Medium and long term temperature prediction method based on differential equation network of graph

Abstract

The invention discloses a medium and long term temperature prediction method based on a graph differential equation network, and the method comprises the steps: obtaining day-by-day temperature sequences of a plurality of meteorological stations, forming an input matrix through the data of adjacent M days of the kth day, and constructing a training and testing sample set through employing the temperature sequence of the future Tau day as a prediction target; calculating a site spacing based on the latitude and longitude information of the site, and selecting the nearest neighbor site to construct a directed adjacency matrix; performing multi-order neighborhood aggregation and linear transformation on the input air temperature data by using the adjacent matrix to extract spatial feature representation; after carrying out linear transformation on the air temperature sequence, combining with the space and time characteristics of the previous moment, and updating the time characteristic representation of the current moment through a gating time sequence module; graph-based differential equation evolution models are established for the space and time features respectively, a spatio-temporal feature evolution sequence is obtained through calculation, and after splicing and fusion, a multi-layer neural network is input to output a multi-site temperature prediction result in the future Tau day. According to the invention, the accuracy and stability of medium-and-long-term temperature prediction are effectively improved.

Description

Technical Field

[0001] This invention relates to the fields of medium- and long-term temperature prediction for urban environments and artificial intelligence technology, and particularly to a medium- and long-term temperature prediction method based on graph differential equation networks. Background Technology

[0002] Temperature is a key meteorological factor affecting human life and socio-economic development, significantly impacting important sectors such as agricultural production and energy utilization, as well as daily life. The ability to make accurate medium- and long-term temperature forecasts will have a significant impact on a range of decisions made by governments and individuals, attracting considerable research attention.

[0003] Numerical weather prediction models are based on physical principles and consider current initial weather conditions, using mathematical models to predict future temperatures. Specifically, the fundamental principles of numerical weather prediction involve estimating future temperatures based on current temperature conditions and applying thermodynamic equations, which are modeled using partial differential equations. The scientific basis of numerical weather prediction lies in the principles of physics and thermodynamics. Applying these principles provides a more objective and scientific basis for forecasts. Therefore, it has become the foundation for large-scale and medium- to long-term temperature forecasts. The prediction accuracy of numerical weather prediction models depends on the resolution of the grid used in the numerical simulation; higher resolution requires significant computational resources.

[0004] Data-driven approaches can effectively overcome the computational limitations of traditional numerical weather prediction methods. Traditional temperature forecasting methods include autoregressive integral moving average models, nonlinear autoregressive models, and support vector regression algorithms, all of which assume that the data follows a statistical distribution. While the value of these statistical and empirical methods is evident, they often face challenges in capturing the complexity and nonlinear patterns of high-dimensional meteorological data. Summary of the Invention

[0005] The purpose of this invention is to overcome the problems of insufficient reliance on cross-city spatial relationships and insufficient modeling of the temporal and spatial characteristics of temperature dynamic evolution in existing medium- and long-term temperature forecasts. It provides a medium- and long-term temperature forecasting method based on graph differential equation networks, which can more accurately and reasonably model the evolution of the temporal and spatial characteristics of temperature data from multiple cities, effectively improving the accuracy and interpretability of medium- and long-term temperature forecasts.

[0006] The technical solution adopted in this invention is:

[0007] A medium- to long-term temperature prediction method based on graph-based differential equation networks is disclosed. The system includes a directed graph adjacency matrix calculation module guided by physical location information, a directed graph-based spatial feature extraction module, a spatiotemporal feature extraction module based on spatiotemporal coupling, a spatiotemporal feature sequence evolution module based on graph-based differential equations, and a spatiotemporal feature fusion output module. The method includes the following steps:

[0008] It includes the following steps:

[0009] Step 1, Data Preparation and Input / Output Construction: Obtain daily temperature sequences from multiple weather stations, and construct the input temperature matrix using the historical data of the M nearest days to day k. In the future Weather temperature series as a prediction target This forms a training sample set and a test sample set;

[0010] Step 2, Construction of the Directed Graph: Based on the latitude and longitude information of each station, the distance between stations is obtained through a distance calculation function. For each station, several nearest neighbor stations are selected to establish location-oriented directed edges, resulting in a directed graph adjacency matrix based on physical information. ;

