SDGs causal network toughness optimization method based on multi-modal data

Abstract

The invention relates to an SDGs causal network toughness optimization method based on multi-modal data, and belongs to the technical field of sustainable development complex network data analysis, and the method comprises the following steps: obtaining multi-modal time sequence data representing SDGs, and carrying out missing value interpolation, standardization and time alignment processing on the data; predicting the future progress of each SDG based on a gated cycle unit model; identifying the causal relationship between the SDGs by using a panel vector autoregression model; calculating a potential interaction probability in combination with a local path index and a weighted random walk restart model, complementing missing links and forming a complete causal network; a multi-scene disturbance experiment is utilized, and a weighted clustering coefficient and weighted global efficiency are adopted to comprehensively calculate the overall toughness index of the network; and taking the toughness index as a fitness function, and performing global optimization by using a genetic algorithm to obtain an optimal network structure configuration and a priority management path. According to the method, the interaction relationship between the SDGs is quantitatively identified, the network structure and function toughness is improved, and technical support is provided for collaborative promotion and policy optimization of the SDGs.

Description

Technical Field

[0001] This invention belongs to the field of data analysis technology for complex networks in sustainable development, and specifically relates to a method for optimizing the resilience of SDGs causal networks based on multimodal data. Background Technology

[0002] The Sustainable Development Goals (SDGs) aim to address the multiple social, economic, and environmental challenges facing the world and promote overall prosperity and peace for humanity and the planet. However, since 2020, the overall progress of the global SDGs has slowed significantly, with most SDGs showing limited progress or even regression. The SDGs and their specific indicators are closely and complexly interconnected. Actions toward one goal often have positive or negative cascading effects on other goals, resulting in synergies and trade-offs. Identifying and leveraging these interactions—for example, maximizing synergies and minimizing trade-offs—is key to achieving coordinated progress on the SDGs and optimizing policy design.

[0003] Currently, numerous studies explore the interactions between SDGs at different scales, primarily including qualitative studies based on expert consultation or literature meta-analysis, and quantitative studies based on correlation, network analysis, and regression models. Among these, network analysis, as a crucial tool of systems thinking, plays a central role in identifying structural relationships and key nodes among SDGs. However, existing research on SDG interaction networks still suffers from two shortcomings: first, the utilization of network structure information is insufficient, making it difficult to comprehensively reflect potential relationships between objectives; second, it largely focuses on static network assessments, lacking characterization of the network's dynamic response and recovery capabilities under external disturbances. Link prediction, as an effective network completion method, can identify potential but unobserved interactions, thereby improving the integrity of the network structure and the accuracy of key node identification. This method has been widely applied in cooperative networks, heterogeneous information networks, and biological networks, but its application in SDG interaction networks remains limited. Meanwhile, robustness and resilience analysis in complex network theory is used to measure the system's ability to maintain function when nodes or links fail. Existing research indicates that a few structurally critical nodes play a decisive role in overall connectivity and function, and their failure can lead to a sharp decline in network performance. However, current research on SDG interactive networks lacks systematic studies on the dynamic resilience evolution and optimization mechanisms of networks under multiple scenario perturbations, making it difficult to achieve controllable optimization of the relationship between cooperation and trade-offs. This deficiency limits the scientific support for SDG policy simulation and the identification of governance priorities.

[0004] Therefore, there is an urgent need to propose a causal network resilience optimization method for SDGs based on multimodal data. This method can integrate multi-source time-series data, identify explicit and potential interaction relationships, quantify the recovery capability of network structure and function under multiple perturbation scenarios, and achieve synergistic reinforcement and trade-off reduction through algorithm optimization to improve the overall resilience of the network and provide technical support for the systematic advancement and scientific decision-making of SDGs. Summary of the Invention

[0005] One of the objectives of this invention is to provide a method for optimizing the resilience of SDG causal networks based on multimodal data. This method addresses the problem that existing SDG interaction assessment methods rely on static structures or qualitative analysis, making it difficult to identify potential interaction relationships, quantitatively characterize network resilience under external disturbances, and achieve coordinated and controllable optimization. This method can quantitatively identify the interaction relationships between SDGs and improve the resilience of network structure and function, providing technical support for the coordinated advancement and policy optimization of SDGs.

[0006] This invention is achieved through the following technical solution: a method for optimizing the resilience of SDGs causal networks based on multimodal data, comprising the following steps:

[0007] A method for optimizing the resilience of SDGs causal networks based on multimodal data includes the following steps:

[0008] Obtain the evaluation metric framework and multimodal time series data representing SDGs; among them, perform missing value imputation, standardization and time alignment on the data to form comparable time series datasets;

[0009] Based on a gated recurrent unit deep learning model, the future progress of each SDG is predicted, and the SDG score sequence for future time periods is output.

