Industrial chain financial risk prediction method based on RGNN-Crossform fusion architecture

Abstract

The invention discloses an industrial chain financial risk prediction method based on RGNN-Crossform fusion architecture. The method comprises a data preprocessing module, a relation extraction module, a feature embedding module and a final prediction module. Firstly, aiming at the problems of high noise and serious loss of financial data, a function type data analysis method is used for preprocessing original data, and then an industry chain upstream and downstream enterprise association network is constructed through a data driving method and a text driving method; and then a routing mechanism and a graph neural network are introduced into a feature extraction part of the deep learning prediction model to help the model to learn enterprise risk association structures from different information sources, and finally a financial risk prediction model RGNN-Crossform considering an enterprise association relationship is constructed. Experimental results show that the prediction effect of the constructed RGNN-Crossform model is obviously superior to that of various leading edge financial risk prediction models. Wherein the routing mechanism and the graph neural network module are adopted, so that the model can learn data internal dependence and external correlation characteristics at the same time, and the performance and robustness of the model are improved.

Description

Technical Field This invention relates to a supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture, which is applied to supply chain financial risk assessment and belongs to the field of financial technology and supply chain management technology. Background Technology Supply chain security is a crucial component of national security, and the struggle for supply chain dominance is a frontier in current great power competition. The financial security of enterprises within the supply chain plays a vital supporting role in maintaining overall supply chain security. Therefore, in-depth research into supply chain financial security and the transmission mechanisms of financial risks among upstream and downstream enterprises is of significant practical importance. Considering that supply chain financial risks often spread among enterprises via the supply chain itself, modeling the risk contagion mechanism is often a primary focus of related research. Scholars have used methods such as financial econometrics, complex networks, and machine learning to construct models of risk transmission mechanisms within the supply chain. Financial econometrics methods are often used to analyze systematic risk factors in data to identify risk factors within the supply chain. However, the indicators used in these methods are often pre-defined, leading to strict assumptions that may overlook complex market behaviors and structural changes. Complex network methods transform collected data into complex networks to simulate supply chain risk contagion under different scenarios, revealing key nodes and connections within the supply chain and identifying the main transmission paths of risk through network statistical characteristics. However, complex network methods have high requirements for data quality; missing or contaminated data can severely affect the accuracy of the results. With the development of data storage and computing technologies, machine learning methods have been widely applied in supply chain financial risk research due to their high adaptability and accuracy in handling big data problems. However, machine learning models may require significant hardware and technical resources, and their generalization ability to new data is somewhat lacking due to overfitting issues. Furthermore, complex machine learning models such as neural networks suffer from insufficient interpretability, which could lead to regulatory dilemmas, a point that requires particular attention when dealing with financial risk issues. Furthermore, in the era of big data, with the rapid development of information technology and the significant improvement in data collection and storage technologies, the operation of financial systems can be characterized in real time and at high frequency. Data is no longer presented as isolated discrete points, but rather as continuous function curves. While high-frequency data sampling helps understand the details of price formation and discovery, numerous theoretical studies and empirical tests have revealed that high-frequency financial data generally faces many challenges that traditional theories and methods struggle to address. These include the coexistence of increased data collection frequency and amplified information noise, the coexistence of expanded data dimensions and structural deficiencies, and the coexistence of increased algorithm complexity and decreased interpretability. Therefore, data preprocessing is often an indispensable step when dealing with complex high-frequency financial data. For example, when processing missing financial time series data, commonly used methods include listwise deletion, single imputation, and multiple imputation. Listwise deletion completely removes any records with missing values, which significantly reduces data utilization efficiency for financial data with mixed frequencies. Single imputation replaces missing values ​​with an estimated value. Common methods include mean imputation, linear imputation, forward imputation (replacing missing values ​​with previous values), and backward imputation (replacing missing values ​​with subsequent values). However, due to the frequent occurrence of prolonged trading halts for individual stocks and inconsistent market closure times caused by different national holidays, the original data often contains a large number of missing values. This can introduce bias into single-value imputation, causing the loss of inherent trends and seasonal variations in the data. Multiple imputation estimates missing values ​​by creating multiple imputation datasets. Each dataset uses a different estimate to replace the missing values, and then multiple independent analyses are performed, with the final result being a synthesis of all the analysis results. However, the results of multiple imputation depend on the chosen model and assumptions, and the method itself cannot handle temporal correlations in the data. This can cause the imputed data to disrupt the latent temporal information of the time series, further amplifying the noise in the original data. When studying financial risk-related issues, the complexity and dynamism of financial markets cause traditional financial risk prediction models such as ARIMA, GARCH, and Probit to exhibit numerous problems, including: 1) Traditional linear econometric methods struggle to handle complex phenomena such as nonlinearity, chaos, and abrupt changes inherent in financial data, which are prevalent in financial markets; 2) The assumption of independence between financial entities in traditional methods often overlooks the interdependencies between them, which are crucial for financial risk prediction. In recent years, deep learning methods, with their significant advantages in modeling complex data, have effectively overcome the limitations of traditional econometric models and demonstrated strong application potential in the field of financial time series forecasting. Among these, the most popular is undoubtedly the Recurrent Neural Network (RNN) model designed for sequential data. However, traditional RNN models, due to the vanishing gradient problem, struggle to capture long-term dependencies between financial time series data. The Transformer series of models provides a solution to this problem. Compared to the sequential processing mechanism of RNNs, the Transformer model achieves parallel computation through a multi-head self-attention mechanism, enabling it to simultaneously focus on the global contextual information of the input sequence, thereby significantly enhancing the model's ability to capture long-range dependencies. However, it should be noted that the Transformer architecture still faces three challenges when applied to financial scenarios: First, the model has a high number of parameters and computational complexity, which can put significant pressure on hardware resources when dealing with massive amounts of financial data; second, the inherent high noise characteristics of financial data can easily lead to overfitting risks; and third, the black-box nature of the self-attention mechanism results in insufficient model interpretability, which can easily lead to model decision bias risks. Recent research indicates that, following the ensemble learning approach, combining Graph Neural Networks (GNNs) with Recurrent Neural Networks (RNNs) to endow models with the ability to simultaneously learn temporal and relational information often improves predictive performance. Taking financial risk prediction as an example, existing model architectures can be broadly categorized into two types based on the order in which temporal and relational information are processed: RNN-GNN architecture and GNN-RNN architecture. In the RNN-GNN architecture, financial time-series data is first input into a recurrent neural network (such as LSTM or GRU) to extract temporal features, and then the hidden features are input into a graph neural network (such as a graph convolutional network (GCN) or graph attention network (GAT)) to perform node classification prediction in conjunction with relational information. In the GNN-RNN architecture, researchers often first use a GNN model to map the stock correlation structure, and then use an RNN model to model the dependencies between different time points and make predictions. From the perspective of research objects, existing financial risk prediction research often focuses on the prediction of single stock prices or exchange stock indices, while research on risk correlation prediction among upstream and downstream enterprises from the perspective of the industrial chain has not yet formed a systematic framework. A comprehensive and objective characterization of the upstream and downstream relationships within an enterprise's industrial chain is crucial for the model's ability to accurately predict the enterprise's financial risk. Current models often construct enterprise industrial chain correlation networks with relatively single dimensions, relying heavily on shallow correlation inferences based on enterprise-related textual information, such as enterprise news, the enterprise's country of origin, and the personal relationships of enterprise executives. They lack in-depth mining of the network topological correlation characteristics hidden in the data (such as power-law distribution, node centrality, connectivity, and clustering coefficients). Furthermore, current financial risk prediction models (such as RNN-GNN and GNN-RNN architectures) often complete the