filled with gray triangles to represent higher-order groups of three or more people (corresponding to...) The key individuals marked by dashed circles (representing higher-order interactions) are the primary targets of regulatory strategies. Because these individuals are located at the intersection of multiple higher-order structures, they significantly influence consensus formation and polarization evolution. The right figure shows the internal cognitive structure of a micro-individual. The large circle represents the individual's cognitive space, and the smaller nodes inside represent different topic layers (e.g., Topic 1-3). These topic layers are connected by dashed lines, visually representing the cognitive coupling relationship where individuals' attitudes influence each other on different topics. This provides structural visualization support for the calculation of multi-topic coupling terms. The points in the multi-layer network topology represent individual nodes in a complex network. Multiple topic layers exist within each individual node, and cognitive dependencies are established between them through a cognitive coupling matrix, simulating the mutual influence of individuals' attitudes on different topics. Edges serve as the network adjacency matrix, representing binary connections between individual nodes. Triangles serve as higher-order association tensors, representing group interactions of three or more people. Core input data includes the network adjacency matrix, higher-order association tensors, and initial phase distribution.

[0019] In this embodiment, the present invention innovatively introduces a simple complex structure to construct a multi-layer network topology. Points and edges represent individual binary connections, and triangles characterize interactions in groups of three or more people. Combined with the cognitive coupling relationships between multiple topic layers within nodes, it accurately captures high-order nonlinear influences in real-world social networks such as group pressure and the echo chamber effect. This improves the fit between the speed and pattern of public opinion dissemination and real data by 15%-20%. Compared to traditional models that only consider binary interactions, it achieves a more realistic topological representation and more accurate evolutionary prediction, effectively reproducing the phenomena of extreme and fragmented viewpoints. By establishing a dynamic equation containing pairwise interaction terms, higher-order interaction terms, and multi-topic coupling terms, and using pairwise interaction strength, higher-order interaction strength, and inter-layer coupling strength as core control parameters, it achieves dynamic control of the interaction strength between individuals and the degree of correlation between topic layers, enabling comprehensive analysis of different topics. The interpenetration of viewpoints across topics provides a more comprehensive and multi-dimensional profile of public opinion. By calculating and comparing the steady-state order parameters of forward and backward evolution, the system can accurately detect bistable risk areas. Strategy A reduces the intensity of higher-order interactions, breaking the solidified echo chamber and eliminating irreversible disorder, thus providing effective early warning for public opinion control. For monostable intervals, non-monotonic peak effects are mined by scanning the parameter space of higher-order interactions. Strategy B adjusts the parameters to the optimal higher-order intensity to maximize consensus through stochastic resonance. At the same time, the complementary relationship between paired interaction intensity and higher-order interaction intensity is utilized to balance the convergence speed of public opinion and the stability of consensus, avoiding the fragmentation of viewpoints that may be caused by traditional linear control strategies. Ultimately, a multi-dimensional balance is achieved in terms of the accuracy of public opinion evolution prediction, the effectiveness of risk prevention and control, and the efficiency of consensus guidance, adapting to the differentiated control needs of different network topologies.

[0020] Furthermore, the core formula of the dynamic equation is as follows: ; In the formula, i is the individual node identifier, i=1, 2, 3, ..., N, N is the total number of nodes, p is the topic layer identifier, p=1, 2, 3, ..., M, M is the total number of topic layers followed by each node; This represents the viewpoint phase of node i at time t in the topic at layer p. Let be the initial phase distribution of individual i on the p-th layer topic, representing the initial viewpoint setting, with the value range corresponding to the viewpoint angle. The intrinsic frequency term represents the inherent viewpoint tendency of individual i towards the topic at layer p, and is the intrinsic frequency when unaffected by external interactions. For paired interaction items, For higher-order interaction items, This is a multi-topic coupling item.

[0021] The core formula for paired interaction terms is as follows: ; In the formula, For pairwise interaction strength, Let i be the network adjacency matrix between node i and node j. =1 indicates that there is a binary connection between node i and node j (such as a friend relationship, peer-to-peer comment / private message interaction). =0 indicates that node i is not connected to node j. This represents the difference in opinion between node j and node i on topic p.

[0022] The core formula for higher-order interaction terms is as follows: ; In the formula, For higher-order interaction strength, The higher-order correlation tensor formed by nodes i, j, and k is generated based on the triangular structure of the simplex complex. =1 indicates that nodes i, j, and k form a high-order group of three or more people, pushing i to align with the group's viewpoint (group pressure). =0 indicates that nodes i, j, and k do not form a higher-order group, and their influence cancels each other out. , where is the sum of the opinion biases between individual i and the higher-order group (i,j,k).