[0010] Based on the panel vector autoregression model, the causal interaction relationship among SDGs is calculated to obtain the causal coefficient matrix;

[0011] A link prediction combined model that combines local path index and weighted random walk restart is adopted to calculate the probability of the existence of potential causal relationships. The obtained scores are then mapped to weights to fill in the unidentified node pairs in the panel vector autoregression model results, keeping the original causal relationship direction and weight unchanged, thus forming a complete SDGs weighted directed causal network.

[0012] Multiple perturbation scenarios were set up on the complete SDGs causal network, including four types of methods: random removal of trade-off edges, removal of trade-off edges sorted by weight, removal of trade-off edges sorted by minimum cut value, and overall enhancement of collaborative edge weights, to simulate the network response under external shocks. For each perturbation scenario, weighted clustering coefficients and weighted global efficiency were calculated, and after standardization, an equal-weighted average was taken to define the overall resilience index. The resilience index is used to characterize the overall stability of the network under both structural connectivity and functional efficiency dimensions.

[0013] Using the comprehensive resilience index as the fitness function, a genetic algorithm is used to globally optimize the network collaborative edge weights. The steps include population initialization, fitness evaluation, selection, crossover, mutation and iterative convergence, and output the optimal edge weight configuration scheme. Based on the optimized SDGs causal network, the changes in resilience index before and after the perturbation are compared to identify the key SDGs interaction relationships in improving network resilience.

[0014] Optionally, the standardization process involves mapping all indicator values ​​to the 0-100 range and performing a linear transformation based on the target and benchmark values ​​to mitigate the potential impact of data distribution skew on the standardization results.

[0015] Furthermore, 100 points are assigned to values ​​exceeding the target value, and 0 points are assigned to values ​​below the benchmark value, in order to ensure the consistency of dimensions and the stability of calculation among indicators. To avoid additional uncertainty caused by subjective weighting, each indicator is aggregated with equal weights under the same specific SDG target to form standardized panel data for causal modeling.

[0016] Optionally, historical time-series data can be modeled, and the SDGs score sequence for future periods can be output through the update gate and reset gate mechanism of the mathematical model.

[0017] Optionally, after parameter estimation, the coefficient matrix is ​​transformed into a weighted directed adjacency matrix, where the coefficient sign indicates the direction of influence, and the absolute value of the coefficient is linearly normalized to [−1,1] as the edge weight.

[0018] Optionally, the local path index can be calculated as follows:

[0019] By inversely weighting the nodes based on the importance of their common neighbors, and taking the minimum value of each node, the result is normalized to prevent nodes with high degrees from dominating the outcome.

[0020] Summing over all common neighbors and adjusting the weights using a damping factor reinforces the effect of common neighbor scarcity.

[0021] The square root of the product of node degrees is taken as the reciprocal and used for global normalization to obtain the local path index.

[0022] Furthermore, based on the original random walk restart algorithm, a weighted random walk restart model is adopted to enhance global metric capabilities. Its calculation method is as follows:

[0023] The node's score is obtained by calculating the weighted sum of the scores of all its neighbors according to their transition probabilities;

[0024] The probability of continuing to walk without restarting controls the degree of exploration of the graph structure, and the weighted random walk restarts;

[0025] Remove the minimum value from the original WRWR values ​​calculated for all node pairs;

[0026] The maximum and minimum values ​​of the original WRWR values ​​calculated for all node pairs are compared to obtain the standardized WRWR value for each node.

[0027] Optionally, to quantify the impact of different external disturbances on the causal network structure and functional stability of SDGs, a network resilience simulation model with edge disturbances is defined. The disturbances are applied to the directed weighted edges in the network resilience simulation model that represent the relationships between SDGs. By simulating the failure and optimization process of the edges, the structural stability and functional recovery capability under different impact scenarios are reflected.

[0028] Furthermore, for each disturbance scenario, the structural and functional resilience of the network before and after the disturbance is calculated to assess the changes in the overall robustness of the system. Structural resilience is measured by weighted clustering coefficients to measure network connectivity, while functional resilience is measured by weighted global efficiency to measure the efficiency of information transmission between nodes.