learning and invocation of temporal and correlation information step by step, making it difficult for the model to organically integrate temporal features and correlation network structure characteristics, resulting in a deficiency in the ability to recognize risk correlations across spatiotemporal dimensions. Summary of the Invention The problem this invention aims to solve is to address the shortcomings of the existing technology by providing a supply chain financial risk prediction method and system based on the RGNN-Crossformer fusion architecture. This addresses the issue that existing methods cannot fully utilize supply chain data with complex characteristics, thus failing to make more accurate predictions of supply chain financial risks. To achieve the above-mentioned objectives of this invention, the technical solution is as follows: a method for predicting supply chain financial risks based on an RGNN-Crossformer fusion architecture, the method comprising the following steps. Step 1: Use functional data analysis methods to preprocess the raw financial data with mixed sampling frequencies, high noise, and outliers; fill in the missing values ​​by using eigenfunction reconstruction. Step 2: Use an adaptive iterative update functional data clustering method to perform cluster analysis on the reconstructed return eigenfunctions, classify volatility categories, extract enterprise relationships from the perspective of return volatility patterns, and characterize the data-driven enterprise relationship network. Step 3: Use text mining methods to extract the associations based on external information of the model from corporate annual reports, news, and stock exchange announcements; Step 4: Use the dimensional segmented embedding method to encode segmented information in the original financial time series data; Step 5: Learn the cross-temporal and cross-dimensional relationships of data based on graph neural networks, two-stage attention layers, and routing mechanisms; Step 6: Generate supply chain financial risk prediction results based on hierarchical encoding and decoding. In step 1, reconstructing the eigenfunction from the original data, which is characterized by uneven frequency and high noise, mainly involves two methods: interpolation and smoothing. The core difference between the two lies in the presence or absence of perturbation factors. Considering the financial raw data Y, which has low signal-to-noise ratio and unequal interval observation characteristics under the functional data analysis framework, i1 ,…,Y iN It can be viewed as an eigenfunction Y i (t j );t j ∈T,i=1,…,N with noise ε i (t j Discrete realization of ), i.e. Therefore, based on the research objectives of this invention, this invention mainly discusses the smoothing of financial functional data and the filling of missing values ​​under error perturbation. In step 2, an adaptive iterative update functional data clustering method is used to perform cluster analysis on the reconstructed return eigenfunction, classify volatility categories, extract enterprise relationships from the perspective of return volatility patterns, and characterize the data-driven enterprise relationship network. In the clustering process, although the observed data is deterministic, the number of potential fluctuations and patterns behind the data is unknown. Determining the number of clusters in the function set and the initial clustering are crucial issues that the clustering model must first address. The results significantly impact not only the computational cost of iterative updates and reclassification and the interpretability of the classification results, but also the accuracy and robustness of subsequent clustering results. In the functional principal component analysis framework, after sufficient dimensionality reduction, the similarity between the original functions is equivalent to the density relationship between their projected scores. Therefore, in the initial clustering process, this invention draws on the method of Chiou and Li, using the classic k-means clustering algorithm to perform cluster analysis on the principal component scores, thereby obtaining the initial classification results of the data. Regarding the determination of the number of clusters, this invention refers to the method given by Pham et al., calculating the f(J) statistic by comparing the dispersion of data within each cluster under different numbers of clusters to determine the optimal number of functional clusters for the data. In step 3, considering the importance of strengthening the chip industry for my country's high-quality economic development, and the urgency and representativeness of achieving breakthroughs for related industrial chain enterprises due to significant risks caused by external sanctions, this invention selects the integrated circuit (IC) industry chain as the research object. The embodiment uses stock data of representative listed companies in the global integrated circuit industry chain from January 1, 2018 to June 30, 2024 as a sample for research. The list of representative listed companies and their related information in the global integrated circuit industry chain are from the Wind industry chain database, and the stock data of listed companies are from the Wind and Bloomberg databases. After excluding companies that have been delisted, listed too late, or whose industry has changed, the final research data sample is obtained, including stock trading data of 83 listed companies worldwide for 1688 trading days, listed in 10 exchanges across 6 countries (China, the United States, Japan, South Korea, Germany, and France) (Shanghai Stock Exchange, Shenzhen Stock Exchange, Taiwan Stock Exchange, Taiwan OTC Market, NASDAQ Stock Exchange, New York Stock Exchange, Tokyo Stock Exchange, Korea Stock Exchange, Frankfurt Stock Exchange, and Paris Stock Exchange). The enterprise relationship data includes 11 types of enterprise relationships, including those extracted from external information such as corporate annual reports, news, and stock exchange announcements using methods like text mining, such as the position of related enterprises in the industry chain, product circulation between enterprises, and the top ten shareholders of enterprises; and data-driven enterprise relationships, such as enterprise stock return clustering. The sample's integrated circuit industry chain is divided into five parts: Electronic Design Automation (EDA), IP, Semiconductor Equipment Manufacturing (SEM), Semiconductor Materials and Chemicals (MC), and IC Manufacturing. In step 4, considering that cutting-edge multidimensional time series prediction models are often based on the Transformer architecture, which was originally developed for natural language processing, where each embedding vector represents a meaningful word, as Zhang and Yan pointed out, in the context of multidimensional time series prediction, the values ​​at a single time step provide very little information. In contrast, a continuous time series often provides richer information. Furthermore, due to the influence of the embedding method, previous models mainly focused on cross-time series correlations while neglecting cross-dimensional correlations, which significantly reduced the model's utilization of known information. Therefore, this invention adopts a Dimension-Segment-Wise Embedding (DSW) method, treating a time series on the same dimension as a segment patch and encoding it to obtain a richer and more meaningful representation. In step 5, a two-stage attention (TSA) mechanism is used to extract cross-temporal and cross-dimensional dependencies in stock return data. Considering that graph convolutional networks can fuse information from a node and its neighbors to handle spatial dependencies in the graph, the model uses a graph neural network to map various upstream and downstream enterprise relationships obtained from external textual information into a relation embedding array. Drawing on methods proposed by Zhang and Yan et al., and DeepSeek-AI, a routing mechanism is established to help the model learn cross-dimensional relationships in enterprise stock return data during time-series prediction. In step 6, the hierarchical structure is widely used in multidimensional time series prediction because it can capture information at different scales. In this invention, the aforementioned DSW embedding, TSA layer, and graph convolutional network are used to construct a hierarchical encoder-decoder (HED) (e.g., ...). Figure 2 (As shown). The upper layer uses coarser-scale information for prediction, while the lower layer uses finer-scale information to simultaneously analyze the long-term trend and short-term fluctuations of the sequence. The predictions at different scales are summed to output the final supply chain financial risk prediction result. Compared with existing technologies, the technical solution adopted in this invention has the following technical effects: This invention's research found that the constructed RGNN-Crossformer model outperforms mainstream financial risk prediction models. Specifically, the routing mechanism and graph neural network used help the model learn internal data dependencies while capturing external enterprise correlation characteristics. The RGNN-Crossformer model maintains high stability in short-term, medium-term, and long-term prediction scenarios, as well as in extreme event scenarios. Analysis of the importance of different types of correlations shows that for most enterprises, the buyer-seller relationship in the supply chain has the most significant impact on the model's final prediction effect, followed by upstream and downstream relationships in the industrial chain and yield clustering relationships. Ablation experiments further indicate that using only data mining or text analysis methods to construct a risk correlation network between upstream and downstream enterprises in the industrial chain cannot fully explore the risk propagation mechanism between enterprises. The RGNN-Crossformer model constructed in this invention can effectively integrate information from two different sources during the prediction process, significantly improving the model's predictive ability. The marginal contribution of this invention is mainly reflected in the following aspects: (1) In order to incorporate the mixed and missing daily trading data of the global stock market into the study of supply chain financial risk, this invention introduces a functional data analysis method to preprocess the stock data of upstream and downstream enterprises in the supply chain. Then, based on the reconstructed intrinsic function, the functional principal component clustering method is used to mine the potential fluctuation pattern clustering characteristics of the enterprise return function, construct a data-driven enterprise relationship network graph, and combine it with the enterprise relationship network extracted from text information as