[0023] The core formula for the multi-topic coupling term is as follows: ; In the formula, D represents the interlayer coupling strength. Let p and q be the cognitive coupling matrix of the topic layers. Let represent the opinion bias of node i on topics p and q.

[0024] In this embodiment, the dynamic equation provided by the present invention innovatively integrates paired interaction terms, higher-order interaction terms and multi-topic coupling terms to construct a complete driving mechanism that takes into account both micro-level individual interaction and macro-level public opinion evolution. This achieves a systematic breakthrough over the core defects of traditional models, with significant technical effects and multi-dimensional synergy. Among them, the pairwise interaction item accurately quantifies the impact of binary connections between individuals (such as friend interaction and peer-to-peer comments) by leveraging the pairwise interaction strength and network adjacency matrix, while also characterizing the driving force of opinion bias on dissemination, ensuring the authenticity and efficiency of basic information dissemination, and providing underlying interaction support for public opinion evolution; the higher-order interaction item captures the group pressure effect of groups of three or more people through higher-order interaction strength and higher-order correlation tensors, and successfully reproduces the phenomenon of opinion extremism and fragmentation that traditional binary models cannot explain by relying on the cumulative sum of opinion bias between individuals and groups, improving the fit between the speed and pattern of public opinion dissemination and real data by 15%-20%, and significantly improving the accuracy of evolution prediction; the multi-topic coupling item quantifies the cognitive dependence between different topic layers by using inter-layer coupling strength and cognitive coupling matrix, while reflecting the cross-topic opinion linkage of individuals, breaking the limitations of single-topic analysis, and clearly presenting the mutual penetration process of opinions on related topics such as policy and people's livelihood, economy and environmental protection, providing a more comprehensive and three-dimensional public opinion profile. Through the synergistic effect of these three factors, the equation not only ensures the basic efficiency of information dissemination through paired interaction strength and accurately characterizes the nonlinear impact of "small group pressure" through higher-order interaction strength, and realizes multi-topic correlation analysis through cognitive coupling matrix, but also provides core quantitative basis for accurate early warning of bistable risks by relying on the non-monotonic effect of higher-order interaction strength and the simple complex structure corresponding to higher-order correlation tensors. It supports the intelligent adaptation of strategy A (reducing higher-order interaction strength to break the echo chamber) and strategy B (adjusting to the optimal higher-order interaction strength to utilize stochastic resonance), which significantly improves the system consensus level (R value). Ultimately, it achieves the technical goal of "more accurate prediction, more multi-dimensional perspective, and more intelligent regulation". It not only solves the shortcomings of traditional models that only consider binary interaction and ignore multi-topic coupling and nonlinear regulation, but also achieves a dynamic balance between public opinion evolution-driven, risk prevention and control and consensus enhancement through flexible iteration and collaborative optimization of various parameters.

[0025] Furthermore, the core formulas for the global order parameters of each topic layer are as follows: ; In the formula, This represents the global order parameter for the topic at level p. The magnitude of the order parameter for the p-th layer topic reflects the group synchronization level of the p-th layer topic. The closer it is to 1, the more concentrated the group's views on the topic and the higher the degree of consensus (as in a fully connected network). ≈1), which can not only clearly distinguish the differences in public opinion convergence under different network structures such as fully connected, group, chain, and center-radial (e.g., in the fully connected structure) ≈1 reflects high consensus in a chain structure. (Long-term moderate level reflects the semi-synchronous dilemma), and can also accurately capture the dynamic impact of pairwise interaction strength and higher-order interaction strength on consensus (such as when pairwise interaction strength increases). Rapidly rising, after the intensity of higher-order interactions exceeds the optimal value. The decline exhibits a non-monotonic effect, which solves the problem that traditional models have difficulty quantifying the degree of consensus; The magnitude of the order parameter for the p-th layer topic corresponds to the core angle in the polar coordinate graph, representing the area where the majority of individuals' opinions are concentrated. It reflects the mainstream attitude tendency of public opinion. For example, when φ = π / 2, it indicates that most people hold the viewpoint corresponding to that angle. This breaks the limitation of only focusing on the strength of consensus while ignoring the direction of attitude, providing an intuitive basis for understanding the core direction of public opinion. Through the synergistic effect of these two factors, this formula achieves a dual quantification of "degree of consensus" and "mainstream attitude" in the evolution of public opinion, providing a basis for bistable risk detection (by comparing forward and backward evolution). Determining bistable states provides key indicator support and lays the foundation for the precise implementation of control strategies—through tracking It can locate the optimal high-order strength to execute strategy B to improve consensus, by monitoring An abnormal decline can be promptly addressed by initiating Strategy A to reduce the intensity of high-order interactions and break the echo chamber, ultimately enabling public opinion analysis to move from "qualitative description" to "quantitative decision-making," significantly improving the accuracy of predictions and the targeted and effective nature of regulation.

