Training method and device and spatio-temporal data prediction method and device

Abstract

The invention discloses a training method and device and a spatio-temporal data prediction method and device, and relates to the technical field of data prediction.The method comprises the steps that an obtained sample is input into a spatio-temporal prediction network for training to obtain a prediction model, and the spatio-temporal prediction network comprises a mapping function, an inverse mapping function and a cross-scale Koopman operator; the spatio-temporal prediction network and the prediction model are used for executing spatio-temporal data prediction according to the input data; the spatio-temporal data prediction comprises the following steps: mapping input data into a first representation space through a mapping function, and at least obtaining a characteristic variable of a current time step; predicting the characteristic variable of the current time step through a cross-scale Koopman operator to obtain a predicted characteristic variable of the next time step; mapping the prediction characteristic variable of the next time step into an observation space through an inverse mapping function to obtain a prediction result; the prediction result comprises the predicted space-time observation data of the next time step. The method can improve the prediction accuracy of the future state of the space-time system.

Description

Technical Field

[0001] The present application relates to the field of data prediction technology, and in particular to a training method and device, and a spatiotemporal data prediction method and device. Background Art

[0002] Real-world spatiotemporal systems, such as transportation networks, atmospheric systems, and epidemiology, are intuitive reflections of the real world, implying the basic laws of natural behavior, and the states of spatiotemporal systems change continuously over time and space.

[0003] Most current studies use a single perspective to analyze space-time systems and predict their future states. However, if they are limited to a specific observation dimension, the prediction of the future state of the space-time system may be inaccurate. Summary of the Invention

[0004] The purpose of this application is to provide a training method and device, and a spatiotemporal data prediction method and device, which can improve the accuracy of prediction of the future state of a spatiotemporal system.

[0005] To achieve the above objectives, this application provides the following solutions: In a first aspect, the present application provides a training method, the method comprising: Acquire samples; each sample includes a sequence of spatiotemporal observation data in an observation space; input the samples into a spatiotemporal prediction network for training to obtain a prediction model, wherein the spatiotemporal prediction network includes a mapping function, an inverse mapping function and a cross-scale Koopman operator; the spatiotemporal prediction network and the prediction model are used to perform spatiotemporal data prediction based on the input data; the spatiotemporal data prediction includes: mapping the input data into a first representation space through a mapping function to obtain at least the feature variables of the current time step; predicting the feature variables of the current time step through the global shared operator, community-specific operator and node-specific operator in the cross-scale Koopman operator respectively to obtain the global prediction feature variables, community prediction feature variables and node prediction feature variables of the next time step, and fusing them to obtain the predicted feature variables of the next time step; mapping the predicted feature variables of the next time step into the observation space through an inverse mapping function to obtain a prediction result; the prediction result includes the predicted spatiotemporal observation data of the next time step.

[0006] In a second aspect, the present application provides a method for spatiotemporal data prediction, the method comprising: Obtain target spatiotemporal observation data; input the target spatiotemporal observation data into a prediction model trained by the training method as described in any one of the first aspects to obtain predicted spatiotemporal observation data within the target time span.

[0007] According to the specific embodiments provided in this application, this application discloses the following technical effects: In this paper, the global shared operator, community-specific operator, and node-specific operator in the cross-scale Koopman operator are used to predict the feature variables of the current time step, obtaining predicted feature variables at different levels, which are then fused. This multi-dimensional feature extraction and fusion approach comprehensively considers the characteristics of the spatiotemporal system at different scales and levels, capturing more comprehensive information and thus more accurately describing the state of the spatiotemporal system. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 Schematic diagram of the observation sequence of the same space-time system at different perspectives in one embodiment of the present application; Figure 2 is a flow chart of a training method according to an exemplary embodiment; Figure 3 2 is an architecture diagram of a spatiotemporal prediction network in one embodiment of the present application; Figure 4 This is a schematic diagram of mapping by a mapping function in one embodiment of the present application; Figure 5 This is a schematic diagram of using a cross-scale Koopman operator for prediction and fusion in one embodiment of the present application; Figure 6 This is a schematic diagram illustrating mapping through an inverse mapping function according to an embodiment of the present application; Figure 7 This is a schematic diagram of a linear decomposition of a Koopman operator according to an embodiment of the present application; Figure 8 The distribution of eigenvalues in Koopman operators and corresponding causal graphs at different scales is shown in an embodiment of the present application; Figure 9 This is a schematic diagram illustrating the reconstruction of an observation data sequence based on an invariant causal pattern according to an embodiment of the present application; Figure 10 A schematic diagram of the third training phase according to an embodiment of the present application; Figure 11 A schematic diagram of the functional modules of a training device provided in one embodiment of the present application; Figure 12 is a flow chart of a spatiotemporal data prediction method according to an exemplary embodiment; Figure 13 A schematic diagram of the functional modules of a null data prediction device provided in one embodiment of the present application; Figure 14 A schematic diagram of comparison results provided in an embodiment of the present application. DETAILED DESCRIPTION

[0009] The technical solutions in the embodiments of the present application will be described below in conjunction with the drawings in the embodiments of the present application.

[0010] Real-world spatiotemporal systems, such as transportation networks, atmospheric systems, and epidemiological systems, are intuitive reflections of the real world and imply fundamental laws of natural behavior. Exploring the inherent causal relationships and dynamical characteristics of spatiotemporal systems is crucial for predicting future states and achieving reliable control. Spatiotemporal representation learning, at the core of understanding spatiotemporal systems, aims to map observable and redundant spatiotemporal data into a low-rank and robust latent representation space. Specifically, it maps data from the observation space into a representation space and vectorizes the data within this representation space, potentially involving the construction of causal relationships. When predicting spatiotemporal data using predictive models, spatiotemporal representation learning is a core technical approach for constructing a stable representation space and is closely interdependent with the predictive model. Constructing a stable representation space not only overcomes the curse of dimensionality but also enhances model generalization, addresses data sparsity challenges, and significantly improves prediction accuracy. This technology has been extensively studied in various tasks, including spatiotemporal series prediction of urban traffic flow and road speeds and anomaly detection.

[0011] A spatiotemporal system can be represented as a spatiotemporal network. In this network, a node represents a region, and its attributes are represented by a sequence of observable spatiotemporal observational data about the region over time. The connections between nodes represent interactions between regions. Due to the limitations of the macroscopic level, real-world spatiotemporal observational data sequences (e.g., traffic flow and road speed) typically lack explicit causal relationships. Instead, they are generated by underlying causal latent variables or causally related confounding factors. Changes in the data distribution arise from changes in the underlying causal latent variables, resulting in the observations relying on nonlinear mixing of these causal latent variables. Causal latent variables describe unobservable but potentially influential travel behaviors of the population in a region, such as specific attributes of the region, economic conditions, education levels, and the ratio of employment to residence.

[0012] In the context of spatiotemporal representation learning, correctly modeling and inferring causal latent variables and causal relationships can produce a more robust representation space, especially with better generalization to out-of-distribution samples, demonstrating that the model overcomes selection bias and statistical shortcuts caused by correlation. However, the approach of tracking causal latent variables alone is insufficient to explain complex urban phenomena. Further exploration of the dynamic interactions between causal latent variables is needed to form nonlinear spatiotemporal dynamics between variables, which describes the causal structure that changes over time.

[0013] At the same time, due to the characteristics of non-stationary, nonlinear, and cross-scale emergence of the causal structure of the spatiotemporal dynamic system, the causal structure between causal latent variables is difficult to be fully described. Compared with single time series data, the spatial dimension in spatiotemporal data has emergence, that is, self-organization at the micro level may show stronger causal relationships at the macro level. At the same time, the observation phenomena of the spatiotemporal system at different spatial scales will also have great differences, that is, the observation sequences in the spatiotemporal system will have great differences at the micro, meso and macro levels, such as Figure 1 As shown, taking the micro as the node perspective, the meso as the community perspective, and the macro as the global perspective as an example, Figure 1 It can be seen that for the same spatiotemporal system on the left, the observation sequences from the global perspective, community perspective, and node perspective show great differences. This will make it difficult for the traditional method of capturing the distribution changes of different spatial scales from the same perspective to explore the causal emergence of different spatial scales, which may lead to inaccurate predictions of the future state of the spatiotemporal system.

[0014] To address the above technical issues, the present disclosure provides a training method, training device, spatiotemporal data prediction method, and spatiotemporal data prediction device. These training methods and training devices are used to train a prediction model. The functions of the spatiotemporal data prediction method and the spatiotemporal data prediction device are implemented based on the prediction model.

[0015] Figure 2 is a flow chart of a training method according to an exemplary embodiment. Figure 2 As shown, the method includes the following steps S101-S102: In step S101 , samples are obtained; each sample includes a spatiotemporal observation data sequence in an observation space.

[0016] The content of a sample may vary across different application areas. For example, in applications such as predicting urban traffic flow data (e.g., average road speed) and detecting anomalies in urban traffic flow data, a sample may include a sequence of spatiotemporal observational data of an urban spatiotemporal system (e.g., one sample corresponds to one time step, and each sample includes the average road speed at each sampling moment for different roads within the same time step).

[0017] For example, spatiotemporal data of areas in a city where data prediction is required can be collected, and the spatiotemporal data can be quantified to obtain time-divided data sets for each area, that is, to obtain spatiotemporal observation data sequences in the observation space.

[0018] In step S102, the samples are input into the spatiotemporal prediction network for training to obtain a prediction model.