the external input of the enterprise relationship of the subsequent supply chain upstream and downstream enterprise financial risk prediction model. Empirical results show that data-driven enterprise financial data fluctuation clustering can provide enterprise relationship information that cannot be obtained from text, which helps the constructed model to integrate information from multiple data sources for collaborative learning and improve the cognitive ability of the relationship structure of upstream and downstream enterprises in the supply chain. (2) In order to integrate enterprise relationship information into the prediction model, this invention draws on the routing mechanism in the hybrid expert model to design a cross-modal information interaction architecture, uses the graph neural network method to encode the external enterprise relationship information of the model, and introduces a routing mechanism to construct the interaction channel between the relationship information and the model input. Experiments show that this mechanism effectively enhances the prediction accuracy and efficiency of the model. (3) In order to improve the accuracy of financial risk prediction for upstream and downstream enterprises in the industrial chain, this invention constructs a financial risk prediction model RGNN-Crossformer that considers enterprise correlation information. Through dimensional segmentation embedding and cross-dimensional attention mechanism, it extracts the time and space dependency features of financial data, and combines multi-head attention mechanism and hierarchical coding mechanism to adaptively adjust model parameters and structure, so as to integrate temporal feature coding and correlation network coding from different information sources.Empirical analysis shows that the RGNN-Crossformer model, which considers external relationships of enterprises, outperforms other mainstream models that can be used to predict financial risks of upstream and downstream enterprises in the industrial chain. Attached Figure Description Figure 1 This is a diagram of the overall architecture of the present invention. Figure 2 This invention provides a hierarchical encoding-decoding prediction architecture. Figure 3 This is a demonstration of the prediction performance of the proposed RGNN-Crossformer model and the baseline model in this embodiment of the invention. Figure 4 This is an illustration of the importance weights of different association relationships to the model prediction results in an embodiment of the present invention. Figure 5 This is a diagram illustrating the model prediction effect under extreme conditions in an embodiment of the present invention. Detailed Implementation To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Example 1: See Figure 1 The supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture includes the following steps in its construction process: Step 1: Use functional data analysis methods to preprocess the raw financial data with mixed sampling frequencies, high noise, and outliers, and use the intrinsic function reconstruction method to fill in the missing values. Specifically, reconstructing eigenfunctions from raw data with uneven frequencies and high noise mainly involves two methods: interpolation and smoothing. The core difference between the two lies in the presence or absence of perturbation factors. Considering the raw stock return data Y, which has low signal-to-noise ratio and unequal interval observation characteristics, within a functional data analysis framework... i1 ,…,Y iN It can be viewed as an eigenfunction Y i (t j );t j ∈T,i=1,…,N with noise ε i (t j Discrete realization of ), i.e. Therefore, based on the practical application scenarios of this invention, this invention mainly discusses the smoothing of functional financial data and the filling of missing values ​​under error disturbances. Suppose that the eigenfunctions of the original financial data are a set of smoothed stochastic processes Y.i (t)∈L 2 (T), i=1,…,N,t∈T, Where N is the number of companies in the sample, and T is the sampling time domain. Its mean function is defined as μ(t). μ(t)=E[Y(t)] (1) The covariance function is G(s,t), where s,t∈T. G(s,t)=Cov[Y(s),Y(t)]=E[(Y(s)-μ(s))(Y(t)-μ(t))] (2) From formula (2), it can be seen that the covariance function Cov[Y(s),Y(t)] is symmetric and positive semi-definite, and its spectral decomposition can be expressed as follows according to Mercer's lemma: Where λ1≥λ2≥…≥0 and They are mutually orthogonal characteristic functions, λ k It is a characteristic function The corresponding eigenvalues. The observed i-th process Y i Karhunen-Loève expands to: in These are the principal component scores with zero mean, and their variance is the corresponding eigenvalue λ. k That is, E(ξ) ik ) = 0, Var(ξ) ik )=λ k , characteristic function It is process Y i The k-th principal component feature function in the expansion space. From formula (4), it can be seen that the functional principal component method utilizes the principal component score ξ. ik Extracting the original sample sequence and the mean function in the feature function The deviation in direction allows for the extraction of information from the original random process sequence into the mean function and principal component scores. By extracting a finite number of K principal components, the projection function of the original sample sequence onto the first K principal components can be obtained. There are various indices for determining the number of principal components K to be extracted, such as AIC and BIC. This invention uses the fraction of variability explained (FVE) score to determine the optimal value of K, and its calculation formula is as follows: In this invention, considering the strong modeling ability of subsequent deep learning models for nonlinear relationships, FVE≥99% was finally selected as the threshold to ensure that the temporal information in the original data is preserved to the greatest extent while improving the signal-to-noise ratio. This invention fills in missing values ​​by dynamically imputing missing segments in the original data. Considering the impact of data leakage on the subsequent deep model training process, during the imputation process, this invention first divides the entire dataset into training and testing sets, then performs sliding window segmentation and selects a shorter window width. Without loss of generality, this invention assumes that the financial data of companies 1,…,m are complete in the time period [t0,t1+Δt], while the data of company m+1 is complete in the time period [t0,t1], but has missing values ​​in the time period [t1,t1+Δt]. Then, according to formula (5), the eigenfunction Karhunen-Loève representation of company m+1 in the time period [t0,t1+Δt] can be estimated as follows: Principal component scores The conditional expectation principal component method proposed by Yao et al. can be used for estimation, which can be specifically expressed as follows: here This is the sample data of the (m+1)th company within the time period [t0, t1]. yes The estimated mean vector over the time interval [t0, t1] Based on data of all samples in the time period [t0, t1] The estimated variance-covariance matrix. By iteratively processing the stock data of each company and using a small window for sliding updates, we can obtain denoised and filled-in, equally spaced regular sampling data. Step 2: Use an adaptive iterative update functional data clustering method to perform cluster analysis on the reconstructed return eigenfunctions, classify volatility categories, extract enterprise relationships from the perspective of return volatility patterns, and characterize the data-driven enterprise relationship network. In the clustering process, although the observed data is deterministic, the number of potential fluctuations and patterns behind the data is unknown. Determining the number of clusters in the function set and the initial clustering are crucial issues that the clustering model must first address. The results significantly impact not only the computational cost of iterative updates and reclassification and the interpretability of the classification results, but also the accuracy and robustness of subsequent clustering results. In the functional principal component analysis framework, after sufficient dimensionality reduction, the similarity between the original functions is equivalent to the density relationship between their projected scores. Therefore, in the initial clustering process, this invention draws on the method of Chiou and Li, using the classic k-means clustering algorithm to perform cluster analysis on the principal component scores, thereby obtaining the initial classification results of the data. Regarding the determination of the number of clusters, this invention refers to the method given by Pham et al., calculating the f(J) statistic by comparing the dispersion of data within each cluster under different numbers of clusters to determine the optimal number of functional clusters for the data. Specifically, I is defined... c The degree of dispersion of the data in the c-th category, d() represents the distance between the two functions, N c Y represents the number of functions belonging to class c. (c) (t) represents the central function of this category, Y x (t) represents the x-th function in this category. The sum of the discreteness of all categories is S. J J represents the total number of categories. The metric f(J) for evaluating clustering effectiveness is defined as follows: Where α J These are weighting coefficients used to balance the dimension N in a dataset. d Impact on classification results. α J S J-1 S represents J Based on S J-1 The estimated value of f(J) represents the ratio of the actual dispersion of the clusters to the estimated dispersion. The smaller f(J) is, the better the effect of the new clusters on reducing the dispersion within the clusters. Therefore, the total number of categories J that minimizes the value of f(J) can be considered as the number of excellent clusters. Without loss of generality, we now assume that there are J types of volatility patterns in the return data, denoted by C, c∈1,…,J. For the function set class C, its conditional mean function is defined as μ. (c) (t) = E(Z(t)|C = c), and the covariance function is defined as Γ. (c)(s,t)=cov[Y(s),Y(t)|C=c]. If any function Y(t) essentially belongs to category c, then by formula (4), the corresponding function Y belonging to category C of the function set is... (c) The KL expansion of (t) is: Among them, eigenvalues ​​and eigenfunctions are pairs satisfy Due to different They are mutually orthogonal, therefore only when k = j hour If Y(t) should not actually belong to category c, then Y (c) There should be a significant difference between Y(t) and Y(t). Based on the above classification principle, the optimal classification c(y) for Y(t) is: Where ||·|| represents Euclidean distance.

