Agricultural pest transmission early warning method

Abstract

This invention discloses an early warning method for the spread of agricultural pests and diseases, implemented based on an improved hyperbolic Bernstein polynomial graph neural network. The method normalizes the feature vectors of nodes in the agricultural pest and disease spread graph and embeds these features into a Poincaré sphere hyperbolic manifold using exponential mapping to obtain a hyperbolic node embedding representation. In the hyperbolic space, linear transformations and bias merging are performed based on Möbius operations, and a recursive hyperbolic spectral filter operator is constructed using the three-term recurrence relation of Jacobi orthogonal polynomials to aggregate multi-order neighborhood information and obtain a hyperbolic feature representation. Logarithmic mapping is then performed on the hyperbolic feature representation to obtain a Euclidean tangent space vector representation. A prediction function is constructed and combined with a loss function for parameter optimization, outputting the spread risk or early warning intensity. This invention eliminates the need for explicit eigenvalue decomposition of the graph operator, reducing computational overhead and improving the stability of the training process, making it suitable for early warning modeling of large-scale spread networks.

Description

Technical Field

[0001] This invention relates to the technical fields of artificial intelligence, graph neural networks and intelligent monitoring and early warning of agricultural pests and diseases, and in particular to an early warning method for the spread of agricultural pests and diseases based on an improved hyperbolic Bernstein polynomial graph neural network. Background Technology

[0002] With the deepening of agricultural informatization and intelligentization, early identification and risk warning of agricultural pests and diseases based on multi-source data has become an important technical direction for ensuring food security and improving agricultural production efficiency. In actual production, the spread of pests and diseases usually exhibits significant spatial diffusion and temporal evolution. The transmission relationships between different plots, regions, or monitoring points are influenced by multiple factors such as geographical proximity, meteorological conditions, crop type, and management measures, presenting a complex structural feature of multi-level branching, hierarchical expansion, and long-range dependence. Therefore, how to structurally model the transmission relationships of agricultural pests and diseases within a unified framework and obtain representation learning results that can both characterize hierarchical topology and express multi-scale transmission features is a key technical problem that urgently needs to be solved in the field of agricultural pest and disease transmission early warning.

[0003] In existing pest and disease early warning methods, some schemes employ statistical regression, spatiotemporal interpolation, or rule-based threshold judgment for risk assessment. While these methods offer some interpretability, they struggle to effectively utilize the propagation patterns inherent in cross-regional and multi-hop paths within the propagation network. With the development of graph neural networks, schemes utilizing graph structures to model propagation relationships are increasingly common. These typically involve directly learning node representations in Euclidean space and achieving feature propagation through local neighborhood aggregation. However, due to the flat geometry and limited spatial capacity of Euclidean space, when the propagation structure exhibits near-tree-like or hierarchical expansion characteristics, Euclidean embeddings often struggle to simultaneously maintain distance metrics and containment relationships between nodes under low-distortion conditions. This can easily lead to crowded, distorted, and insufficiently discriminative node representations at different propagation levels, thus affecting the early warning model's ability to characterize propagation paths and long-range spread risks. To overcome these limitations, researchers have proposed transferring graph representation learning to hyperbolic spaces with negative curvature. Hyperbolic manifolds such as Poincaré spheres are used to express hierarchical structures in a more natural way, mitigating the distortion problem in Euclidean space representations to some extent.

[0004] While hyperbolic graph neural networks have advantages in hierarchical modeling, most existing methods still have shortcomings in frequency domain filtering and characterization of higher-order propagation patterns. They generally use first-order message passing or non-orthogonal spectral polynomial basis for feature aggregation. Different-order spectral components are prone to strong correlation and overlap in the frequency domain, leading to filter coefficient coupling, parameter redundancy, and decreased training stability. At the same time, in scenarios that need to capture multi-hop propagation paths and multi-scale diffusion patterns, the computational efficiency and engineering feasibility of higher-order spectral aggregation become bottlenecks. Some spectral graph convolution schemes rely on explicit eigenvalue decomposition or direct computation of higher-order polynomials when extracting higher-order features, resulting in high computational overhead and storage pressure, which is not conducive to end-to-end training and real-time early warning deployment on large-scale agricultural propagation maps.