[0019] Among them, such as Figure 3As shown, the spatiotemporal prediction network architecture includes a spatiotemporal synchronization network and a dynamics layer. The spatiotemporal synchronization network includes an encoder and a decoder. The encoder fits the mapping function, the dynamics layer fits the cross-scale Koopman operator, and the decoder fits the inverse mapping function. The following is a detailed introduction. Figure 3 Each data stream in .

[0020] The spatiotemporal prediction network and prediction model are used to perform spatiotemporal data prediction based on input data. The spatiotemporal prediction network performs spatiotemporal data prediction based on input data during the training phase, while the prediction model performs spatiotemporal data prediction based on input data during the inference phase. This is an application of the trained spatiotemporal prediction network.

[0021] In one example, performing spatiotemporal data prediction includes the following sub-steps A1-A3: A1. Map the input data into the first representation space through a mapping function to obtain at least the feature variables of the current time step.

[0022] It should be noted that when the spatiotemporal prediction network performs spatiotemporal data prediction based on input data, the input data is the samples in S101; when the prediction model performs spatiotemporal data prediction based on input data, the input data is the spatiotemporal observation data sequence in the observation space to be predicted.

[0023] Consider a controlled input The affected space-time system , Indicates the time span; Indicates the time span is The control input or control variable, Represents any time step t The control input or control variable; N Indicates the number of spatial nodes, T +1 indicates the total length of time, m Indicates the control information dimension.

[0024] Taking the application field of predicting urban traffic flow data (such as average road speed) as an example, It can include variables such as the attributes of each region (spatial node), weather conditions, and regional gathering activities. The spatiotemporal observation data sequence in the affected spatiotemporal system is , ; Represents the observation sequence dimension.

[0025] Continuing with the previous example, assuming that the sampling period of traffic flow data for the above urban spatiotemporal system is 1 minute and 5 minutes is a time step, the traffic flow data with a total time length of 1 hour can be divided into 12 time steps, namely T =11, Contains 12 time steps of spatiotemporal observation data, which can be used express Any time step t The spatiotemporal observation data of Including a time step t The average road speed in different areas at each sampling time.

[0026] The following introduces the mapping function, inverse mapping function, and Koopman operator , the relationship between the first representation space, etc.: Establishing the Koopman operator The key is to discover the observation space and representational space The mapping function of the reversible mapping relationship between and the inverse mapping function ,in, Represents the dimension of the representation space.

[0027] The representation space is the subspace spanned by the mapping function , if for any mapping function All satisfied , that is, in the Koopman operator Under the action of , the representation space is complete, then it is called the representation space is the Koopman invariant subspace. At this time, the mapping function The nonlinear dynamics of a space-time system can be encapsulated into a linear Koopman operator In the observation space Mapping to representation space and satisfy the following dynamic evolution equation: ; in, Representation Space A characterization element in , also called a characteristic variable at any time step t, is a D dimensional vector, Indicates t At time t, the characteristic variable of node 1, t means [0: T ], Indicates t At this moment, the characteristic variable of node N is Indicates the next time stept +1 predictive feature variable, Indicates t +1 moment, the predicted feature variable of node 1, Indicates t +1 time, the predicted feature variable of node N. The first representation space in the present disclosure can also be referred to as a representation space.

[0028] Therefore, the first representation space in this application is the Koopman invariant subspace.

[0029] The present disclosure uses any spatiotemporal synchronous network to obtain the mapping function and the inverse mapping function Any neural network that can simultaneously extract spatial and temporal features from a spatiotemporal system can be used as a spatiotemporal synchronization network, without any specific requirements. Therefore, the present disclosure is highly flexible, allowing users to design appropriate spatiotemporal synchronization networks based on specific tasks. For example, a conventional GraphGRU can be used as a spatiotemporal synchronization network.

[0030] like Figure 4 As shown, the spatiotemporal observation data sequence of the current time step is Through the mapping function Mapped into the first representation space, the characteristic variables of the current time step are obtained , here, for , , , that is, ,for , .

[0031] A2. Predict the feature variables of the current time step using the global shared operator, community-specific operator, and node-specific operator in the cross-scale Koopman operator to obtain the global prediction feature variables, community prediction feature variables, and node prediction feature variables for the next time step, and fuse them to obtain the prediction feature variables for the next time step.

[0032] like Figure 1 As shown in Figure 1, causal emergence leads to different observation sequences at different spatial scales, and the evolutionary laws within these phenomena also follow different dynamics. Koopman theory, one of the main methods for analyzing complex dynamics, can model arbitrary nonlinear dynamics in representational space using the linear Koopman operator. Similar to spatiotemporal causal structures, the core of the Koopman operator also encapsulates the dynamics of the input sequence into a linear matrix and uses this matrix to encode the temporal transition process between latent variables. Therefore, methods based on the Koopman operator are suitable for learning nonlinear spatiotemporal dynamics.

[0033] In order to adapt to the nonlinearity and emergence of spatiotemporal systems, this paper proposes a cross-scale Koopman operator to encapsulate the dynamics at different scales into their respective linear matrices, thereby limiting the representation space to a Koopman invariant subspace.

[0034] For the non-stationary and emergent properties of spatiotemporal systems, this paper uses the Koopman operator It is divided into three scales, and Koopman operators are established from the macro, meso and micro scales. Among them, the global shared operator represents the Koopman operator at the macro scale, the community-specific operator represents the Koopman operator at the meso scale, and the node-specific operator represents the Koopman operator at the micro scale. The global shared operator can also be called the global shared Koopman operator, the community-specific operator can also be called the community-specific Koopman operator, and the node-specific operator can also be called the node-specific Koopman operator. The following is a detailed introduction to each Koopman operator: 1. Globally shared Koopman operator: Globally shared Koopman operator is a The learnable matrix is shared in both time and space dimensions and is used to characterize the trend and behavior of global dynamics. The update equation is as follows: ; in, Represents the use of globally shared Koopman operator Calculate the global prediction feature variables for the next time step t+1.

[0035] 2. Community-specific Koopman operator: The emergence of spatiotemporal systems is mainly manifested in the fact that spatial nodes have community characteristics, that is, nodes in the same community have similar dynamics. Since the prior knowledge of the nodes is unknown, this paper uses the concept of prototype learning to construct community models.

[0036] Initialization of this disclosure Learnable prototype embedding vectors , as a latent factor representing the community pattern, C It is a hyperparameter, which is given manually based on experience or statistical methods. It can be set differently according to different application scenarios. The original embedding vector is randomly initialized and updated during the training process. After training, it becomes the model parameter. The total dimension is , each D The vector represents the community c ( CThe implicit regularities within any of the communities are directly used during inference and are not updated. This indicates that the prototype embedding vectors and regularities in the dataset were learned during training.

[0037] Based on the prototype embedding vector, when predicting the feature variables of the current time step using the community-specific Koopman operator to obtain the community predicted feature variables for the next time step, the following operations can be performed: Operation 1: Calculate the similarity between the node embedding vector and the prototype embedding vector, and divide the nodes into communities based on the similarity.

[0038] First, use any multi-layer perceptron MLP to compress the feature variables The time dimension is obtained as shown in formula (1) , the node embedding matrix The node embedding vectors of N nodes are: ; (1) Then, the similarity between the node embedding vector and the prototype embedding vector is calculated, and the Gumbel-Softmax technique is used to obtain the indicator variable to classify the nodes into the corresponding community class. The formula can be expressed as follows:

[0039] in, ;make c ∈[1, C ], express Any vector in , Is an indicator variable, refers to the similarity, indicating which node belongs to communities; represents the node embedding matrix; Represents the prototype embedding vector The transpose of Represents the temperature coefficient, which is used to control the smoothness of the softmax function output. Represents the inner product of the matrix. The value after the inner product represents the similarity, specifically the node embedding matrix Each node embedding vector in C Prototype embedding vector Multiply each of the transposes of ; Indicates from Randomly sampled noise in .

[0040] Operation 2: Calculate the community prediction feature variables of each community at the next time step based on the community-specific Koopman operator.

[0041] This disclosure defines the community-specific Koopman operator is a The learnable matrix is shared across time dimensions and independent between different communities. The update formula is as follows: ;

[0042] in, Indicates the use of the community-specific Koopman operator The community prediction feature variables of the next time step are calculated, which include the community prediction feature variables of the next time step corresponding to each community; N Each node may belong to different communities, so Indicates belonging to the community c The community prediction feature variables for the next time step corresponding to all nodes, indicator variables Will belong to the community c Filter out the nodes Indicates the The Koopman operator is unique to each group. Represents the Hadamard product.

[0043] In order to ensure the effectiveness of prototype learning, this paper designs a prototype embedding orthogonal loss function, which is defined as follows: ; Where, represents the identity matrix, express C Prototype embedding vector Combined The matrix is multiplied by the transpose of this matrix, and the loss function is used for training C Prototype embedding vector , so that the cluster centers have sufficient recognition.

[0044] It should be noted that the initialization C prototype embedding vectors, which are orthogonal to each other. The similarity between orthogonal vectors is 0, and the inner product between two orthogonal vectors is 0. Ideally, if the learned C The prototype embedding vectors are orthogonal to each other, then The resulting matrix is a diagonal matrix (elements on the main diagonal are not 0, and the other elements are 0).

[0045] If the inner product of any prototype embedding vector and its transposed vector is equal to 1, then the learned C When the prototype embedding vectors are pairwise orthogonal, The resulting matrix is the identity matrix.

