Network public opinion phase transition analysis and early warning system fusing information entropy and physical field theory

Abstract

This invention discloses a network public opinion phase transition analysis and early warning system that integrates information entropy and physical field theory, belonging to the field of network public opinion data processing technology. It includes a public opinion data processing module, a model building module, an energy landscape modeling module, a phase transition precursor extraction module, and a risk warning discrimination module. The public opinion data processing module is used to preprocess the acquired network public opinion data, mapping the network public opinion text to individual opinion state variables. The model building module is used to construct a nonlinear dynamic model based on the individual opinion state variables. The energy landscape modeling module is used to introduce the concept of physical energy modeling, mapping the macroscopic state of the public opinion system to an energy function. The phase transition precursor extraction module is used to extract precursor indicators that reflect the system approaching the critical state of phase transition. The risk warning discrimination module is used to discriminate the public opinion risk state and output the public opinion risk warning result when preset criteria are met.

Description

Technical Field

[0001] This invention relates to the field of online public opinion data processing technology, and in particular to an online public opinion phase transition analysis and early warning system that integrates information entropy and physical field theory. Background Technology

[0002] With the rapid development of social media, news commentary platforms, and online communities, online public opinion has become a significant factor influencing social operations and public governance. How to effectively identify and provide early warnings of online public opinion risks has become a key technical issue in the field of cyberspace governance.

[0003] Existing methods for assessing and warning about online public opinion risks mainly include statistical analysis methods based on the popularity or scale of dissemination, analysis methods based on sentiment polarity and intensity, and prediction and classification methods based on machine learning or deep learning models. These methods typically rely on historical data for trend extrapolation and assume that the evolution of public opinion is continuous and gradual.

[0004] From the perspective of complex systems science, online public opinion, as an open information-energy system, exhibits profound similarities in its evolutionary patterns to nonlinear dynamic systems in physics. On one hand, the collaboration and competition among different actors within the public opinion system can be seen as the intrinsic driving force behind the evolution of the system's macroscopic state. On the other hand, the process by which the system maintains or disrupts its equilibrium through information exchange and emotional dissipation conforms to the characteristics of dissipative structures. This suggests that the phase transition of the public opinion system is essentially an external manifestation of the instability of its internal energy structure. Traditional methods have failed to construct a unified framework similar to the energy function in physical systems to quantify and describe the changes in system stability generated by microscopic interactions and ultimately leading to macroscopic phase transitions. Therefore, abstracting the public opinion system as an energy system driven by collaborative dynamics and possessing dissipative characteristics, and using the topological changes in its energy landscape to predict phase transitions, is a possible way to fundamentally break through the limitations of existing technological paradigms. In major emergencies or highly controversial issues, the state of public opinion may suddenly leap from a relatively stable state of consensus to a radicalized or polarized state within a short period. Before this leap occurs, traditional methods often struggle to provide clear risk signals. From a research perspective, this invention possesses the following three important aspects: From a macro-social and governance perspective, the real-world complexity of public opinion risks continues to increase. With the widespread adoption of social media and mobile internet, online public opinion has become a crucial vehicle for expressing social opinions, releasing emotions, and engaging in debates on public issues. Public opinion events often exhibit characteristics such as large scale, rapid speed, numerous participants, and significant emotional amplification effects during their dissemination. Once the public opinion situation becomes unstable, it can easily evolve into a large-scale public opinion risk event within a short period, significantly impacting social order, public governance, and institutional decision-making. In actual governance and intervention, public opinion risks are not simply caused by the accumulation of public opinion intensity or negative information, but often manifest as a sudden change in the overall public opinion structure within a short time. What was originally a relatively neutral discussion space may quickly shift to a radicalized or polarized state, and the overall stability of the public opinion system will significantly decline in a short period. These sudden risks have obvious irreversibility and amplification effects, placing higher demands on public opinion monitoring and early warning capabilities.

[0005] From a technical and methodological perspective, traditional public opinion early warning methods have paradigmatic limitations. Current technical means for identifying and warning of online public opinion risks mainly rely on methods such as time-series trend analysis, sentiment polarity statistics, keyword monitoring, or machine learning classification. While these methods are effective in routine public opinion monitoring scenarios, their core logic remains based on linear trend assumptions or threshold-based judgments. However, before a public opinion system approaches a risk outbreak, key changes often do not manifest as a significant increase in public opinion intensity or sentiment ratio, but rather as a gradual destabilization of the system's internal structure, such as increased opinion volatility, intensified group differentiation, and a decreased ability to recover from disturbances. These changes are difficult to effectively capture using traditional methods based on single-point indicators or short-term trends, leading to delayed or even ineffective early warnings. Technically, there is an urgent need to break through the limitations of single indicators and linear predictions, and introduce analytical methods capable of characterizing the overall evolution and stability of the public opinion system.

[0006] From the perspective of theoretical paradigm innovation, the shift from trend prediction to phase transition early warning requires a multidisciplinary integration and innovation mechanism. Theoretically, the online public opinion system is essentially a complex system formed by the interaction of numerous individual opinions, and its evolutionary process exhibits significant nonlinearity, feedback, and abrupt changes. This characteristic is highly similar to phase transition processes in physical systems; that is, a system may undergo state transitions near a critical point as external conditions or internal parameters change slowly. Phase transition theory focuses on the system's stable state, potential barrier structure, and critical behavior, providing an effective tool for understanding the sudden changes in complex systems. Introducing phase transition theory into public opinion risk research helps elevate the issue from the traditional judgment of whether public opinion risk is rising to the identification of whether the system is approaching a critical point of instability. From a theoretical paradigm perspective, it is necessary to reformulate the public opinion risk early warning problem as an early warning problem based on system stability and phase transition mechanisms, achieving ex-ante identification and explanatory early warning of public opinion risks through energy potential landscapes and phase transition precursor indicators.