[0011] Step 3, Spatial Feature Extraction Based on Directed Graph: The input temperature matrix is ​​processed using adjacency matrix A through multi-order neighborhood aggregation and linear transformation to obtain the corresponding spatial feature representation. ;

[0012] Step 4, Temporal Feature Extraction Based on Spatiotemporal Coupling: The input temperature matrix... After linear transformation, the spatial characteristics compared to the previous time step and time characteristics The common input gating timing module obtains the updated candidate state. In order to calculate the time feature representation of the current moment. ;

[0013] Step 5, calculation of spatiotemporal feature sequence evolution based on graph differential equations: for spatial features and time characteristics A differential equation evolution model is established, and the spatial feature sequence is obtained by solving it. and time feature sequences ;

[0014] Step 6, Spatiotemporal Feature Fusion and Prediction Output: This involves processing the spatial feature sequence... and time feature sequences The components are spliced ​​and fused together, and the future output is generated through a multi-layer neural network. Multi-site temperature forecast results for the day.

[0015] Furthermore, step 2 involves a directed adjacency matrix. Distance-based weight decay and normalization are employed, and a preset number of outgoing edges are retained for each vertex to form a sparse directed graph.

[0016] Furthermore, the directed adjacency matrix elements in The calculation formula is as follows:

[0017]

[0018] in It is the th adjacency matrix line, number Column elements; σ is a coefficient. For the first The weather station and the first The distance between weather stations; and They represent the first Weather station and the The set of adjacent weather stations Indicates the first Adjacent stations of the weather station Indicates the first Adjacent stations to the weather station; No. The weather station and the first The first weather station The distance between adjacent stations; No. The weather station and the first The first weather station The distance between adjacent stations.

[0019] Furthermore, in step 3, after expanding the input sequence over time, the directed adjacency matrix is ​​calculated respectively. The spatial features of the temperature data are obtained by aggregating neighborhood features from order 0 to order L and by linear mapping and weighted summation. The expression is:

[0020] ;

[0021] ;

[0022] ;

[0023] in, For the first Temperature data collected from all stations Spatial characteristics; The spatial characteristic order, For the largest order, Z represents the learnable coefficients, and Z is the linear transformation matrix. It is the size of The matrix, M represents the number of monitoring stations, and M represents the number of historical neighboring days for the temperature data on day k. For the first The temperature data collected that day Rank space aggregation features; Indicates the first Temperature data collected from all stations throughout the day, express An adjacency matrix of order 1.

[0024] Furthermore, the gating timing module in step 4 includes update gate calculation and candidate state fusion, and time features. The update formula is:

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] in, To update the gate output, Let be the characteristic matrix, and ⊙ denote element-wise multiplication; It is a coefficient matrix; , , , , , The coefficient matrix to be determined , The bias matrix to be designed, for function, For activation functions; Z represents the input temperature matrix after linear transformation, where Z is the linear transformation. and is the coefficient matrix to be determined, and tanh is the hyperbolic tangent activation function.

[0030] Furthermore, step 5, the graph-based differential equations, include: characterizing the diffusion / smoothing effect of features on the graph using the graph Laplacian operator, and adjusting the diffusion intensity using learnable coefficients to obtain spatial features. With time characteristics Evolution equation

[0031] Furthermore, the differential equation evolution model in step 5 includes:

[0032] Spatial feature evolution equation:

[0033] ;

[0034] Where L is a scaled version of the normalized Laplacian matrix based on the adjacency matrix A. ; It is the normalized Laplace matrix. ; It is a matrix The largest eigenvalue; It is composed of adjacency matrix Calculate the degree matrix; The coefficient matrix, , and These are coefficients to be determined. , It is the maximum order; yes function, This represents element-wise multiplication of two matrices; tanh is the hyperbolic tangent activation function.

[0035] Evolutionary equation of time characteristics:

[0036] ;

[0037] in, Indicates time characteristics; , and The coefficients are to be determined.

[0038] Furthermore, in step 5, a fixed-step numerical integration method is used with a neural network constant differential equation solver to obtain a spatial feature sequence of β steps. With time feature sequence ,Right now:

[0039] ;

[0040] ;

[0041] in, For each time point corresponding to the feature sequence to be calculated, a total of spatial features need to be calculated. With time characteristics of Step evolution sequence.