[0046] Therefore, the above prototype embedding orthogonal loss function is intended to make the learned C The prototype embedding vectors are as orthogonal as possible.

[0047] In one example, a condition may be set for learning the prototype embedding vector, which stipulates that the inner product of any learned prototype embedding vector and its transposed vector is equal to 1.

[0048] 3. Node-specific Koopman operator: In order to capture the local dynamics of each node and adapt to local distribution changes, this disclosure proposes a node-specific Koopman operator to capture the node-specific dynamics. Indicates the The node-specific Koopman operator of nodes, then is calculated as follows: ; in, It means the first The node embedding vector of the nodes, and represents the learnable parameters, is the number of nodes.

[0049] The aforementioned "predicting the characteristic variables of the current time step through the node-specific operator to obtain the node predicted characteristic variables of the next time step" can be obtained using the following formula:

[0050] in, Indicates the The node has its own Koopman operator The calculated t +1 node prediction feature variable at time (time step); express The transpose of . It represents the node prediction feature variable of the next time step, which contains the node prediction feature variable of the next time step of each node.

[0051] Here's how to integrate: like Figure 5 As shown, in Figure 4 Lieutenant General Through the mapping function Mapped into the first representation space, the characteristic variables of the current time step are obtained Afterwards, Obtain global prediction feature variables through the globally shared Koopman operator ,right The community prediction feature variables are obtained through the community-specific Koopman operator ,right Obtain node prediction feature variables through the node-specific Koopman operator For different nodes, the Koopman operators of different scales have different capabilities. This paper uses learnable scalar weights. , fuse the calculation results under the action of the cross-scale Koopman operator to obtain the predicted characteristic variables for the next time step t+1 : , at this time .

[0052] A3. Mapping the predicted feature variables of the next time step to the observation space through an inverse mapping function to obtain a prediction result; the prediction result includes the predicted spatiotemporal observation data of the next time step.

[0053] like Figure 6 As shown, the predicted feature variables for the next time step are obtained After that, each Mapping to the above observation space to obtain the prediction results .

[0054] In this disclosure, since the Koopman operator used to predict spatiotemporal observation data is refined into a global shared operator, a community-specific operator, and a node-specific operator, when predicting spatiotemporal observation data, predictions will be made from three different scales, making the predicted spatiotemporal data more accurate.

[0055] The following is an introduction to how to train.

[0056] In one embodiment, a three-stage training is used to obtain a prediction model. The following details the training process of each stage: First training phase: The spatiotemporal prediction network performs the above spatiotemporal data prediction to obtain the prediction result; Please refer to the above record for how to perform spatiotemporal data prediction, which will not be described in detail here.

[0057] Perform the first loss calculation: use the first loss function to obtain the first loss based on the prediction results and samples obtained in the current training phase; Update the spatiotemporal prediction network according to the first loss mentioned above.

[0058] In one embodiment, the first loss function at least includes a spatial loss function , reconstruction loss function And the prediction loss function .

[0059] In one example, the first loss function includes a spatial loss function, a reconstruction loss function, a prediction loss function, and a prototype embedding orthogonal loss function, i.e. . Represents the first loss function.

[0060] The above method uses the first loss function to obtain the first loss based on the prediction results and samples obtained in the current training phase, including the following sub-steps B1-B3: B1. Calculate the spatial loss using the spatial loss function according to the first predicted feature variable and the first actual feature variable.

[0061] In one example, in order to make the Koopman operator With the ability to characterize nonlinear dynamics, the present disclosure designs a spatial loss function to constrain the first representation space into a Koopman invariant subspace. The spatial loss function is defined as follows: ; in, represents the mean square error, Represents the time step t The actual characteristic variable of +1 (which can be called the first actual characteristic variable) is obtained by sampling from the posterior distribution; represents the first predictive feature variable, Represents the time step t The actual characteristic variable of (which can be called the second actual characteristic variable) is also sampled from the posterior distribution.

[0062] The following describes how to determine the first or second actual feature variable from the posterior distribution.

[0063] In the first training phase, when determining the first or second actual feature variable, in order to increase randomness, the first representation space is fitted The posterior distribution of The specific definitions are as follows:

[0064] Specifically, in this disclosure, a learnable Gaussian distribution is used to fit the posterior distribution. is a Gaussian distribution with mean and variance These two learnable parameters; The calculated result is the mean and variance of the Gaussian distribution, so the posterior distribution is equal to this mapping function, that is, , by the posterior distribution Sampling can get and .

[0065] B2. The reconstruction loss is calculated by the reconstruction loss function according to the spatiotemporal observation data sequence in the sample and the above-mentioned second actual characteristic variable.

[0066] In order to ensure the reversibility of the mapping function and the inverse mapping function, the present disclosure designs a reconstruction loss function : ; in, represents the reconstruction loss function, Indicates that the time step in the sample is t The spatiotemporal observation data sequence of Represents the time step t The actual characteristic variable of (which can be called the second actual characteristic variable), By mapping function The fitted posterior distribution is sampled, Represents the cross-scale Koopman operator in the current training stage; Represents the inverse mapping function in the current training stage.

[0067] B3. The prediction loss function is used to calculate the prediction loss based on the spatiotemporal observation data sequence in the sample and the above-mentioned second actual characteristic variable; the above-mentioned first loss includes spatial loss, reconstruction loss and prediction loss.

[0068] To ensure that the cross-scale Koopman operator It can fit the dynamics of the spatiotemporal system, and the present disclosure designs a prediction loss function : ; in, represents the prediction loss function, Indicates that the time step in the sample is t+ 1's spatiotemporal observation data sequence; Represents the time step t The actual characteristic variable of (which may be called the second actual characteristic variable); Represents the cross-scale Koopman operator in the current training stage (the cross-scale Koopman operator updated in the previous training stage or the previous iteration).

[0069] After obtaining the first loss, the mapping function in the spatiotemporal prediction network can be updated according to the first loss , cross-scale Koopman operator and the inverse mapping function .

[0070] After the first training phase, the mapping function, cross-scale Koopman operator and inverse mapping function obtained through training can be called the first mapping function , the first cross-scale Koopman operator and the first inverse mapping function .

[0071] The second training phase includes C1-C3: C1. The target spatiotemporal prediction network performs the above spatiotemporal data prediction to obtain the prediction result; the target spatiotemporal prediction network is the spatiotemporal prediction network updated in the previous training stage.

[0072] C2. Perform the second loss calculation to obtain the second loss. C2 includes C21-C23: C21. Execute the above first loss calculation to obtain the first loss of the current training stage.

[0073] How to perform the first loss calculation can be found in the above description and will not be elaborated here.

[0074] In step C21, 、 and Replace B1-B3 respectively 、 and , recalculate the first loss and get the first loss of the second training stage.

[0075] C22. Use the prediction results of the current training stage to perform spectral decomposition on the cross-scale Koopman operator in the above target spatiotemporal prediction network to obtain multiple eigenvalues and corresponding eigenvectors.

[0076] C23. Calculate a spectral loss based on the multiple eigenvalues; the second loss includes the first loss and the spectral loss in the current training stage.

[0077] The spectral loss may be obtained according to a unit matrix, a diagonal matrix composed of the plurality of eigenvalues, and a complex conjugate matrix of the diagonal matrix.

[0078] C3. Update the target spatiotemporal prediction network based on the second loss.

[0079] Because the Koopman operator is a linear operator, its eigenvalues can be analyzed using spectral decomposition techniques to understand the dynamical evolution process. Spectral decomposition can then be used to identify stable and unstable states. Spectral decomposition is a fundamental concept in matrix theory, enabling the eigendecomposition of matrices.

[0080] The following describes the principles of finding stable and unstable states: By the first cross-scale Koopman operator Decomposed eigenvalue and eigenvectors The following relationship is satisfied:

[0081] Among them, the first representation space i The node in feature variables at each time step , can be calculated from the above eigenvectors and eigenvalues.

[0082] For each feature variable The spectrum can be decomposed to obtain i The transpose of the initial feature variables of the nodes Hedi i The node in The transpose of the characteristic variables of time steps The relationship between:

[0083]

[0084] in, represents the first cross-scale Koopman operator Power, It is i The initial characteristic variables of the nodes In the eigenvector The projection onto , also called the magnitude, pass and The inner product of the above formula is obtained. T Indicates transpose.

[0085] like Figure 7 As shown in Figure 1, based on the Koopman pattern decomposition technique, the Koopman operator is linearly decomposed into eigenvectors and eigenvalues. The eigenvectors are the basis of the representation space, containing basic information about the underlying dynamics and describing the temporal transition patterns between latent variables. The eigenvalues, on the other hand, capture the evolution of the corresponding dynamical pattern.

[0086] It is worth noting that Figure 7 The first cross-scale Koopman operator in is the globally shared Koopman operator obtained after the first training phase , community-specific Koopman operator and node-specific Koopman operator A linear combination of .

[0087] In order to more clearly understand the oscillation and frequency of the dynamic evolution process, the eigenvalues can be converted to continuous time: ( is a microelement, representing a very small numerical difference, the difference between two consecutive time points), where and (θ represents the argument, which represents the angle formed by rotating counterclockwise from the positive x-axis to the vector corresponding to the eigenvalue in the complex plane.) Since the eigenvalue belongs to the complex space , so the real part of the time-continuous eigenvalue represents the evolution growth rate of the corresponding dynamic mode, and the imaginary part represents the evolution frequency of the corresponding dynamic mode. It can be regarded as a dynamic evolution process, representing the contribution rate of the corresponding dynamic mode to the space-time system. considered as a kinetic mode. or Can be used to determine the Whether the mode is decaying, static or diverging. The real part of the continuous-time eigenvalue represents the growth rate of the corresponding mode, while the imaginary part represents the mode frequency. The relative size of the eigenvalue basically determines the contribution of the corresponding dynamic mode to the system.

