An air quality prediction method based on a deep Gaussian diffusion model

Abstract

The present invention relates to an air quality prediction method based on a deep Gaussian diffusion model. In order to facilitate the efficient learning of the geographical spatio-temporal coupling relationship of spatio-temporal data between different regions by the model, the method first designs a planar Gaussian diffusion equation to represent the asymmetric diffusion relationship of pollutants in a single region, and then parameterizes the planar Gaussian diffusion equation through a geospatial coupling learner to improve its generalization ability. Finally, the automatic learning of the geographical spatio-temporal coupling relationship is realized by combining the backpropagation technique with a recurrent neural network, and the air quality of multiple regions in the city is accurately predicted.

Description

Technical Field

[0001] The present invention relates to the fields of smart cities, pervasive computing, and data mining, and particularly to a method for spatio-temporal data modeling and prediction using a deep learning model. Background Art

[0002] In recent years, the continuous urbanization and industrialization have caused serious air pollution in urban areas and their surrounding regions, and have also had a greater impact on the daily travel and physical health of the public. Therefore, a reliable and accurate method is needed to predict the future air quality of cities. Nowadays, air quality monitoring stations have been widely deployed in different regions of major cities in China to monitor the air quality of the surrounding areas in real time, thus generating a large amount of spatio-temporal data. If these monitoring data can be fully utilized, analyzed, and the internal relationships of spatio-temporal data in different regions can be used for modeling and prediction, it will enable us to better understand the diffusion patterns and changing trends of air pollution in cities, and then provide assistance when the government and the public formulate response measures for air pollution, such as vehicle restrictions, reduction of outdoor work, and school closures.

[0003] Currently, the methods for air quality prediction are mainly divided into two categories: traditional methods simulate the diffusion process of pollutants in the surrounding environment through mathematical modeling to achieve the prediction task. However, such models rely heavily on domain knowledge and have insufficient generalization ability, and are only applicable to the prediction scenarios of single-point source pollutants for specific tasks. In recent years, more advanced deep learning methods have taken advantage of their superiority in learning complex non-linear relationships and achieved good results in spatio-temporal data prediction problems. However, in Figure 1 the scenario shown, the geospatial relationships between different monitoring points are asymmetric and interact with each other, and their relationships are related to their geographical locations. When the wind direction changes, the relative relationships will also change. The potential dependence relationships captured by existing deep learning methods are only topological spatial relationships, and there is no targeted design for the dependencies related to the geographical location information shown in Figure 1 , and the complex diffusion relationships of pollutants in multiple regions cannot be effectively modeled. Considering the impact of environmental air quality on various aspects such as society and public health, how to use the spatio-temporal dependence relationships between the data of multi-region monitoring stations in cities for modeling and prediction is of great significance for the government and the public to formulate response strategies for air pollution problems. Summary of the Invention

[0004] Technical Problems to be Solved

[0005] Aiming at the limitation that the existing air quality prediction methods cannot learn the geospatial coupling relationships in spatio-temporal data, the present invention proposes an air quality prediction method based on a deep Gaussian diffusion model.

[0006] Technical Solutions

[0007] The present invention first establishes a planar Gaussian diffusion equation to represent the asymmetric diffusion relationship from the target area to its surroundings, where the Brownian motion of pollutant molecules and the influence of wind on pollutant diffusion are decoupled into two perpendicular directions of the plane, thereby simplifying the difficulty of modeling. Subsequently, a geospatial coupling learner is designed to parameterize the planar Gaussian diffusion equation, so as to learn the geospatial coupling relationship of the mutual influence of multi-region diffusion. In addition, a recurrent neural network is used to capture the temporal coupling relationship of each region, and combined with the geospatial coupling learner through backpropagation technology to achieve joint training, enhancing the generalization ability of the model when capturing geospatial coupling.