[0029] Optionally, to further enhance the overall resilience and synergistic effect of the SDGs causal network, a genetic algorithm is used to globally optimize the weights of the synergistic edges in the network. The genetic algorithm uses the overall resilience index as the fitness function and searches through multiple generations of iterative evolution to identify the optimal edge weight configuration that achieves overall synergistic enhancement.

[0030] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0031] 1. This invention introduces a gated recurrent unit deep learning model to perform time series prediction on multi-source social, economic, resource and environmental data, which can dynamically simulate the progress trend of future SDGs and provide reliable input for subsequent causal identification and network construction.

[0032] 2. This invention quantitatively identifies causal relationships among SDGs based on a panel vector autoregression model, avoiding the subjective bias of traditional expert consultation methods, achieving objectivity, standardization, and repeatability of causal relationship identification, and ensuring the robustness and verifiability of the model results.

[0033] 3. This invention identifies and completes missing potential interaction relationships by combining the local path index with the link prediction algorithm of weighted random walk restart, forming a more complete and information-rich SDGs weighted directed causal network.

[0034] 4. This invention utilizes various network disturbance scenarios to systematically evaluate the structural stability and functional recovery capability of the network under external shocks. With the comprehensive resilience index as the optimization target, a genetic algorithm is used to globally optimize the cooperative edge weights, thereby improving the overall resilience and cooperative effect of the causal network.

[0035] 5. Based on the changes in network structure and resilience index before and after the disturbance, this invention can quantitatively identify the key causal chains and edge weight adjustment directions that have the highest priority impact on system stability and recovery capability, providing a scientific basis for formulating targeted intervention measures and optimizing policy paths, and realizing the direct transformation from resilience quantification to governance action.

[0036] 6. This invention has good scalability and can be applied to SDGs causal network modeling and optimization in different regions, providing technical support for global SDGs policy evaluation and collaborative governance. Attached Figure Description

[0037] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0038] Figure 1 This is a flowchart illustrating the overall workflow of the present invention.

[0039] Figure 2 This is a diagram showing the causal matrix and link prediction results of the SDGs of this invention.

[0040] Figure 3 This is a schematic diagram of the SDGs causal network structure of the present invention.

[0041] Figure 4 This is a schematic diagram of the SDGs causal network disturbance scenario of the present invention.

[0042] Figure 5 The diagram shows the optimization results of SDGs causal network perturbation and resilience in this invention. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0044] Example 1

[0045] like Figure 1 As shown in the figure, this embodiment provides a method for optimizing the resilience of SDGs causal networks based on multimodal data, including the following steps:

[0046] S1: Obtain the evaluation indicator framework and multimodal time series data representing the SDGs. The data includes indicators from multiple fields such as society, economy, resources and environment. To achieve comparability between different SDG indicators, the original data is imputed for missing values, standardized and time aligned based on the multimodal time series data to form a comparable time series dataset.

[0047] The standardization process maps all index values ​​to the 0-100 range and performs a linear transformation based on the target value (upper bound) and the benchmark value (lower bound) to mitigate the potential impact of data distribution skew on the standardization results. The standardization formula is as follows:

[0048] ;

[0049] In the formula, This represents the standardized value of a specific SDG indicator. These are the original values. and These are the target value and the baseline value, respectively.

[0050] The setting of target and baseline values ​​should follow these principles:

[0051] (1) The target values ​​are determined based on the latest sustainability report released by the United Nations Sustainable Development Solutions Network;

[0052] (2) For some indicators, the target value can be determined by using absolute quantification thresholds or zero deprivation criteria;

[0053] (3) The average value of the best-performing sample during the reference period is used as the target value for the remaining indicators;

[0054] (4) The benchmark values ​​are uniformly set according to the latest sustainable development report released by the United Nations Sustainable Development Solutions Network, or determined according to the bottom 2.5 percentile of the historical data distribution.

[0055] Based on this, values ​​exceeding the target are assigned 100 points, while values ​​below the benchmark are assigned 0 points, ensuring consistency in dimensionality and computational stability among the indicators. To avoid additional uncertainty caused by subjective weighting, each indicator is aggregated with equal weights under the same specific SDG objective, forming standardized panel data for causal modeling.

[0056] S2: Based on the GatedRecurrentUnit deep learning model, it models historical time series data, predicts the future progress of each SDG, and outputs the progress score of SDGs in future time periods (i.e., the score sequence of SDGs in future time periods).