[0001] Although the expansion in equation (13) is infinite-dimensional, in practical applications, to simplify the computational cost of iterative updates during classification and prediction, selecting a finite number of feature components is sufficient to effectively approximate the function trajectory without loss of core information. This reduces the computational cost during clustering by significantly lowering the dimensionality. The KL expansion of the corresponding function set category C after truncation is as follows: In equation (15), M c The optimal number of principal components is determined based on the Explanation of Variability Score (FVE). To ensure robustness of classification and accuracy of prediction, the model needs to iteratively update the initial classification results until a stable cluster is obtained. Assume the result of the l-th iteration is... make and The function Y is not included in category c. i Find the mean and principal component characteristic functions of the set (t). Calculate Y. i The projection of (t) into category c, c∈1,…,J is [t] in, For Y i The expansion coefficients of (t) in each category, i.e., Y i (t) is the score of the kth principal component in category c. Furthermore, based on the optimization results of the lth iteration, Y is optimized according to equation (16). i Optimize the category assignment of (t), let Y i The classification result of (t) after the (l+1)th iteration optimization is: All functions are iteratively updated, and the result of the (l+1)th iteration is: The entire process described above is repeated until no more functions need to be reclassified, i.e., when R... (l+1) =R (l) When the iteration stops, the final classification result is determined. Step 3: Using text mining and other methods, extract the association relationships based on external information from corporate annual reports, news, and stock exchange announcements. Taking the implementation sample of this invention as an example, considering the importance of strengthening the chip industry for my country's high-quality economic development, and the urgency and representativeness of breakthroughs needed for related industrial chain enterprises due to significant risks caused by external sanctions, this invention's implementation sample selects the integrated circuit (IC) industrial chain as the research object. The example uses stock data of representative listed companies in the global integrated circuit industrial chain from January 1, 2018 to June 30, 2024 as a sample for research. The list of representative listed companies and their association information in the global integrated circuit industrial chain comes from the Wind industrial chain database, and the stock data of listed companies comes from the Wind and Bloomberg databases. After excluding companies that were delisted, listed too late, or whose industries had changed, the final research data sample was obtained, including stock trading data from 1688 trading days for 83 listed companies worldwide. These companies were listed on 10 stock exchanges in 6 countries (China, the United States, Japan, South Korea, Germany, and France) (Shanghai Stock Exchange, Shenzhen Stock Exchange, Taiwan Stock Exchange, Taiwan OTC Market, NASDAQ, New York Stock Exchange, Tokyo Stock Exchange, Korea Exchange, Frankfurt Stock Exchange, and Paris Stock Exchange). The corporate relationship data included 11 types of relationships, including those extracted from corporate annual reports, news, and exchange announcements using text mining methods, such as the position of related companies in the industry chain, product circulation between companies, and the top ten shareholders; and data-driven relationships, such as clustering of corporate stock returns. The integrated circuit industry chain in the sample was divided into five parts: Electronic Design Automation (EDA), IP, Semiconductor Equipment Manufacturing (SEM), Semiconductor Materials and Chemicals (MC), and IC Manufacturing. Step 4: The original financial time series data was segmented and encoded using a dimensional segmented embedding method. Specifically, state-of-the-art multidimensional time series prediction models are often based on the Transformer architecture, which was originally developed for natural language processing, where each embedding vector represents a meaningful word. However, as Zhang and Yan pointed out, in the context of multidimensional time series prediction, values ​​at a single time step provide very little information. In contrast, a continuous time series often provides richer information. Furthermore, due to the influence of the embedding method, previous models mainly focused on cross-time series correlations while neglecting cross-dimensional correlations, which significantly reduced the model's utilization of known information. Therefore, this invention employs a Dimension-Segment-Wise Embedding (DSW) method, treating a time series on the same dimension as a segment patch and encoding it to obtain a richer and more meaningful representation.