[0008] An air quality prediction method based on a deep Gaussian diffusion model, characterized by the following steps:

[0009] Step 1: Description and formal definition of the multi-region air quality prediction problem;

[0010] Step 2: Planar Gaussian diffusion equation

[0011] First, based on the theoretical assumption that the diffusion of pollutants under windless conditions is molecular motion, a binary joint Gaussian diffusion equation is established in two perpendicular directions of the two-dimensional plane; subsequently, the influence of wind speed and wind direction is introduced to further improve the equation, and finally a single-region pollutant asymmetric diffusion equation is established;

[0012] Step 3: Geospatial coupling learning

[0013] The planar Gaussian diffusion equation is extended from single-region diffusion to a general paradigm of multi-region mutual diffusion, and the parameters in the equation are automatically learned through a neural network to capture the geospatial coupling relationship between different regions;

[0014] Step 4: Geospatiotemporal coupling learning

[0015] The intrinsic temporal coupling of each region's data is learned through a recurrent neural network, and the spatial coupling between different regions is learned by the geospatial coupling learner; the recurrent neural network and the geospatial coupling learner are combined through the backpropagation method of a deep neural network to realize the collaborative relationship modeling of geospatiotemporal coupling, and the final output of the model is used as the prediction result of the future air quality of multiple regions;

[0016] Step 5: Model training

[0017] A deep neural network is built on a cloud server, and the original air quality geospatiotemporal data of multiple regions are preprocessed and divided into training and test samples; the model is trained batch by batch, and a parameter search algorithm is designed to realize automatic model parameter tuning, and the model finally converges to complete the training process by reducing the model loss function.

[0018] A further technical solution of the present invention: In step 1, based on the research problem of multi-variable spatio-temporal data modeling and prediction, the prediction problem of air quality is specifically described and formally defined:

[0019] Geographical spatio-temporal data: Given N air monitoring stations distributed in different urban areas, the geographical spatial data G = {g1, g2, …, g N} represents the set of their true geographical locations, where g n = (x n , y n ), n ∈ {1, 2, …, N} records the coordinates of each station, and x n and y n represent its longitude and latitude respectively; each monitoring station records the hourly air quality observation values in the past h time periods to generate a time series That is where represents an element in the time series, indicating the observation value of the nth station at time t; the multi-variable time series corresponding to all regions forms the time series data of a two-dimensional tensor;

[0020] External features: including undirected features and directed features. The undirected features U 1:K = {U1, U2, … U k …, U K}, where K is the number of undirected features, k ∈ {1, 2, …, K} is the sequence of the kth time-varying feature corresponding to the time series data; the directed feature where v t and θ t are the wind speed and wind direction at time t respectively, and the wind direction is represented by the angle between the due north direction and the direction from which the wind blows;

[0021] Geographical spatio-temporal coupling: The set of all geographical spatial couplings corresponding to the area related to station n is

[0022] Problem definition: Based on the definitions of the above parameters and concepts, the definition of the current research problem is as follows:

[0023] For a given time t, the air quality prediction problem aims to learn a mapping function F ω (·), by learning the hidden relationship between the geographical spatio-temporal data of the past length h and the relevant external features, to predict the air quality of multiple urban areas within the future l time; ω represents all learnable parameters of the function, F ω(·) requires three inputs: the geospatial data G of N monitoring stations in the past time periods {t - h + 1, …, t - 1, t} and its historical time series data and the external features [U 1:K ; V] (t-h+1):(t+l) ; the model output is a two-dimensional tensor representing the predicted results of the air quality multivariate time series in the regions where the corresponding monitoring stations are located, for the expansion of one of them, the research problem is defined as follows:

[0024]

[0025] A further technical solution of the present invention: the diffusion equation under the condition of no wind described in step 2 is expressed as:

[0026]

[0027] where P(A|B) is the joint probability of the pollutant diffusing from point B to point A, σ x and σ y are the standard deviation parameters of each Gaussian equation, φ x and φ y respectively represent the relative distance from B to A in the X-Y plane.

[0028] A further technical solution of the present invention: the asymmetric diffusion equation of pollutants in a single region described in step 2 is expressed as:

[0029]

[0030] where, and are the projections in the X-Y direction at time t.