[0057] The mathematical model includes update gates and reset gates, and the calculation expression is as follows:

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] In the formula, To update the door, The reset gate takes values ​​in the range [0,1]; the update gate determines whether to retain the hidden state from the previous time step. Which parts of the reset gate are used to determine the hidden state of the previous time step? Which parts need to be ignored; This is the Sigmoid function, which restricts the output to the range [0,1]. , , and These are the weight matrices for the update gate, reset gate, candidate hidden state, and fully connected layer, respectively. Input for the current time step t; , , and These are the update gate, reset gate, candidate hidden state, and bias vector of the fully connected layer, respectively. This is the candidate hidden state; Given a hyperbolic tangent function, the output is restricted to the range [−1, 1]. This is the final hidden state; For Hadamard product, For the future Time node or future Progress score of SDGs for each sample.

[0064] The model parameters are trained using the backpropagation algorithm to obtain the predicted score sequence of SDGs for future time periods.

[0065] S3: After obtaining the time series of SDGs, the causal interaction relationship between each SDG is calculated based on the panel vector autoregressive model to obtain the weighted directed adjacency matrix (i.e., the causal coefficient matrix), which is used to construct the initial causal network.

[0066] The model is in the following form:

[0067] ;

[0068] In the formula, Indicates the first One sample in SDGs score at any given moment; Individual fixed effects; This is a time-fixed effect; The lag order; The autoregressive term represents the effect of lagged terms of the explained variable on the current value. Multiply by a sign; For parameter matrices; for of lag term; This is a random disturbance term.

[0069] After parameter estimation, the coefficient matrix is ​​transformed into a weighted directed adjacency matrix. The sign of the coefficient indicates the direction of influence (positive for cooperation, negative for trade-off). The absolute value of the coefficient is linearly standardized to [−1,1] as the edge weight.

[0070] S4: For the node pairs not identified by the panel vector autoregression model in step S3, a link prediction combination model of Local Path Index (LPI) and Weighted Random Walk with Restart (WRWR) is adopted to calculate the probability of the existence of potential edges between nodes (i.e., the probability of the existence of potential causal relationships). The obtained scores are mapped to weights to fill in the unidentified node pairs in the panel vector autoregression model results, keeping the original causal relationship direction and weight unchanged, thereby forming a complete SDGs weighted directed causal network.

[0071] Among them, the local path index The calculation formula is defined as follows:

[0072] ;

[0073] In the formula, i is the given node, and j is all other nodes; and Let i and j be the sets of neighbors of nodes i and j, respectively; z is the common neighbor of i and j. , and Let i, j, and z be the degrees of nodes i, j, and z, respectively. This is a damping factor, usually set to less than 1, to reduce the weight influence of longer paths and is used to characterize the potential connection strength of node pairs in a local ternary closed structure.

[0074] The importance of common neighbors is inversely weighted; the smaller the degree of a common neighbor, the greater its contribution to the local association between i and j. To obtain the minimum value of nodes i and j for normalization, and to avoid nodes with high degree dominating the result; It is the sum of all common neighbors z, which is the reciprocal of the degree. The smaller the degree of the common neighbors, the stronger their contribution to the path between node i and node j (because nodes with small degrees are scarcer in the network, and the paths they connect are more distinctive).

[0075] To cube the summation result, and through Adjusting the weights further strengthens the impact of the scarcity of common neighbors.

[0076] This is the square root and reciprocal of the product of the degrees of nodes i and j, used for global normalization. Because the larger the degree of a node, the more potential connections it has, this term can weaken the natural advantage of high-difficulty nodes for LPI, making the metric more focused on the intrinsic connections of local paths.

[0077] Based on the original random walk restart algorithm, a weighted random walk restart model is proposed to enhance global metric capabilities. Its calculation formula is as follows:

[0078] ;

[0079] In the formula, Represents a node With nodes Standardized WRWR value; The restart probability is denoted as 0.15 in this invention; N is the total number of nodes. node The score is obtained by weighting the scores of all neighbors z according to their transition probabilities; Represents a node The standardized weighted transition probability to node z. Represents a node The set of all neighboring nodes (i.e., with) Directly connected nodes). Represents a node The weight of the edge to node z reflects The intensity transferred directly to z. For random walk from node To the node The cumulative walk probability; Let Kronecker function be used when = The value is 1 for the time period and 0 for the rest. and These are the maximum and minimum values ​​among the original WR values ​​calculated for all node pairs. This indicates the probability of continuing to roam without restarting, controlling the degree of exploration of the graph structure; This is a restart item.

[0080] After obtaining the above two metrics, a combined link prediction model is constructed, which weights and fuses local structure information and global walk information. The combined score is defined as:

[0081] ;

[0082] In the formula, This represents the combined link prediction score between nodes i and j; The weighting coefficient is 0.5 in this invention.

