A spatio-temporal differential equation network for urban traffic prediction

Abstract

The application provides a kind of space-time differential equation network for urban traffic prediction, comprising: deep learning model and physical dynamic process integrated in a framework, physical dynamic process is based on energy transfer differential equation constructs the traffic potential field sequence evolution dynamic equation of road network node;Deep learning model: including encoder, space-time differential equation network and decoder;Encoder is used to map traffic flow into potential field, then space-time differential equation network is used to predict the change of potential field, and finally the potential field is converted into traffic flow by a decoder.The application can bridge the gap between data-driven models and physical-driven models, and the model can have the performance advantages of data-driven models and the interpretability of physical models.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent transportation, in particular to a spatiotemporal differential equation network for urban traffic flow prediction. BACKGROUND

[0002] Current traffic flow prediction methods can be mainly divided into two categories: physical information based models and data driven models. The first method relies on traffic flow theory, representing the traffic system as coupled differential equations, and then achieving traffic flow prediction through differential equation driven traffic system simulation. This method ensures that the simulation results can represent the global traffic dynamic changes, not just the fitting based on historical observation data. However, such models usually make strong assumptions about traffic flow movement, which may not be able to capture complex human behavior and other uncertain factors in the real world. Moreover, the simulation process relies on a large number of numerical differentiation and integration operations, which usually requires a large amount of computing resources.

[0003] The second method is data driven, first training a statistical learning model according to historical observation data, and then generating prediction results through the model. The most representative of which is the deep learning based traffic flow prediction model. For example, using recurrent neural networks or temporal convolution to model temporal dependence, then modeling spatial dependence through convolutional neural networks, and introducing road network information using graph convolution technology. In recent years, with the significant increase in the amount of traffic data, data driven methods based on deep learning have attracted widespread attention in the industry and have achieved great success in many practical applications. However, this deep learning data driven method also has certain disadvantages. First, since there is no physical knowledge to guarantee the universality of the results, the model may fail in scenarios not contained in the training data. Secondly, the black box structure of the deep learning model may also introduce unknown risks, which may pose a potential threat to urban safety.

[0004] Therefore, how to provide a spatiotemporal differential equation network for urban traffic flow prediction that combines traffic dynamics knowledge and end-to-end deep learning method is a problem that those skilled in the art need to solve. SUMMARY

[0005] Therefore, the present application provides a spatiotemporal differential equation network for urban traffic flow prediction, which can bridge the gap between data driven models and physical driven models, and the model can have the performance advantages of data driven models and the interpretability of physical models.

[0006] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0007] A kind of space-time differential equation network for urban traffic prediction, comprising: deep learning model and physical dynamic process integrated in a framework, wherein,

[0008] Physical dynamic process: the traffic potential energy field sequence evolution dynamic equation of road network node is constructed based on energy transfer differential equation;

[0009] Deep learning model: including encoder, space-time differential equation network and decoder;

[0010] The encoder is used to encode the historical traffic flow sequence into the initial state of traffic potential energy field

[0011] The space-time differential equation network introduces traffic potential energy field sequence evolution dynamic equation into residual graph convolutional network, in combination with the initial state Potential energy field sequence is predicted via neuron ordinary differential equation calculator t0 For initial time, H time to be predicted in the future;

[0012] The decoder generates predicted traffic flow sequence based on traffic flow and potential energy gradient relationship model from predicted potential energy field sequence

[0013] Preferably, the traffic potential energy field sequence evolution dynamic equation is:

[0014]

[0015] Wherein, z=(z1,…,z n ) T Traffic potential energy field of whole road network, Traffic potential energy of road network node i, α is shared parameter, φ=(φ1,…,φi,…,φ n T , φ i Training parameter, ⊙ Hadamard product, Δ Laplace operator for calculating the difference between the state z i Of node i and neighbor.

[0016] Preferably, the space-time differential equation network is:

[0017]

[0018] Wherein, function Residual graph convolutional network, wherein the repeated neural network layer in it is

[0019]

[0020] ​​Φ represents all trainable parameters, uses α as a convolution kernel to aggregate node states within a given receptive field, Tanh(·) is an activation function, and the result of convolution is weighted by φ i Weighted summation.