[0031] A further technical solution of the present invention: the geospatial coupling relationship between different regions described in step 3 is expressed as:

[0032]

[0033]

[0034] where f embedding (·) is a geographical location embedding function that converts the coordinates of each monitoring point into a hidden state representation; f unique (·) is a multi-layer perceptron that takes undirected features and geographical location information as inputs and automatically learns the features of each region according to meteorological conditions and relevant location information

[0035] Further technical solution of the present invention: The model described in step 4 is expressed as:

[0036]

[0037]

[0038]

[0039]

[0040] Among them, the first formula: f encoder (·) is a recurrent neural network that can capture the temporal coupling within the region based on the time series data of each monitoring site. It takes the original time series as the input and outputs a one-dimensional vector representing the hidden state The second formula: Multiply the diffusion probability calculated by the planar Gaussian diffusion model by the data hidden state representation of region m to obtain the geospatial coupling; Multiple geospatial coupling learners can calculate the geospatial coupling relationships between all regions in parallel; The third formula: The intra-regional temporal coupling of each region is fused with its associated inter-regional geospatial coupling, and the output is finally received by the decoder f decoder (·) based on the recurrent neural network to generate the next time prediction result in the fourth formula

[0041] A computer system, characterized in that it includes: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are caused to implement the above method.

[0042] A computer-readable storage medium, characterized in that it stores computer-executable instructions, and the instructions are used to implement the above method when executed.

[0043] Beneficial effects

[0044] An air quality prediction method based on a deep Gaussian diffusion model provided by the present invention represents the asymmetric diffusion relationship from the target region to its surroundings through the planar Gaussian diffusion equation and parameterizes it through a deep neural network model, enabling it to simultaneously learn the shared and unique characteristics of geospatial-temporal data, thereby enhancing the generality and effectiveness of the model, and finally achieving accurate and efficient air quality prediction.

[0045] The present invention proposes an air quality prediction method based on a deep Gaussian diffusion model. To facilitate the efficient learning of the geographical spatio-temporal coupling relationship of spatio-temporal data between different regions by the model, the method first designs a planar Gaussian diffusion equation to represent the asymmetric diffusion relationship of pollutants in a single region. Subsequently, a geospatial coupling learner is used to parameterize the planar Gaussian diffusion equation to enhance its generalization ability. Finally, the combination of backpropagation technology and a recurrent neural network is utilized to automatically learn the geographical spatio-temporal coupling relationship and accurately predict the air quality of multiple regions in the city.

[0046] Compared with existing air quality prediction methods, it can automatically model the complex geographical spatio-temporal coupling relationship by considering the influence of relative positions. At the same time, the invention can provide interpretability for the model through visualizing the coupling relationship, explore the coupling relationship between air quality changes in different regions, which is of great significance for the government and the public to formulate response strategies for air pollution problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The drawings are only for the purpose of illustrating specific embodiments and are not considered to be a limitation of the present invention. Throughout the drawings, the same reference signs denote the same components.

[0048] Figure 1 Schematic diagram of multi-region air quality geographical spatio-temporal data and its complex coupling relationship provided for the embodiments of the present invention.

[0049] Figure 2 Schematic diagram of the planar Gaussian diffusion equation under windless and windy conditions. Figure 3 Schematic diagram of the geospatial coupling learner inside the model.

[0050] Figure 3 Schematic diagram of the geospatial coupling learner inside the model.

[0051] Figure 4 Detailed design diagram of the air quality prediction model based on the learning of geographical spatio-temporal coupling relationship.

[0052] Figure 5 Visualization result of the geographical spatio-temporal coupling relationship learned by the model. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0053] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0054] Such as Figure 4As shown, the present invention designs an air quality prediction method based on a deep Gaussian diffusion model. The asymmetric diffusion relationship from the target area to its surroundings is represented by the planar Gaussian diffusion equation, and its parameters are parameterized by a deep neural network model, enabling it to simultaneously learn the shared and unique characteristics of geographical spatio-temporal data, thereby enhancing the generality and effectiveness of the model, and finally achieving accurate and efficient air quality prediction. To facilitate the model's efficient learning of the geographical spatio-temporal coupling relationship between different regions, the method first designs a planar Gaussian diffusion equation to represent the asymmetric diffusion relationship of pollutants in a single region, and then parameterizes the planar Gaussian diffusion equation through a geographical space coupling learner to improve its generalization ability. Finally, the automatic learning of the geographical spatio-temporal coupling relationship is realized by combining the backpropagation technique with a recurrent neural network, and the air quality of multiple regions in the city is accurately predicted. The main steps are as follows:

[0055] Step 1: Description and formal definition of the air quality prediction problem. The present invention takes the prediction of multi-variable spatio-temporal data as the basic research problem, and uses Figure 1 (a) The geographical spatio-temporal data collected from multiple different regions to establish Figure 1 (b) A complex geographical spatio-temporal coupling relationship model between regions, and gives a formal definition of the symbols and specific tasks in the air quality prediction problem:

[0056] ① Geographical spatio-temporal data. Given N air monitoring stations distributed in different urban regions, the geographical space data G = {g1, g2,..., g N} represents the set of their true geographical locations, where g n = (x n , y n ), n ∈ {1, 2,..., N} records the coordinates of each station, and x n and y n represent their longitude and latitude respectively. At the same time, each monitoring station records the hourly air quality observation values in the past h time periods to generate a time series That is where represents an element in the time series, indicating the observation value of the nth station at time t. Finally, the multi-variable time series corresponding to all regions forms a two-dimensional tensor of time series data.

[0057] ② External features. The diffusion of air pollutants is generally affected by two types of external factors: a) Undirected features. As the name implies, they are scalar features related to air quality such as temperature, humidity, and atmospheric pressure, which are defined as U 1:K = {U1, U2,..., U K}, where K is the number of undirected features. is the sequence of the k-th time-varying feature corresponding to the time series data. b) The directed feature, i.e., the impact of wind on pollutant diffusion, is a geometric vector including wind speed and wind direction, and its impact is usually related to the relative position of the monitoring site. It can be defined as where v t and θ t are the wind speed and wind direction at time t respectively, and the wind direction is represented by the angle between the due north direction and the direction from which the wind blows. Similar to the undirected feature, the time series corresponding to the directed feature can be expressed as:

[0058] ③ Geographical spatio-temporal coupling. Geographical spatio-temporal coupling generally refers to the data similarity, correlation, deep dependence relationship, etc. at the geographical space level and time level. In addition, many time-related inherent information in the time series data, such as historical trends, cycles, mutation factors, etc., play an important role in its future changes. To represent such information, we define as the time coupling of site n at time t. In addition, there is a geographical space coupling between the relevant area of the target site n and its surrounding area m, which can be expressed as: Therefore, the set of all geographical space couplings corresponding to the relevant area of site n is

[0059] Problem definition: Based on the above definitions of parameters and concepts, the definition of the current research problem is as follows:

[0060] For a given time t, the air quality prediction problem aims to learn a mapping function F ω (·), which predicts the air quality of multiple urban areas in the future l time by learning the hidden relationship between the geographical spatio-temporal data and relevant external features in the past length h. ω represents all the learnable parameters of the function, and F ω (·) requires three inputs: the geographical space data G of N monitoring sites in the past time period {t - h + 1, …, t - 1, t} and its historical time series data and the external features [U 1:K ; V] in the historical and future time periods (t-h+1):(t+l) . The model output is a two-dimensional tensor representing the prediction results of the air quality multivariate time series in the areas corresponding to the above-mentioned monitoring sites, is the expansion of one of them. Specifically, the research problem is defined as follows:

[0061]