[0083] By mapping the combined scores to corresponding edge weights, and assigning these weights only to node pairs not identified by the panel vector autoregressive model, while maintaining the original causal relationships' directions and weights, a structurally complete weighted directed causal network of SDGs can be constructed. In this network, nodes represent specific objectives of different SDGs, edges represent the positive or negative impact of one SDG objective on another; the direction of the edges reflects the flow of influence, and the edge weights reflect the intensity of the interaction.

[0084] S5: Multiple perturbation scenarios are set up on the complete SDGs causal network, including four methods: random removal of trade-off edges, removal of trade-off edges sorted by weight, removal of trade-off edges sorted by minimum cut value, and overall enhancement of collaborative edge weights, to simulate the network response under external shocks. For each perturbation scenario, weighted clustering coefficients and weighted global efficiency are calculated, and after standardization, an equal-weighted average is taken to define the overall resilience index. The resilience index is used to characterize the overall stability of the network under both structural connectivity and functional efficiency dimensions.

[0085] To quantify the impact of different external disturbances on the structural and functional stability of the causal network of SDGs, this invention designs a network resilience simulation model based on edge perturbation. The perturbation is applied to the directed weighted edges representing the relationships between SDGs in the network resilience simulation model. By simulating the failure and optimization process of the edges, the structural stability and functional recovery capability of the system under different impact scenarios are reflected.

[0086] The disturbance scenarios include:

[0087] (1) Randomly select and remove several edges with negative effects to simulate the trade-off between randomness and reduction;

[0088] (2) Remove the weighted edges in descending order of their absolute weight values;

[0089] (3) Use the minimum cut algorithm to identify the set of key edges that minimize the total weight under the condition of completely cutting off the path from the source node to the target node, and remove them in order of importance;

[0090] (4) Implement overall enhancement of the weights of all positive collaborative edges to simulate collaborative reinforcement caused by external intervention or resource input.

[0091] For each perturbation scenario, the structural and functional resilience of the network before and after the perturbation is calculated to assess the change in the overall robustness of the system. Structural resilience is assessed using weighted clustering coefficients. Network connectivity and functional resilience are measured using weighted global efficiency. The efficiency of information transmission between nodes is calculated using the following formula:

[0092] ;

[0093] ;

[0094] In the formula, N is the total number of nodes; Let i represent the set of neighbors of node i; , and These represent the edge weights from node i to node j, from node j to node k, and from node k to node i, respectively. This represents the shortest path between nodes i and j; Representing a path Above The weight.

[0095] After standardization, the overall toughness function is defined. :

[0096] ;

[0097] In the formula, and These are the standardized weighted clustering coefficients and the weighted global efficiency, respectively.

[0098] S6: The comprehensive resilience index is a fitness function. A genetic algorithm is used to globally optimize the network's collaborative edge weights. The steps include population initialization, fitness evaluation, selection, crossover, mutation, and iterative convergence, outputting the optimal edge weight configuration. Based on the optimized SDGs causal network, the changes in the resilience index before and after the perturbation are compared to identify the key SDGs interactions in improving network resilience.

[0099] To further enhance the overall resilience and synergistic effect of the SDGs causal network, a genetic algorithm is used to globally optimize the weights of the synergistic edges in the network. The genetic algorithm uses the overall resilience index as the optimization factor. Using the fitness function, the optimal edge weight configuration that achieves overall synergistic enhancement is identified through multi-generation iterative evolutionary search.

[0100] The main steps of the algorithm include:

[0101] (1) Randomly generate an initial population of collaborative edge weights, where each individual represents a possible combination of edge weights;

[0102] (2) Calculate the fitness of each individual based on the comprehensive resilience index;

[0103] (3) Use the Tournament Selection strategy to replicate based on the individual with the highest fitness;

[0104] (4) Perform a single-point crossover operation with the set crossover probability, and generate a new offspring by mixing the edge weight information of the two groups of individuals;

[0105] (5) Randomly perturb the individual partial edge weights with a set mutation probability;

[0106] (6) Set the maximum number of iterations and population size, and terminate the iteration when the fitness no longer improves for several consecutive generations;

[0107] (7) Output the individual with the highest fitness as the optimal solution, which corresponds to the optimal weight configuration of the collaborative edges in the network.

[0108] The general form of the algorithm can be expressed as:

[0109] ;

[0110] In the formula, This generation represents evolution. Indicates the next generation of evolution; The fitness function is used to evaluate an individual. Comprehensive resilience; , , These represent the selection, crossover, and mutation operators, respectively.