[0002] Let x 1:T Given the original sample data from time 1 to T, split it into segments along each dimension, where the length is L. seg The data is divided into segments. This represents the i-th segment in the d-th dimension. Then, using linear mapping and position embedding methods, each segment is mapped to a vector h. i,d in For a learnable projection matrix, This is a learnable embedding vector used for positional encoding. Therefore, we obtain a two-dimensional vector array: Where h i,d This represents the i-th segment of the next-dimensional time series in the d-th dimension. Step 5: Learn the temporal and dimensional relationships of data based on graph neural networks, two-stage attention layers, and routing mechanisms; specifically, this invention uses a two-stage attention (TSA) mechanism to extract the temporal and dimensional dependencies of data. Given a two-dimensional array as input to the TSA layer... Where L and D are the number of segments and the number of dimensions, respectively. Z can be the output of the DSW embedding or the output of a lower-level TSA layer. i,: Z represents a vector of all dimensions at time step i. :,dThis represents the vector across all time steps in dimension d. This invention employs a multi-head self-attention (MSA) mechanism for each dimension to extract cross-temporal correlations. Here, LayerNorm is the layer normalization method, MLP represents a multilayer perceptron, MSA(Q,K,V) represents multi-head self-attention, and Q, K, and V are the query, key, and value, respectively. All dimensions 1≤d≤D share the same multi-head self-attention. and Z time These represent the outputs of MSA and MLP, respectively. After this, Z... time It can capture the dependencies between different time periods within the same dimension. Considering that graph convolutional networks can fuse information from a node and its neighboring nodes to handle spatial dependencies in a graph, this invention uses a graph neural network to map various upstream and downstream enterprise relationships obtained from external text information into a relationship embedding array. The graph convolutional network used in this invention contains two hybrid jump propagation layers, respectively used to process inflow and outflow information transmitted through each node. The outputs of these two hybrid jump propagation layers are summed to obtain the net inflow information. The hybrid jump propagation layer consists of two steps: information propagation and information selection. Information propagation is used to represent the influence of neighboring nodes on the root node, while information selection is used to generate a relationship representation filtered by information importance. Without loss of generality, if a relationship is randomly selected, and A is the enterprise relationship matrix under this relationship, then the hybrid jump propagation layer used can be defined as follows: Where β is a hyperparameter used to control the proportion of the original state of the root node preserved. K is the propagation depth, and H... in H represents the input hidden state of the output of the previous layer. out H represents the output hiding state of the current layer. (0) =H in , This invention draws upon methods proposed by Zhang and Yan, Dai, and DeepSeek-AI to establish a routing mechanism to help the model learn cross-dimensional relationships in corporate financial data during time series forecasting. For each time step, a fixed number of learnable arrays (called routers) are set up to aggregate information from all dimensions, and then this information is distributed to each dimension. This invention embeds the acquired multiple relationships into the initial router R to input external relationship information during the cross-dimensional relationship extraction process. Specifically, Routers that integrate external correlation information and internally learned correlation information It is an aggregated message from all dimensions. This is the output of the routing mechanism. Z dim These represent the output results of skip connections and MLP, respectively. Step 6: Generate supply chain financial risk prediction results based on hierarchical encoding and decoding; Specifically, hierarchical structures are widely used in multidimensional time series prediction because they can capture information at different scales. In this invention, the aforementioned DSW embedding, TSA layer, and graph convolutional network are used to construct a hierarchical encoder-decoder (HED) (e.g., ...). Figure 2 (As shown). The upper layer uses coarser-scale information for prediction, while the lower layer uses finer-scale information to simultaneously analyze the long-term trend and short-term fluctuations of the sequence. The predictions at different scales are summed to output the final result. In each encoder layer (except the first layer), two vectors from each adjacent time step in the time domain are merged to obtain a coarser representation for that layer. A TSA layer is then applied to capture dependencies across time and dimensions. Where H represents a two-dimensional array obtained by DSW embedding; Z enc,l This represents the output of the l-th layer encoder; L represents a learnable matrix used for fragment merging; l-1 This represents the number of segments in each dimension of the (l-1)th layer. This represents the array after segment merging at the i-th layer. Assuming the encoder has N layers, Z is used. enc,0 Z enc ,1 ,…,Z enc,N ,(Z enc,0 =H) to represent the N+1 outputs of the encoder. The decoder's task is to reconstruct future time series from information at different levels of the encoder. It receives the output of the last layer from the encoder, along with positional encoding, and progressively recovers details until it reaches the finest-grained prediction. The decoder also employs a structure similar to the encoder, fusing information at different scales by aggregating predictions layer by layer to obtain the final prediction result. in This represents the learnable position embedding of the decoder. It is the output of the TSA layer, and the MSA layer passes through... Set as a query, Set as key and value to establish a connection between the encoder and decoder; the output of the MSA layer is... Z dec,l These represent the outputs of skip connections and the MLP, respectively. dec,0 Z enc,1 ,…,Z dec,N This represents the N+1 outputs of the decoder. Finally, linear projection is used on the output of each layer to obtain the prediction for that layer, and the predictions of each layer are added together to obtain the final prediction result. in It is a learnable matrix used to project vectors onto a time series segment. This is the prediction for the i-th segment in the d-th dimension. The predictions from each layer are summed to obtain the final prediction result. Example 2: The technical solution of this application is applicable to application scenarios that require financial risk assessment of the industry chain, such as the semiconductor-integrated circuit industry chain. Enterprise Relationship Network Feature Analysis To capture the external relationship structure between enterprises, this invention-embodiment constructs eight types of enterprise relationship diagrams. Among them, seven types are based on network information text mining, including (country (region) of enterprise location, position of enterprise in industry chain, stock exchange of enterprise, legal nature of enterprise, supply chain relationship of enterprise, location of enterprise headquarters, and common shareholders of enterprise), and one type of enterprise relationship is based on data mining (clustering of enterprise stock return function). The diagram showing the relationship between the country of origin, stock exchange, and headquarters location of listed companies reveals that global listed integrated circuit (IC) companies are mainly concentrated in China, the US, Japan, South Korea, and Europe. Breaking down the concentration by provincial-level administrative division, the most concentrated areas for IC company headquarters are Taiwan, California (USA), and Tokyo (Japan), followed by Jiangsu, Zhejiang, and Beijing (China). Apart from my country's five state-owned enterprises, the rest are private companies. The phenomenon of multiple IC companies sharing the same major shareholder is common both domestically and internationally. my country's National Integrated Circuit Industry Investment Fund is among the top 10 shareholders of the 23 Chinese listed IC companies in the sample, highlighting its important role in promoting the independent development of my country's IC industry and enhancing the self-sufficiency and controllability of the industrial chain. Common major shareholders abroad are often large US investment companies, such as BlackRock, Blackstone, and Vanguard Group. These groups have appeared multiple times in the major shareholder lists of IC companies in the US, Europe, Japan, South Korea, and China, demonstrating the undeniable influence of US investment companies on the global IC industry chain. A company's position in the industry chain and the supply chain relationships between companies have the most direct impact on its operating performance. As shown in the figure, most listed companies in my country's integrated circuit industry chain are concentrated in the fields of semiconductor materials and chemicals (MC), IC manufacturing, and semiconductor equipment manufacturing (SEM), while there is a relative lack of listed companies in the fields of IP and electronic design automation (EDA). Clustering results based on corporate stock return functions show that Category 1 contains 68 stocks, with a complex composition involving all parts of the integrated circuit industry chain and various countries. This illustrates the complexity of the interrelationships between companies within the industry chain; a qualitative analysis of the relationship structure between companies based solely on textual information such as their position in the industry chain or their country of origin is insufficient to characterize these complex relationships. Category 2, on the other hand, has a much simpler composition, containing 15 stocks, 13 of which are from China. This indicates that the stock returns of listed integrated circuit companies in my country often exhibit synchronous fluctuations. The reasons for this phenomenon may include: 1. The integrated circuit industry is globalized and heavily influenced by the international market. Disruptions in the international chip supply chain can simultaneously damage the profits of Chinese companies, thus affecting stock performance. 2. my country's integrated circuit industry receives significant government policy support, and national industrial policies have a significant impact on the overall stock performance of the industry. 3. Many domestic integrated circuit companies exhibit a degree of homogenization in technology and products, such as a concentration in the low-to-mid-end chip market. When competition is intense or prices fluctuate, company profits are prone to synchronous changes. This invention-embodiment uses the generated enterprise association graphs under various relationships as prior associations to input into the prediction model. This helps the model learn objectively existing external relationships while adaptively learning the internal dependencies of the data itself, thereby improving the model's final prediction accuracy and interpretability. Experimental setup Considering the significant fluctuations in global stock markets during the sampling period, to ensure the model's effectiveness during periods of market turmoil, and referencing experimental setups in stock prediction literature, this invention employs a sequential iterative training method. The entire dataset is divided into multiple subsets chronologically, and each subset is then trained using the classic three-stage partitioning of training, validation, and testing. Taking into account both model performance and computational efficiency, this invention ultimately divides the training, validation, and test sets in a 7:1:2 ratio. Furthermore, the model uses a rolling time window prediction method, with rolling prediction window widths set to 1 day, 5 days, and 20 days (simulating predictions of return fluctuations for the next day, week, and month). The setting of hyperparameters often has a significant impact on model performance. This invention employs a combination of random search and grid search to determine optimal hyperparameters. First, random search is used to broadly and efficiently explore the hyperparameter space, initially locating potential optimal hyperparameter regions. Then, within these regions, a grid search method is used for detailed and systematic searching to ensure the finding of the optimal hyperparameter combination, aiming to improve search efficiency while maintaining result quality. This invention uses the Adam optimizer, adaptively adjusting the learning rate based on gradient descent, and pre-sets several tuning ranges for model hyperparameters: the learning rate range is 10. -5 Up to 10 -3 The weight decay range is 10. -5 Up to 10 -4 Simultaneously, the ReLU function is used as the activation function to alleviate the gradient vanishing problem. This invention-embodiment uses MSE (mean squared error) and MAE (mean absolute error) as evaluation metrics for the model's predictive ability. benchmark model To verify the effectiveness of the model proposed in this invention-embodiment, this invention-embodiment not only focuses on the performance of the model's prediction metrics but also compares the prediction results with several mainstream and state-of-the-art models. Specifically, this invention-embodiment compares the prediction accuracy of the proposed RGNN-Crossformer model with cutting-edge prediction models such as MICN, Transformer, PatchTST, TimesNet, Crossformer, iTransformer, and TimeXer under the same settings. The baseline models used for comparison can be broadly categorized into three types: ① Multi-scale isometric convolutional network (MICN) models, which combine local features and global correlations to obtain a holistic view of the time series. This type of model was selected to compare the prediction performance differences between RGNN-Crossformer and non-Transformer architecture models; ② Transformer, PatchTST, and TimesNet models for one-dimensional time series, which encode the time series structurally along the temporal direction to obtain correlation information for different time periods. These models were selected to compare the prediction performance differences between one-dimensional Transformer models that do not specifically consider cross-dimensional dependencies in multi-dimensional time series and RGNN-Crossformer models that do consider cross-dimensional dependencies; ③ Crossformer, iTransformer, and TimeXer models, which are suitable for multi-dimensional time series, consider both cross-time and cross-dimensional dependencies, making them more suitable for multi-dimensional time series prediction scenarios. However, the cross-dimensional dependencies in these models are often learned adaptively by the model and do not consider external objective correlations. Therefore, these models are compared with RGNN-Crossformer to study the impact of introducing external correlation information on the model's prediction accuracy. Performance evaluation and comparative analysis Figure 3Table 1 details the prediction performance of several benchmark models and the RGNN-Crossformer model proposed in this embodiment of the invention under the same settings. It can be seen that, compared to other benchmark models, the RGNN-Crossformer model proposed in this embodiment of the invention exhibits the best performance in both evaluation metrics related to prediction accuracy. In contrast, the MICN model performs worse in prediction accuracy compared to other models. A deeper analysis reveals that, because the underlying architecture is a convolutional neural network model originally designed for image recognition, the MICN model tends to focus more on local information when modeling the dependencies between time-series data, and may not be able to accurately characterize long-distance dependencies. This limitation results in the MICN model's insufficiency in capturing global information, thus affecting its prediction accuracy. Among the three prediction models for one-dimensional time series (PatchTST, TimesNet, and Transformer), the classic Transformer model performs best. This is likely because PatchTST and TimesNet perform initial data segmentation and normalization to improve computational efficiency. However, this can lead to insufficient accuracy when predicting shorter time series. The Transformer model, by incorporating finer-grained temporal dependencies, ensures the model can fully learn the internal relationships within the data, but this significantly reduces its computational speed, resulting in a computational complexity of O(T0). 2 This indicates that when the model data increases significantly, the training time of the model will become unacceptable. Table 1 Comparison of prediction performance between RGNN-Crossformer and benchmark models