[0062] Step 2: Planar Gaussian diffusion equation. Due to the diffusion of air pollutants, the air quality changes between different urban areas are coupled. Under windless conditions, the diffusion of pollutants is molecular Brownian motion, and its concentration is assumed to be normally distributed. Therefore, we established a planar Gaussian diffusion equation to simulate the asymmetric diffusion relationship of air quality between cities in a two-dimensional plane. To simplify the modeling difficulty, it is assumed that the distribution of pollutant concentration in two perpendicular directions of the plane is independent, that is, X is perpendicular to Y. X and Y correspond to the east-west and north-south directions in the real world respectively, so the diffusion in any direction can be decoupled into a combination of the above two directions. We first construct the planar Gaussian diffusion equation under windless conditions, that is, the pollutant diffusion is only affected by molecular motion. Figure 2 (a) is a schematic diagram of the diffusion of pollutants from a single area to its surrounding environment under windless conditions. Point B is the coordinate origin, representing the location of the area related to a specific monitoring site. Point A is the location representing the area around site B, and the X-Y axes are perpendicular to form a two-dimensional plane to describe the relative positions of the two points. Another time axis simulates the continuous diffusion of pollutants in the current area over time, where any cross-section represents the diffusion range of pollutants at the corresponding time. Specifically, the distribution in each direction is independent of each other and has its own unique diffusion coefficient. Therefore, the bivariate joint Gaussian distribution formula under windless conditions is expressed as:

[0063]

[0064] where P(A|B) is the probability density of the pollutant diffusing from point B to point A, φ x and φ y respectively represent the relative distances from B to A in the X-Y plane. Σ is a matrix describing the bivariate relationship between A and B. Since the distribution of pollutant concentration in the X-Y directions is independent of each other, the bivariate relationship matrix should be which contains two parameters σ x and σ y which are the standard deviation parameters of each Gaussian equation respectively. They are related to meteorological conditions and control the diffusion speed and shape of air pollutants, so they are defined as diffusion coefficients. Substituting them into the above formula for simplification, the diffusion equation under windless conditions can be expressed as:

[0065]

[0066] Furthermore, the presence of wind will change the shape, speed, direction, etc. of pollutant diffusion, so it also needs to be taken into account in the equation design. The schematic diagram of the influence of wind on the diffusion of pollutants in a single area is as shown in Figure 2 (b), where point B′ is the virtual center of the diffusing pollutants moved by the wind, where Represents its movement trajectory. In this way, affected by the wind, the diffusion probability from point B to point A can be regarded as the diffusion probability from point B' to point A under windless conditions, that is, P(A|B'). According to geometric vector conversion, we can get Therefore, the calculation of the relative position between B' and A can be converted into the above two steps, where Is opposite to the wind direction, that is Since Has been decomposed into φ x And φ y , so the characteristics of the wind Should also be decomposed into the same directions for separate calculations. Specifically And Are The projections in the X-Y direction at time t and can be calculated through trigonometric transformation: Therefore, the diffusion equation under windy conditions is updated to:

[0067]

[0068] Step 3: Geospatial coupling learner. The geospatial coupling learner enhances its generalization ability by parameterizing the planar Gaussian diffusion equation, enabling the model to model the dynamically evolving geospatial coupling while learning the shared and unique characteristics of air quality data in different regions. Figure 3 Is a schematic diagram of the internal details of the geospatial coupling learner. First, the calculation of the relative distance between two points in the diffusion equation is converted into two confusion matrices Φ x , Φ y To record the relative distances between all pairs of regions. The specific calculation method is:

[0069]

[0070] Where φ x,mn Represents an element in the matrix Φ x And is used to record the relative distance from the source region m to the target region n in the x direction. (x n , y n ), (x m , y m ) ∈ G are the coordinates of the site-related regions, and φ y,mn Similarly.

[0071] At the same time, the geospatial coupling learner sets time-varying parameters Through sharing and continuous learning in the deep neural network, the common characteristics of diffusion within the region can be captured, improving the generalization ability of the model. The parameters can be achieved through the following formula:

[0072]

[0073] where f shared (·) is a multi-layer perceptron with time-varying undirected features as input. Its deep neural network will learn the non-linear dependence between various meteorological conditions and diffusion coefficients through backpropagation.