[0088] in: or It means that the contribution of the corresponding dynamical pattern to the system does not change over time, so the dynamical pattern captures stable information, which is defined in this disclosure as an invariant causal pattern, such as Figure 7 As shown, the sequence recovered based on the invariant causal pattern ( Figure 7 The waveform referred to by the invariant causal pattern in the data can accurately reflect the stable trend of the observation sequence; and If the values are close to 0 (e.g., between -0.1 and 0.1), it indicates that the contribution change frequency of the corresponding dynamic mode is relatively low and follows a certain change law. Therefore, the mode captures the causal relationship of the change and is a supplementary information to the static information. This disclosure defines it as a time-varying causal mode. Figure 7 As shown, the sequence recovered based on the time-varying causal pattern ( Figure 7 (where the waveform refers to the time-varying causal model) can reflect the degree of fluctuation of the observation sequence and characterize the degree of local change. For example, the location with a smaller value of the observation sequence has a larger fluctuation, and the location with a larger value of the observation sequence has a smaller fluctuation. Smaller (e.g. to -0.1) or larger (e.g. 0.1 to ), it indicates that the eigenvalue is far away from the unit circle of the complex space, indicating that the contribution evolution frequency of the corresponding dynamic mode is large and irregular, which is defined as a noise mode in this disclosure. Figure 7 As shown, the sequence recovered based on the noise pattern ( Figure 7 The noise pattern (the waveform referred to in the figure) is irregular and random noise.

[0089] According to the above analysis, relatively stable dynamic patterns and causal relationships are closely related. Therefore, this disclosure regards relatively stable dynamic evolution patterns (invariant causal patterns and time-varying causal patterns) as causal patterns, and the linear matrix reconstructed based on this is regarded as a causal structure.

[0090] Relatively stable dynamic patterns can be separated and used to reconstruct a linear matrix. It can be found from the sequence results restored under different dynamic matrices that a stable dynamic pattern can effectively restore the stable trend in the observed sequence, which the present invention refers to as a causal component. Therefore, this application uses the stability of the dynamic evolution process reflected by the eigenvalue as the link between dynamics and causality, regards a relatively stable dynamic evolution pattern as a causal pattern, and regards the linear matrix reconstructed based on this as a causal structure.

[0091] In the context of deep learning, this embodiment explores the dynamic processes and causal relationships between latent variables. The present disclosure can discover interpretability from eigenvalues at different scales. The core of this embodiment is to explore the connection between linear dynamics and causal structure, so as to reconstruct the causal structure from a dynamic perspective.

[0092] The following explains the connection between spatiotemporal dynamics and spatiotemporal causality captured by the corresponding Koopman operators at different scales, demonstrating the interpretability and effectiveness of this disclosure at the underlying principle: Figure 8 The distribution of eigenvalues in the Koopman operator and the corresponding causal graph at different scales is shown. When conducting interpretability experiments, that is, Figure 8 In the figure, the Koopman operators of different scales are spectrally decomposed separately, and the causal graph obtained is a causal graph of a specific scale obtained by decomposing the Koopman operator of a certain scale. It is worth noting that this is only for the purpose of illustrating the relationship between the Koopman operator and the causal graph at each scale, and what kind of features each scale can capture in the spatiotemporal system, just for the purpose of interpretability.

[0093] The global shared Koopman operator uses a learnable matrix to capture the dynamics of spatial node sharing. It is stable in the spatiotemporal dimension and depicts global behaviors and trends. Figure 8As shown in Figure 2, this stability ensures that all eigenvalues of the globally shared Koopman operator are close to the unit circle, preserving the contribution of the corresponding modes to the system dynamics (i.e., stable or causal modes). This property also conforms to the intuition of causality, which is the law of stability.

[0094] The community-specific Koopman operator captures several typical patterns that follow the assumption that nodes in the same community have similar dynamical systems. In addition, to prevent over-smoothing, the community-specific Koopman operator is often used as a compensation for the globally shared Koopman operator to improve the overall performance. Figure 8 As shown in Figure 2, the discrete eigenvalues of the community-specific Koopman matrix are mostly concentrated in the region where the real part is positive. or will cause the pattern to eventually decay to zero over time, while or This fact becomes the key principle for separating causality (relative stability) from dynamics, i.e. or Therefore, the community-specific Koopman operator mainly extracts low-frequency dynamic patterns. The present disclosure defines the matrix recovered from these patterns as invariant causal relationships, which is more important in self-mapping.

[0095] The node-specific Koopman operator is more flexible and is designed to capture the specific properties caused by the local dynamics of each node and adapt to distribution changes. Figure 8 As shown, the eigenvalues of the node-specific Koopman operator are mainly distributed in the left half of the unit circle, where The larger the value, the higher the frequency of change of the corresponding dynamic pattern. This also proves that the node-specific Koopman operator focuses more on local changes and can effectively capture the non-stationarity of spatiotemporal series. This disclosure defines the matrix recovered from these patterns as a time-varying causal relationship.

[0096] The darker points in the causal diagram indicate causal relationships. Figure 8 As can be seen in the causal graphs corresponding to the globally shared Koopman operator and the community-specific Koopman operator, there are causal relationships. However, the causal graph corresponding to the node-specific Koopman operator has fewer darker points, indicating that the causal relationships are sparse. In contrast, the causal graph induced by the node-specific Koopman operator is very sparse, indicating that the local dynamics of high-frequency changes have fewer causal relationships.

[0097] The present invention extracts all invariant causal patterns (i.e., satisfying eigenvalues) of the complete cross-scale Koopman operator. or ), and reconstruct the observation data sequence according to the invariant causal pattern, the result is as follows Figure 9 As shown (second row), in Figure 9 In the second row, the components are the sequences predicted by the new Koopman operator composed of the eigenvectors after eigenvalue constraints, that is, the things decomposed from the observation sequence are predicted by the new Koopman operator. Figure 9 As can be seen in the second row, the sequence predicted by the invariant causal component effectively captures the core patterns of the observed sequence while ignoring local oscillations. This is also the main task of causal representation learning, which involves extracting core rules from redundant and noisy data and possessing a certain degree of transfer and scalability, namely, causal structure.

[0098] In addition, the present disclosure extracts time-varying causal patterns from the node-specific Koopman operator and reconstructs the observation data sequence based on them (the reconstruction here is also equivalent to prediction, which is also the sequence predicted by the new Koopman operator composed of eigenvectors after eigenvalue constraints, that is, it refers to the decomposition from the observation sequence, which is predicted by the new Koopman operator). The results are shown in Figure 9. It can be observed that the reconstruction result ( Figure 9 The time-varying causal component in the causal relationship has an opposite trend to the invariant causal component. This is because the nodes pay more attention to local oscillations. When the value of the series is large, small changes will not have a significant impact on the entire series, thus masking the local oscillations. When the value of the series is small, oscillations become the main factor, and even small changes will cause fluctuations. The main task of the time-varying causal component is to extract causal patterns from these fluctuations. Figure 9 The noise component in is irregular random noise.

[0099] Based on the above principles, in order to ensure the effectiveness of decoupling stable causal patterns, this paper proposes a spectral loss function to regularize the eigenvalues: ; in, Indicates finding the complex conjugate matrix of the matrix, represents the identity matrix, Represents a diagonal matrix consisting of multiple eigenvalues.

[0100] The purpose of the spectral loss function is to make the modulus of the eigenvalue close to 1. In the second training stage, spectral normalization is added to make the Koopman eigenvalue close to the unit circle of the complex space, which enhances the stability of the dynamic mode. The loss function in this stage is .

[0101] As mentioned above, the target spatiotemporal prediction network can be updated according to the second loss. Specifically, in the second training phase, the first mapping function in the spatiotemporal prediction network can be updated according to the second loss. , the first cross-scale Koopman operator and the first inverse mapping function After the second training phase, the second mapping function is obtained , the second cross-scale Koopman operator and the second inverse mapping function .

[0102] The third training phase includes D1-D7: D1. The target spatiotemporal prediction network performs the above spatiotemporal data prediction to obtain the prediction results.

[0103] The target spatiotemporal prediction network here may specifically refer to the spatiotemporal prediction network trained in the second training stage.

[0104] D2. Execute the above second loss calculation.

[0105] In this step, use 、 and Replace C1-C3 respectively 、 and , recalculate the second loss and get the second loss of the third training stage.

[0106] D3. Obtain a target eigenvalue that meets preset conditions from the multiple eigenvalues obtained in the current training phase; the eigenvector corresponding to the target eigenvalue is the target eigenvector.

[0107] It should be noted that the eigenvalues and eigenvectors in the current training phase are the second cross-scale Koopman operator Obtained by spectral decomposition.

[0108] The preconditions will be introduced later.

[0109] D4. Construct a causal graph using target eigenvalues and target eigenvectors.

[0110] D5. Based on the above causal graph, the feature variables of the current time step are mapped to a second representation space with causal constraints through a causal flow network; the above second representation space is a subspace of the above first representation space.