[0021] Preferably, the neuron ordinary differential equation calculator predicts a potential energy field sequence is:

[0022]

[0023] where is sampled from a distribution , the distribution is a conditional probability distribution calculated according to a historical traffic flow sequence.

[0024] Preferably, is sampled from a distribution During the sampling process, the corresponding mean and variance are obtained from a historical traffic flow sequence :

[0025]

[0026] GRU is used as an encoder to extract information from , g(·) is a fully connected network that converts the final hidden state into the mean and variance of

[0027] The reparameterization method is used to calculate the of each node according to the following formula

[0028]

[0029] where ∈ i is sampled from a standard normal distribution, and T represents the length of the historical traffic flow sequence.

[0030] Preferably, the traffic flow and potential energy gradient relationship model is:

[0031]

[0032] In the present application, is the graph gradient operator, and the negative sign represents the direction of flow, z = (z1, …, z n ) T is the traffic potential energy field of the entire road network, is the traffic potential energy of road network node i, and the traffic flow of the entire road network is vector |ε| is the size of the edge set, and the edge set is a set of directed edges between two road network nodes.

[0033] Preferably, the framework is trained by a backward iterative algorithm aiming at minimizing the log-likelihood of the traffic flow sequence.

[0034] Via the technical solutions described above, compared with the prior art, the present application has the following beneficial effects:

[0035] The traffic flow of the present application is always from a point with high potential energy to a point with low potential energy, and the gradient of the potential energy also reflects the size of the corresponding traffic flow, indicating that the potential energy driven by the physical equation can capture the internal of the traffic flow and can be explained as a factor driving the flow. The physical-guided deep learning model used in the present application can bridge the gap between data-driven models and physically-driven models, and the model can have the performance advantages of data-driven models and the interpretability of physical models. At the same time, the differential equation calculator can achieve a dynamic balance between prediction accuracy and computational complexity. BRIEF DESCRIPTION OF DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings;

[0037] Figure 1 The figure is a space-time differential equation network model architecture for urban traffic prediction provided by the embodiments of the present application;

[0038] Figure 2 The figure is a traffic flow and potential energy field schematic diagram on a road network provided by the embodiments of the present application;

[0039] Figure 3 The figure is a comparison diagram of potential energy field differential equation results on different data sets provided by the embodiments of the present application;

[0040] Figure 4 The figure is a computational complexity vs. prediction accuracy schematic diagram provided by the embodiments of the present application;

[0041] Figure 5 The figure is a potential energy field and real traffic flow schematic diagram learned on GT-221 data set provided by the embodiments of the present application. DETAILED DESCRIPTION

[0042] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work are within the protection scope of the present application.

[0043] The embodiments of the present application propose a model named space-time differential equation network (STDEN) which combines traffic dynamics knowledge and end-to-end deep learning method to perform traffic flow prediction.

[0044] Traffic flow on the road is driven by a potential potential field (similar to water flow driven by gravity field). The potential potential field follows a physical law represented by a differential equation. In order to further illustrate the technical solutions of the present application, the related professional terms are explained as follows:

[0045] Road network: the road network is represented as a directed graph Wherein represents a set of points, represents a set of edges, W∈R n×n represents an adjacency matrix, point represents an intersection or road end, e ij ∈ε represents a directed edge from node v i to v j .

[0046] Traffic flow: traffic flow is an attribute of an edge in the road network. Given an edge e ij , the flow of the edge in a given time period is defined as f ij , and the flow of the entire road network is defined as vector where |ε| is the size of the edge set.

[0047] Potential field: for a node i in the road network, define the traffic potential as an attribute of his, and the traffic potential field of the entire road network is defined as

[0048] As shown in Figure 2 , the potential field of the road network is the potential driving force of the traffic flow, similar to the gravity field driving the water flow, and the flow of an edge is the potential gradient of its two end points.