[0005] In summary, existing agricultural pest and disease transmission early warning technologies suffer from at least the following problems: (1) insufficient fit between the node representation space and the hierarchical topology of the transmission network; (2) non-orthogonal filtering basis, weak decoupling ability of high-order spectral components, and limited training stability; (3) computational efficiency of high-order feature aggregation is insufficient to meet the needs of large-scale transmission graph modeling and engineering deployment. Therefore, there is an urgent need for an improved hyperbolic polynomial graph neural network scheme for agricultural pest and disease transmission early warning, which can improve the independence of spectral filtering and recursive computation efficiency while maintaining the advantages of hyperbolic geometry, thereby achieving more stable and efficient transmission risk prediction and early warning output. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings and deficiencies of existing technologies and provide an agricultural pest and disease transmission early warning method based on an improved hyperbolic Bernstein polynomial graph neural network. This method orthogonals the non-orthogonal spectral filtering basis into a Jacobi polynomial spectral basis and constructs a recursive hyperbolic spectral convolution operator using its three recursive relations. It combines exponential mapping on the Poincaré spherical manifold, Möbius operations, and logarithmic mapping to achieve geometrically consistent representation learning and efficient multi-order feature aggregation. This effectively characterizes the hierarchical topology and long-range dependency features in the agricultural pest and disease transmission graph without the need for explicit eigenvalue decomposition, improving the stability, convergence efficiency, and accuracy of transmission risk prediction and early warning output.

[0007] To achieve the above objectives, the technical solution provided by this invention is: an early warning method for the spread of agricultural pests and diseases, which is based on an improved hyperbolic Bernstein polynomial graph neural network for accurate early warning of agricultural pests and diseases; the improved hyperbolic Bernstein polynomial graph neural network is based on the original hyperbolic Bernstein polynomial graph neural network with the following two improvements: the first part is to orthogonalize the spectral filtering basis in the hyperbolic Bernstein polynomial graph neural network, that is, by replacing the original non-orthogonal polynomial feature aggregation mechanism with a Jacobi polynomial spectral basis with orthogonal properties, and using the Jacobi polynomial under a preset weight function. The first part is to improve the orthogonality of the hyperbolic spectral components by decoupling and aggregating different orders of spectral components in the hyperbolic spectral domain to reduce parameter coupling and spectral component redundancy in the feature aggregation process. The second part is to improve the spectral convolution calculation operator in the hyperbolic Bernstein polynomial graph neural network by recursion. That is, by using the three-term recursive relation of the Jacobi polynomial, a recursive form of hyperbolic spectral convolution operator is constructed in the hyperbolic space. By decomposing the high-order hyperbolic spectral filtering process into multiple low-order recursive calculation steps based on Möbius operation, a recursive calculation mechanism in which the computational complexity of high-order feature aggregation increases linearly with the filtering order is realized, thereby avoiding explicit eigenvalue decomposition of the graph operator.

[0008] The specific implementation of this agricultural pest and disease transmission early warning method includes the following steps:

[0009] S1: Normalize the original feature vectors of nodes in the agricultural pest and disease transmission graph to obtain normalized node feature vectors. Then, map the normalized node feature vectors to the Poincaré spherical manifold in hyperbolic space using the exponential mapping operator to obtain an agricultural pest and disease transmission graph carrying hyperbolic node embedding representation.

[0010] S2: The agricultural pest and disease transmission graph carrying hyperbolic node embeddings is input into an improved hyperbolic Bernstein polynomial graph neural network for training. A linear transformation and bias merging process are performed on the hyperbolic node embeddings in hyperbolic space based on Möbius operations to obtain hyperbolic feature vectors. Then, multi-order recursive spectral filtering and aggregation are performed on the hyperbolic feature vectors based on the three-term recurrence relation of Jacobi polynomials to obtain a deep hyperbolic feature representation that integrates long-range dependencies and hierarchical topological information of agricultural pest and disease transmission. A logarithmic mapping operation is performed on the deep hyperbolic feature representation to map it from hyperbolic space to the corresponding Euclidean tangent space, obtaining a vector representation in the Euclidean tangent space. During training, the network parameters are backpropagated and iteratively optimized according to a preset loss function until the loss function converges, resulting in the network with optimal performance.

[0011] S3: By using the network with the best performance to model and predict the spread of agricultural pests and diseases, early warning results for the spread of agricultural pests and diseases can be obtained.