[0007] This study proposes a hypothesis that before a risk erupts, the internal structure of the online public opinion system undergoes significant changes, including a sustained increase in the amplitude of individual opinion fluctuations, a significant decrease in the system's ability to recover from external disturbances, and a shift in the distribution of group opinions from a concentrated to a differentiated state. These changes are not necessarily accompanied by a significant increase in public opinion intensity, and therefore are difficult to capture by existing technologies based on thresholds or trends.

[0008] The above phenomena indicate that the online public opinion system conforms to the phase transition behavior characteristics of complex systems, that is, during the slow change of external conditions or internal parameters, the system will undergo a sudden structural transition near a critical point. Current technologies generally lack a method to characterize the formation mechanism of public opinion risks from the perspective of system stability and structural evolution, and also lack technical means to quantitatively identify the precursors of public opinion phase transitions. Therefore, this paper proposes an early warning method and system for online public opinion phase transitions based on physical energy and phase transition theory, in order to achieve early identification and warning of sudden risks in online public opinion. Summary of the Invention

[0009] This application provides a network public opinion phase transition analysis and early warning system that integrates information entropy and physical field theory. This solves the problems of existing technologies, such as reliance on single indicator trends, difficulty in characterizing system stability, and inability to timely identify nonlinear mutation risks. It constructs an engineered system capable of providing early warning of public opinion structural risks from the perspective of overall system stability. Traditional early warning methods mainly rely on surface-level indicators of information dissemination, such as public opinion heat and sentiment distribution, which are insufficient to discern instability and mutations within the internal structure of the public opinion system. This invention, by introducing phase transition theory and energy landscape modeling, views public opinion evolution as a stability transition process of a nonlinear dynamic system, thereby achieving an essential characterization and forward-looking early warning of public opinion risks.

[0010] This application provides a network public opinion phase transition analysis and early warning system that integrates information entropy and physical field theory, including: a public opinion data processing module, a model building module, an energy landscape modeling module, a phase transition precursor extraction module, and a risk warning discrimination module; wherein, the public opinion data processing module is used to acquire network public opinion data through a preset data acquisition mechanism, and to preprocess the network public opinion data, mapping the network public opinion text into individual opinion state variables; the model building module is used to construct a nonlinear dynamic model based on the individual opinion state variables, to characterize the dynamic evolution process of the public opinion system under the combined effects of social influence, individual response differences, and random disturbance factors, the nonlinear dynamic model includes The system includes attenuation terms, social interaction terms, and random noise terms. The energy landscape modeling module introduces the concept of physical energy modeling on the basis of nonlinear dynamics models, mapping the macroscopic state of the public opinion system to an energy function to describe the stability characteristics of the system under different opinion structures. The stable state corresponds to the energy minimum, and the unstable state corresponds to the energy saddle point. The phase transition precursor extraction module is used to extract precursor indicators that can reflect the system approaching the critical state of phase transition by analyzing the changes in the energy potential landscape structure and statistical characteristics during the evolution of the public opinion system. The risk warning and discrimination module is used to judge the public opinion risk state based on the changes in the phase transition precursor indicators, and output the public opinion risk warning result when the preset criteria are met.

[0011] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: First, it overcomes the limitations of linear indicator-based public opinion early warning systems, enabling systematic identification of sudden changes in public opinion structure. Existing public opinion early warning technologies mostly rely on indicators such as sentiment polarity ratio, dissemination speed, or keyword frequency for trend analysis or threshold judgment, typically assuming that the evolution of public opinion has continuous and gradual characteristics. When sudden structural changes occur in the public opinion system, these methods often fail to provide timely and effective early warnings. This invention models the online public opinion system as a nonlinear dynamic system. By constructing a minimum social dynamics model and introducing an energy landscape, it analyzes the overall stability of the public opinion system, enabling the identification of the transition process from one stable state to another. This allows for the identification of systemic instability risks that are difficult to capture using traditional methods, improving the foresight and reliability of public opinion early warning.

[0012] Secondly, by introducing phase transition theory and energy landscape models, the interpretability of public opinion risk early warning is improved. This invention constructs an energy function and potential energy landscape for the public opinion system, corresponding the stability of the public opinion state to the system's energy structure. This allows different states of the public opinion system to be characterized by physical quantities such as energy minima and potential barrier height. Compared to existing technologies that rely on empirical thresholds or black-box models, the early warning judgment process of this invention has a clear theoretical basis, can explain the causes and evolution of public opinion risks, and helps improve the credibility of early warning results and the understandability of decision support.

[0013] Third, this invention characterizes the impact of opinion interaction on public opinion evolution, enabling early identification of unstable trends in the public opinion system. In the process of public opinion modeling, this invention considers the interaction between individual opinions and describes the impact of group interaction on public opinion evolution through a nonlinear response mechanism. When a public opinion system approaches an unstable state, it often exhibits characteristics such as enhanced response to disturbances and increased amplitude of opinion fluctuations. By analyzing the energy potential landscape structure and dynamic characteristics, this invention can identify unstable trends in the public opinion system before it enters a state of significant differentiation or confrontation, providing a technical basis for public opinion guidance and risk intervention.