[0003] The Crossformer model, designed for multidimensional time series prediction problems, boasts the highest prediction accuracy among all benchmark models. This is likely because, compared to one-dimensional time series prediction models, Crossformer comprehensively considers both cross-temporal and cross-dimensional dependencies, enabling it to incorporate information from other dimensions into the prediction process for the target dimension, thereby improving information utilization. However, the Crossformer model obtains cross-dimensional information transmission through adaptive learning, failing to fully utilize objectively existing external correlation information, resulting in lower prediction accuracy compared to the RGNN-Crossformer model, which considers external correlations. Table 2 Prediction Performance of Short-Term, Medium-Term, and Long-Term Models

[0004] Given that Yang Qing and Wang Chenwei believe that for stock prediction, the trading data of the first 60 days already contains sufficient information, and information beyond 60 trading days has very little impact on the 61st day, this invention—an embodiment—conducts three sets of comparisons, taking into account both the theoretical and practical application value of prediction: predicting the next day's data based on the previous 5 days' data (predicting the next day's return based on the previous week's stock information), predicting the next 5 days' data based on the previous 20 days' data (predicting the next week's return based on the previous month's stock information), and predicting the next 20 days' data based on the previous 60 days' data (predicting the next month's return based on the previous quarter's stock information). The results are shown in Table 2. It can be observed that, regardless of whether it's short-term, medium-term, or long-term prediction, the RGNN-Crossformer model, which considers external objective correlation information, outperforms the Crossformer model. This demonstrates that the model proposed in this invention—an embodiment—has high robustness for prediction tasks across different periods. Importance analysis of relational variables This invention further examines the impact of different external correlations on the model prediction results. Figure 4 The report examines the importance of different relationships to the model's final prediction results. The results show that the importance of the same relationship to the model's prediction results is not constant for different companies; however, for most companies, the buyer-seller relationship in the supply chain has the most significant impact on the final prediction effect, followed by the upstream and downstream relationships in the industrial chain and the yield clustering relationship. This may be because business transactions between buyers and sellers have a rapid and significant impact on the company's operating performance, and information flow between buyers and sellers is fast. Financial conditions or market fluctuations can be quickly transmitted through supply chain relationships, thus directly affecting the performance of the prediction model. In contrast, the upstream and downstream relationships in the industrial chain are usually transmitted through multiple links, and their influence may be weakened by intermediate links. Furthermore, the upstream and downstream relationships in the industrial chain cover a wide range of companies, and the impact on individual companies also has a certain degree of uncertainty. The yield clustering relationship ranks third in influence, indicating that the historical synchronicity of corporate stock returns plays a role in the prediction. This may be because the yield clustering relationship can reveal the industry-specific or market-specific systemic risks faced by companies, and companies with similar yield patterns often have stronger commonalities in their investor sentiment. robustness test Preventing and mitigating major financial risks and safeguarding national financial security are among the goals of establishing financial forecasting models. Therefore, the stability of the model under extreme conditions is of great significance for research. This invention—an embodiment—samples the period from January 1, 2018 to June 30, 2024, to examine the model's predictive performance and robustness. Two datasets of equal length are selected: June 1, 2019 to March 31, 2020, and June 1, 2020 to March 31, 2021, to test the model's predictive performance under extreme conditions. From Table 3 and Figure 5 As can be seen, the model's prediction accuracy dropped significantly when it first encountered sudden and extreme events, causing the MSE and MAE to reach 32.664 and 2.047, respectively. This decline may be due to the fact that in the early stages of the event, the data contained a lot of uncertainty and sudden factors, and the model failed to adjust in time to adapt to the rapidly changing market environment. However, as relevant data information about the event was continuously added to the model, the model gradually learned the new normal characteristics in the data and their medium- and long-term impact on the financial market, resulting in a significant reduction in prediction error. Table 3 Model Prediction Accuracy under Extreme Conditions MSE MAE RGNN-Crossformer(2019.06-2020.03) 32.664 2.739 RGNN-Crossformer(2020.06-2021.03) 2.047 0.796