[0026] Furthermore, the steps for detecting the existence of bistable regions in the evolution of complex network public opinion based on global order parameters include: under the same pairwise interaction strength and inter-layer coupling strength, the higher-order interaction strength is gradually increased from 0 to a preset maximum value, and the magnitude of the order parameter when the system reaches steady state is recorded as the forward-evolving steady-state order parameter; the higher-order interaction strength is gradually decreased from the maximum value to 0, and the magnitude of the order parameter when the system reaches steady state is recorded as the backward-evolving steady-state order parameter; the absolute deviation between the forward-evolving steady-state order parameter and the backward-evolving steady-state order parameter is recorded as the bistable deviation, and the bistable deviation is compared with a preset bistable determination threshold. If the bistable deviation exceeds the bistable determination threshold, a bistable region is determined to exist; if the bistable deviation does not exceed the bistable determination threshold, a bistable region is determined not to exist.

[0027] If a bistable region exists, the difference between the bistable deviation and the bistable determination threshold is recorded as the bistable risk excess. Based on the bistable risk excess, a pre-stored excess-adjustment step size combination mapping model is dynamically invoked to obtain the adjustment step size. The excess-adjustment step size combination mapping model is based on pre-stored multiple sets of numerical simulation data, establishing the correspondence rules between each bistable risk excess range and the adjustment step size. It can dynamically output an adjustment step size adapted to the bistable risk excess. The more excesses remain, the larger the step size. The maximum step size does not exceed the pre-stored safe upper limit of pairwise interaction strength to avoid over-enhancement leading to viewpoint polarization. The real-time values ​​of high-order interaction strengths in the current multi-layer network topology are extracted. Based on the network topology structure type (including fully connected structure, cluster structure, chain structure, and center-radial structure) and the current values ​​of pairwise interaction strengths, a pre-stored topology-pairwise interaction strength combination mapping model is dynamically invoked to obtain an adjustment step size adapted to the current network state. The destabilization threshold for higher-order interaction strength is determined by a topology-paired interaction strength combination mapping model. This model is based on pre-stored multiple sets of numerical simulation data. It establishes a correspondence rule between the combination relationship between network topology structure type and paired interaction strength and the destabilization threshold for higher-order paired interaction strength. This model can dynamically output a mapping model that adapts to the current topology characteristics and the destabilization threshold for higher-order paired interaction strength. The real-time value of the higher-order interaction strength is adjusted by gradually decreasing the adjustment step size. After each adjustment, the bistable deviation and the order parameters of each topic are recalculated by substituting them into the dynamic equation to verify whether the deviation does not exceed the judgment threshold. If it still does not meet the requirement, the above incremental optimization process is repeated until the bistable deviation drops below the judgment threshold and the system order parameters show a stable upward trend. This achieves coordinated control of the destabilization threshold for paired interaction strength and higher-order interaction strength, completely eliminating the bistable risk until the bistable deviation does not exceed the bistable judgment threshold.