[0014] Fourth, early warning of public opinion risks can be achieved based on pre-phase transition precursors, improving the timeliness of risk management. The dynamic characteristics of the public opinion system before a state transition occur, such as decreased system resilience, increased opinion volatility, and increased structural disorder, can be monitored and jointly identified. By continuously monitoring and jointly identifying these pre-phase transition precursor characteristics, early warning information can be output before the explicit outbreak of public opinion risks, thus providing more sufficient response time for public opinion management and risk management, and improving the initiative in public opinion risk prevention and control.

[0015] Fifth, it assists in the analysis, decision-making, and intervention of public opinion trends. This invention can output analytical results reflecting the stable state and evolutionary trend of the public opinion system, including changes in energy landscape, time-series characteristics of key parameters, and indicators of precursors to phase transitions. Presenting these results in a visual manner helps users intuitively understand the current state and changing trends of the public opinion system, thereby providing a reference for the analysis and intervention strategy formulation. Attached Figure Description

[0016] Figure 1 A schematic diagram of the structure of the network public opinion phase transition analysis and early warning system that integrates information entropy and physical field theory, provided in an embodiment of this application; Figure 2 A flowchart of a network public opinion phase transition analysis and early warning method that integrates information entropy and physical field theory, provided in an embodiment of this application; Figure 3 A flowchart of a risk warning system for multi-event iterative verification and learning provided in an embodiment of this application. Detailed Implementation

[0017] This application provides a network public opinion phase transition analysis and early warning system that integrates information entropy and physical field theory. It introduces phase transition theory and potential energy landscape models to perform unified modeling and evolutionary analysis of cross-platform public opinion data. This promotes the upgrade of the early warning mechanism from traditional indicator trend monitoring to a phase transition early warning paradigm based on system stability mutations and structural leaps, providing more forward-looking and systematic technical support for public opinion risk identification and intervention. Its core invention includes: First, construct a dynamic and energy model framework that can characterize the stability of the public opinion system. By collecting public opinion data from multiple platforms and mapping opinion states, a minimal social dynamics model is constructed that includes a dispute function and a nonlinear social response based on homogeneity mechanisms. Then, an energy function describing the macroscopic state of the system is defined, and a corresponding potential energy landscape model is established. This provides a unified model basis for quantitatively representing different stable states such as consensus, radicalization, and polarization, as well as the conditions for their mutual transformation.

[0018] Second, establish a public opinion status identification and early warning indicator system based on phase transition precursors.

[0019] By analyzing the topological structure of the potential energy landscape (potential well merging, potential barrier reduction) and its corresponding system dynamics, characteristic indicators reflecting the system's approach to the critical point are extracted, including slowed recovery speed (critical slowdown), amplified internal fluctuations (increased variance), increased structural disorder (entropy change), potential barrier height, fluctuation amplitude, and other pre-phase transition signals, in order to identify structural risk signs before the public opinion system transitions from a consensus state to a radical or polarized state.

[0020] Third, establish a closed-loop judgment and decision support mechanism from risk identification to early warning triggering.

[0021] By continuously monitoring and jointly judging the aforementioned phase transition precursor indicators from multiple dimensions, the system automatically triggers public opinion risk warnings when the preset phase transition criteria are met, and outputs the current stable state type, evolution trend, and critical risk level of the system, thereby completing the closed loop of early identification, warning, and decision support for sudden structural changes in online public opinion.

[0022] Furthermore, this invention aims to achieve further technological breakthroughs in the following aspects: First, by introducing time-varying coupling strength and group heterogeneity parameters, the model can dynamically respond to event popularity and group differences, improving the adaptability and explanatory power of the early warning system to real public opinion scenarios; Second, by constructing a reverse reasoning logic from system phase variable analysis to steady-state jump identification to public opinion risk early warning, a closed-loop connection between theoretical models and engineering early warning is achieved; Third, by providing a visualized potential energy landscape evolution diagram and sequence parameter transition trajectory, decision-makers can intuitively grasp the evolution path and critical state of system stability, enhancing the understandability and credibility of early warning results.

[0023] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0024] like Figure 1 The diagram shown illustrates the structure of the network public opinion phase transition analysis and early warning system integrating information entropy and physical field theory provided in this embodiment. Using multi-platform network public opinion data as input, it achieves public opinion risk identification and early warning by performing dynamic and energy modeling on the evolution process of the public opinion system. The network public opinion phase transition analysis and early warning system integrating information entropy and physical field theory provided in this embodiment includes: a public opinion data processing module, a model building module, an energy landscape modeling module, a phase transition precursor extraction module, and a risk early warning identification module. The public opinion data processing module and the dynamic model building module are connected via a data interaction link; the dynamic model building module and the energy landscape modeling module are connected via a model parameter interaction link; the energy landscape modeling module and the phase transition precursor extraction module are connected via a landscape feature interaction link; and the phase transition precursor extraction module and the risk early warning identification module are connected via an indicator data interaction link.