[0074] On this basis, the geospatial coupling learner also adds a direction parameter to simulate the asymmetric geospatial coupling between multiple regions. It is a learnable parameter that varies within the range of [-1, 1], determining the state of the current region in the directed geospatial coupling structure. For example, the closer the value is to 1, the worse the air quality in the current region, indicating that pollutants are diffusing to the surroundings, and vice versa. The parameters of each region are learned independently:

[0075]

[0076] where f embedding (·) is a geographical location embedding function that converts the coordinates of each monitoring point into a hidden state representation. f unique (·) is a multi-layer perceptron that takes undirected features and geographical location information as input and automatically learns the features of each region according to meteorological conditions and relevant location information

[0077] Based on this, taking the pollutant diffusion process from region m to region n as an example, the parameterized planar Gaussian diffusion model can be expressed as:

[0078]

[0079] Step 4: Geospatiotemporal coupling learning. The geospatiotemporal coupling relationship of air quality in multiple regions is learned through an integrated deep neural network model, which is composed of multiple layers of spatiotemporal coupling blocks connected in series, generating prediction results step by step, as Figure 4 shown. Each module includes four main components: a time encoder / updater, a geospatial coupling learner, a coupling relationship integrator, and an output decoder. Taking the air quality prediction of region n as an example, the detailed mechanism of a module can be summarized as follows:

[0080]

[0081]

[0082]

[0083]

[0084] Specifically, f in Equation 9 encoder(·) is a recurrent neural network that can capture the temporal coupling within the region based on the time series data of each monitoring site. It takes the original time series as input and outputs a one-dimensional vector representing the hidden state Equation 10 multiplies the diffusion probability calculated by the planar Gaussian diffusion model (taking the region "m - n" as an example) with the data hidden state representation of region m to obtain the geospatial coupling. Multiple geospatial coupling learners calculate in parallel to obtain the geospatial coupling relationships among all regions. In Equation 11, the intra-regional time coupling of each region is fused with its associated inter-regional geospatial coupling, and the output is finally received by the decoder f based on the recurrent neural network decoder (·) to generate the next time prediction result in Equation 12

[0085] In the cyclic prediction stage, the output of the first-layer geospatiotemporal coupling block is transmitted to the updater of the next layer. The updater takes the hidden state representation of the previous step and the prediction result at the current moment as input:

[0086]

[0087] The model concatenates multiple geospatiotemporal coupling blocks to generate prediction results step by step to achieve multi-step prediction.

[0088] Step 5: Model training and prediction. The test data set based on the true results is represented as follows: T1' :N = [T1', T2', …, T' N T , where Since the model is smooth and continuously differentiable, it can be trained using backpropagation. Here, the mean squared error (MSE) is used as the loss function:

[0089]

[0090] where T1' :N , represent the true value and the predicted value respectively. Due to parallel training of multi-region data and parameter sharing, the loss function is the average of the MSE calculated for each region's time series. The entire data set is divided into non-overlapping training set, validation set, and test set in a ratio of 7:2:1 for model training, and finally the prediction results are output and the coupling relationships automatically learned by the model are visualized (as Figure 5 shown).

[0091] ​As described above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the present invention.

Claims

1. An air quality prediction method based on a deep Gaussian diffusion model, characterized in that The steps are as follows: Step 1: Description and formal definition of the multi-region air quality prediction problem; Step 2: Planar Gaussian diffusion equation First, based on the theoretical assumption that the diffusion of pollutants under windless conditions is molecular motion, a binary joint Gaussian diffusion equation is established in two perpendicular directions in the two-dimensional plane; Subsequently, the influence of wind speed and wind direction is introduced to further improve the equation, and finally, an asymmetric diffusion equation for pollutants in a single region is established; Step 3: Geospatial coupling learning The planar Gaussian diffusion equation is extended from single-region diffusion to a general paradigm of multi-region mutual diffusion, and the parameters in the equation are automatically learned through a neural network to capture the geospatial coupling relationship between different regions; Step 4: Geospatiotemporal coupling learning The internal time coupling of the data in each region is learned through a recurrent neural network, and the spatial coupling of the data between different regions is learned by a geospatial coupling learner; the recurrent neural network and the geospatial coupling learner are combined through the backpropagation method of a deep neural network to realize the collaborative relationship modeling of geospatiotemporal coupling, and the final output of the model is used as the prediction result of the future air quality in multiple regions; Step 5: Model training A deep neural network is built on a cloud server, and the original air quality geospatiotemporal data of multiple regions are preprocessed and divided into training and test samples; the model is trained batch by batch, and a parameter search algorithm is designed to realize automatic model parameter tuning, and the model finally converges to complete the training process by reducing the model loss function.