[0042] Furthermore, in step 6, the spatial feature sequence... and time feature sequences After splicing and fusion, the mixture undergoes linear transformation and nonlinear activation before being input into a multilayer perceptron for prediction.

[0043] The present invention adopts the above technical solution, and compared with traditional methods, the beneficial effects of the present invention are as follows: The present invention utilizes the latitude and longitude information of temperature monitoring stations to construct a location-oriented directed graph for extracting the temporal and spatial features of temperature changes, and models the temporal and spatial feature evolution sequence of temperature data based on the differential equation of the graph, significantly improving the accuracy and stability of medium- and long-term temperature forecasts without increasing a large amount of computational overhead; Compared with traditional baseline model-based schemes, the present invention accurately models the spatial and temporal evolution mechanism of temperature across cities, and has stronger interpretability and generalization ability; The modular architecture facilitates practical deployment and updates, and can be extended to the joint forecasting of multiple meteorological elements such as humidity and wind speed, thus having significant application value in medium- and long-term decision-making in agricultural production, energy dispatch, transportation, and urban management. Attached Figure Description

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments;

[0045] Figure 1 This is a schematic diagram of the overall framework of a medium- to long-term temperature prediction method based on graph differential equation networks according to the present invention.

[0046] Figure 2 This is a schematic diagram comparing the average prediction errors of each site within a 2, 3, 4, and 5-day prediction range in this invention.

[0047] Figure 3 This is a schematic diagram comparing the performance of spatiotemporal feature sequence evolution modules with and without graph-based differential equations in the embodiments. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0049] like Figures 1 to 3As shown in the figure, this invention discloses a medium- to long-term temperature prediction method based on graph differential equation networks. This method comprises five modules: a directed graph adjacency matrix calculation module guided by physical location information, a directed graph-based spatial feature extraction module, a temporal feature extraction module based on spatiotemporal coupling, a spatiotemporal feature sequence evolution module based on graph differential equations, and a spatiotemporal feature fusion output module. This method effectively improves the accuracy of medium- to long-term temperature prediction by modeling the temporal and spatial evolution mechanism of temperature data across cities. The proposed method is applicable to guiding scenarios such as agricultural production, transportation, and industrial operations.

[0050] like Figure 1 As shown, the present invention provides a medium- to long-term temperature prediction method based on graph differential equation networks, comprising the following steps:

[0051] 1) Data preparation: Temperature data collected by the monitoring station is used for... It indicates that the size is ,in, The number of monitoring stations. To determine the length of the collected data, use Indicates the first Temperature monitoring station All collected temperature data, using Indicates the first This invention utilizes historical temperature data collected from all stations over the past day. The study focuses on the problem of temperature prediction, namely:

[0052] ;

[0053] in, The length of the sliding window; that is Indicates the first Historical temperature data for a specified window length M starting from today;

[0054] In this temperature prediction problem, the latitude and longitude of the temperature monitoring station are considered:

[0055] ;

[0056] in, This represents a set of location information for temperature monitoring stations; This provides the location information for the i-th station. This refers to the number of monitoring stations. The goal is to predict the future. The temperature data for the day, i.e.:

[0057] ;

[0058] in, Indicates the first Tianqi's Predicted Future Temperature data for the day;

[0059] Therefore, the problem of medium- and long-term temperature prediction is expressed as:

[0060] ;

[0061] in, It is a directed adjacency matrix based on the latitude and longitude data of monitoring stations. It is the medium- to long-term temperature prediction model to be designed.