[0005] ablation experiment

[0006] To further evaluate the role of various relationships in the prediction process of the RGNN-Crossformer model, this invention designed two variant models for ablation experiments: RGNN-Crossformer-DataDriven and RGNN-Crossformer-TextDriven. The RGNN-Crossformer-DataDriven model, when constructing external relationships between upstream and downstream enterprises in the industry chain, uses only a data-driven approach to obtain the relationship network between enterprises, without considering textual information such as the country of origin or the position of the enterprise in the industry chain. This design aims to explore whether a data-driven method alone can fully reveal the relationships between upstream and downstream enterprises in the industry chain. In contrast, the RGNN-Crossformer-TextDriven model considers only textual information when obtaining enterprise relationships, ignoring the enterprise relationship network extracted using data analysis methods, to verify the independent role and completeness of textual information in revealing relationships between enterprises. The results are shown in Table 4. Table 4 Comparison of results in ablation experiments RGNN-Crossformer-DataDriven RGNN-Crossformer-TextDriven RGNN-Crossformer MSE 3.606 3.605 3.603 MAE 0.532 0.530 0.528

[0007] The experiments revealed that the two variants (RGNN-Crossformer-DataDriven and RGNN-Crossformer-TextDriven) exhibited decreased prediction accuracy compared to the original RGNN-Crossformer model. This verifies the effectiveness of the RGNN-Crossformer model constructed in this invention-embodiment in integrating information obtained from data mining and text. Specifically, without considering data mining information, the RGNN-Crossformer-TextDriven model can only utilize textual information to construct a network of relationships between upstream and downstream enterprises in the industry chain, leading to a decline in the model's predictive ability. This demonstrates that introducing data mining information during modeling can effectively improve the model's predictive ability. The RGNN-Crossformer-DataDriven model shows a more significant decrease in prediction accuracy compared to the RGNN-Crossformer-TextDriven model. This phenomenon may be due to the fact that data mining information is inherently more ambiguous than clearly expressed textual information, causing the model's learning process to be more affected by noise, resulting in a decline in predictive performance. Analysis shows that the RGNN-Crossformer model excels in both performance and effectiveness in predicting financial risks for upstream and downstream enterprises in the industrial chain. The routing mechanism and graph neural network introduced into the model help it simultaneously learn the learnable dependencies inherent in the data and the objectively existing external relationships between related enterprises, thereby improving the model's predictive ability. Comparative experiments show that the RGNN-Crossformer model outperforms cutting-edge deep learning time-series prediction models such as Transformer, PatchTST, TimesNet, and Crossformer in terms of prediction accuracy; and it maintains high stability in short-term, medium-term, and long-term prediction scenarios, as well as in extreme event scenarios. Analysis of the importance of different relationships indicates that for most enterprises, the buyer-seller relationship in the supply chain has the most significant impact on the final prediction effect, followed by the upstream and downstream relationships in the industrial chain and the yield clustering relationship. Ablation experiments further indicate that using only data mining or text analysis methods to construct a risk relationship network for upstream and downstream enterprises in the industrial chain cannot fully explore the risk propagation mechanism between enterprises. The RGNN-Crossformer model can effectively integrate information from two different sources during the prediction process, improving the final prediction effect. It should be noted that the above embodiments are not intended to limit the scope of protection of the present invention. Equivalent transformations or substitutions made based on the above technical solutions all fall within the scope of protection of the claims of the present invention.

Claims

1. A supply chain financial risk prediction method based on an RGNN-Crossformer fusion architecture, characterized in that, The method Includes the following steps, Step 1: Use functional data analysis methods to preprocess the raw financial data with mixed sampling frequencies, high noise, and outliers; use eigenfunction reconstruction to fill in missing values ​​for missing value segments. Step 2: Use an adaptive iterative update functional data clustering method to perform cluster analysis on the reconstructed return intrinsic function, classify volatility categories, extract enterprise relationships from the perspective of return volatility patterns, and characterize the data-driven enterprise relationship network. Step 3: Use text mining methods to extract the associations based on external information of the model from corporate annual reports, news, and stock exchange announcements; Step 4: Use the dimensional segmented embedding method to encode segmented information in the original financial time series data; Step 5: Learn the cross-temporal and cross-dimensional relationships of data based on graph neural networks, two-stage attention layers, and routing mechanisms; Step 6: Generate supply chain financial risk prediction results based on hierarchical encoding and decoding.

2. The supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture as described in claim 1, characterized in that, Step 1 is as follows: Reconstructing the eigenfunction from the original data, which has uneven frequencies and high noise, mainly involves two methods: interpolation and smoothing. The core difference between the two lies in the presence or absence of perturbation factors. Considering the original stock return data Y, which has low signal-to-noise ratio and unequal interval observation characteristics under the functional data analysis framework, i1 ,…,Y iN It can be viewed as an eigenfunction Y i (t j );t j ∈T,i=1,…,N with noise ε i (t j Discrete realization of ), i.e. Suppose that the eigenfunctions of the original financial data are a set of smoothed stochastic processes Y. i (t)∈L 2 (T), i=1,…,N,t∈T, Where N is the number of companies in the sample, T is the sampling time domain, and its mean function is defined as μ(t). μ(t)=E[Y(t)] (1) The covariance function is G(s,t), where s,t∈T. G(s,t)=Cov[Y(s),Y(t)]=E[(Y(s)-μ(s))(Y(t)-μ(t))] (2) From formula (2), it can be seen that the covariance function Cov[Y(s),Y(t)] is symmetric and positive semi-definite, and its spectral decomposition can be expressed as follows according to Mercer's lemma: Where λ1≥λ2≥…≥0 and They are mutually orthogonal characteristic functions, λ k It is a characteristic function The corresponding eigenvalue, the observed i-th process Y i Karhunen-Loève expands to: in These are the principal component scores with zero mean, and their variance is the corresponding eigenvalue λ. k That is, E(ξ) ik ) = 0, Var(ξ) ik )=λ k , characteristic function It is process Y i The k-th principal component feature function in the expansion space, as shown in formula (4), utilizes the principal component score ξ. ik Extracting the original sample sequence and the mean function in the feature function The deviation in direction allows for the extraction of information from the original random process sequence into the mean function and principal component scores. By extracting a finite number of K principal components, the projection function of the original sample sequence onto the first K principal components is obtained. There are several indicators for determining the number of principal components K to be extracted. The optimal value of K is determined by the fraction of variability explained (FVE) score, and its calculation formula is as follows: Considering the powerful modeling capabilities of subsequent deep learning models for nonlinear relationships, an FVE ≥ 99% was ultimately selected as the threshold to ensure that the temporal information in the original data is preserved to the greatest extent while improving the signal-to-noise ratio. To fill missing values ​​in the original data by dynamically imputing missing segments, considering the impact of data leakage on the subsequent deep model training process, the entire dataset is first divided into training and test sets, and then a sliding window is segmented with a shorter window width selected. Without loss of generality, assuming that the financial data of companies 1,…,m are complete in the time period [t0,t1+Δt], and the data of company (m+1) is complete in the time period [t0,t1], but there are missing values ​​in the time period [t1,t1+Δt], then according to formula (5), the Karhunen-Loève representation of the intrinsic function of company (m+1) in the time period [t0,t1+Δt] is estimated as follows: Principal component scores The conditional expectation principal component method proposed by Yao et al. can be used for estimation, which can be specifically expressed as follows: here This is the sample data of the (m+1)th company within the time period [t0, t1]. yes The estimated mean vector over the time interval [t0, t1] Based on data of all samples in the time period [t0, t1] The estimated variance-covariance matrix can be obtained by iteratively processing the stock data of each company and using a small window for sliding updates, resulting in denoised and filled-in equally spaced regular sampling data.