2. The air quality prediction method based on the deep Gaussian diffusion model according to claim 1, wherein: Step 1 takes the multi-variable spatio-temporal data modeling prediction as the basic research problem, and specifically describes and formally defines the air quality prediction problem: Geospatial and Temporal Data: Given N air quality monitoring stations distributed in different urban areas, the geospatial data G = {g1, g2, …, g N} represents the set of their true geographical locations, where g n = (x n , y n ), n ∈ {1, 2, …, N} records the coordinates of each station, and x n and y n represent its longitude and latitude respectively; each monitoring station records the hourly air quality observations for the past h hours, generating a time series namely where represents an element in the time series, indicating the observation value of the nth station at time t; the multivariate time series corresponding to all regions forms the time series data of a two-dimensional tensor. External features: including undirected features and directed features, the undirected feature U 1:K ={U1,U2,…U k …,U K}, where K is the number of undirected features, k∈{1,2,…,K} is the sequence of the k-th time-varying feature corresponding to the time series data; the directed feature where v t and θ t are the wind speed and wind direction at time t respectively, and the wind direction is represented by the angle between the due north direction and the direction from which the wind blows; Geographical spatio-temporal coupling: The set of all geographical spatial couplings corresponding to the relevant area of site n is Problem definition: Based on the above definitions of parameters and concepts, the definition of the current research problem is as follows: For a given time t, the air quality prediction problem aims to learn a mapping function F ω (·) that predicts the air quality of multiple urban areas in the next l time steps by learning the hidden relationships between the spatio-temporal data and relevant external features of the past length h; ω represents all learnable parameters of the function, and F ω (·) requires three inputs: the geospatial data G of N monitoring stations in the past time period {t - h + 1, …, t - 1, t} and its historical time series data as well as the external features in the historical and future time periods [U 1:K ; V] (t-h+1):(t+l) ; the model output is a two-dimensional tensor representing the prediction results of the multi-variable time series of the air quality in the regions corresponding to the above monitoring stations, where is the expansion of one of them, and the research problem is defined as follows:

3. The air quality prediction method based on the deep Gaussian diffusion model according to claim 2, characterized in that: The diffusion equation under windless conditions described in Step 2 is expressed as: Among them, P(A|B) is the joint probability of pollutant diffusion from point B to point A, σ x and σ y are the standard deviation parameters of each Gaussian equation, φ x and φ y respectively represent the relative distance from B to A in the X-Y plane.

4. The air quality prediction method based on the deep Gaussian diffusion model according to claim 3, characterized in that: The asymmetric diffusion equation for pollutants in a single region described in Step 2 is expressed as: Among them, and are the projections in the X-Y direction at time t.

5. The air quality prediction method based on the deep Gaussian diffusion model according to claim 4, wherein: The geospatial coupling relationship between different regions described in Step 3 is expressed as: Among them, f embedding (·) is a geographical location embedding function that converts the coordinates of each monitoring point into a hidden state representation; f unique (·) is a multi-layer perceptron that takes undirected features and geographical location information as inputs and automatically learns the features of each region according to meteorological conditions and relevant location information 6. The air quality prediction method based on the deep Gaussian diffusion model according to claim 5, wherein: The model described in Step 4 is expressed as: Among them, the first formula: f encoder (·) is a recurrent neural network that can capture the temporal coupling within the region based on the time series data of each monitoring site; it takes the original time series as input and outputs a one-dimensional vector representing the hidden state The second formula: Multiply the diffusion probability calculated by the planar Gaussian diffusion model by the data hidden state representation of region m to obtain the geospatial coupling; multiple geospatial coupling learners can calculate the geospatial coupling relationships between all regions in parallel; The third formula: The intra-regional temporal coupling of each region is fused with its related inter-regional geospatial coupling, and the output is finally received by the decoder f decoder (·), generating the next time prediction result in the fourth formula 7. A computer system, characterized in that Including: One or more processors, a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method according to claim 1.

8. A computer-readable storage medium, characterized in that Stored with computer-executable instructions, the instructions are used to implement the method according to claim 1 when executed.

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