[0062] 2) Calculation of the adjacency matrix of a directed graph guided by physical location information: The distance between different stations is calculated using the latitude and longitude information of multiple meteorological monitoring stations, i.e.:

[0063] ;

[0064] in, Indicates the first Station and the The distance between stations , This indicates that the hasersine function is used to calculate the distance between stations. Represents a size of The directed adjacency matrix, A directed adjacency matrix The elements in the formula are calculated as follows:

[0065] ;

[0066] in, It is the th adjacency matrix line, number Column elements; σ is a coefficient; and They represent the first Weather station and the The set of adjacent weather stations; Indicates the first Index of adjacent stations of the weather station; Indicates the first Index of adjacent stations of the weather station; For the first The weather station and the first The first weather station The distance between adjacent stations; For the first The weather station and the first The first weather station Distance between adjacent stations

[0067] 2) Spatial feature extraction based on directed graphs: Definition of The characteristics of the order space are:

[0068] ;

[0069] in, Indicates the first The temperature data collected from all stations over the past day is a file of size [size missing]. The vector, , Let be the order of the spatial characteristics, then the th order of the medium- and long-term temperature forecast... The spatial characteristics of the order space can be defined as:

[0070] ;

[0071] in It is the size of The matrix. A linear transformation. Applied to The spatial characteristics of the first order are used to obtain the first order after linear transformation. Rank space features :

[0072] ;

[0073] in It is a dimension with size The coefficient matrix. Finally, the linear combination expression of the spatial features is obtained:

[0074] ;

[0075] in For the first Temperature data collected from all stations Spatial features, size , These are coefficients to be determined.

[0076] 4) Temporal feature extraction based on spatiotemporal coupling: First, extract historical temperature sequences... Perform linear transformation

[0077] ;

[0078] Obtain input data with aligned channel dimensions Then calculate the update gate. The calculation formula is as follows:

[0079] ;

[0080] in , , , , , The coefficient matrix to be determined , The bias matrix to be designed, for function, Let be the activation function. Then, the temporal features can be obtained using the following formula. :

[0081] ;

[0082] Among them, the feature matrix The calculation formula is as follows:

[0083] ;

[0084] coefficient matrix The calculation formula is as follows:

[0085] ;

[0086] and is the coefficient matrix to be determined, and tanh is the hyperbolic tangent activation function.

[0087] 5) Spatiotemporal feature sequence evolution calculation based on graph-based differential equations:

[0088] S1: First, from the adjacency matrix Calculate the degree matrix Construct the normalized Laplace matrix :

[0089] ;

[0090] in, It is the identity matrix;

[0091] Scaling the Laplacian matrix yields The calculation formula is as follows:

[0092] ;

[0093] in It is a matrix The largest eigenvalue.

[0094] S2: Spatial Features The dynamic evolution can be calculated using the following formula:

[0095] ;

[0096] Where the coefficient matrix It can be calculated using the following formula:

[0097] ;

[0098] in and These are coefficients to be determined. yes function, This represents the element-wise multiplication of two matrices.

[0099] S3: Time Characteristics The dynamic evolution can be calculated using the following formula:

[0100] ;

[0101] in Defined as:

[0102] ;

[0103] and The coefficient to be designed.

[0104] S4: Solving differential equations using a neural network ODE solver yields spatial feature sequences. With time feature sequence ,Right now:

[0105] ;

[0106] ;

[0107] in, For each time point corresponding to the feature sequence to be calculated, a total of spatial features need to be calculated. With time characteristics of Step evolution sequence.

[0108] 6) Spatiotemporal feature fusion output: for the aforementioned and Feature fusion is performed using the formula shown below:

[0109] ;

[0110] in This represents the concatenation of two matrices, i.e. Integrating time features and spatial features Then, a multi-layer neural network was designed for medium- to long-term temperature forecasting, which outputs multi-site temperature forecasts for the next τ days. ,Right now:

[0111] ;

[0112] in The calculation formula is as follows:

[0113] ;

[0114] in It is a linear transformation applied to spatiotemporal characteristics.

[0115] Verification experiment:

[0116] 1) Data selection: 100 cities in southern China were selected, and the daily maximum temperature from January 1, 2018 to December 31, 2018 (a total of 365 days) was used.

[0117] 2) Baseline comparison: CST-GL (correlation-driven spatiotemporal graph learning model) was used as the baseline comparison method.

[0118] Experimental steps: Implement the medium- and long-term temperature prediction method based on graph differential equation networks according to the following procedure.

[0119] 1) Data preprocessing: Daily maximum temperature data for 365 days from 100 cities were read and divided into training / validation / test sets with a ratio of 0.45:0.05:0.50. Historical input was generated using a sliding window method. (close (Tian), the goal is to predict the temperature for the next 5 days.