[0012] Furthermore, the improved hyperbolic Bernstein polynomial graph neural network includes a hyperbolic transformation module, a Jacobi recursive hyperbolic spectral convolution aggregation module, an Euclidean mapping module, and an early warning prediction module. Specifically, the hyperbolic transformation module performs linear transformation and bias merging processing on the hyperbolic node embedding representation based on Möbius operations to obtain hyperbolic feature vectors. The Jacobi recursive hyperbolic spectral convolution aggregation module performs multi-order recursive spectral filtering aggregation on the hyperbolic feature vectors based on the three-term recursive relationship of the Jacobi polynomial to obtain deep hyperbolic feature representations. The Euclidean mapping module performs logarithmic mapping on the deep hyperbolic feature representations to obtain a vector representation of the Euclidean tangent space. The early warning prediction module outputs early warning results for agricultural pest and disease transmission based on the vector representation of the Euclidean tangent space, and iteratively updates the network parameters during the training phase using backpropagation with a preset loss function.

[0013] Furthermore, step S1 specifically includes:

[0014] S11: Original feature vectors of nodes in the agricultural pest and disease transmission graph. Normalization is performed to obtain the normalized node feature vectors. The normalization process satisfies the following form:

[0015] ;

[0016] in, express Victorious space, To prevent division by zero of constants;

[0017] S12: Assume the hyperbolic space uses a curvature parameter of... The Poincaré spherical manifold, in which There is a non-zero vector , Poincaré spherical manifold Defined as:

[0018] ;

[0019] The normalized node feature vector Considered to be located at the origin of the Poincaré sphere The tangent vector in the tangent space;

[0020] S13: Map the tangent vector onto the Poincaré spherical manifold using the exponential mapping operator to obtain the hyperbolic node embedding vector. The exponential mapping satisfies:

[0021] ;

[0022] in, Indicates at the origin The curvature parameter is The exponential mapping operation is performed; the hyperbolic node embedding vector is used as the hyperbolic node embedding representation of the agricultural pest and disease propagation graph to obtain the agricultural pest and disease propagation graph carrying the hyperbolic node embedding representation.

[0023] Furthermore, in step S2, the agricultural pest and disease transmission graph carrying hyperbolic node embeddings obtained in step S1 is first input into an improved hyperbolic Bernstein polynomial graph neural network. The hyperbolic transformation module performs a linear transformation based on Möbius operations on the hyperbolic node embeddings in the agricultural pest and disease transmission graph. This linear transformation is performed by a learnable weight matrix. The definition is that the corresponding Möbius matrix multiplication result is expressed as:

[0024] ;

[0025] in, Indicates curvature parameter as The Möbius matrix multiplication is performed; after the Möbius matrix multiplication is completed, the bias vector is transformed by the hyperbolic transformation module. By merging the results of Möbius addition and transformation, the hyperbolic eigenvectors are obtained. The merging form satisfies:

[0026] ;

[0027] In the formula, The curvature parameter defined under the Poincaré spherical manifold is... Möbius addition operation;

[0028] Based on the adjacency matrix corresponding to the agricultural pest and disease transmission map and its degree matrix Construct a normalized graph operator to describe the transmission relationships of agricultural pests and diseases. ,satisfy:

[0029] ;

[0030] The obtained hyperbolic feature vector Using node feature input and normalized graph operators as graph structure operators, the Jacobi recursive hyperbolic spectral convolution aggregation module constructs a spectral filter based on Jacobi orthogonal polynomials in hyperbolic space and performs multi-order recursive spectral filtering aggregation. The filtering form is defined as follows:

[0031] ;

[0032] In the formula, Indicates the first Jacobi orthogonal polynomial of order 1 These are the learnable spectral filter coefficients for the corresponding order. These are the polynomial parameters used to adjust the shape of the spectral response;

[0033] To avoid explicitly calculating higher-order Jacobi polynomials, the Jacobi recursive hyperbolic spectral convolution aggregation module recursively constructs multi-order spectral filtering results based on the three-term recursive relation of the Jacobi polynomials. The recursive form satisfies:

[0034] when hour:

[0035] ;

[0036] when hour:

[0037] ;

[0038] when hour:

[0039] ;

[0040] In the formula, , , They are composed of polynomial parameters and order Determined recursive coefficients; multi-order hyperbolic spectral filtering results are constructed step-by-step through the above three recursive relations, decomposing the high-order feature aggregation process into a series of low-order recursive computation steps based on Möbius operations. Thus, without performing eigenvalue decomposition on the graph operator, a deep hyperbolic feature representation incorporating multi-scale neighborhood structure information is obtained. This serves as the input for subsequent mapping and early warning prediction steps;

[0041] The deep hyperbolic feature representation is obtained by the Euclidean mapping module. Mapping to the corresponding Euclidean tangent space, we obtain the vector representation of the Euclidean tangent space by performing a logarithmic mapping operator at the origin of the Poincaré sphere. :

[0042] ;