[0111] D6. Calculate the KL divergence between the posterior distribution of the current training stage and the prior distribution of the second representation space.

[0112] D7. Update the current target spatiotemporal prediction network based on the third loss; the third loss includes the second loss and KL divergence obtained in the current training phase.

[0113] The following is a detailed introduction.

[0114] In the third training phase, if Figure 10 As shown, this involves a causal structure extractor and a causal flow network. The causal structure extractor considers relatively stable dynamical patterns as causal patterns and the linear matrix reconstructed from the stable patterns as a causal graph. It decouples the evolution of relatively stable dynamical patterns and, based on this, reconstructs a linear matrix as a causal structure. The causal flow network fits structural causal equations based on the extracted causal graph to ensure the identifiability of causal variables and model the subspace of causal structural constraints. The aforementioned representation space constraint method narrows the distribution distance between the Koopman subspace (the first representation space in the above embodiment) and the causal constraint subspace (the second representation space in the above embodiment), resulting in a robust representation space.

[0115] For the second cross-scale Koopman operator Perform spectral decomposition:

[0116] (For specific methods, please refer to the description of the second training phase), where: , is the left eigenvector, is the right eigenvector, and the eigenvalue is .

[0117] The matrix composed of eigenvectors is , the matrix composed of eigenvalues is This disclosure extracts the corresponding causal pattern by constraining the eigenvalue range. The calculation process is as follows:

[0118] in, and represents the matrix composed of all invariant causal patterns and time-varying causal patterns, is a relaxation factor used to control the strictness of the causal model and is an empirical value. is the reconstructed causal graph, which is also a matrix, because the reconstructed matrix A is the stable part of the Koopman operator matrix K. The matrix established by this stable part is regarded as a causal graph in this application. The constraint shows that and is a matrix composed of eigenvectors whose modulus satisfies 1±δ, It is a matrix composed of eigenvalues whose modulus satisfies 1±δ.

[0119] The aforementioned preconditions include the above-mentioned constraints on the range of eigenvalues.

[0120] exist Figure 10 In the causal structure extractor part, find a matrix composed of eigenvectors that meet the requirements, with dimension ,so The dimension transformation is , after dimension transformation The left eigenvectors form a time-varying causal pattern and an invariant causal pattern. , the right eigenvectors also form the time-varying causal pattern and the invariant causal pattern .

[0121] Obtaining a cause-and-effect diagram Finally, we need to establish a causal structural equation based on the causal edge To clarify the generation mechanism of latent variables, Represents the characteristic variables in the representation space; express According to the cause-effect diagram Obtained The parent variable set of right The causal effect of is obtained by sampling from the posterior distribution, and The direct cause of the generation of represents an exogenous variable that follows a standard Gaussian distribution , is randomly sampled from a standard Gaussian distribution, which is The generated external cause is usually a random noise with no practical meaning. This disclosure proposes to use an affine transformation modulated by the causal parent variable as a structural causal equation, which is defined as follows:

[0122] Among them, such as Figure 10 The causal flow network shown, SNet is a multi-layer perceptron, whose purpose is to obtain the time step in the affine transformation The corresponding scaling factor , TNet is a multi-layer perceptron whose purpose is to obtain time steps The corresponding translation factor , is a vector of alternating 0 / 1, whose purpose is to convert the time step The corresponding exogenous variable Divide into two groups and , Used to find the scaling factor and translation factor, expressed as Multiply The remaining part is 0; the other part Used to calculate the result of affine transformation, Indicates that the modulation parameters are generated by the multilayer perceptron based on the parent variable , modulation parameters Used to correct the scaling factor and translation factor , modulation parameters Used to correct the translation factor , thereby achieving causal effect transmission. The purpose of the last formula in the structural causal equation is to convert the exogenous variable into a causal variable based on the influence of the causal parent variable. The causal structural equation designed in this disclosure is a reversible function, which can effectively improve the identifiability of causal variables. For convenience, this disclosure records .

[0123] The causal effects contained in the causal graph can be embedded into the causal variables through the structural causal equation. Since the parent variable of the causal variable comes from the second representation space, the generated causal variable also belongs to the second representation space. Therefore, the present disclosure uses the causal flow network to obtain the prior distribution of the second representation space. , thereby forming a representation space of structural causal constraints and enhancing the causality of the characteristic variables.

[0124] This paper uses the variable theorem to convert the prior distribution Decomposition into exogenous variable distribution The product of is defined as follows: ; in, represents the distribution of exogenous variables; yes The k elements, representing the causal variables Switching to exogenous variables process; Indicates the i Node, t time step, the k the value of an exogenous variable; Represents the function f from Calculated to The Jacobian matrix of , , express The identity matrix of dimension; It means to find the determinant of the Jacobian matrix. Indicates the i Node, t time step, the kThe causal variable of an exogenous variable, Represents a diagonal matrix. The above formula can be used to solve the prior distribution .

[0125] In the third training phase, the target spatiotemporal prediction network characterizes the evolution of the spatiotemporal system dynamics based on the posterior distribution fitted by the second cross-scale Koopman operator, while the prior distribution fitted by the causal structural equation contains the causal relationship that naturally exists in the system. By reducing the distribution distance between the prior distribution and the posterior distribution, the spatiotemporal system can be driven to operate in a causal dynamic manner in the representation space. Specifically, this application calculates their KL divergence as a constraint. Since there is no explicit analytical expression for the prior distribution, it is calculated by sampling. : ;in, Used to seek expectations.

[0126] In the third training phase, structural causal constraints are added with the goal of propagating causal relationships throughout the representation space. The loss function for this phase is , the loss obtained is the third loss.

[0127] In this training phase, the second mapping function is updated according to the third loss , the second span-scale operator and the second inverse mapping function After the third training phase, the mapping function, cross-scale operator and mapping function can be expressed as 、 and , that is, the parameters in the prediction model are 、 and .

[0128] Of course, in other embodiments, the training phase may not be divided into two stages, and the loss function may be used. Conduct training.

[0129] It is worth noting that during training, the spatiotemporal observation data sequence can be used The spatiotemporal observation data corresponding to each time step in the model is used to predict the spatiotemporal data of the next time step, and then the model is trained based on the predicted spatiotemporal data and the corresponding spatiotemporal observation data. For example: T +1 is 3 minutes, and each time step is 1 minute, then , using the spatiotemporal observation data of the first minute To predict the spatiotemporal data of the second minute , using the spatiotemporal observation data of the second minute To predict the spatiotemporal data of the 3rd minute , at least using and ,as well as, and Conduct model training.

[0130] This embodiment describes the equivalence between spacetime dynamics and causal structure from another perspective, understanding the evolutionary mechanism of causal structure from the perspective of the dynamic evolution process. Spacetime causal structure describes the causal dependencies between latent variables in space that change over time, while spacetime dynamics describes the evolution of the state of a spatial system over time. The two are inherently related. This disclosure uses the Koopman operator to linearize the representation space and then uses spectral analysis techniques to explain the relationship between the dynamics and causal structure of a spacetime system.

[0131] It's important to note that existing methods for learning spatiotemporal representations assume that causal structures are stable and globally shared. They typically use a learnable causal matrix to learn causal relationships between latent variables in an unsupervised manner. However, excessive pursuit of global causal relationships between latent variables can lead to over-stationarity in the learned causal structure. This means that the learned causal matrix contains only a small number of edges, while the majority are zero. This results in a loss of variability in the learned causal structure, making it difficult to generalize to specific scenarios.

[0132] In response to the above problems, the present disclosure provides a solution based on a structural causal constrained Koopman operator model. Starting from the perspective of spatiotemporal dynamics, the present disclosure explores the stable modes in the evolution process, thereby revealing the generation principle of causal structures that emerge across scales, and constraining the representation space. This application regards relatively stable dynamic evolution patterns as causal patterns, and the linear matrix reconstructed based on this as a causal structure. To this end, the present disclosure proposes a structural causal constrained Koopman neural operator model (Structural Causality-Constrained Koopman Neural Operator Model, SCKNO) to learn a robust representation space in a spatiotemporal system. Its core idea is to reconstruct the causal structure by decomposing stable dynamic patterns, and thereby impose causal constraints in the representation space. First, in order to adapt to the nonlinearity and emergence of spatiotemporal systems, a cross-scale Koopman neural operator is proposed to encapsulate the dynamics at different scales into their respective linear matrices, thereby limiting the representation space to a Koopman invariant subspace. Secondly, due to the linear characteristics of this space, the model can perform spectral analysis and examine its eigenvalues, thereby better understanding the oscillation frequency. To this end, this paper decomposes the Koopman pattern to decouple relatively stable dynamical patterns and extract causal structures. Third, this paper proposes a causal flow network to fit the causal structural equations, thereby generating a subspace with structural causal constraints. Finally, this paper approximates the distribution of the Koopman subspace and the structural causal constraint subspace to generate a robust representation space.

[0133] In summary, the advantages of the present disclosure over the prior art are: Different from the traditional method of calculating feature variables through complex encoders, the present invention explores the stable patterns in the evolution process from the perspective of spatiotemporal dynamics, thereby revealing the generation principle of causal structures that emerge across scales and constraining the representation space. Traditional methods only focus on the fact that the generation of observation sequences depends on feature variables, but ignore the generation principle of feature variables. This application further explores the generation principle of feature variables and defines that the generation of feature variables comes from the causal structure between variables, and the generation of causal structures depends on the stable patterns of spatiotemporal dynamics.