[0111] Through the above steps, the global optimization of the collaborative edge weights can be achieved, thereby maximizing the overall resilience index of the network while reducing trade-offs, resulting in an optimized and resilient network structure.

[0112] Example 2

[0113] Based on Example 1, to address the problem that existing technologies rely heavily on qualitative analysis and lack quantitative analysis of systemic resilience in SDGs interaction research, this example provides an SDGs causal network resilience optimization method based on multimodal data. This method integrates multi-source time-series data, deep learning prediction models, panel causal analysis, link prediction algorithms, and network optimization simulation to achieve dynamic identification of SDGs interaction relationships and overall resilience improvement.

[0114] like Figure 1 As shown, this embodiment includes the following steps:

[0115] S1: Referring to the global SDGs indicator framework proposed by the United Nations Statistics Division, the World Bank, the United Nations Sustainable Development Solutions Network, OurWorldinData, the World Health Organization, and the Food and Agriculture Organization of the United Nations, 45 indicators (Table 1) were selected to assess the six SDGs and their 33 specific targets related to resources, economy, climate, and ecology. Annual data for these indicators from 162 countries from 2000 to 2023 were collected.

[0116] The data underwent imputation for missing values ​​(using methods such as linear interpolation, spline interpolation, and interpolation based on equal values ​​or mean values ​​between preceding and following years), standardization, and time alignment. To ensure comparability between different indicators, the original data was standardized to a range of 0-100 points, and a target value (upper bound) and a benchmark value (lower bound) were set for each indicator.

[0117] The determination of the target value (upper bound) follows four principles:

[0118] (1) Adopt the target setting (8 of the 45 SDG indicators) in the latest "Sustainable Development Report 2025: Financing Sustainable Development to 2030 and Mid-Century" published by the United Nations Sustainable Development Solutions Network.

[0119] (2) Use relevant absolute quantitative thresholds for some indicators (9 indicators), such as SDG indicator 2.2.1 (proportion of moderately or severely overweight children, %).

[0120] (3) Based on the principle of “leaving no one behind”, set target values ​​for zero deprivation or universal accessibility (6 indicators), such as SDG indicator 6.2.2 (percentage of the population using at least basic health services, %).

[0121] (4) For the remaining 22 indicators, the average of the five best-performing countries will be used as the target value. The benchmark (lower bound) will be uniformly set in the latest "Sustainable Development Report 2025: Financing Sustainable Development to 2030 and Mid-Century" published by the United Nations Sustainable Development Solutions Network, or the bottom 2.5% percentile of each country's performance. Based on this, the distribution characteristics of each indicator will be examined, and 100 points (best performance) will be assigned to those exceeding the target value, and 0 points (worst performance) will be assigned to those below the benchmark value.

[0122] To avoid introducing additional uncertainty due to subjective weighting, all indicators were aggregated with equal weights under the same specific SDG objective. This resulted in panel data on the specific SDG objectives for each country from 2000 to 2023.

[0123] In this embodiment, the research scope is global, and Table 1 shows the framework of SDGs evaluation indicators selected in this embodiment.

[0124] Table 1. Evaluation Indicator Framework for SDGs and Their Specific Objectives

[0125]

[0126] Note: The definitions of the SDGs and their specific targets are consistent with the 2030 Agenda for Sustainable Development. UN refers to the United Nations; WB refers to the World Bank; SDSN refers to the Sustainable Development Solutions Network; FAO refers to the Food and Agriculture Organization of the United Nations.

[0127] S2: A gated recurrent unit deep learning model is used to predict the annual scores of specific targets of each country's SDGs in a time series.

[0128] For example, in this embodiment, the standardized SDGs scores from 2000 to 2023 obtained in step S1 are used as model input to predict the annual SDGs scores from 2024 to 2026. The model input can be expressed as:

[0129]

[0130] In the formula, Let represent the input time series of the i-th country; n is the number of samples, n=162; T is the time step, T=24; F is the number of features, F=33; For the set of input time series; It is a collection of multi-dimensional input time series.

[0131] In model training, this embodiment sets an appropriate number of hidden units and a dropout ratio to prevent overfitting, uses the Adam adaptive moment estimator to update network parameters, and achieves model convergence through iterative training. Through model training and prediction, prediction scores for specific targets in 162 countries from 2000 to 2026 are obtained, providing dynamic input data for subsequent causal identification and network construction.