[0043] in, Indicated by Origin, curvature parameter is Logarithmic mapping under;

[0044] The early warning prediction module is based on the vector representation of the Euclidean tangent space. Constructing prediction functions And generate the corresponding prediction output. :

[0045] ;

[0046] In the formula, The predicted output represents the set of parameters to be learned in the network. Used to characterize the risk of agricultural pest and disease transmission or the intensity of early warning;

[0047] The early warning prediction module outputs the prediction. Corresponding actual annotation information Construct the loss function :

[0048] ;

[0049] Based on the loss function, gradient descent is used to adjust the parameter set. The parameter update process, which performs iterative updates, satisfies the following:

[0050] ;

[0051] In the formula, Indicates the learning rate. Indicates the number of iterations. Indicates the first The set of parameters updated in each iteration. No. The parameter set is updated in multiple iterations, and the loss function is converged through multiple iterations to obtain the network with optimal performance.

[0052] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0053] 1. This invention addresses the structured modeling needs for early warning of agricultural pest and disease transmission. It uses an improved hyperbolic Bernstein polynomial graph neural network as the core computational model. By embedding and propagating the node features of the agricultural pest and disease transmission graph in the hyperbolic space of the Poincaré sphere, it achieves a geometrically consistent characterization of the hierarchical topology, near-tree-like diffusion structure, and long-range dependencies in the transmission network. It can make full use of the advantages of negative curvature space in expressing hierarchical structures, thereby improving the ability to represent complex transmission relationships and the effect of early warning modeling.

[0054] 2. This invention proposes a spectral basis improvement strategy based on Jacobi orthogonal polynomials. In the hyperbolic feature aggregation stage, orthogonal basis functions are used to achieve decoupling and aggregation of spectral components of different orders. This can reduce redundant components and parameter coupling in the spectral filtering process, reduce instability factors in high-order filtering training, improve the numerical stability and convergence efficiency of model training, and enable the network to obtain more robust hyperbolic embedding representation and more reliable propagation risk characterization when learning multi-layer propagation features.

[0055] 3. This invention constructs a recursive hyperbolic spectral convolution operator and uses the three-term recursive relation of the Jacobi polynomial to organize the high-order feature extraction process. It decomposes multi-order neighborhood information aggregation into a series of low-order recursive calculation steps based on Möbius operations, thereby completing deep spectral filtering aggregation without explicit eigenvalue decomposition of the graph operator. This makes the computational complexity increase linearly with the filtering order, effectively reducing the computational overhead and storage occupation when modeling large-scale agricultural pest and disease transmission graphs, and is more suitable for engineering deployment and continuous online early warning.

[0056] 4. This invention forms a complete closed loop in the early warning function: by embedding node features into hyperbolic space through exponential mapping, obtaining deep hyperbolic feature representation through Möbius linear transformation and Jacobi recursive spectrum filtering, and then obtaining Euclidean tangent space vector representation through logarithmic mapping and outputting the propagation risk or early warning intensity, it realizes an integrated process from propagation relationship modeling to early warning result output. It can be used in application scenarios such as agricultural pest and disease propagation risk assessment, early warning level determination and key prevention and control area identification, and has strong practical application value and promotion significance. Attached Figure Description

[0057] Figure 1 This is a framework diagram of the method of the present invention; in the diagram, These are the eigenvalues ​​of the Laplace matrix. This represents the response of the spectral filter at different frequencies. Detailed Implementation

[0058] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0059] like Figure 1As shown in the figure, this embodiment discloses an early warning method for the spread of agricultural pests and diseases. This method is based on an improved hyperbolic Bernstein polynomial graph neural network for accurate early warning of agricultural pests and diseases. This improved hyperbolic Bernstein polynomial graph neural network is based on the original hyperbolic Bernstein polynomial graph neural network and makes the following two improvements: The first part is to orthogonalize the spectral filtering basis in the hyperbolic Bernstein polynomial graph neural network. That is, by replacing the original non-orthogonal polynomial feature aggregation mechanism with the Jacobi polynomial spectral basis with orthogonal properties, the orthogonality of the Jacobi polynomial under the preset weight function is used to decouple and aggregate spectral components of different orders in the hyperbolic spectral domain, so as to reduce parameter coupling and spectral component redundancy in the feature aggregation process. The second part is to recursively improve the spectral convolution calculation operator in the hyperbolic Bernstein polynomial graph neural network. That is, by using the three recursive relations of the Jacobi polynomial, a recursive form of hyperbolic spectral convolution operator is constructed in hyperbolic space. By decomposing the high-order hyperbolic spectral filtering process into multiple low-order recursive calculation steps based on Möbius operation, a recursive calculation mechanism in which the computational complexity of high-order feature aggregation increases linearly with the filtering order is realized, thereby avoiding explicit eigenvalue decomposition of the graph operator.