[0134] This paper proposes to use the cross-scale Koopman operator to encapsulate non-stationary, nonlinear, cross-scale emergent dynamics into a linear matrix, and uses spectral decomposition technology to analyze the connection between stable dynamic patterns and causal relationships, explaining the generation mechanism of causal structures.

[0135] This paper uses prototype learning technology to divide spatial nodes into communities. The same community has similar dynamic processes, while the dynamic processes between different communities are different. This helps to capture spatial emergence in spatiotemporal systems and improve the model's cross-scale feature extraction capabilities.

[0136] The present invention uses linear dynamics and causal structure to jointly constrain the representation space to obtain robust characteristic variables. In this space, nonlinear dynamics are described by linear operators, and characteristic vectors with structural causal constraints are generated according to the causal direction. By narrowing the distance between the prior distribution and the posterior distribution, the robustness of the representation space is increased.

[0137] In summary, this paper utilizes the globally shared operator, community-specific operator, and node-specific operator in the cross-scale Koopman operator to predict the feature variables of the current time step, obtaining predicted feature variables at different levels and then fusing them. This multi-dimensional feature extraction and fusion method can comprehensively consider the characteristics of the spatiotemporal system at different scales and levels, capturing more comprehensive information and thus more accurately describing the state of the spatiotemporal system. For example, the globally shared operator can capture the macroscopic characteristics of the entire system, the community-specific operator can take into account the specific characteristics of different communities or sub-regions in the system, and the node-specific operator focuses on the unique properties of each node. By fusing these different levels of feature variables, the model can better grasp the complex characteristics of the spatiotemporal system.

[0138] The use of the mapping function and the inverse mapping function in the present disclosure enables the model to perform nonlinear mapping on spatiotemporal data, and better adapt to the complex dynamic changes of the spatiotemporal system. The state changes of the spatiotemporal system are often nonlinear, and the traditional single-perspective analysis method may be difficult to accurately describe this nonlinear relationship. The disclosed solution maps the data to a feature space that is more suitable for model processing through a mapping function, in which the nonlinear characteristics of the data can be more effectively captured, and then the prediction results are mapped back to the observation space through the inverse mapping function, so that the prediction results can correspond to the actual spatiotemporal observation data. At the same time, the cross-scale Koopman operator can model the dynamic changes of the spatiotemporal system. By processing features of different scales through different operators, the evolution law of the spatiotemporal system over time and space can be more accurately captured, thereby improving the accuracy of prediction of future states.

[0139] The present invention trains a spatiotemporal prediction network by acquiring a large amount of sample data, and the model can automatically learn the potential patterns and regularities in the spatiotemporal data. During the training process, the model continuously adjusts its own parameters based on the input sample data to minimize the error between the prediction results and the actual observation data. This data-driven adaptive learning method enables the model to adapt to different spatiotemporal systems and various complex situations, unlike the existing technology that is limited to specific observation dimensions or fixed analysis methods. The model can automatically extract appropriate features based on the specific data set and problem, and establish a corresponding prediction model, thereby improving the accuracy and generalization ability of the prediction.

[0140] Based on the same inventive concept, the present application also provides a training device for implementing the aforementioned training method. The solution provided by this device is similar to the solution described in the aforementioned method. Therefore, the specific limitations of one or more training device embodiments provided below can be found in the above-mentioned limitations of the training method and will not be repeated here.

[0141] In an exemplary embodiment, Figure 11 As shown, a training device is provided, comprising: A sample acquisition module 11 is used to acquire samples; each sample includes a sequence of spatiotemporal observation data in an observation space; a training module 12 is used to input the samples into a spatiotemporal prediction network for training to obtain a prediction model, wherein the spatiotemporal prediction network includes a mapping function, an inverse mapping function and a cross-scale Koopman operator; the spatiotemporal prediction network and the prediction model are used to perform spatiotemporal data prediction based on the input data; wherein the above-mentioned spatiotemporal data prediction includes: mapping the input data into a first representation space through a mapping function to obtain at least the feature variables of the current time step; predicting the feature variables of the current time step through the global shared operator, community-specific operator and node-specific operator in the cross-scale Koopman operator respectively to obtain the global prediction feature variables, community prediction feature variables and node prediction feature variables of the next time step, and fusing them to obtain the predicted feature variables of the next time step; mapping the predicted feature variables of the next time step into the observation space through the inverse mapping function to obtain a prediction result; the prediction result includes the predicted spatiotemporal observation data of the next time step.

[0142] In one embodiment, the above-mentioned training includes a first training stage, and the training module 12 is specifically used to: perform the above-mentioned spatiotemporal data prediction by the spatiotemporal prediction network to obtain a prediction result; perform a first loss calculation: use the first loss function to obtain the first loss based on the prediction results and samples obtained in the current training stage; and update the spatiotemporal prediction network according to the above-mentioned first loss.

[0143] In one embodiment, the above-mentioned first loss function includes a spatial loss function, a reconstruction loss function and a prediction loss function; in the aspect of using the first loss function to obtain the first loss based on the prediction results and samples obtained in the current training stage, the training module 12 is specifically used to: calculate the spatial loss by the spatial loss function based on the first predicted feature variable and the first actual feature variable; wherein the first predicted feature variable is determined by the second actual feature variable and the current cross-scale Koopman operator; the first actual feature variable and the second actual feature variable are both determined by the posterior distribution corresponding to the sample and the first representation space in the current training stage; the reconstruction loss is calculated by the reconstruction loss function based on the spatiotemporal observation data sequence in the sample and the second actual feature variable; the prediction loss is calculated by the prediction loss function based on the spatiotemporal observation data sequence in the sample and the second actual feature variable; the first loss includes spatial loss, reconstruction loss and prediction loss.

[0144] In one embodiment, the above-mentioned training also includes a second training stage, and the training module 12 is specifically used to: execute the above-mentioned spatiotemporal data prediction by the target spatiotemporal prediction network to obtain a prediction result; the target spatiotemporal prediction network is the spatiotemporal prediction network updated in the previous training stage; execute a second loss calculation to obtain a second loss: execute the above-mentioned first loss calculation to obtain the first loss of the current training stage; use the prediction result of the current training stage to perform spectral decomposition on the cross-scale Koopman operator in the above-mentioned target spatiotemporal prediction network to obtain multiple eigenvalues and corresponding eigenvectors; calculate the spectral loss based on the above-mentioned multiple eigenvalues; the above-mentioned second loss includes the first loss and spectral loss of the current training stage; and update the above-mentioned target spatiotemporal prediction network based on the above-mentioned second loss.

[0145] In terms of calculating the spectral loss based on the multiple eigenvalues, the training module 12 is specifically configured to obtain the spectral loss based on a unit matrix, a diagonal matrix composed of the multiple eigenvalues, and a complex conjugate matrix of the diagonal matrix.

[0146] In one embodiment, the above-mentioned training also includes a third training stage, and the training module 12 is specifically used to: execute the above-mentioned spatiotemporal data prediction by the target spatiotemporal prediction network to obtain a prediction result; execute the above-mentioned second loss calculation; obtain the target eigenvalue that meets the preset conditions from the multiple eigenvalues obtained in the current training stage; the eigenvector corresponding to the target eigenvalue is the target eigenvector; construct a causal graph through the target eigenvalue and the target eigenvector; based on the above-mentioned causal graph, map the feature variables of the current time step to a second representation space with causal constraints through the causal flow network; the above-mentioned second representation space is a subspace of the above-mentioned first representation space; calculate the KL divergence between the posterior distribution of the current training stage and the prior distribution of the above-mentioned second representation space; update the current target spatiotemporal prediction network according to the third loss; the above-mentioned third loss includes the second loss and KL divergence obtained in the current training stage.

[0147] Figure 12 is a flow chart of a spatiotemporal data prediction method according to an exemplary embodiment. Figure 12 As shown, the method includes the following steps S201-S202: In step S201, target spatiotemporal observation data is obtained. In step S202, the target spatiotemporal observation data is input into a prediction model to obtain predicted spatiotemporal observation data within a target time span.

[0148] The prediction model is obtained through training. For related introduction, please refer to the above records and will not be elaborated here.

[0149] In one example, the target predicted spatiotemporal observation data includes predicted spatiotemporal observation data of at least one time step; obtaining the predicted spatiotemporal observation data of the target time span in step S202 includes the following sub-steps S2021-S2022: S2021. Input the input data into the above-mentioned prediction model to obtain the predicted spatiotemporal observation data for the next time step.

[0150] S2022. Use the predicted spatiotemporal observation data of the next time step to update the above input data until the predicted spatiotemporal observation data of all time steps in the above target time span are obtained.

[0151] After the prediction model is obtained through the above embodiment, when the prediction model needs to be used to predict spatiotemporal data, the target spatiotemporal observation data is first obtained, and the target spatiotemporal observation data is used as input data, and the target spatiotemporal observation data is used as input data through the mapping function. The target spatiotemporal observation data is mapped to the first representation space to obtain the characteristic variables of the current time step, and the characteristic variables of the current time step are transformed through the cross-scale Koopman operator The global shared operator, community-specific operator and node-specific operator in the prediction are used to obtain the global prediction feature variables, community prediction feature variables and node prediction feature variables of the next time step, and then they are fused to obtain the prediction feature variables of the next time step; through the inverse mapping function The predicted feature variables of the next time step are mapped to the above observation space to obtain the predicted spatiotemporal observation data of the next time step. After obtaining the predicted spatiotemporal observation data of the next time step, the predicted spatiotemporal observation data of the next time step is used to update the input data, and the predicted spatiotemporal observation data of the next time step is obtained again based on the new input data through the prediction model, and so on, until the predicted spatiotemporal observation data of all time steps in the target time span are obtained. With the above spatiotemporal observation data sequence For example, the predicted spatiotemporal observation data for the next time step is ;use Update the input data to obtain a new spatiotemporal observation data sequence As new input data, the prediction model is based on Get the predicted spatiotemporal observation data for the next time step ; Reuse Update the input data to obtain a new spatiotemporal observation data sequence As input data, and so on, no further details are given.