[0025] The public opinion data processing module is used to acquire online public opinion data related to the target event / topic from multiple online platforms through a preset data collection mechanism. It then preprocesses the data, mapping online public opinion texts into numerical individual opinion state variables based on semantic analysis or sentiment analysis techniques. This allows data from different platforms to be described within a unified opinion space. Online public opinion data includes, but is not limited to, public opinion text content, publication time information, and platform source identifiers. Data preprocessing includes cleaning, noise reduction, and normalization. Online public opinion is dispersed across numerous platforms, with diverse forms and expressions; any single data source may introduce perspective bias. To construct a comprehensive and objective digital image of the public opinion field, a distributed collection network covering mainstream social media, news aggregation platforms, and important online forums must be established. This network consists of multiple scalable collection nodes, each adapted to the specific platform's interface specifications and page structure. Using a streaming processing approach, it continuously captures raw public opinion data units based on a preset keyword library, event tags, or community discovery algorithms. These data units contain at least text content, publisher anonymization markers, precise timestamps, and interaction metadata representing influence (such as the number of reposts, comments, and likes). The raw data stream undergoes a series of preprocessing pipelines, including rule-based and machine learning model-based spam filtering, cross-platform deduplication, removal of irrelevant topics, and text encoding standardization. Finally, it is neatly stored in a time-series database or distributed file system, forming a spatiotemporally aligned, structurally clear, large-scale public opinion data warehouse. The result of this step is the generation of a high-quality, highly available foundational dataset that not only records who said what and when, but also implicitly reveals the network structure and interaction intensity of information dissemination, providing a real-world foundation for subsequent quantitative modeling.

[0026] The model building module is used to construct a nonlinear dynamic model describing the interaction between individual opinions based on individual opinion state variables. This model is used to characterize the dynamic evolution of the public opinion system under the combined influence of social impact, individual response differences, and random disturbance factors. The nonlinear dynamic model includes a decay term, a social interaction term, and a random noise term.

[0027] After constructing the minimum dynamic model, the next step is to extract a framework describing the macroscopic stability of the system from this microscopic dynamics, namely, to construct the system's free energy function and potential energy landscape. Directly analyzing the stability of high-dimensional nonlinear differential equations is extremely difficult. Statistical physics provides a powerful tool: in systems with a large number of interacting individuals, their collective behavior is often dominated by a few order parameters, and the stable equilibrium state of the system corresponds to a minimum point of a generalized free energy function. By constructing this free energy function, the complex dynamic stability problem can be transformed into a geometric problem of analyzing the energy terrain in a low-dimensional order parameter space. The energy landscape modeling module is used to introduce the idea of ​​physical energy modeling on the basis of the nonlinear dynamic model, mapping the macroscopic state of the opinion system to an energy function. By constructing the energy potential landscape, the stability characteristics of the system under different opinion structures are described. The stable state corresponds to the energy minimum, and the unstable state corresponds to the energy saddle point. Specifically, the dynamic equations can be formally written as: ,in This is the system's free energy function. By integrating the deterministic part on the right-hand side of the equation, the expression for the free energy function can be derived.

[0028] The phase transition precursor extraction module is used to extract precursor indicators that reflect the system approaching the critical state of phase transition by analyzing the changes in the energy potential landscape structure and statistical characteristics during the evolution of the public opinion system; the risk warning and discrimination module is used to judge the state of public opinion risk based on the changes in the phase transition precursor indicators, and output the public opinion risk warning result when the preset criteria are met.

[0029] like Figure 2 The diagram shows a flowchart of the network public opinion phase transition analysis and early warning method that integrates information entropy and physical field theory, provided in this application embodiment. The logical starting point of the entire method lies in a renewed understanding of the essence of the network public opinion system: viewing it as a complex dynamic system formed by the nonlinear interaction and coupling of a large number of heterogeneous individuals. The macroscopic behavior of this system—consensus, differentiation, polarization, or radicalization—is not the result of simple linear accumulation, but rather a macroscopic manifestation of the system's inherent stability undergoing abrupt changes (i.e., phase transitions) under external conditions. Therefore, the core of early warning shifts from threshold monitoring of surface indicators (such as heat and sentiment ratios) to the detection of the system's underlying stability and critical precursors of phase transitions, thus classifying the study of public opinion risk as the study of the stability of complex public opinion systems. The implementation of this invention revolves around this core idea, constructing a closed-loop technical system from microscopic data to macroscopic early warning.

[0030] In this embodiment, the present invention constructs a closed-loop technical system around system stability detection, from microscopic data collection, opinion quantification, and model building to macroscopic energy landscape analysis, phase transition precursor identification, and risk warning output. It engineered the theoretical methods of information entropy and physical field theory into the scenario of network public opinion early warning, which not only improves the adaptability and explanatory power of the early warning system to real public opinion scenarios, but also provides scientific and practical technical support for public opinion management. It can accurately identify unstable trends before the explicit outbreak of public opinion risks, reserve sufficient response time for risk disposal, and greatly improve the initiative and effectiveness of network public opinion risk prevention and control. It also provides a new technical path for the forward-looking risk governance of complex systems in cyberspace.

[0031] Furthermore, the step of mapping public opinion texts into numerical individual opinion state variables includes: determining the probability distribution of the input text belonging to a preset ordered category for the target issue; aggregating the probability distribution into a single scalar value as the individual opinion base value through a mapping function; the ordered categories include strongly opposed, opposed, neutral, supported, and strongly supported; aggregating the probability distributions of each online public opinion text corresponding to the ordered category into the base scalar value; matching the degree of opinion fluctuation in users' historical speaking behavior with a preset opinion fluctuation-perturbation variance mapping table to generate the random perturbation variance of the corresponding user; the opinion fluctuation-perturbation variance mapping table is a lookup table used to quantify the degree of opinion fluctuation into random perturbation variance; and based on the random perturbation variance of each user, adding personalized perturbations to the corresponding base scalar value to obtain the initial value of the individual opinion state, which serves as the initial opinion state of the nonlinear dynamics model.