[0132] S3: After completing the time series forecasting of SDGs, further identification of causal relationships between different SDGs is based on a panel vector autoregressive model. This model integrates the characteristics of time series and cross-sectional data, and can quantitatively characterize the mutual influence and feedback paths between multidimensional variable systems.

[0133] For example, in this embodiment, the SDGs scores of various countries from 2000 to 2026 obtained in step S2 are used as input to construct a panel vector autoregressive model.

[0134] To ensure the robustness of the estimation results, the model first performs a stationarity test on the variables and determines the optimal lag order using the information criterion. Finally, the coefficient matrix is ​​transformed into a weighted directed adjacency matrix, where the sign of the coefficients indicates the direction of influence (positive for synergy, negative for trade-off), and the absolute values ​​of the coefficients are linearly standardized to the interval [-1,1] to represent the strength of the causal effect.

[0135] S4: To supplement the potential interactions not identified by the panel vector autoregressive model, a link prediction algorithm combining local path index and weighted random walk restart is adopted to calculate the potential interaction strength between different SDGs, which is used to construct a complete weighted causal network of SDGs. In this network, nodes represent specific objectives of different SDGs related to resources, economy, climate, and ecology, and edges represent the causal relationships between these SDGs; the direction of the edges reflects the flow of influence, and the thickness and color of the edges reflect the intensity of influence. The colors of the edges from red to blue represent negative (trade-off) and positive (synergistic) relationships, respectively.

[0136] For example, Figure 2 a shows the initial causal relationship matrix identified based on the panel vector autoregressive model in this embodiment. Figure 2b is the potential causal relationship matrix obtained based on the link prediction algorithm. Figure 2 c represents the final causal matrix integrating both factors. Cell colors, from red to blue, represent negative (trade-off) and positive (synergistic) relationships, respectively, with color intensity indicating the strength of causal impact. Based on this, a complete weighted directed causal network of resource-economy-climate-ecology related SDGs is constructed, as follows: Figure 3 As shown.

[0137] S5: In this embodiment, to quantify the impact of external disturbances on the structural and functional stability of the SDGs causal network, a network resilience simulation and optimization scheme based on edge perturbation is designed. This scheme models the process of removing edges and adjusting weights in the network to simulate the structural changes and resilience response of the system under different disturbance scenarios. Figure 4 (1) represents the random removal and weight adjustment process of the trade-off edge. Figure 4 (2) Represents the process of edge removal and weight adjustment based on edge weight. Figure 4 (3) represents the process of edge removal and weight adjustment based on the minimum cut value. Figure 4 (4) Adjustment of collaborative edge weights. To enhance the overall collaborative effect of the network and reduce the impact of trade-offs, a genetic algorithm is used to globally optimize the edge weights of the SDGs causal network, aiming to maximize the overall resilience index of the network. The optimal path for achieving overall synergistic enhancement and robustness improvement is identified by minimizing trade-offs. After optimization, the optimal edge weight configuration is mapped back to the SDG causal network to generate the optimized resilience enhancement network.

[0138] For example, Figure 5 The diagram shows the causal network perturbation and resilience optimization results of the resource-economy-climate-ecology related SDGs provided in this embodiment. Among them, Figure 5 'a' represents the simulation results of 100 perturbations with the trade-off edge randomly removed; the black curve represents the average of the 100 simulations; and the green shaded area represents the 95% confidence interval. Figure 5 b represents the edge removal results based on two deterministic trade-offs: edge weight and minimum cut value. Figure 5 c shows a comparison of the network structure before and after removing the top 20% of the weighted edges; Figure 5 d represents the network structure before optimization; Figure 5 e represents the optimized network structure.

[0139] In the actual operation of this embodiment, a removal simulation was performed on 407 negative trade-off edges in the network, and the weights of 649 positive cooperative edges were adaptively optimized. The results show that the overall resilience index of the optimized network is improved, and the connectivity and information propagation efficiency of the network structure are both improved.

[0140] Based on the optimization results, priority actions can be identified to enhance the resilience of the causal network of resource-economy-climate-ecology related SDGs in the future:

[0141] The study focuses on reducing the top 20% of weighted trade-offs while strengthening 84% of the synergies, thereby achieving a simultaneous improvement in overall network synergy and robustness. Among these, the positive impact of SDG 6.6 (water-related ecosystems) on SDG 2.c (limiting food price anomalies) was identified as a key synergistic path to enhance network resilience and propagation capabilities.