[0028] If no bistable region exists, then the optimization parameter space for high-order interaction strength is dynamically obtained based on the multi-topic coupling matrix and the network adjacency matrix [K2]. min K2 max ], where K2 min It is the minimum value of the higher-order interaction strength optimization parameter, with the goal of stimulating effective higher-order interactions, and its value is related to... The spectral radius is positively correlated when When the spectral radius is large, indicating tight cognitive coupling between topics, individuals exhibit strong cross-topic viewpoint linkages, K2 min It can be appropriately reduced, as topic coupling can already help the group resonate, and there is no need for excessively high-level intensity; when When the spectral radius is small, i.e. the topics are relatively independent, K2 min Improvements are needed to compensate for the lack of natural connections between topics, while also combining... average degree The lower the average degree, the sparser the node connections. K2min A higher value enhances propagation efficiency through higher-order group interactions. K2 max It is the maximum value of the higher-order interaction strength optimization parameter, to avoid viewpoint fragmentation as a constraint, and its value is related to... The clustering coefficients are positively correlated; the higher the clustering coefficient, the denser the local node connections. max Lower values ​​prevent the formation of closed high-order groups in dense local areas, which could lead to polarization; at the same time, reference is made to... The higher the proportion of non-zero elements (the broader the topic relevance), the better. max It needs to be appropriately lowered to avoid over-amplifying differences in viewpoints due to the cross-coupling of multiple topics, and ultimately through integration. The correlation strength index and The density, clustering coefficient, and other characteristic parameters are used to determine the boundary of the optimization interval suitable for the current network structure through simulation fitting. The average amplitude of the order parameter of each topic layer is used as the objective function, and a gridded scan of the higher-order interaction intensity is performed within the optimization parameter space according to a preset scan step size. For the higher-order interaction intensity value of each traversed node, iterative calculation is performed through the dynamic equation until the system reaches a steady state. The steady state is defined as the continuous iterative change in the amplitude of the order parameter of each topic layer being less than a preset steady-state threshold. The objective function value under steady state is recorded. The non-monotonic characteristic curve of the objective function changing with the higher-order interaction intensity is identified, and the optimal value of the higher-order interaction intensity corresponding to the peak of the curve is determined, i.e., when the curve shows… When the curve exhibits a peak-and-trend effect, the highest-order interaction intensity corresponding to the peak value is determined as the optimal value. The current highest-order interaction intensity is dynamically adjusted to this optimal value. During this adjustment, the evolution trend of the order parameters and the distribution of viewpoints at each topic layer are monitored in real time. If the objective function reaches the preset optimal threshold and the viewpoint distribution at each topic layer exhibits a single-peak concentration without fragmentation characteristics of multi-peak separation, then the optimization is confirmed to be complete. If the objective function does not reach the preset optimal threshold or the viewpoint distribution at each topic layer does not exhibit fragmentation characteristics, the optimization parameter space is updated based on the current network topology changes and multi-topic coupling relationships. Regarding network topology changes, if the node connection density increases (…), the optimization parameter space is updated accordingly. An increase in average degree indicates that the basic propagation efficiency of binary interactions is enhanced, which can moderately reduce K2. min To reduce redundant investment in higher-order interactions; if the network clustering coefficient increases (local node connections are denser) or the number of simple complex groups increases (more high-order interaction structures with three or more people), then K2 needs to be lowered. max To avoid the risk of viewpoint polarization caused by locally closed groups; if the topology changes (e.g., a chain structure evolves into a center-radial structure), then based on the connectivity characteristics of the new topology (e.g., the efficiency of propagation dominated by the central hub), and referring to pre-existing different topology-parameter mapping relationships, K2 is recalibrated. min With K2 maxThe baseline range. Secondly, regarding the changes in multi-topic coupling relationships, if the cognitive coupling matrix... The increased spectral radius (closer cognitive coupling between topics) and enhanced cross-topic viewpoint linkage among individuals can reduce K2. min To reduce the activation cost of higher-order interactions; if The increased proportion of non-zero elements (expanded scope of topic relevance) increases the risk of over-amplifying differences in viewpoints due to the cross-coupling of multiple topics, necessitating further compression of K2. max The upper limit; if the coupling relationship between topics weakens ( If the spectral radius decreases and the proportion of non-zero elements decreases, then K2 needs to be increased. min This ensures that higher-order interactions contribute to consensus. Finally, the dynamic change indicators of the aforementioned topology and coupling are integrated, based on the updated... Feature parameters (average degree, clustering coefficient, density) and The correlation strength index is used to fit the steady-state order parameter and fragmentation risk under different high-order interaction strength values ​​through multiple sets of short-period numerical simulations, and to redetermine the K2 value that is suitable for the current network state. min (Minimum threshold for effective higher-order interaction excitation) and K2 max (without significant fragmentation of the maximum critical value), forming an updated optimization parameter space to ensure that the interval is accurately matched with the real-time network status and topic-related features, until the optimal control effect is achieved.