[0032] Opinion dynamics models require inputs to be scalars defined over a continuous domain, while opinions expressed in human language are ambiguous, implicit, and highly context-dependent. Simple positive / negative counting methods based on sentiment dictionaries cannot capture the strength, complexity, and subtle attitudes such as irony and skepticism of opinions. Therefore, this invention employs a hybrid quantization framework based on deep semantic understanding. At the core of this framework is a pre-trained language model fine-tuned with a large-scale social media corpus, trained as a position classifier. For a target issue, it determines the probability distribution of the input text belonging to one of five ordered categories: strongly opposed, opposed, neutral, supported, and strongly supported. Subsequently, this probability distribution is aggregated into a single scalar value through a defined mapping function, such as a weighted summation. : This is the baseline value for the corresponding category [-1.0, -0.5, 0.0, 0.5, 1.0]. To more realistically simulate the differences and uncertainties in individuals' initial opinions in the real world, we do not directly use... Instead of using them as initial values ​​for the dynamic model, a personalized random perturbation is added to them: ,in The key here is the variance of the noise. It's not fixed, but rather estimated based on the user's historical posting behavior—users with large fluctuations in their historical viewpoints are assigned higher [status]. Conversely, assign a smaller amount of... This step ultimately produces an N-dimensional real vector. It is not only a digital snapshot of the initial opinion state of the group, but also embeds the initial uncertainty determined by user heterogeneity, providing a high-fidelity initial condition that is both representative and random for subsequent dynamic evolution.

[0033] Furthermore, the fundamental purpose of the nonlinear dynamics model provided by this invention is to capture the most critical mechanisms driving the evolution of public opinion in the simplest possible mathematical form, while maintaining the analytical tractability of the model. This model is described by a set of coupled stochastic differential equations, for the system... Individual opinions The evolution follows the following equation: ; In the formula, This represents the rate of change of individual opinions over time, which is a basic description of dynamics. `i` represents the individual's ID, where `i = 1, 2, 3, ..., N`, and `N` is the total number of individuals. The decay term represents individual i, simulating the individual's viewpoint tending towards a neutral state. The inherent inertia or forgetting effect, similar to the linear restoring force experienced by a particle in a potential well in a physical system, ensures that an individual's extreme opinions will naturally moderate in the absence of external social influences. For the social interaction term between individual i and all other individuals j, it encodes the complex rules of inter-individual interaction, specifically the summation of opinion interactions between individual i and each interacting individual j. It is a time-varying social coupling strength, a key regulatory parameter that characterizes the modulating effect of the social environment, such as event popularity, media attention, and platform algorithm recommendation strength, on the overall interaction effectiveness. Its dynamic nature... It is the core of the model for capturing the energy fluctuations in the public opinion field; These are elements of the network adjacency matrix, defining whether individuals i and j have an actual interactive relationship. A value of 1 indicates interaction, while a value of 0 indicates no interaction. This defines who can interact with whom; it originates from an actual social relationship graph or a transient interaction graph constructed based on jointly participated interactive events. It is a homogeneity function of individual i with respect to individual j, and its core characterizes the tolerance characteristic of individual i towards the opinions of other individuals j, based on the opinions of individual i. and individual j's opinion The absolute value of the difference is the core input, combined with the individual i's own opinion tolerance radius. To determine whether individual j's opinion falls within the acceptable range for individual i, and thus whether individual j's opinion can have a social impact on individual i, that is, when... hour Otherwise threshold Individual The tolerance radius for others' opinions is limited to the opinions of others. Falling to Centered on It will only be effective when the interval is within the radius. To have an impact; function It is a nonlinear social response function that describes how the influence of others' opinions is perceived and transformed by the recipient. The S-shaped curve characteristic of the hyperbolic tangent function means that weak opinions produce an approximately linear influence, while strong opinions produce a saturated nonlinear influence. (Parameters...) The steepness of this curve is controlled by the individual's response sensitivity. The higher the value, the stronger the individual's reaction to differing opinions, and the more likely they are to go to extremes. Finally, This is a Gaussian white noise term with zero mean and constant variance, representing random factors that cannot be captured by deterministic models, such as an individual's momentary emotional fluctuations or other accidental information. The profound aspect of this minimum system equation lies in its ability to... These three core parameters and network structure This approach closely links the macro-level shift in public opinion with the heterogeneity and interactive rules of individual behavior at the micro-level. To apply this theoretical equation to real-world data, parameters must be identified and defined. Ultimately, this parameterized system of differential equations constitutes a digitally simulated public opinion system capable of predicting possible future evolutionary paths based on the current state and parameter settings.

[0034] In addition, the dynamics model construction module is also used to identify and set the parameters in the minimum social dynamics model. Specifically, it sets the time-varying social coupling strength by matching and inverting the model output with the observed opinion fluctuations or by associating it with the observed macro-interaction indicators; it fits the individual's response sensitivity parameters by analyzing the statistical relationship between the volatility of the user's historical speech sequence and the social influence it receives; and it estimates the actual range of opinions accepted by the user by analyzing the opinion distribution of the user's interaction objects, thus obtaining the individual's opinion tolerance radius.