[0120] 2) Construct a directed graph based on location information: Calculate and normalize the pairwise distances of temperature monitoring stations based on their latitude and longitude, and establish a directed sparse adjacency matrix for each city by selecting the four nearest neighbor stations. .

[0121] 3) Feature Extraction and Fusion: After two steps, spatial feature extraction and temporal feature extraction, spatial features are obtained. and time characteristics Based on the characteristic calculation of graph differential equations, spatial feature sequences characterizing the spatiotemporal feature evolution are obtained. With time feature sequence Finally, the time features are integrated through the output fusion module. and spatial features Features .

[0122] 4) Model training, prediction, and comparison: using features As input, the model is trained to calculate medium- and long-term temperature forecasts. Then, the prediction performance of the two methods is compared with that of the baseline method CST-GL under the same dataset partitioning and training strategy.

[0123] Experimental results: such as Figure 2 As shown, the four subplots (a–d) in the figure respectively show the comparison of the average prediction error of 100 stations under the prediction range of 2, 3, 4, and 5 days. The red line (the model in this paper) is lower than the black line (CST-GL) for almost all stations, and the gap between the two gradually widens from 2 days to 5 days. At the same time, the red line fluctuates less, showing better stability.

[0124] Figure 3 As shown, the impact of having and not having a graph-based differential equation spatiotemporal feature sequence evolution module on the model's predictive performance was compared for each station. The red solid line represents the average prediction error with this module, and the black dashed line represents the prediction error without it. It can be seen that the red line is significantly lower than the black line for almost all stations, with less fluctuation and a smoother curve, indicating that introducing the graph-based differential equation spatiotemporal feature sequence evolution module makes the model more stable and robust.

[0125] Compared to existing baseline-based models, this invention integrates geographical priors with continuous-time dynamics to accurately model cross-city temperature variations in both spatial and temporal dimensions. The proposed graph-based differential equation network-based medium- to long-term temperature prediction method has been validated on real-world datasets in South China, demonstrating superior performance in medium- to long-term temperature prediction. It can be widely applied to medium- to long-term decision support in meteorological operational platforms, agricultural production, and transportation organization.

[0126] In summary, the medium- and long-term temperature prediction method proposed in this invention can solve the technical problem that existing methods are unable to effectively characterize the spatiotemporal evolution mechanism of temperature characteristics. The method and apparatus of this invention have a clear structure and strong modularity, enabling efficient deployment. They are also adaptable to different regions, seasons, and site sizes, providing reliable medium- and long-term decision support for a wide range of economic activities such as agricultural production, transportation, and industrial operations.

[0127] Obviously, the described embodiments are only a part of the embodiments of this application, not all of them. Without conflict, the embodiments and features in the embodiments of this application can be combined with each other. The components of the embodiments of this application described and illustrated herein can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A medium- to long-term temperature prediction method based on graph-based differential equation networks, characterized in that: It includes the following steps: Step 1, Data Preparation and Input / Output Construction: Obtain daily temperature sequences from multiple weather stations, and construct the input temperature matrix using the historical data of the M nearest days to day k. In the future Weather temperature series as a prediction target This forms a training sample set and a test sample set; Step 2, Construction of the Directed Graph: Based on the latitude and longitude information of each station, the distance between stations is obtained through a distance calculation function. For each station, several nearest neighbor stations are selected to establish location-oriented directed edges, resulting in a directed graph adjacency matrix based on physical information. ; Step 3, Spatial Feature Extraction Based on Directed Graph: The input temperature matrix is ​​processed using adjacency matrix A through multi-order neighborhood aggregation and linear transformation to obtain the corresponding spatial feature representation. ; Step 4, Temporal Feature Extraction Based on Spatiotemporal Coupling: The input temperature matrix... After linear transformation, the spatial characteristics compared to the previous time step and time characteristics The common input gating timing module obtains the updated candidate state. In order to calculate the time feature representation of the current moment. ; Step 5, calculation of spatiotemporal feature sequence evolution based on graph differential equations: for spatial features and time characteristics A differential equation evolution model is established, and the spatial feature sequence is obtained by solving it. and time feature sequences ; Step 6, Spatiotemporal Feature Fusion and Prediction Output: This involves processing the spatial feature sequence... and time feature sequences The components are spliced ​​and fused together, and the future output is generated through a multi-layer neural network. Multi-site temperature forecast results for the day.