[0029] In this embodiment, during the bistable detection stage, the present invention, through a bidirectional evolution experiment of forward and reverse decrease in high-order interaction intensity, combined with the deviation comparison of forward and backward steady-state order parameters and threshold determination, can accurately identify whether the system has an irreversible "echo chamber" bistable risk. This solves the defect of traditional models in being unable to warn of the risk of solidified public opinion, and provides a scientific basis for subsequent regulation. When a bistable region exists, the step size is dynamically matched and adjusted based on the bistable risk overscalar, while also considering four different topologies: fully connected, clustered, chained, and centrally radiating. The adaptation relationship between connectivity characteristics and pairwise interaction strength is dynamically obtained through a mapping model constructed from pre-stored simulation data to obtain the destabilization threshold, achieving precise matching between the destabilization threshold and the network structure. The fully connected structure adapts to a higher destabilization threshold based on high connectivity, the group structure avoids subgroup solidification through negative correlation adjustment, the chain structure prevents fragmentation from intensifying with a low threshold, and the central radial structure adapts to a stability threshold slightly lower than that of the fully connected structure. Through gradual reduction adjustment and real-time deviation monitoring, the system ensures efficient elimination of bistable risks and restoration of monostable state, breaking the limitations of the traditional "one-size-fits-all" control. When bistable regions are absent, a high-order interaction intensity optimization space is dynamically constructed based on the spectral radius and non-zero element ratio of the multi-topic cognitive coupling matrix, the average degree of the network adjacency matrix, and the clustering coefficient. This space adapts to the current network state and ensures effective activation of high-order interactions through the correlation features of the cognitive coupling matrix, while avoiding viewpoint fragmentation through the constraints of network adjacency matrix density and clustering coefficient. This solves the problem of mismatch between fixed optimization intervals and dynamic networks. Using the average amplitude of multi-topic hierarchical parameters as the objective function, the optimal high-order interaction intensity (i.e., the peak value of the camel hump effect) is accurately located through gridded scanning, dynamic iterative simulation, and non-monotonic feature curve identification. The consensus level is maximized by utilizing stochastic resonance, which significantly improves consensus quality compared to traditional linear enhancement strategies. Simultaneously, the optimization space boundary and benchmark range are updated in real time to address the dynamic changes in network topology (node ​​density, clustering coefficient, structural type conversion) and multi-topic coupling relationships (spectral radius and non-zero element ratio of the cognitive coupling matrix). This ensures that the control strategy always adapts to the network evolution state, avoiding redundant investment in high-order interactions and effectively mitigating the risk of viewpoint polarization caused by local closed groups. Overall, this strategy achieves both accurate early warning and efficient resolution of bistable risks, and fully utilizes higher-order nonlinear effects to enhance consensus through a dynamic optimization mechanism. It balances the targeted nature (adapting to different topologies and coupling characteristics), dynamism (responding to network and topic evolution), and robustness (balancing consensus enhancement and fragmented prevention and control) of public opinion regulation. It completely overcomes the singleness and rigidity of traditional linear regulation strategies, and provides reliable technical support for guiding consensus on complex online public opinion in different scenarios.

[0030] Furthermore, based on the aforementioned model structure and algorithm, this invention conducted multiple sets of numerical simulations, respectively analyzing differences in network structure and pairwise interaction strength. Impact on the synchronization of viewpoints, intensity of higher-order interactions The impact of fragmentation, and The effectiveness of the method was verified in three aspects: non-monotonic effects. Typical results are as follows: ① Synchronous evolution results under the same network structure like Figure 4 The diagram shown illustrates the evolution of order parameters over time in different network structures provided in this application embodiment, with a fixed... Under these conditions, four typical network structures were constructed: fully connected structure (irreducible), group structure (reducible, with several dense subgroups), chain structure (reducible, with weak linear connections), and center-radial structure (irreducible, with a central hub). Each structure simultaneously tracks the synchronization order parameters of multiple topic layers. Simulation results show that: In a fully connected and centrally radiating architecture, the order parameters of all topic layers All parameters rapidly increase and approach 1, indicating strong network connectivity at this point. Under the combined effect of high-order and pairwise interactions, the system can reach a high degree of consensus in a short time. In the group structure, the order parameters of different topics can still gradually approach 1, but the convergence speed is significantly lower than in the fully connected structure, indicating a certain lag in viewpoints and differences between circles within the internal groups. In the chain structure, the order parameters of some topics... The initial rise followed by a decline, and even a prolonged stagnation at a moderate level, indicates that when network connections exhibit weak, chain-like coupling, even if individual small groups are relatively consistent, overall public opinion is prone to prolonged semi-synchronous states, hindering the formation of a unified consensus. These results demonstrate that different topologies have a significant impact on the evolution of public opinion. The high-order model of this invention can distinguish and quantify these structural differences, providing a basis for implementing differentiated regulation on different types of platforms or communities.

[0031] ② The impact of pairwise interaction intensity on the viewpoint synchronization process like Figure 5The figure shows the evolution of the order parameter for different pairwise interaction intensities under different higher-order interaction intensities provided in the embodiments of this application. The vertical axis in the figure is the average order parameter R, and the horizontal axis is time t. This invention presents the influence of pairwise interaction strength (0.1-2.0) on the evolution of the order parameter R(t) under four fixed higher-order interaction strengths of 0.0, 0.3, 0.6, and 0.9 in the form of subgraphs: within the same subgraph, the greater the pairwise interaction strength, the faster the order parameter rises and the higher the final value, reflecting the monotonically enhancing effect of pairwise interaction strength on synchronization speed and consensus. Furthermore, there exists a critical pairwise interaction strength dependent on the higher-order interaction strength; below this value, the system remains in a state of low synchronization for a long period. Horizontal comparison between subgraphs shows that when the higher-order interaction strength is 0.3 and 0.6, all curves shift upwards, indicating higher synchronization and faster convergence at the same pairwise interaction strength, suggesting that moderate higher-order interaction can lower the critical threshold of pairwise interaction strength. When the higher-order interaction strength is 0.9, diminishing marginal returns occur, and the improvement in synchronization is limited under high pairwise interaction strength, confirming the complementary regulatory relationship between pairwise interaction strength (controlling propagation efficiency) and higher-order interaction strength (influencing consensus form).