[0035] Furthermore, under the mean-field approximation, assuming the system is fully connected and individual parameters are uniform, the macroscopic state of the system can be derived from the average opinion. This is described by order parameters. At this point, the mean-field dynamic equation is: The corresponding mean field free energy function It can be obtained through integration. For more general network structures and heterogeneous parameters, this invention employs a numerical method based on large deviation theory to reconstruct the free energy landscape. In this invention, the system's average opinion is typically selected. As the main order parameter, it most directly reflects the overall tendency; at the same time, the opinion variance is selected. As an auxiliary order parameter, it distinguishes between states such as consensus (low variance) and polarization (high variance). Given the minimal system equations, it can be analytically derived using the mean-field approximation, or, in a more general case, numerical methods can be used to construct the free energy surface. The numerical construction method involves running the parameterized dynamic model to ensure the noise term... There exists a method to traverse the state space and perform long-scale Monte Carlo simulations or numerical integrations. During the simulation, a massive number of system states are sampled, and the corresponding state is recorded. Values. Statistics on these sampling points. Empirical probability density of occurrence in a two-dimensional plane According to fundamental principles of statistical physics, at a given temperature (corresponding to system noise intensity), the probability of a state occurring is related to its free energy. Satisfies the Boltzmann distribution relation: Therefore, it is possible to... To numerically calculate the free energy surface, where This is a proportionality constant related to the effective temperature. After obtaining the free energy grid data, numerical optimization algorithms (such as gradient descent combined with Hessian matrix analysis) are used to find all local minima (steady states) on the surface and the first-order saddle points connecting different minima. The potential barrier height between adjacent minima is calculated. It quantitatively characterizes the energy barrier that needs to be overcome to transition from one stable state to another. Thus, we obtain a visualized landscape of public opinion potential energy. This map clearly shows which stable states (depressions) the system might settle in under the current parameters, and the difficulty of transitioning between these states (potential barrier height). By continuously monitoring this landscape... The dynamic evolution of parameters can intuitively predict the changing trend of system stability. For example, a deep single-well (consensus) may change with... The gradual increase in size and the subsequent splitting into two symmetrical double wells (polarization) indicate an impending phase transition.

[0036] Furthermore, phase transition theory indicates that near the critical point where a system transitions from one stable state to another, several universal early warning signals will emerge. These signals are independent of the microscopic details of a specific system, providing a reliable basis for early risk identification. We continuously calculate the following multidimensional indicators: First, the critical slowing down indicator, calculated by analyzing the time series of order parameters. Fit a low-order autoregressive model and calculate its first-order autoregressive coefficients. When a system approaches instability, its characteristic time to restore equilibrium tends to infinity, exhibiting the following characteristics: The coefficient continuously approaches 1, indicating that the system's response to external disturbances becomes abnormally sluggish, like a relaxation process being extremely stretched. Secondly, the volatility amplification index calculates the variance of the entire group's opinions in real time. The study analyzes the trend and fluctuation amplitude of the macroscopic order parameter within the sliding time window. Near the critical point, due to the disappearance of system resilience, small fluctuations at the microscopic individual level are strongly amplified, leading to an abnormally large increase in the fluctuation amplitude of the macroscopic order parameter and exhibiting violent oscillation characteristics. Third, the structural entropy increase index discretizes the continuous opinion value range into several intervals, calculates the empirical probability of the opinion distribution at each time step, and then calculates the information entropy. As the system tends towards disorder and differentiation, the opinion distribution changes from a sharp unimodal to a flat multimodal distribution, and the entropy value... It will show a monotonically increasing trend, and its rate of change The acceleration of [something] is a sensitive indicator of the exacerbation of system disorder. Fourth, the barrier decay index is the most direct and physically meaningful stability indicator. Based on the dynamically updated free energy surface, the depth of the current dominant stable state (the depression in which the system is most likely to be located) and the height of the barrier separating it from adjacent competing states are continuously calculated. A significant reduction in the potential barrier height means that the energy barrier for system state switching has almost disappeared. A tiny random perturbation can drive the system to cross the barrier and fall into another depression, i.e., a macroscopic state transition occurs. These four indicators detect stability erosion from the perspectives of system dynamic response, macroscopic fluctuations, structural disorder, and energy topography, respectively, forming a three-dimensional monitoring network.

[0037] Furthermore, a single early warning indicator may produce false alarms due to data noise, model errors, or special circumstances. To improve the accuracy, robustness, and reliability of the early warning system, this invention employs a risk early warning discrimination module for public opinion risk discrimination and early warning output. Based on a rule-based multi-indicator fusion and hierarchical triggering mechanism, all real-time calculated indicator sequences are standardized, and their short-term and medium-term trends are analyzed within a sliding time window. Corresponding level early warnings are triggered based on the characteristics of indicator changes.

[0038] The risk warning and judgment module includes three warning levels: Level 1, Level 2, and Level 3. Level 1 warnings are triggered when the volatility amplification index and the structural entropy increase index simultaneously exceed the preset volatility amplification threshold and the preset structural entropy increase threshold, respectively, and maintain an upward trend for more than a preset duration. This level of warning indicates that the system is showing signs of anomalies and differentiation, and manual intervention and mild intervention are recommended. Level 2 warnings are triggered when, in addition to meeting the conditions for Level 1 warnings, the critical slowing index also exceeds the critical slowing threshold, and the trends of the critical slowing index, volatility amplification index, and structural entropy increase index continue to worsen. This level of warning indicates that the system not only experiences increased internal volatility but also a significant decrease in self-recovery capability, and the risk of instability has entered an upward channel. A warning consultation should be initiated, and corresponding contingency plans should be prepared. Level 3 warnings are triggered when, in addition to meeting the conditions for Level 2 warnings, the barrier height index drops below the preset barrier height threshold (which can be determined through historical data statistics or theoretical analysis). This generates the highest-level alarm and outputs a structured analysis report containing system state diagnosis, target state prediction, identification of key influencing nodes, and suggested intervention directions. The collapse of the potential barrier is strong scientific evidence that an irreversible state transition is imminent in the system. Once triggered, the system will automatically generate the highest-level alert and output a structured analysis report containing a diagnosis of the current system state, a prediction of the most likely transition state, identification of key influencing nodes (such as highly connected or highly influential individuals), and suggested intervention directions. This report requires decision-makers to immediately activate the emergency response mechanism. The warning results are presented through a visualized command cockpit, including indicator time series diagrams, free energy landscape evolution animations, and warning event timelines, providing intuitive and comprehensive situational awareness support for decision-making.