[0049] Traffic flow sequence and potential field sequence: divide time into regular time slices, let f (t) represent the observed traffic flow in time slice . The traffic flow sequence is represented as the time sequence F (0:t) on the traffic flow f (0) ,…,f (t)), the potential field sequence is Z (0:t) = (z (0) ,…,z (t) ).

[0050] Based on the above basic concepts, the traffic flow prediction problem is defined as follows.

[0051] Input: historical flow sequence F from t-T+1 to t (t-T+1:t) , future flow sequence F from t+1 to t+H (t +1:t+H) , the corresponding road network

[0052] Output: the model m(·) satisfies

[0053] Objective: minimize the prediction error of the training data.

[0054] The relevant mathematical symbols are shown in Table 1:

[0055] Table 1

[0056]

[0057] The space-time differential equation network for urban traffic flow prediction provided in this embodiment is a physical knowledge guided traffic flow prediction framework, and a data driven method generates a prediction result by modeling the relationship between F (t-T+1:t) and F (t+1:t+T) . In order to realize a learnable potential field differential equation, an existing ordinary differential equation network is expanded by replacing the differential operator with a graph Laplacian operator to design a graph neural network. It includes two parts: an explicit deep learning model STDEN and an implicit physical dynamic process PGFM. In the implicit physical dynamic process, a deep neural network is implemented, which is a space-time differential equation network.

[0058] Physical dynamic process: based on the energy transfer differential equation, the evolution dynamic equation of the traffic potential field sequence of the road network node is constructed; in the PGFM, a continuous equation based on physical knowledge is used to represent the conversion relationship between the potential field and the traffic flow.

[0059] Deep learning model: STDEN includes three parts: an RNN-based encoder encodes the traffic flow sequence into the initial state of the potential field, a differential equation network predicts the change of the potential field, and a decoder generates the traffic flow from the predicted potential energy according to formula 1.

[0060] The encoder is used to encode the historical traffic flow sequence into the initial state of the traffic potential field

[0061] The spatio-temporal differential equation network introduces a traffic potential field sequence evolution dynamic equation into a residual graph convolutional network, in combination with an initial state The potential field sequence is predicted via a neuron ordinary differential equation calculator t0 is an initial time, and H is a future time to be predicted;

[0062] The decoder generates a predicted traffic flow sequence based on a traffic flow and potential gradient relationship model from the predicted potential field sequence The predicted traffic flow sequence is generated.

[0063] In one embodiment, the potential field of the road network is the potential driving force of the traffic flow, similar to the gravity field driving water flow, and the flow of an edge is the potential gradient of its two endpoints.

[0064]

[0065] wherein is a graph gradient operator, and the negative sign in front represents the direction of the flow. According to equation (1), the traffic flow can be considered as an energy transfer process on the potential field, which is the basis of the model.

[0066] In physics, a continuity equation is often used to describe the transfer between physical quantities, such as gravity, energy, momentum. Taking energy transfer as an example, under the continuity equation, the energy transfer process can be expressed as

[0067]

[0068] wherein u is the energy density, q is the energy flux, and div is the differential operator. The differential equation represented by equation (2) shows the relationship between the energy size and the energy transfer, i.e. the change in energy density leads to the energy transfer in space. For example, heat always transfers from a hot location to a cold location.

[0069] The traffic flow driven by the potential field in the road network is an example of the continuity equation. In Table 2, the potential-driven traffic flow is compared with the energy continuity equation, and the traffic flow on the road can be considered as the energy transfer on the potential field.

[0070] Table 2

[0071]

[0072] In one embodiment, given a road network For a node We define his corresponding energy density as u i . v i The potential energy of v is proportional to his energy density z i = φ i · u i , wherein φ iare trainable parameters representing the energy volume. For a point set The potential energy z = (z1,..., z n ) T The relationship between the energy density u = (u1,..., u n ) T is

[0073] z = φ ⊙ u (3)

[0074] where φ = (φ1,..., φ n ) T is the Hadamard product.

[0075] In a traffic system of road network , the potential energy can only be transmitted through edges. We define the energy flux of edge as q ij , which is mainly composed of traffic flow f ij . To measure the relationship between them, we introduce a shared parameter a.