2. The medium- to long-term temperature prediction method based on graph differential equation networks according to claim 1, characterized in that: In step 2, there is a directed adjacency matrix. Distance-based weight decay and normalization are employed, and only a preset number of outgoing edges are retained for each vertex to form a sparse directed graph.

3. The medium- to long-term temperature prediction method based on graph differential equation networks according to claim 1, characterized in that: Directed adjacency matrix elements in The calculation formula is as follows: ； in It is the th adjacency matrix line, number Column elements; σ is a coefficient. For the first The weather station and the first The distance between weather stations; and They represent the first Weather station and the The set of adjacent weather stations Indicates the first Adjacent stations of the weather station Indicates the first Adjacent stations to the weather station; No. The weather station and the first The first weather station The distance between adjacent stations; No. The weather station and the first The first weather station The distance between adjacent stations.

4. The medium- to long-term temperature prediction method based on graph differential equation networks according to claim 1, characterized in that: In step 3, after expanding the input sequence by time, the directed adjacency matrix is ​​calculated respectively. 0th order to The spatial features of the temperature data are obtained by aggregating neighborhood features and performing linear mapping and weighted summation. The specific process expression is as follows: ; ； ； in, For the first Temperature data collected from all stations Spatial characteristics; The spatial characteristic order, For the largest order, Z represents the learnable coefficients, and Z is the linear transformation matrix. It is the size of The matrix, M represents the number of monitoring stations, and M represents the number of historical neighboring days for the temperature data on day k. For the first The temperature data collected that day Rank space aggregation features; Indicates the first Temperature data collected from all stations throughout the day, express An adjacency matrix of order 1.

5. The medium- to long-term temperature prediction method based on graph differential equation networks according to claim 1, characterized in that: Step 4, the gating timing module includes update gate calculation and candidate state fusion, and time features. The update formula is: ; ; ; ; in, To update the gate output, Let be the characteristic matrix, and ⊙ denote element-wise multiplication; It is a coefficient matrix; , , , , , The coefficient matrix to be determined , The bias matrix to be designed, for function, For activation functions; Z represents the input temperature matrix after linear transformation, where Z is the linear transformation. and is the coefficient matrix to be determined, and tanh is the hyperbolic tangent activation function.

6. The medium- to long-term temperature prediction method based on graph differential equation networks according to claim 1, characterized in that: Step 5, the graph-based differential equations, includes: characterizing the diffusion / smoothing effect of features on the graph using the graph Laplacian operator, and adjusting the diffusion intensity using learnable coefficients to obtain spatial features. With time characteristics The evolution equation.

7. A medium- to long-term temperature prediction method based on graph differential equation networks according to claim 1 or 6, characterized in that: The differential equation evolution model in step 5 includes: Spatial feature evolution equation: ； Where L is a scaled version of the normalized Laplacian matrix based on the adjacency matrix A. ; It is the normalized Laplace matrix. ; It is the normalized Laplace matrix The largest eigenvalue; It is composed of adjacency matrix Calculate the degree matrix; The coefficient matrix, , and These are coefficients to be determined. , It is the maximum order; yes function, This represents element-wise multiplication of two matrices; tanh is the hyperbolic tangent activation function. Evolutionary equation of time characteristics: ； in, Indicates time characteristics; , and The coefficients are to be determined.

8. The medium- to long-term temperature prediction method based on graph differential equation networks according to claim 7, characterized in that: In step 5, a numerical integration method with a fixed step size of β is used to obtain the spatial feature sequence of β steps by employing a neural network constant differential equation solver. With time feature sequence ,Right now: ； ； in, The time corresponding to the feature sequence to be calculated.

9. A medium- to long-term temperature prediction method based on graph differential equation networks according to claim 7, characterized in that: Step 6 involves spatial feature sequences. and time feature sequences After splicing and fusion, the mixture undergoes linear transformation and nonlinear activation before being input into a multilayer perceptron for prediction.

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