[0142] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for SDGs causal network resilience optimization based on multi-modal data, characterized in that, The method comprises the following steps: Obtaining an evaluation index framework representing the SDGs and multi-modal time series data; wherein the data is subjected to missing value interpolation, standardization and time alignment processing to form a comparable time series data set; Based on the gated recurrent unit deep learning model, the future progress of each SDG is predicted, and the score sequence of the SDGs in the future period is output. Based on the panel vector autoregressive model, the causal interaction relationship between the SDGs is calculated, and a causal coefficient matrix is obtained. A link prediction combination model combining the local path index and the weighted random walk restart is used to calculate the existence probability of the potential causal relationship, and the obtained score is mapped as a weight to complete the node pairs in the panel vector autoregressive model result, and the original causal relationship direction and weight are kept unchanged, so as to form a complete SDGs weighted directed causal network. On the complete SDGs causal network, various disturbance scenarios are set, including randomly removing the trade-off edge, removing the trade-off edge according to the weight order, removing the trade-off edge according to the minimum cut value order and overall enhancement of the collaborative edge weight, to simulate the network response under external impact. For each disturbance scenario, the weighted clustering coefficient and the weighted global efficiency are calculated, and after standardization processing, the equal weight average is taken to define the overall resilience index, which is used to represent the overall stability of the network in the two dimensions of structural connectivity and functional efficiency. Taking the comprehensive resilience index as the fitness function, a genetic algorithm is used to globally optimize the network collaborative edge weight, including population initialization, fitness evaluation, selection, crossover, mutation and iteration convergence, and an optimal edge weight configuration scheme is output. Based on the optimized SDGs causal network, the change of the resilience index before and after the disturbance is compared to identify the key SDGs interaction relationship in the network resilience improvement.

2. The method of claim 1, wherein, The standardization process is to uniformly map all index values to the 0-100 interval, and perform linear conversion based on the target value and the reference value to weaken the potential influence of data distribution skew on the standardization result.

3. The method of claim 2, wherein, 100 points are given to the case of exceeding the target value, and 0 points are given to the case of being lower than the reference value, to ensure the dimensional consistency and calculation stability of the indicators. To avoid additional uncertainty caused by subjective weighting, the indicators are aggregated with equal weight under the same SDG specific target to form the standardized panel data for causal modeling.

4. The method of claim 1, wherein, The historical time series data is modeled, and through the update gate and reset gate mechanism of the mathematical model, the score sequence of the SDGs in the future period is output.

5. The method of claim 1, wherein, After parameter estimation, the coefficient matrix is converted into a weighted directed adjacency matrix, the coefficient sign represents the influence direction, and the coefficient absolute value is linearly standardized to [−1, 1] as the edge weight.

6. The method of claim 1, wherein, The local path index is calculated as follows: The importance of the common neighbor is inversely weighted, and the minimum value of the node is taken for normalization to avoid the dominance of the node with high degree; The sum of all common neighbors is adjusted by a damping factor to strengthen the influence of the scarcity of common neighbors; The product of the node degree is squared and then inverted for global normalization to obtain the local path index.

7. The method of claim 6, wherein, On the basis of the original random walk restart algorithm, a weighted random walk restart model is used to enhance the global measurement capability, and the calculation method is as follows: The score of a node is obtained by summing the scores of all its neighbors weighted by the transition probabilities; The probability of continuing the walk without restarting controls the degree of exploring the graph structure, and the weighted random walk restarts; The minimum value of the WRWR original value calculated for all node pairs is removed; The maximum and minimum values of the WRWR original value calculated for all node pairs are compared to obtain the normalized WRWR value of the node.

8. The method of claim 1, wherein, To quantify the influence of different external disturbances on the structural and functional stability of the SDGs causal network, a network resilience simulation model of edge disturbance is defined, in which the directed weighted edges representing the relationships between SDGs are disturbed. Through the simulation of edge failure and optimization process, the structural stability and functional recovery ability under different impact scenarios are reflected.

9. The method of claim 8, wherein, For each disturbance scenario, the structural and functional resilience of the network before and after the disturbance is calculated to evaluate the overall robustness change. The structural resilience is measured by the weighted clustering coefficient to measure the network connectivity, and the functional resilience is measured by the weighted global efficiency to measure the information transmission efficiency between nodes.

10. The method of claim 1, wherein, To further improve the overall resilience and synergistic effect of the SDGs causal network, a genetic algorithm is used to globally optimize the weights of the synergistic edges in the network. The overall resilience index is used as the fitness function of the genetic algorithm, and through multiple generations of iterative evolution search, the optimal edge weight configuration that achieves overall synergistic enhancement is identified.

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