[0032] from Figure 5 The following conclusions can be drawn: 1. Under a given high-order interaction strength, pairwise interaction strength has a monotonically reinforcing effect on synchronization speed and final consensus. In each subgraph, the higher the curve and the faster it saturates, the larger the corresponding pairwise interaction strength value. When the pairwise interaction strength is small, R(t) rises slowly and eventually remains at a low level, indicating that when pairwise interaction is too weak, opinions in the network are difficult to fully converge through one-to-one propagation. As the pairwise interaction strength increases, the curve becomes significantly steeper, and R(t) approaches 1 in a short time, indicating that enhancing point-to-point communication (such as forwarding, commenting, liking, private messages, and friend relationships) can significantly accelerate consensus formation. This shows that within the model framework of this invention, there exists a critical strength of pairwise coupling and pairwise interaction that depends on the high-order interaction strength: when the pairwise interaction strength is below this critical value, the system remains in a low-synchronization or semi-synchronization state for a long time; only when the pairwise interaction strength is above this value can a high degree of consensus be formed.

[0033] 2. Higher-order interaction intensity modulates the critical threshold and efficiency of pairwise interaction intensity. A horizontal comparison of the four sub-graphs shows that: when the higher-order interaction intensity = 0.0 (almost no higher-order grouping effect), R(t) can only rise to a relatively high level within a finite time when the pairwise interaction intensity is large; when the higher-order interaction intensity increases to 0.3 and 0.6, all curves shift upwards overall. For the same pairwise interaction intensity value, the final synchronization degree of the system is higher and the convergence is faster, indicating that moderate higher-order interaction can lower the threshold of pairwise interaction and alleviate the pressure on the platform to maximize one-to-one interaction; when the higher-order interaction intensity further increases to 0.9, although the synchronization degree is still improved under small pairwise interaction intensity conditions, the improvement is no longer significant for already large pairwise interaction intensity conditions, exhibiting diminishing marginal returns: at this point, further increasing the pairwise interaction intensity brings limited improvement in synchronization.

[0034] 3. Paired interaction strength and higher-order interaction strength are complementary in terms of regulation. Combined with subsequent results regarding the fragmentation and non-monotonic effects of higher-order interaction strength, it can be seen that paired interaction strength and higher-order interaction strength are not simply superimposed, but rather serve different functions: paired interaction strength primarily controls whether information can spread smoothly and whether convergence is fast enough; higher-order interaction strength mainly affects consensus patterns and risk structures. Too weak a strength makes it difficult to stimulate group resonance, while too strong a strength can easily lead to fragmentation and bistable risks. Therefore, in practical applications, we can first use the results of this section to select a paired interaction strength range that ensures convergence speed and basic synchronization. Then, combined with the analysis of fragmentation and non-monotonic effects of higher-order interaction strength in subsequent sections, we can comprehensively determine the joint operating point of (paired interaction strength, higher-order interaction strength) to achieve both rapid and robust public opinion guidance.

[0035] ③ Impact on the fragmentation of viewpoints like Figure 6 The diagram shown illustrates the influence of high-order interaction intensity on viewpoint fragmentation, as provided in this embodiment of the application. In the case of taking respectively , and Three representative high-order intensities are used to analyze the steady-state opinion distribution of a specific topic layer. Each column has a polar coordinate plot at the top (angles represent the opinion phase) and a corresponding linear histogram at the bottom.

[0036] Simulation shows: When When (higher-order effects are weak), the distribution of viewpoints is concentrated in a narrow angular range, the polar plot shows a single sector, and the histogram shows a unimodal distribution, indicating that the system as a whole tends to be mild and consistent, with a low degree of fragmentation; when At (moderate intensity), the distribution of viewpoints begins to show significant stretching, with the main peak widening and secondary peaks appearing locally, indicating that subgroup differentiation begins to emerge within the group under the impetus of higher-order interactions; when When higher-order effects are excessively strong, the viewpoint distribution exhibits two or more distinct peaks. The fan-shaped regions in the polar plot are far apart, and the histogram shows a multi-peak structure. This is accompanied by higher variance and a greater number of viewpoints, indicating that the system has entered a stage of significant viewpoint fragmentation and polarization. Therefore, the intensity of higher-order simplex complexes... Bigger isn't always better: too small It is difficult to generate effective consensus; the scale is too large. This can amplify differences within a group, leading to severe fragmentation. This aligns perfectly with the theoretical assessment in this invention that higher-order interactions are a double-edged sword.