[0060] This method has been implemented on the PyCharm platform, which is based on the Python language, and includes the following steps:

[0061] S1: Normalize the original feature vectors of nodes in the agricultural pest and disease transmission graph to obtain normalized node feature vectors. Then, map the normalized node feature vectors to a Poincaré spherical manifold in hyperbolic space using an exponential mapping operator to obtain an agricultural pest and disease transmission graph carrying hyperbolic node embedding representations; specifically including:

[0062] S11: Original feature vectors of nodes in the agricultural pest and disease transmission graph. Normalization is performed to obtain the normalized node feature vectors. The normalization process satisfies the following form:

[0063] ;

[0064] in, express Victorious space, To prevent division by zero of constants;

[0065] S12: Assume the hyperbolic space uses a curvature parameter of... The Poincaré spherical manifold, in which There is a non-zero vector , Poincaré spherical manifold Defined as:

[0066] ;

[0067] The normalized node feature vector Considered to be located at the origin of the Poincaré sphere The tangent vector in the tangent space;

[0068] S13: Map the tangent vector onto the Poincaré spherical manifold using the exponential mapping operator to obtain the hyperbolic node embedding vector. The exponential mapping satisfies:

[0069] ;

[0070] in, Indicates at the origin The curvature parameter is The exponential mapping operation is performed; the hyperbolic node embedding vector is used as the hyperbolic node embedding representation of the agricultural pest and disease propagation graph to obtain the agricultural pest and disease propagation graph carrying the hyperbolic node embedding representation.

[0071] S2: The agricultural pest and disease transmission graph carrying hyperbolic node embeddings is input into an improved hyperbolic Bernstein polynomial graph neural network for training. A linear transformation and bias merging process are performed on the hyperbolic node embeddings in hyperbolic space based on Möbius operations to obtain hyperbolic feature vectors. Then, multi-order recursive spectral filtering aggregation is performed on the hyperbolic feature vectors based on the three-term recurrence relation of Jacobi polynomials to obtain a deep hyperbolic feature representation that integrates long-range dependencies and hierarchical topological information of agricultural pest and disease transmission. A logarithmic mapping operation is performed on the deep hyperbolic feature representation to map it from hyperbolic space to the corresponding Euclidean tangent space, obtaining a vector representation in Euclidean tangent space. During training, the network parameters are backpropagated and iteratively optimized according to a preset loss function until the loss function converges, resulting in the network with optimal performance.

[0072] Specifically, the improved hyperbolic Bernstein polynomial graph neural network includes a hyperbolic transformation module, a Jacobi recursive hyperbolic spectral convolution aggregation module, an Euclidean mapping module, and an early warning prediction module. The hyperbolic transformation module performs linear transformation and bias merging processing on the hyperbolic node embedding representation based on Möbius operations to obtain hyperbolic feature vectors. The Jacobi recursive hyperbolic spectral convolution aggregation module performs multi-order recursive spectral filtering aggregation on the hyperbolic feature vectors based on the three-term recursive relationship of the Jacobi polynomial to obtain deep hyperbolic feature representations. The Euclidean mapping module performs logarithmic mapping on the deep hyperbolic feature representations to obtain a vector representation of the Euclidean tangent space. The early warning prediction module outputs early warning results for the spread of agricultural pests and diseases based on the vector representation of the Euclidean tangent space, and iteratively updates the network parameters during the training phase using backpropagation with a preset loss function.

[0073] Specifically, the training process of the improved hyperbolic Bernstein polynomial graph neural network is as follows:

[0074] First, the agricultural pest and disease transmission graph carrying hyperbolic node embeddings obtained in step S1 is input into an improved hyperbolic Bernstein polynomial graph neural network. The hyperbolic transformation module performs a linear transformation based on Möbius operations on the hyperbolic node embeddings in the agricultural pest and disease transmission graph. This linear transformation is performed by a learnable weight matrix. The definition is that the corresponding Möbius matrix multiplication result is expressed as:

[0075] ;

[0076] in, Indicates curvature parameter as The Möbius matrix multiplication is performed; after the Möbius matrix multiplication is completed, the bias vector is transformed by the hyperbolic transformation module. By merging the results of Möbius addition and transformation, the hyperbolic eigenvectors are obtained. The merging form satisfies:

[0077] ;

[0078] In the formula, The curvature parameter defined under the Poincaré spherical manifold is... Möbius addition operation;

[0079] Based on the adjacency matrix corresponding to the agricultural pest and disease transmission map and its degree matrix Construct a normalized graph operator to describe the transmission relationships of agricultural pests and diseases. ,satisfy:

[0080] ;

[0081] The obtained hyperbolic feature vector Using node feature input and normalized graph operators as graph structure operators, the Jacobi recursive hyperbolic spectral convolution aggregation module constructs a spectral filter based on Jacobi orthogonal polynomials in hyperbolic space and performs multi-order recursive spectral filtering aggregation. The filtering form is defined as follows:

[0082] ;

[0083] In the formula, Indicates the first Jacobi orthogonal polynomial of order 1 These are the learnable spectral filter coefficients for the corresponding order. These are the polynomial parameters used to adjust the shape of the spectral response;

[0084] To avoid explicitly calculating higher-order Jacobi polynomials, the Jacobi recursive hyperbolic spectral convolution aggregation module recursively constructs multi-order spectral filtering results based on the three-term recursive relation of the Jacobi polynomials. The recursive form satisfies:

[0085] when hour:

[0086] ;

[0087] when hour:

[0088] ;

[0089] when hour:

[0090] ;

[0091] In the formula, , , They are composed of polynomial parameters and order Determined recursive coefficients; multi-order hyperbolic spectral filtering results are constructed step-by-step through the above three recursive relations, decomposing the high-order feature aggregation process into a series of low-order recursive computation steps based on Möbius operations. Thus, without performing eigenvalue decomposition on the graph operator, a deep hyperbolic feature representation incorporating multi-scale neighborhood structure information is obtained. This serves as the input for subsequent mapping and early warning prediction steps;

[0092] The deep hyperbolic feature representation is obtained by the Euclidean mapping module. Mapping to the corresponding Euclidean tangent space, we obtain the vector representation of the Euclidean tangent space by performing a logarithmic mapping operator at the origin of the Poincaré sphere. :

[0093] ;

[0094] in, Indicated by Origin, curvature parameter is Logarithmic mapping under;

[0095] The early warning prediction module is based on the vector representation of the Euclidean tangent space. Constructing prediction functions And generate the corresponding prediction output. :

[0096] ;

[0097] In the formula, The predicted output represents the set of parameters to be learned in the network. Used to characterize the risk of agricultural pest and disease transmission or the intensity of early warning;

[0098] The early warning prediction module outputs the prediction. Corresponding actual annotation information Construct the loss function :

[0099] ;

[0100] Based on the loss function, gradient descent is used to adjust the parameter set. The parameter update process, which performs iterative updates, satisfies the following:

[0101] ;

[0102] In the formula, Indicates the learning rate. Indicates the number of iterations. Indicates the first The set of parameters updated in each iteration. No. The parameter set is updated in multiple iterations, and the loss function is converged through multiple iterations to obtain the network with optimal performance.

[0103] S3: By using the network with the best performance to model and predict the spread of agricultural pests and diseases, early warning results for the spread of agricultural pests and diseases can be obtained.

[0104] To comprehensively evaluate the performance of the proposed method, this paper applies it to the link prediction task of a propagation graph and conducts experiments on a disease propagation dataset. AUC (Area Under the ROC Curve) and total runtime are used as evaluation metrics to comprehensively measure the model's predictive performance and computational efficiency. Several representative models are selected as baselines for comparison, covering three categories: shallow embedding and non-graph convolution methods, Euclidean graph neural network methods, and hyperbolic graph neural network methods. These include hyperbolic space shallow embedding models Poincaré Embedding (HYP), Multilayer Perceptron (MLP), classic message passing models GCN and GAT, and spectral methods BernNet, ARMA, and JacobiConv. HNN, HGCN, and the hyperbolic Bernstein graph neural network (HBNN) using polynomial spectral convolution in hyperbolic space are also introduced to systematically compare the performance gains of higher-order spectral filtering mechanisms in hyperbolic geometric modeling. All models are trained and evaluated under the same dataset partitioning and experimental configuration. The experimental results are shown in Tables 1 and 2.

[0105] Table 1. AUC values ​​of each method in the link prediction task on disease datasets (higher is better).