[0039] like Figure 3 The diagram shown is a flowchart of the risk warning system for multi-event iterative verification and learning provided in this application embodiment. The network public opinion phase transition analysis and warning system integrating information entropy and physical field theory also includes a model self-optimization module. This module is connected to the dynamics model construction module, energy landscape modeling module, and risk warning discrimination module via parameter feedback links. The model self-optimization module is used to realize system verification, calibration, and adaptive learning, specifically including the following steps: Using historically established events with significant public opinion shifts and consensus collapse and sudden polarization characteristics, such as typical black swan events, the entire process is backtested. By comparing the warning time points automatically issued by the system with the actual time points of drastic turning points in the events, the key performance indicators such as the lead time, accuracy, and recall rate of the warnings are quantitatively evaluated, thereby scientifically verifying the effectiveness of this method. Based on this, Bayesian inference methods are used to analyze key parameters (such as baseline coupling strength) in the model (a composite analysis and warning system containing nonlinear dynamics models, energy landscape models, and phase transition precursor indicator extraction logic, used to simulate how public opinion changes, the system's stable state, and how far it is from collapse (phase transition)). Modulation coefficient Different user groups , The calibration process involves global calibration of the model output with historical observation data, using prior distributions and warning thresholds to achieve optimal fit. First, initial distributions are set for key parameters and warning thresholds based on prior knowledge. Then, using historical event data, the differences between the model's output warning time points, phase transition precursor sequence, and actual observation results under given parameter combinations are calculated. Based on this, performance metrics such as warning lead time, accuracy, and recall are evaluated, and a likelihood function is constructed to quantify the consistency between the model and historical data. Using Bayes' theorem, the prior distribution and likelihood function are combined to derive the posterior distribution of the parameters. The goal of calibration is to find an optimal set of parameters that minimizes the warning lead time error of the model output, while simultaneously meeting the preset loss threshold requirements for accuracy and recall, thus achieving optimal fit between the model output and historical observation data. This process is typically achieved by solving for the expected or maximum value of the posterior distribution, ensuring that the model not only conforms to historical patterns but also that the predictive performance is controlled within an acceptable range, thereby achieving optimal fit between parameters and thresholds. After the system is officially launched, an online adaptive learning mechanism will be established. The system continuously records each warning trigger and the actual development of public opinion over a subsequent period (whether a phase shift or intense conflict actually occurred), forming a warning-result feedback loop. Using this incremental feedback data, the system dynamically fine-tunes the warning threshold and some model parameters through online learning. This allows the system to gradually adapt to new public opinion environments, new platform characteristics, and new information manipulation methods, achieving continuous optimization of warning performance and resistance to aging, thus forming a self-improving intelligent warning system.

[0040] In summary, through the aforementioned interconnected and meticulous implementation steps, this invention successfully engineered the phase transition theory of physics, the energy landscape framework, and the scientific concepts of complex systems into an end-to-end, data-driven, model- and indicator-driven intelligent early warning system for network public opinion risks. It not only provides a novel solution that breaks through the traditional linear threshold early warning paradigm, but also ensures the unity of scientific validity, practicality, and scalability through a complete technical chain from the construction of the minimum system equation to the fusion of multiple indicators for early warning. This provides solid technical support for achieving forward-looking risk governance in complex cyberspace systems.

[0041] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0042] This invention is described with reference to flowchart illustrations and / or block diagrams of systems, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0043] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0044] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0045] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0046] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A network public opinion phase transition analysis and early warning system that fuses information entropy and physical field theory, characterized in that, It includes modules for public opinion data processing, model building, energy landscape modeling, phase change precursor extraction, and risk warning and discrimination. The public opinion data processing module is used to preprocess the acquired online public opinion data, mapping the online public opinion text to individual opinion status variables. The online public opinion data includes, but is not limited to, public opinion text content, release time information and platform source identifier. The data preprocessing includes cleaning, noise reduction and normalization processing. The model building module is used to construct a nonlinear dynamic model based on individual opinion state variables. The nonlinear dynamic model includes a decay term, a social interaction term, and a random noise term. The energy landscape modeling module is used to introduce the concept of physical energy modeling on the basis of nonlinear dynamics model, and to map the macroscopic state of the public opinion system into an energy function; The phase transition precursor extraction module is used to extract precursor indicators that reflect the system approaching the critical state of phase transition by analyzing the changes in the energy potential landscape structure and statistical characteristics during the evolution of the public opinion system. The risk warning and discrimination module is used to judge the public opinion risk status based on the changes in the phase transition precursor indicators, and output the public opinion risk warning result when the preset criteria are met.