[0037] ④ Non-monotonic effects and optimal control point like Figure 7 The figure shown is a non-monotonic effect curve of high-order interaction intensity provided in the embodiments of this application. The present invention systematically scans... In the interval The values ​​within the range are used to perform multiple simulations and calculate the steady-state order parameters for each value. The time average and its standard deviation are obtained. – Relationship curve.

[0038] As can be seen: when As the average steady-state order parameter increases slowly from 0, The gradual increase in interaction at the higher levels indicates that appropriately enhancing interaction within higher-level groups is beneficial for promoting consensus and improving system synchronization. Increase to approximately At this point, the curve reaches a significant peak. The system achieves its maximum value while maintaining a relatively small standard deviation range, demonstrating both high consensus and good stability. After continuing to increase beyond this peak value, Instead, it begins to decline, accompanied by a significant increase in standard deviation, indicating that the system is gradually entering an unstable or even fragmented state. This curve clearly demonstrates the intensity of higher-order interactions. The non-monotonic response relationship of the system synchronization level verifies the existence of an optimal higher-order intensity proposed in this invention. Rather than adhering to the view that 'the bigger the better', this invention selects the area near the peak point marked by the red dashed line as the optimal operating point in its control strategy: near this point, it can fully utilize the accelerated consensus advantage brought by higher-order interactions; while avoiding entering bistable and severely fragmented regions, ensuring the controllability and recoverability of public opinion.

[0039] Through the above description of the implementation methods, those skilled in the art can clearly understand that, for the sake of convenience and brevity, only the division of the above functional modules is used as an example. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the above functions can be divided into different functional modules to complete all or part of the functions described above.

[0040] In the several embodiments provided in this application, it should be understood that the disclosed methods can be implemented in other ways. For example, the embodiments described above are merely illustrative; for instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between devices or units, and may be electrical, mechanical, or other forms.

[0041] The units described as separate components may or may not be physically separate. A component shown as a unit can be one or more physical units, located in one place or distributed in multiple different locations. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0042] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0043] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling, characterized in that, Includes the following steps: A multi-layer network topology is constructed based on a simple complex structure, and core input data is dynamically determined based on the multi-layer network topology. The simple complex structure includes points, edges, and triangles. Using the core dynamic control parameters as weighting coefficients, and based on the core input data, the interaction strength between individuals and the correlation between topic layers are dynamically controlled through dynamic equations. The interaction terms of all individual nodes in the multi-layer network topology are iteratively calculated until the system reaches a steady state, and the global order parameters of each topic layer are obtained. The core dynamic control parameters include pairwise interaction strength, higher-order interaction strength, and inter-layer coupling strength. The interaction terms include pairwise interaction terms, higher-order interaction terms, and multi-topic coupling terms. The core input data are used as the calculation input and structural basis of the corresponding interaction terms to drive and quantify the dynamic process simulated by the interaction terms. Based on the global order parameter, the system dynamically detects whether there is a bistable region in the evolution of public opinion in complex networks. If it exists, the higher-order interaction intensity is dynamically destabilized to eliminate the risk of bistable interaction and restore the system to monostable state. If it does not exist, the higher-order interaction intensity is dynamically optimized using the global order parameter as the objective function. The global order parameter includes the forward-evolved steady-state order parameter and the backward-evolved steady-state order parameter.

2. The method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling as described in claim 1, characterized in that: The points in the multi-layer network topology represent individual nodes in a complex network. Each individual node contains multiple topic layers, and cognitive dependencies are established between topic layers through a cognitive coupling matrix. Edges serve as the network adjacency matrix, representing the binary connection relationships between individual nodes. Triangles serve as higher-order correlation tensors, representing group interactions of three or more people. The core input data includes the network adjacency matrix, higher-order correlation tensors, and initial phase distribution.

3. The method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling as described in claim 1, characterized in that: The core formula of the dynamic equation is as follows: ； In the formula, i is the individual node identifier, i=1, 2, 3, ..., N, N is the total number of nodes, p is the topic layer identifier, p=1, 2, 3, ..., M, M is the total number of topic layers followed by each node; This represents the viewpoint phase of node i at time t in the topic at layer p. Let i be the initial phase distribution of individual i to the topic at the p-th layer. For the natural frequency term, For paired interaction items, For higher-order interaction items, This is a multi-topic coupling item.

4. The method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling as described in claim 3, characterized in that: The core formula for the pairwise interaction terms is as follows: ； In the formula, For pairwise interaction strength, Let i be the network adjacency matrix between node i and node j. This represents the difference in opinion between node j and node i on topic p.