3. The supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture as described in claim 1, characterized in that, Step 2 is as follows: Definition I c The degree of dispersion of the data in the c-th category, d() represents the distance between the two functions, N c Y represents the number of functions belonging to class c. (c) (t) represents the central function of this category, Y x (t) represents the x-th function in this category, and the sum of the discreteness of all categories is S. J If J is the total number of categories, then the metric f(J) for evaluating the clustering effect is defined as follows: Where α J These are weighting coefficients used to balance the dimension N in a dataset. d The impact on classification results, α J S J-1 S represents J Based on S J-1 The estimated value, f(J), represents the ratio of the actual cluster dispersion to the estimated dispersion. Assume there are J volatility pattern categories in the return data, denoted as C, c∈1,…,J. For the function set category C, its conditional mean function is defined as μ. (c) (t) = E(Z(t)|C = c), and the covariance function is defined as Γ. (c) (s,t)=cov[Y(s),Y(t)|C=c], if any function Y(t) essentially belongs to category c, then by formula (4), the corresponding function Y belonging to category C of the function set is... (c) The KL expansion of (t) is: Among them, eigenvalues ​​and eigenfunctions are pairs satisfy Due to different They are mutually orthogonal, therefore only when k = j When k≠j The optimal class decision c(y) for Y(t) is: Where ||·|| represents Euclidean distance. The KL expansion of the truncated set of corresponding functions of category C is: In equation (15), M c The optimal number of principal components is determined based on the Explanation of Variability (FVE) score. Assume the result of the l-th iteration is make and The function Y is not included in category c. i Given the set of (t) and its principal component eigenfunctions, calculate Y. i The projection of (t) into category c, c∈1,…,J is [t] in, For Y i The expansion coefficients of (t) in each category, i.e., Y i (t) is the score of the kth principal component in category c, and then, according to equation (16), Y is optimized based on the result of the lth iteration. i Optimize the category assignment of (t), let Y i The classification result of (t) after the (l+1)th iteration optimization is: All functions are iteratively updated, and the result of the (l+1)th iteration is: The entire process described above is repeated until no more functions need to be reclassified, i.e., when R... (l+1) =R (l) When the iteration stops, the final classification result is determined.

4. The supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture as described in claim 1, characterized in that, Step 3 is as follows: The list of representative listed companies in the global integrated circuit industry chain and information on their related relationships are sourced from the Wind Industry Chain Database. Stock data for listed companies comes from Wind and Bloomberg databases. After excluding companies that have been delisted, listed too late, or whose industry has changed, the final research data sample includes stock trading data from 1688 trading days for 83 listed companies worldwide. These companies are listed on 10 stock exchanges in 6 countries (China, the United States, Japan, South Korea, Germany, and France) (Shanghai Stock Exchange, Shenzhen Stock Exchange, Taiwan Stock Exchange, Taiwan OTC Market, NASDAQ, New York Stock Exchange, Tokyo Stock Exchange, Korea Exchange, Frankfurt Stock Exchange, and Paris Stock Exchange). The data on related relationships includes 11 types of relationships, including those extracted from company annual reports, news, and exchange announcements using text mining and other methods. These relationships are based on external information, including the companies' positions in the industry chain, product distribution between companies, and their top ten shareholders. In addition, data-driven corporate relationships, including corporate stock return clustering, are analyzed. The entire integrated circuit industry chain in the sample is distributed across five parts: electronic design automation (EDA), IP, semiconductor equipment manufacturing (SEM), semiconductor materials and chemicals (MC), and IC manufacturing.

5. The supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture as described in claim 1, characterized in that, Step 4 is as follows: A dimensional segmented embedding method is adopted, treating a time series on the same dimension as a segment patch and encoding it to obtain a richer and more meaningful representation. Let x 1:T Given the original sample data from time 1 to T, split it into segments along each dimension, where the length is L. seg The data is divided into segments. This represents the i-th segment in the d-th dimension. Then, using linear mapping and position embedding methods, each segment is mapped to a vector h. i,d in For a learnable projection matrix, These are learnable embedding vectors used for positional encoding, thus resulting in a two-dimensional vector array: Where h i,d This represents the i-th segment of the next-dimensional time series in the d-th dimension.

6. The supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture as described in claim 1, characterized in that, Step 5 is as follows: A two-stage attention (TSA) mechanism is used to extract cross-temporal and cross-dimensional dependencies in the data, given a two-dimensional array as input to the TSA layer. Where L and D are the number of segments and the number of dimensions, respectively, and Z is the output of the DSW embedding or the output of a lower-level TSA layer. i,: Z represents a vector of all dimensions at time step i. :,d Let d represent the vector at all time steps along dimension d. Multi-head self-attention (MSA) is applied to each dimension to extract cross-temporal relationships. Here, LayerNorm is the layer normalization method, MLP represents a multilayer perceptron, MSA(Q,K,V) represents multi-head self-attention, Q, K, and V are the query, key, and value, respectively, and all dimensions 1≤d≤D share the same multi-head self-attention. and Z time These represent the outputs of MSA and MLP, respectively. After this, Z... time Capture the dependencies between different time periods within the same dimension.

7. The supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture as described in claim 1, characterized in that, Step 6 is as follows: The DSW embedding, TSA layer, and graph convolutional network described above are used to construct a hierarchical encoder-decoder (HED). In each encoder layer (except the first layer), two vectors from each adjacent time step in the time domain are merged to obtain a coarser representation for that layer. Then, a TSA layer is applied to capture dependencies across time and dimensions. Where H represents a two-dimensional array obtained by DSW embedding; Z enc,l This represents the output of the l-th layer encoder; L represents a learnable matrix used for fragment merging; l-1 This represents the number of segments in each dimension of the (l-1)th layer. This represents the array after merging segments at the i-th layer. Assuming the encoder has N layers, Z is used. enc,0 Z enc ,1 ,…,Z enc,N ,(Z enc,0 =H) to represent the N+1 outputs of the encoder, The decoder's task is to reconstruct future time series from information at different levels of the encoder. It receives the output of the last layer of the encoder along with positional codes, gradually recovering details until the finest-grained prediction is achieved. The decoder then aggregates these predictions layer by layer to fuse information at different scales, thus obtaining the final prediction result. in This represents the learnable position embedding of the decoder. It is the output of the TSA layer, and the MSA layer passes through... Set as a query, Set as key and value to establish a connection between the encoder and decoder; the output of the MSA layer is... Z dec,l Z represents the output of the skip connection and the MLP, respectively. dec,0 Z enc,1 ,…,Z dec,N This represents the N+1 outputs of the decoder. Finally, linear projection is applied to the output of each layer to obtain the prediction for that layer, and the predictions from all layers are summed to obtain the final prediction result. in It is a learnable matrix used to project vectors onto a time series segment. The prediction is for the d-th dimension and the i-th segment. The predictions from each layer are summed to obtain the final prediction result.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the computer instructions are executed by the processor, they implement the supply chain financial risk prediction method based on the RGNN-Crossformer fusion architecture as described in any one of claims 1-7.

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