2. The network public opinion phase transition analysis and early warning system that fuses information entropy and physical field theory according to claim 1, wherein, The step of mapping public opinion text into numerical individual opinion state variables includes: The probability distribution of the input text belonging to a preset ordered category is determined for the target issue. The probability distribution is aggregated into a single scalar value as the base value of individual opinions through a mapping function. The ordered categories include strongly opposed, opposed, neutral, supported, and strongly supported. Aggregate the probability distributions of each online public opinion text corresponding to an ordered category as the base scalar value; The user's historical speaking behavior is matched with a preset opinion fluctuation-perturbation variance mapping table to generate the corresponding user's random perturbation variance. The opinion fluctuation-perturbation variance mapping table is a lookup table used to quantify the degree of opinion fluctuation into random perturbation variance. Based on the random perturbation variance of each user, a personalized perturbation is added to the corresponding basic scalar value to obtain the initial value of the individual opinion state, which is used as the initial opinion state of the nonlinear dynamic model.

3. The network public opinion phase transition analysis and early warning system that fuses information entropy and physical field theory according to claim 1, characterized in that, The nonlinear dynamic model is as follows: ； wherein, represents the rate of change of opinion over time for individual i, i is the individual number, i = 1, 2, 3,..., N, N is the total number of individuals, represents the decay term for individual i, is the social interaction term for individual i with all other individuals j, where is the time-varying social coupling strength; is the element of the network adjacency matrix; function is the homophily function for individual i with respect to individual j, threshold is the opinion tolerance radius of individual ; function is the nonlinear social response function, parameter is the response sensitivity of the individual, is the Gaussian white noise term.

4. The network public opinion phase transition analysis and early warning system that fuses information entropy and physical field theory according to claim 3, characterized in that, The dynamics model building module is also used to identify and set the parameters in the minimum social dynamics model, specifically: By matching and inverting the model output with observed opinion fluctuations, or by correlating it with observed macro-level interaction indicators, the time-varying social coupling strength is set. By analyzing the statistical relationship between the volatility of users' historical speech sequences and the social influences they receive, we can fit the individual's response sensitivity parameters. By analyzing the distribution of opinions among users' interactions, the actual range of opinions accepted can be estimated, thus obtaining the individual's opinion tolerance radius.

5. The network public opinion phase transition analysis and early warning system integrating information entropy and physical field theory as described in claim 1, characterized in that, The steps for constructing the free energy function and potential energy landscape of the system include: The average opinion of the system is selected as the main order parameter, and the opinion variance is selected as the auxiliary order parameter. The free energy landscape is dynamically reconstructed using the main order parameter and auxiliary order parameter to obtain the free energy surface; The local minimum points on the free energy surface are taken as the stable state of the public opinion system. First-order saddle points connecting different minimum points are identified, and the potential barrier height between adjacent minimum points and corresponding saddle points is calculated. Continuously monitor the dynamic evolution of the potential energy landscape to predict the changing trend of system stability.

6. The network public opinion phase transition analysis and early warning system integrating information entropy and physical field theory as described in claim 5, characterized in that, The steps for reconstructing the free energy landscape using a numerical method based on large deviation theory include: Monte Carlo simulations were performed on the nonlinear dynamic model, and the system states were sampled in large quantities during the simulation process, recording the two-dimensional plane values ​​corresponding to each state. The empirical probability density of statistical sampling points appearing on a two-dimensional plane; The free energy surface is dynamically calculated based on the proportionality constant related to the effective temperature in the Boltzmann distribution relationship of statistical physics.

7. The network public opinion phase transition analysis and early warning system integrating information entropy and physical field theory as described in claim 1, characterized in that, The extracted precursor indicators of phase transition include critical slowing indicators, fluctuation amplification indicators, structural entropy increase indicators, and barrier decay indicators.

8. The network public opinion phase transition analysis and early warning system integrating information entropy and physical field theory as described in claim 7, characterized in that, The risk warning and judgment module performs public opinion risk judgment and warning output. It adopts a multi-indicator fusion and hierarchical triggering mechanism. Within the sliding time window, it triggers the corresponding level of warning based on the change characteristics of the phase change precursor indicators and the phase change precursor threshold indicators. The phase change precursor threshold indicators include the fluctuation amplification threshold, the structural entropy increase threshold, the critical slowing threshold, and the barrier height threshold.

9. The network public opinion phase transition analysis and early warning system integrating information entropy and physical field theory as described in claim 8, characterized in that, The specific steps for triggering corresponding level early warnings based on changes in phase transition precursor indicators within the sliding time window are as follows: The risk warning judgment module has three warning levels: Level 1, Level 2, and Level 3. Level 1 warning is triggered when the fluctuation amplification index and the structural entropy increase index simultaneously exceed the preset fluctuation amplification threshold and the preset structural entropy increase threshold, respectively, and maintain an upward trend for more than a preset duration. Level 2 warning is triggered when, in addition to meeting the conditions for Level 1 warning, the critical slowing index also exceeds the critical slowing threshold, and the trends of the critical slowing index, fluctuation amplification index, and structural entropy increase index continue to deteriorate. Level 3 warning is triggered when, in addition to meeting the conditions for Level 2 warning, the barrier height index drops below the preset barrier height threshold, generating the preset highest-level alarm and outputting a structured analysis report.

10. The network public opinion phase transition analysis and early warning system integrating information entropy and physical field theory as described in claim 1, characterized in that, It also includes a model self-optimization module for public opinion verification, calibration, and adaptive learning, specifically including the following steps: Retrospective testing of historical public opinion events is conducted to compare the automatically issued warning time points with the actual turning points of the events, and the warning performance indicators are evaluated. The warning performance indicators include, but are not limited to, warning lead time, accuracy, and recall rate. Based on the results of the backtest, the key parameters and the phase transition precursor threshold index are globally calibrated so that the loss function value between the model output and the historical observation data is lower than the preset loss threshold. The key parameters include baseline coupling strength, modulation coefficient, and prior distribution parameters of different user groups.

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