5. The method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling as described in claim 3, characterized in that: The core formula for the higher-order interaction term is as follows: ； In the formula, For higher-order interaction strength, Let i be the higher-order correlation tensor formed by nodes i, j, and k, where , where is the sum of the opinion biases between individual i and the higher-order group (i,j,k).

6. The method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling as described in claim 3, characterized in that: The core formula for the multi-topic coupling term is as follows: ； In the formula, D represents the interlayer coupling strength. Let p and q be the cognitive coupling matrix of the topic layers. Let represent the opinion bias of node i on topics p and q.

7. The method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling as described in claim 3, characterized in that: The core formulas for the global order parameters of each topic layer are as follows: ； In the formula, This represents the global order parameter for the topic at level p. Let be the magnitude of the order parameter for the topic at level p. Let be the magnitude of the order parameter of the topic at layer p.

8. The method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling as described in claim 1, characterized in that: The steps for detecting whether a bistable region exists in the evolution of complex network public opinion based on the global order parameter include: Under the same pairwise interaction strength and interlayer coupling strength, the higher-order interaction strength gradually increases from 0 to the preset maximum value of the higher-order interaction strength. The magnitude of the order parameter when the system reaches steady state is recorded as the steady-state order parameter of forward evolution. The higher-order interaction strength gradually decreases from the maximum value to 0. The magnitude of the order parameter when the system reaches steady state is recorded as the steady-state order parameter of backward evolution. The absolute deviation between the forward-evolved steady-state sequence parameter and the backward-evolved steady-state sequence parameter is denoted as the bistable deviation. The bistable deviation is compared with a preset bistable determination threshold. If the bistable deviation exceeds the bistable determination threshold, it is determined that a bistable region exists. If the bistable deviation does not exceed the bistable determination threshold, then it is determined that there is no bistable region.

9. The method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling as described in claim 8, characterized in that: The steps for dynamically destabilizing higher-order interaction strengths include: The difference between the bistable deviation and the bistable judgment threshold is recorded as the bistable risk exceedance, and the adjustment step size is dynamically obtained based on the bistable risk exceedance. Extract the real-time values ​​of high-order interaction strengths in the current multi-layer network topology; The destabilization threshold of high-order interaction strength is dynamically obtained based on network topology type and pairwise interaction strength. The real-time value of the higher-order interaction intensity is adjusted by gradually decreasing the adjustment step size, and the bistable deviation is recalculated after each adjustment. If the recalculated bistable deviation does not exceed the bistable determination threshold, and the adjusted higher-order interaction strength is not lower than the higher-order interaction strength destabilization threshold, then the adjustment stops. If the recalculated bistable deviation still exceeds the bistable determination threshold, and the adjusted higher-order interaction strength is greater than the higher-order interaction strength destabilization threshold, then the higher-order interaction strength is gradually adjusted based on the adjustment step size. If the recalculated bistable deviation still exceeds the bistable determination threshold, and the adjusted higher-order interaction strength is not greater than the higher-order interaction strength destabilization threshold, then the paired interaction strength is simultaneously optimized until the bistable deviation does not exceed the bistable determination threshold.

10. The method for predicting the evolution of complex online public opinion based on high-order interaction and multi-topic coupling as described in claim 8, characterized in that: The step of dynamically optimizing the higher-order interaction strength using the global order parameter as the objective function includes: The optimization parameter space for high-order interaction intensity is dynamically obtained based on the multi-topic coupling matrix and network adjacency matrix; Using the average magnitude of the order parameter of each topic layer as the objective function, the higher-order interaction intensity is scanned in a gridded manner within the optimization parameter space according to the preset scanning step size; for the higher-order interaction intensity value of each traversed node, iterative calculation is performed through the dynamic equation until the system reaches a steady state. The steady state is when the continuous iterative change of the magnitude of the order parameter of each topic layer is less than the preset steady state threshold, and the objective function value under the steady state is recorded. Identify the non-monotonic characteristic curve of the objective function as a function of higher-order interaction intensity, and determine the optimal value of higher-order interaction intensity corresponding to the peak of the curve. Dynamically adjust the current higher-order interaction intensity to the optimal value of higher-order interaction intensity. During the adjustment process, monitor the evolution trend of the order parameters and the distribution pattern of viewpoints in each topic layer in real time. If the objective function reaches the preset optimal threshold and the distribution of viewpoints in each topic layer is fragmented, the optimization is confirmed to be complete. If the objective function does not reach the preset optimal threshold or the distribution of viewpoints in each topic layer is not fragmented, update the optimization parameter space based on the current network topology changes and multi-topic coupling relationships until the optimal control effect is achieved.

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