[0076] f = a -1 q (4)

[0077] where f = (f ij ) T , q = (q ij ) T .

[0078] Substituting formula (3) and formula (4) into formula (2), we get

[0079]

[0080] which is the energy transmission continuity equation of the potential field. According to formula (1), the traffic flow on the road network is the potential gradient between adjacent nodes Substituting it into formula (5), we get

[0081]

[0082] The graph Laplacian operator Δ is defined as the gradient differential So formula (6) can be transformed into

[0083]

[0084] Formula (7) is the dynamic equation of the potential field sequence evolution. In the discrete angle, formula (7) can be written as

[0085] z (t+1) = z (t) - φ ⊙ (a Δz (t) ) (8)

[0086] In one embodiment, based on the neuron ordinary differential equation network, it can generalize the standard layer-connected network into a continuous form, and the state update process between layers can be written as

[0087]

[0088] where h t is the hidden state of the t-th layer, is the repeated structure in the residual network, and θ t is the network parameter of the t-th layer.

[0089] Equation (9) can also be written as

[0090]

[0091] where l represents the step size, which is equal to 1 in the residual network. When l→0, the update process of the state h becomes

[0092]

[0093] i.e. the continuous form of the residual network. In equation (11), the deep residual network becomes a dynamic process driven by the ordinary differential equation.

[0094] Inspired by the deep residual network driven by the ordinary differential equation, the potential field differential equation of equation (7) is written as

[0095]

[0096] where Φ represents all trainable parameters, and the function is the neural network in equation (7). According to equation (7), the function is taken as a residual graph convolutional network, and the repeated neural network layer therein is

[0097]

[0098] where Δ is the Laplacian of the difference between the state z i of the neighbor of the calculation node i. This is equivalent to using α as the convolution kernel to aggregate the node states within a certain receptive field. The result of the convolution is weighted and summed by the weight φ i .

[0099] In this embodiment, it can be seen from the spatial perspective that if t is taken as a discrete variable, equation (13) is equivalent to a residual graph convolutional network, and the input of each layer is the state z (t) of all nodes in the road network. From the time perspective, the time t is a continuous variable, which means that any corresponding state z (t)Therefore, the network model provided by the application is a space-time differential equation network.

[0100] In one embodiment, the potential field sequence can be calculated by a given initial state by a neuron ordinary differential equation solver (ODE solver) that predicts the potential field sequence is:

[0101]

[0102] where is sampled from a distribution , which is a conditional probability distribution calculated according to a historical traffic flow sequence.

[0103] In this embodiment, the mean and variance corresponding to the sampling process from the distribution are obtained from a historical traffic flow sequence , specifically, are sampled from a Gaussian distribution, and the mean and variance corresponding thereto are obtained from .

[0104]

[0105] GRU is used as an encoder to extract information from , and g(·) is a fully connected network that converts the final hidden state into the mean and variance of T represents the length of the historical traffic flow sequence, which can be understood as predicting the future H time data using the past T time data.

[0106] In order to obtain a differentiable sampling process, the reparameterization method is used to calculate the of each node according to the following formula

[0107]

[0108] where, ∈ i is sampled from a standard normal distribution. In this way, for a given batch of training data, is fixed, so formula (16) can be trained by backpropagation through time. In the prediction process, ∈ i is sampled for each input respectively. Given the initial , the entire potential field sequence in the future can be calculated.

[0109] In one embodiment, the framework is trained by a backward iterative algorithm, targeting at minimizing the log-likelihood of the traffic flow sequence. The only difference from the standard neural network is that the forward iteration of the differential equation network needs to be calculated by the differential equation calculator in equation (14).

[0110] The embodiments of the present application are described below in conjunction with specific data:

[0111] The dataset collected by the transportation committee of City A is adopted to evaluate the performance of our model, which includes the trajectory data of about 40000 taxis in City A from April 1, 2015 to June 31, 2015. First, the trajectories are mapped onto the real road network by the road network matching algorithm. The traffic flow of each road in each time slice is calculated, so there are 288 data points in a day.