[0152] Based on the same inventive concept, the embodiment of the present application also provides a spatiotemporal data prediction device for implementing the spatiotemporal data prediction method involved above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme described in the above method, so the specific limitations in the embodiments of one or more spatiotemporal data prediction devices provided below can refer to the limitations of the spatiotemporal data prediction method above, and will not be repeated here. In an exemplary embodiment, Figure 13 As shown, a spatiotemporal data prediction apparatus is provided, comprising: an acquisition module 21 for acquiring target spatiotemporal observation data; and a prediction module 22 for inputting the target spatiotemporal observation data into a prediction model trained using any of the training methods described in the above embodiments to obtain predicted spatiotemporal observation data within a target time span.

[0153] In one embodiment, the predicted spatiotemporal observation data within the above-mentioned target time span includes predicted spatiotemporal observation data of at least one time step; in terms of obtaining the predicted spatiotemporal observation data of the target time span, the prediction module 22 is specifically used to: input the input data into the above-mentioned prediction model to obtain the predicted spatiotemporal observation data of the next time step; use the predicted spatiotemporal observation data of the next time step to update the above-mentioned input data until the predicted spatiotemporal observation data of all time steps in the above-mentioned target time span are obtained.

[0154] The following is a further explanation of the above model using the urban highway speed spatiotemporal system specifically involved in this embodiment. The globally shared Koopman operator is used to model the common information within all regions. The community-specific Koopman operator is used to model the unique information within the same type of community. The dynamic evolution process of the same community is similar, while the dynamic evolution process of different communities is different. The node-specific Koopman operator is used to model the private information within a single region, with the aim of capturing regional specificity and local detail characteristics.

[0155] For the prediction of spatiotemporal data of multi-regional urban highway speeds, the multi-regional urban highway speeds themselves form a spatiotemporal system. The spatiotemporal system is mapped into a high-dimensional space through deep learning technology, which is called a representation space. The characteristic variables in the representation space are unobservable latent variables that affect the regional highway speed. This application uses deep learning technology to mine the latent variables to model and explain the generation process of urban road speed. During the training process, the characteristic variables are constrained by the causal flow network, so that causal effects are generated between the characteristic variables, and then the characteristic variables are converted into causal variables. In this application, the latent variables obtained by spatiotemporal dynamics mining are defined as characteristic variables, and the characteristic variables are converted into causal variables after passing through the causal flow network. In order to make the representation space cover both spatiotemporal dynamics and causality, this application uses the structural causal constraint method to narrow the distribution distance between the characteristic variable distribution (located in the Koopman invariant subspace) and the causal variable distribution (located in the subspace subject to causal constraints) to obtain a robust representation space. Finally, the inverse mapping function is used from this robust representation space to predict spatiotemporal data.

[0156] Characteristic variables for highway speeds in various urban areas may include, but are not limited to, the following (data on population density, building density, economic activity intensity, and traffic conditions are difficult to collect): Population density: Population density is an important spatial characteristic because areas with high population density often have greater traffic demand to meet people's daily and commercial needs. For example, highway speeds in large cities are slower than those in ordinary urban areas because cities have more people and more commercial activities. Building density: Building density is also an important spatial characteristic because areas with high building density require more traffic to meet people's daily needs such as work and entertainment. For example, during the evening rush hour, traffic speeds in commercial areas are generally slower than those in residential areas because commercial areas have higher building density and people travel more frequently. Economic activity intensity: Economic activity intensity is also a significant factor influencing traffic speeds. Developed areas often require more traffic to meet higher demand for work and trade. For example, traffic speeds in a highly industrialized area may be slower than those in a more agricultural area. The purpose of this application is to infer characteristic variables that may influence highway speeds within a region from observable highway speed data for various urban areas, establish causal relationships between these characteristic variables, and then model and explain the generation patterns and causal structure of highway speeds in various regions within a complex urban system. In addition, this application takes variables that affect the operation of the space-time system, such as the region's own attributes, weather conditions, and regional gathering activities, as system control variables, and summarizes the time series pattern of traffic speed in each region into a node embedding vector to characterize the operation mode. For example, the time series pattern of traffic speed in each region is periodic, trendy, seasonal, and sudden. When exogenous variables such as weather change, the time series pattern of traffic speed in the region will also change. At the same time, sudden regional gathering activities will also cause dynamic changes in the regional traffic speed pattern. Therefore, the dynamic process and causal structure of the characteristic variables will be affected by the control variables.

[0157] The following examples of this application are used to compare the performance of the SCKNO of this application with the baseline model. The representation space dimension is set for all SCKNO components. For the hyperparameter, the number of communities For fairness, the hidden layers of all baseline models were adjusted to 64 while ensuring consistent input information, and all models were optimized for a maximum of 300 epochs using the Adam optimizer. The optimal parameters of all deep learning models were selected through a careful parameter tuning process on the validation set.

[0158] Example 1: The prediction performance of SCKNO is evaluated on a real-world public spatiotemporal dataset collected by the Performance Measurement System (PeMS) of the Transportation Bureau A, which consists of the average speed of Area B. The research node is roads, the time interval is 5 minutes (every 5 minutes is a time step), and the observation dimension is Using data from the past hour ( ) to predict the next hour's data ( ). This dataset records the average speed of each road in 170 road areas in District B from July 2016 to August 2016, with a sampling period of 1 minute. For the stability of the time series, this application deletes the areas with missing values and splits the dataset at intervals of 5 minutes to obtain 17,833 samples of the PeMS08 dataset. One sample includes the average speed of each of the 170 roads in one time step (5 minutes) (if the sampling period is 1 minute, the average speed includes the average of 5 1-minute road speed samples). This application uses data from the past hour ( ) to predict the next hour's data ( ). 60% of the data is used for training, 20% for validation, and the rest for testing.

[0159] This application uses the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) methods to evaluate model performance. This application compares SCKNO with the current advanced spatiotemporal representation learning methods / models (DGCRN, DMSTGCN, PDFormer, and STNSCM) to verify the prediction performance of SCKNO. The final average results are shown in Table 1: Table 1 Quantitative analysis results of the prediction model of this application and other baseline models on the PeMS08 dataset

[0160] Figure 14 The figure shows the change in MAE and MAPE between the proposed model and the baseline model in the multi-step forecasting task on the PeMS08 dataset as the time step increases. Thanks to its ability to extract causal structure from stable dynamic patterns, the proposed model performs best in all time periods, reflecting its stability. It is worth noting that Figure 14 The quantitative analysis results of other baseline models outside Table 1, GCIM, ST-SSL, DSTAGNN, RGSL, D2STGNN and KNF are also shown.

[0161] Example 2: The prediction performance of SCKNO was evaluated on a real-world public spatiotemporal dataset, namely the BJ2022 dataset. This dataset records traffic flow data of various modes of transportation in 235 areas of District B from January 2022 to December 2022, including the inflow and outflow of bicycles, the inflow and outflow of taxis, the inflow and outflow of buses, and the average speed of regional roads, with a sampling period of 30 minutes. This application also splits the dataset at intervals of 30 minutes to obtain 17,518 samples of the BJ2022 dataset. One sample includes traffic flow data within one time step (30 minutes) for each of the 235 areas. This application uses 4 hours of historical data To predict the data for the next 90 minutes 60% of the data is used for training, 20% for validation, and the rest for testing.

[0162] This application uses root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) to evaluate model performance. This application compares SCKNO with current state-of-the-art spatiotemporal representation learning methods / models to verify SCKNO's prediction performance. The final average results are shown in Table 2: Table 2 Quantitative analysis results of the prediction model of this application and other models on the BJ2022 dataset

[0163] Example 3: The present disclosure evaluates the prediction performance of SCKNO on a real-world public spatiotemporal dataset, namely the NYC2016 dataset. This dataset records traffic flow data for various modes of transportation in 51 areas of District D in City C from April to June 2016, including the inflow and outflow of bicycles and taxis, with a sampling period of 30 minutes. The present application splits the dataset at 30-minute intervals to obtain 4,358 samples of the NYC2016 dataset, where one sample includes traffic flow data for one time step (30 minutes) for each of the 51 areas. The present application uses 4 hours of historical data. To predict the data for the next 90 minutes 60% of the data is used for training, 20% for validation, and the rest for testing.

[0164] This application uses root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) to evaluate model performance. This application compares SCKNO with current state-of-the-art spatiotemporal representation learning methods / models to verify SCKNO's prediction performance. The final average results are shown in Table 3: Table 3 Quantitative analysis results of the prediction model of this application and other models on the NYC2016 dataset

[0165] For spatiotemporal sequences, the higher the observation dimension, the more complex the causal relationships within the system. The MAPE effectively reflects a model's ability to withstand random fluctuations. The MAPEs corresponding to various models show that the SCKNO method proposed in this paper consistently outperforms the baseline model by a significant margin. In particular, SCKNO demonstrates significant improvements in MAPE on the multimodal traffic datasets BJ2022 and NYC2016 (Tables 2 and 3). Furthermore, the Koopman operator method based on nonlinear dynamics has a natural advantage in multi-step spatiotemporal sequences on the PeMS08 dataset (Table 1), making the proposed method even more advantageous on the BJ2022 dataset.