[0106]

[0107] Table 2. Total runtime of each method in the link prediction task (in seconds)

[0108]

[0109] The experimental results show that, in terms of prediction accuracy, the method of this invention significantly outperforms shallow embedding methods and Euclidean graph neural network models on the disease transmission dataset, and even surpasses the hyperbolic polynomial spectral convolution model HBNN on the same dataset. This indicates that the proposed recursive spectral filtering mechanism based on Jacobi orthogonal polynomials can more effectively capture the multi-scale and hierarchical dependencies in the transmission structure. Table 2 shows that, in terms of computational efficiency, although the method of this invention introduces multi-order spectral filtering operations, its total running time is still significantly lower than that of HBNN, indicating that the three-term recursive computation can reduce the engineering overhead of high-order spectral filtering. Combining the results in terms of both accuracy and running time, it can be seen that the method of this invention achieves a better balance between accuracy and efficiency in disease transmission graph link prediction tasks, providing effective and engineering-feasible technical support for modeling transmission networks with hierarchical diffusion characteristics, such as agricultural pest and disease transmission early warning, and is worthy of promotion.

[0110] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An agricultural disease and pest transmission early warning method, characterized by, This method uses an improved hyperbolic Bernstein polynomial graph neural network for accurate early warning of agricultural pests and diseases. The improved hyperbolic Bernstein polynomial graph neural network is based on the original hyperbolic Bernstein polynomial graph neural network with the following two improvements: The first part is to orthogonalize the spectral filtering basis in the hyperbolic Bernstein polynomial graph neural network. Specifically, the original non-orthogonal polynomial feature aggregation mechanism is replaced with an orthogonal Jacobi polynomial spectral basis. Utilizing the orthogonality of Jacobi polynomials under a preset weight function, different orders of spectra are separated within the hyperbolic spectral domain. The first part decouples and aggregates the parameters to reduce parameter coupling and spectral component redundancy in the feature aggregation process. The second part recursively improves the spectral convolution operator in the hyperbolic Bernstein polynomial graph neural network. That is, it uses the three-term recursive relation of the Jacobi polynomial to construct a recursive form of the hyperbolic spectral convolution operator in the hyperbolic space. By decomposing the high-order hyperbolic spectral filtering process into multiple low-order recursive calculation steps based on Möbius operation, it realizes the recursive calculation mechanism in which the computational complexity of the high-order feature aggregation process increases linearly with the filtering order, thereby avoiding explicit eigenvalue decomposition of the graph operator. The specific implementation of this agricultural pest and disease transmission early warning method includes the following steps: S1: Normalize the original feature vectors of nodes in the agricultural pest and disease transmission graph to obtain normalized node feature vectors. Then, map the normalized node feature vectors to the Poincaré spherical manifold in hyperbolic space using the exponential mapping operator to obtain an agricultural pest and disease transmission graph carrying hyperbolic node embedding representation. S2: The agricultural pest and disease transmission graph carrying hyperbolic node embeddings is input into an improved hyperbolic Bernstein polynomial graph neural network for training. A linear transformation and bias merging process are performed on the hyperbolic node embeddings in hyperbolic space based on Möbius operations to obtain hyperbolic feature vectors. Then, multi-order recursive spectral filtering and aggregation are performed on the hyperbolic feature vectors based on the three-term recurrence relation of Jacobi polynomials to obtain a deep hyperbolic feature representation that integrates long-range dependencies and hierarchical topological information of agricultural pest and disease transmission. A logarithmic mapping operation is performed on the deep hyperbolic feature representation to map it from hyperbolic space to the corresponding Euclidean tangent space, obtaining a vector representation in the Euclidean tangent space. During training, the network parameters are backpropagated and iteratively optimized according to a preset loss function until the loss function converges, resulting in the network with optimal performance. S3: By using the network with the best performance to model and predict the spread of agricultural pests and diseases, early warning results for the spread of agricultural pests and diseases can be obtained.

2. The agricultural disease and pest transmission early warning method according to claim 1, characterized in that, The improved hyperbolic Bernstein polynomial graph neural network includes a hyperbolic transformation module, a Jacobi recursive hyperbolic spectral convolution aggregation module, an Euclidean mapping module, and an early warning prediction module. Specifically, the hyperbolic transformation module performs linear transformation and bias merging processing on the hyperbolic node embedding representation based on Möbius operations to obtain hyperbolic feature vectors. The Jacobi recursive hyperbolic spectral convolution aggregation module performs multi-order recursive spectral filtering aggregation on the hyperbolic feature vectors based on the three-term recursive relationship of the Jacobi polynomial to obtain a deep hyperbolic feature representation. The Euclidean mapping module performs logarithmic mapping on the deep hyperbolic feature representation to obtain a vector representation in the Euclidean tangent space. The early warning prediction module outputs early warning results for agricultural pest and disease transmission based on the vector representation in the Euclidean tangent space, and iteratively updates the network parameters during the training phase using backpropagation with a preset loss function.