[0112] Due to the complexity of the road network in City A, three regions of City A are selected to construct the dataset. The first one is around the Workers' Stadium, including 221 road segments; the second one is around the West Railway Station, including 393 road segments; and the third one is around Zhongguancun, including 564 road segments. The three datasets are named GT-221, WRS-393 and ZGC-564 respectively, and then the three datasets are divided into training set, validation set and test set according to the ratio of 7:1:2. For multi-step prediction, the historical one hour (12 time slices) data is used to predict the future one hour.

[0113] Three categories of ten baseline models are adopted for comparison. The first category is the time series model, including the historical average method (HA), vector autoregression (VAR) and GRU model. This method regards the historical traffic flow sequence as a pure time series to model, without considering the spatial dependence. The second category is the graph-based spatio-temporal method, which compares with traditional graph-based traffic prediction methods such as DCRNN, STGCN, GWNET, AGCRN and MTGNN. The third category is the neural differential equation-based network, which uses two traditional models: Latent-ODE and ODE-LSTM. Latent-ODE uses ordinary differential equations to generalize RNN to continuous time variation, and ODE-LSTM is a new type of long short-term memory network.

[0114] The setting of STDEN includes two aspects. The first one is the differential equation network part, which uses an adaptive method dopri5 to model the potential energy change of the hidden space, and then searches the dimension of the hidden space on the set {1, 2, 4, 8}. The second one is the encoder part, which uses GRU to encode the distribution of the initial value of the potential field sequence, and searches the dimension of the hidden layer of GRU on the set {16, 32, 64, 128}.

[0115] Table 3

[0116]

[0117] Table 3 shows the prediction results of different methods on three datasets in three dimensions: 15 minutes, 30 minutes, and 1 hour. In this example, three different evaluation functions are used: the minimum absolute difference (MAE), the minimum mean square error (RMSE), and the minimum absolute percentage difference (MAPE).

[0118] From Table 3, four points can be observed. The first is that the model based on graph neural networks outperforms the pure time series model, which demonstrates the importance of spatial information. The second point is that the performance of STDEN is also improved compared to the spatio-temporal model. Compared to the second best model, the performance of the model of the present invention is the best in all dimensions, with a performance improvement of 10.29%, 13.49%, and 6.03% in MAE, RMSE, and MAPE, respectively, which demonstrates the importance of the potential field differential equation. The third point is that due to the neglect of the importance of spatial information, the performance of pure neural differential equations is weaker than that of spatio-temporal models, but their performance is better than that of traditional time series models. The fourth point is that traditional models such as HA and VAR do not perform well because it is difficult for them to capture complex non-linear spatio-temporal data. And because HA does not rely on short-term data, its results remain unchanged in each dimension.

[0119] To better illustrate the importance of the potential field differential equation in formula (7), STDEN and its two variants are compared. The first variant replaces the potential field differential equation with a fully connected network, i.e., removes the physical knowledge (UnkP) in the network. In the second variant, the parameter φ in the potential field differential equation is removed, and the physical knowledge is incomplete (IncP).

[0120] Figure 3 The results of the comparison of the two variants in different evaluation methods on different datasets are shown. From the graph, it can be observed that the effect of STDEN is much better than that of UnkP, which demonstrates the important role of the potential field in traffic flow prediction. And the performance of IncP also leads UnkP, which shows the effectiveness of the potential field differential equation. The potential field differential equation shows the diffusion of energy in space, so that IncP can capture the trend of the potential field. However, the performance of IncP is slightly lower than that of STDEN, which is due to the lack of the energy volume parameter φ in IncP. At this time, IncP can only infer the potential energy through the energy density, similar to calculating the physical mass only through the physical density.