[0166] Regarding correlation-based representation learning methods, DGCRN and DMSTGCN embed the spatiotemporal correlations of the training data into a learnable implicit graph. The difference lies in that DMSTGCN learns an implicit graph structure at each time step. While this maximizes data information, it hinders model generalization and significantly degrades performance when handling complex scenarios (such as multimodal data). PDFormer focuses on using complex attention to extract long-term spatiotemporal correlations. While competitive, it lacks stable causal guidance and is insufficient when handling complex non-stationary environments. In contrast, methods based on causal representation learning have significant advantages in complex scenarios (i.e., multimodal datasets such as BJ or NYC). STNSCM eliminates confounding factors in spatiotemporal representations based on causal interventions, but does not model causal relationships between latent variables. STNSCM assumes that the causal graph is globally shared and stable, which can lead to over-stationarity and poor performance in multi-step prediction tasks (i.e., PeMS datasets).

[0167] In an exemplary embodiment, a computer device is provided, comprising a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of each of the aforementioned training method embodiments are implemented. The computer device may be a server or a terminal. Exemplarily, the computer device specifically comprises a processor, a memory, an input / output (I / O) interface, and a communication interface. The processor, the memory, and the I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O interface. The processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operating system and computer program in the non-volatile storage medium to run. The I / O interface of the computer device is configured to exchange information between the processor and an external device. The communication interface of the computer device is configured to communicate with an external terminal via a network connection. When the processor executes the computer program, a training method is implemented. In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the processor executes the computer program, the steps of each of the aforementioned training method embodiments are implemented. In an exemplary embodiment, a computer program product is provided, comprising a computer program. When executed by a processor, the computer program implements the steps of each of the aforementioned training method embodiments. In an exemplary embodiment, a computer device is also provided, comprising a memory and a processor. The memory stores a computer program. When the processor executes the computer program, the steps of each of the aforementioned spatiotemporal data prediction method embodiments are implemented. The computer device may be a server or a terminal. In an exemplary embodiment, the computer device specifically includes a processor, a memory, an input / output (I / O) interface, and a communication interface. The processor, the memory, and the I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O interface. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operating system and computer program in the non-volatile storage medium. The I / O interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a spatiotemporal data prediction method. In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, which, when executed by a processor, implements the steps in the above-mentioned embodiments of the spatiotemporal data prediction method.In an exemplary embodiment, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the steps of each of the aforementioned spatiotemporal data prediction method embodiments. Those skilled in the art will appreciate that all or part of the processes in the aforementioned method embodiments can be implemented by instructing the relevant hardware through a computer program. The aforementioned computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the aforementioned method embodiments. The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may be, but are not limited to, general-purpose processors, central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), programmable logic units (PLCs), data processing logic units based on quantum computing, and the like. The technical features of the aforementioned embodiments may be arbitrarily combined. For the sake of brevity, not all possible combinations of the various technical features in the aforementioned embodiments are described. However, as long as there are no inconsistencies in the combinations of these technical features, they should be considered within the scope of this specification. This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A training method, characterized in that: The method comprises: Acquire samples; each sample includes a sequence of spatiotemporal observation data in an observation space; Inputting the sample into a spatiotemporal prediction network for training to obtain a prediction model, wherein the spatiotemporal prediction network includes a mapping function, an inverse mapping function, and a cross-scale Koopman operator; the spatiotemporal prediction network and the prediction model are used to perform spatiotemporal data prediction based on the input data; The spatiotemporal data prediction includes: Mapping the input data to the first representation space through a mapping function to obtain at least the feature variables of the current time step; The feature variables of the current time step are predicted respectively by the global shared operator, the community-specific operator, and the node-specific operator in the cross-scale Koopman operator to obtain the global prediction feature variables, the community prediction feature variables, and the node prediction feature variables of the next time step, and are fused to obtain the prediction feature variables of the next time step; The predicted characteristic variables of the next time step are mapped to the observation space through an inverse mapping function to obtain a prediction result; the prediction result includes the predicted spatiotemporal observation data of the next time step.

2. The training method according to claim 1, characterized in that The training comprises a first training phase: Executing the spatiotemporal data prediction to obtain a prediction result; Perform the first loss calculation: use the first loss function to obtain the first loss based on the prediction results and samples obtained in the current training phase; The spatiotemporal prediction network is updated according to the first loss.

3. The training method according to claim 2, characterized in that The first loss function includes a spatial loss function, a reconstruction loss function and a prediction loss function; The first loss function is used to obtain the first loss according to the prediction results and samples obtained in the current training phase, including: A spatial loss is calculated using a spatial loss function based on a first predicted feature variable and a first actual feature variable; wherein the first predicted feature variable is determined by the second actual feature variable and a current cross-scale Koopman operator; and both the first actual feature variable and the second actual feature variable are determined by a posterior distribution corresponding to the sample and the first representation space in the current training phase; The reconstruction loss is calculated by a reconstruction loss function according to the spatiotemporal observation data sequence in the sample and the second actual characteristic variable; The prediction loss is calculated by the prediction loss function according to the spatiotemporal observation data sequence in the sample and the second actual feature variable; the first loss includes spatial loss, reconstruction loss and prediction loss.

4. The training method according to claim 3, characterized in that The training also includes a second training phase: The target spatiotemporal prediction network performs the spatiotemporal data prediction to obtain a prediction result; the target spatiotemporal prediction network is the spatiotemporal prediction network updated in the previous training stage; Perform the second loss calculation to get the second loss: Execute the first loss calculation to obtain the first loss of the current training stage; Using the prediction results of the current training phase to perform spectral decomposition on the cross-scale Koopman operator in the target spatiotemporal prediction network, a plurality of eigenvalues and corresponding eigenvectors are obtained; Calculating a spectral loss according to the plurality of eigenvalues; wherein the second loss includes the first loss and the spectral loss of the current training stage; The target spatiotemporal prediction network is updated according to the second loss.

5. The training method according to claim 4, characterized in that Calculating spectral loss according to the plurality of eigenvalues comprises: The spectral loss is obtained according to a unit matrix, a diagonal matrix composed of the multiple eigenvalues, and a complex conjugate matrix of the diagonal matrix.

6. The training method according to claim 4, characterized in that The training also includes a third training phase: The target spatiotemporal prediction network performs the spatiotemporal data prediction to obtain a prediction result; performing the second loss calculation; Obtain a target eigenvalue that meets preset conditions from multiple eigenvalues obtained in the current training phase; The eigenvector corresponding to the target eigenvalue is the target eigenvector; Construct a causal graph through target eigenvalues and target eigenvectors; Based on the causal graph, mapping the feature variables of the current time step into a second representation space with causal constraints through a causal flow network; The second representation space is a subspace of the first representation space; Calculating the KL divergence between the posterior distribution of the current training stage and the prior distribution of the second representation space; The current target spatiotemporal prediction network is updated according to the third loss; the third loss includes the second loss and KL divergence obtained in the current training stage.

7. A training device, characterized in that: The device comprises: A sample acquisition module is used to acquire samples; each sample includes a sequence of spatiotemporal observation data in an observation space; A training module, configured to input samples into a spatiotemporal prediction network for training to obtain a prediction model, wherein the spatiotemporal prediction network includes a mapping function, an inverse mapping function, and a cross-scale Koopman operator; the spatiotemporal prediction network and the prediction model are configured to perform spatiotemporal data prediction based on the input data; The spatiotemporal data prediction includes: Mapping the input data to the first representation space through a mapping function to obtain at least the feature variables of the current time step; The feature variables of the current time step are predicted respectively by the global shared operator, the community-specific operator, and the node-specific operator in the cross-scale Koopman operator to obtain the global prediction feature variables, the community prediction feature variables, and the node prediction feature variables of the next time step, and are fused to obtain the prediction feature variables of the next time step; The predicted characteristic variables of the next time step are mapped to the observation space through an inverse mapping function to obtain a prediction result; the prediction result includes the predicted spatiotemporal observation data of the next time step.

8. A method for predicting spatiotemporal data, characterized in that: The method comprises: Acquire target spatiotemporal observation data; The target spatiotemporal observation data is input into a prediction model trained by the training method according to any one of claims 1 to 6 to obtain predicted spatiotemporal observation data within a target time span.

9. The method according to claim 8, characterized in that The predicted spatiotemporal observation data within the target time span includes predicted spatiotemporal observation data of at least one time step; The method of obtaining the predicted spatiotemporal observation data of the target time span includes: Inputting the input data into the prediction model to obtain the predicted spatiotemporal observation data for the next time step; The input data is updated using the predicted spatiotemporal observation data of the next time step until the predicted spatiotemporal observation data of all time steps in the target time span are obtained.

10. A spatiotemporal data prediction device, characterized in that: The device comprises: Acquisition module, used to obtain target spatiotemporal observation data; A prediction module is used to input the target spatiotemporal observation data into a prediction model trained by the training method according to any one of claims 1 to 6 to obtain predicted spatiotemporal observation data within a target time span.

Images