3. The method of claim 2, wherein the method further comprises: Step S1 specifically includes: S11: Normalizing the original feature vector of the node in the agricultural pest transmission graph S12: Obtaining a normalized node feature vector by performing normalization processing wherein the normalization processing satisfies the following form: ； wherein denotes Von Neumann space, is a constant to prevent division by zero; S12: Let the hyperbolic space adopt the curvature parameter as Poincaré ball manifold, where , has a nonzero vector , dimensional Poincaré ball manifold is defined as: ； normalizing the node feature vectors a tangent vector at the origin of the Poincaré sphere a tangent vector at the origin of the Poincaré sphere S13: mapping the tangent vector into the Poincaré ball manifold by an exponential mapping operator to obtain a hyperbolic node embedding vector The exponential mapping satisfies: ； wherein, represents an exponential mapping operation with a curvature parameter of at the origin ; and obtaining the agricultural pest transmission graph carrying the hyperbolic node embedding representation.

4. The method for early warning of agricultural pest and disease transmission according to claim 3, characterized in that: In step S2, the agricultural pest propagation graph carrying the hyperbolic node embedding representation obtained in step S1 is first input into the improved hyperbolic Bernstein polynomial graph neural network, and a linear transformation based on Möbius operation is performed on the hyperbolic node embedding representation in the agricultural pest propagation graph by the hyperbolic linear transformation module, and the linear transformation is represented by a learnable weight matrix Definition, the corresponding Möbius matrix multiplication result is represented as: ； wherein, represents a Möbius matrix multiplication with a curvature parameter After the Möbius matrix multiplication is completed, a bias vector is merged with the transformation result by Möbius addition to obtain a hyperbolic feature vector , and the merged form satisfies: ； wherein represents the curvature parameter defined under the Poincaré ball model Möbius addition operation; According to the adjacency matrix corresponding to the agricultural pest transmission graph and the degree matrix , a normalized graph operator for describing the agricultural pest transmission relationship is constructed , which satisfies: ； The resulting hyperbolic eigenvectors As node feature input and with the normalized graph operator as the graph structure operator, the Jacobi recursive hyperbolic spectral convolution aggregation module constructs a spectral filter based on Jacobi orthogonal polynomials in hyperbolic space and performs multi-order recursive spectral filter aggregation, whose filtering form is defined as: ； In the formula, Indicates the first Jacobi orthogonal polynomial of order 1 These are the learnable spectral filter coefficients for the corresponding order. These are the polynomial parameters used to adjust the shape of the spectral response; To avoid explicitly calculating higher-order Jacobi polynomials, the Jacobi recursive hyperbolic spectral convolution aggregation module recursively constructs multi-order spectral filtering results based on the three-term recursive relation of the Jacobi polynomials. The recursive form satisfies: when hour: ； when hour: ； when hour: ； In the formula, , , They are composed of polynomial parameters and order Determined recursive coefficients; multi-order hyperbolic spectral filtering results are constructed step-by-step through the above three recursive relations, decomposing the high-order feature aggregation process into a series of low-order recursive computation steps based on Möbius operations. Thus, without performing eigenvalue decomposition on the graph operator, a deep hyperbolic feature representation incorporating multi-scale neighborhood structure information is obtained. This serves as the input for subsequent mapping and early warning prediction steps; The deep hyperbolic feature representation is obtained by the Euclidean mapping module. Mapping to the corresponding Euclidean tangent space, we obtain the vector representation of the Euclidean tangent space by performing a logarithmic mapping operator at the origin of the Poincaré sphere. : ； in, Indicates Origin, curvature parameter is Logarithmic mapping under; The early warning prediction module is based on the vector representation of the Euclidean tangent space. Constructing prediction functions And generate the corresponding prediction output. : ； In the formula, The predicted output represents the set of parameters to be learned in the network. Used to characterize the risk of agricultural pest and disease transmission or the intensity of early warning; The early warning prediction module outputs the prediction. Corresponding actual annotation information Construct the loss function : ； Based on the loss function, gradient descent is used to adjust the parameter set. The parameter update process, which performs iterative updates, satisfies the following: ； In the formula, Indicates the learning rate. Indicates the number of iterations. Indicates the first The set of parameters updated in each iteration. No. The parameter set is updated in multiple iterations, and the loss function is converged through multiple iterations to obtain the network with optimal performance.

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