[0121] In the training process of the differential equation network, a differential equation calculator is used to achieve a dynamic balance between prediction accuracy and computational complexity. For example,Figure 4 -a, 4-b, 4-c show that with the increase of training rounds, the required function verification times (NFE) also increase synchronously, and due to the early end strategy, there is no stable stage. And with the different task difficulty, the required NFE is also different. For example, the GT-221 dataset is more difficult to predict due to its more intense traffic flow changes, so the NFE required by the GT-221 dataset is about 80% more than that of the ZGC-564. From Figure 4 -d, 4-e, 4-f can be seen that the more NFE, the smaller the prediction error, which makes the application more from the production environment to cope with emergency situations.

[0122] Next, the potential learned by the application and the predicted traffic flow will be shown to analyze the better performance of the network model of the application. Figure 5 Two kinds of model learned potential are shown, Figure 5 -a and Figure 5 -c shows the STDEN and UnkP learned potential in the form of a heat map, and the arrow shows the real traffic flow at that time. In order to make the potential clearer, how the flow is driven, this example selects a roundabout area for detailed analysis. In Figure 5 -b, the traffic flow is always from the point with high potential to the point with low potential, and the gradient of the potential also reflects the size of the corresponding traffic flow. This shows that the potential driven by the physical equation can capture the inherent of the traffic flow and can be explained as a factor driving the flow. However, without the guidance of the physical equation, Figure 5 -d neural network learned energy does not have physical meaning, and cannot meet the prediction data accuracy requirement.

[0123] The above experimental data fully show that the physical guided deep learning model proposed by the application can bridge the gap between data driven models and physical driven models, and the model can have the performance advantages of data driven models and the explainability of physical models.

[0124] The above provides a detailed introduction to the spatial-temporal differential equation network for urban flow prediction provided by the application, and the principles and implementation modes of the application are described by applying specific examples in this paper. The above example is only used to help understand the method of the application and its core idea; at the same time, for those skilled in the art, according to the idea of the application, the specific implementation mode and application range will be changed, and the above description should not be understood as a limitation of the application.

[0125] The foregoing description of the disclosed embodiments enables a person skilled in the art to make or use the application. Modifications of these embodiments will occur to persons of skill in the art, and that the appended claims are intended to cover all such modifications that do not depart from the true spirit and scope of the application. Therefore, the application is not limited to the embodiments shown but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A spatio-temporal differential equation network for urban traffic prediction, characterized in that, Comprise: The deep learning model and the physical dynamic process integrated in one framework, the trajectory data is mapped to the real road network through the road network matching algorithm, the calculated traffic of each road in the unit time slice is taken as the input of the deep learning model and the physical dynamic process, and the city traffic is predicted; wherein, The physical dynamic process: a traffic potential field sequence evolution dynamic equation of road network nodes is constructed based on energy transfer differential equation; The deep learning model: comprising an encoder, a space-time differential equation network and a decoder; the encoder is configured to encode the historical traffic flow sequence into an initial state of a traffic potential field The spatiotemporal differential equation network introduces a traffic potential energy field sequence evolution dynamic equation into a residual graph convolutional network, in combination with the initial state Predicting the potential energy field sequence via a neuron ordinary differential equation calculator t0 is an initial time, and H is a future time to be predicted. The traffic potential field sequence evolution dynamic equation is: wherein, is the traffic potential field of the whole road network, is the traffic potential of the road network node i, and a is a shared parameter, φ i is the training parameter, is the Hadamard product, and Δ is the Laplacian operator that calculates the difference between the state z i of the node i and its neighbors. The space-time differential equation network is: where the function is a residual graph convolutional network, where the repeated neural network layers are Φ represents all trainable parameters, uses a as a convolutional kernel to aggregate node states within a given receptive field, Tanh(·) is an activation function, and the result of the convolution is weighted by φ i weighted sum; The neuron ordinary differential equation calculator predicts a potential energy field sequence Is: wherein, from a distribution wherein the distribution is a conditional probability distribution computed from a historical traffic flow sequence; from a distribution wherein the corresponding mean and variance are obtained from a historical traffic flow sequence ​ Using GRU as the encoder to extract information from g(·) is a fully connected network to transform the final hidden state into the mean and variance The reparameterization method is used to calculate each node's where ∈ i is sampled from the standard normal distribution, and T represents the length of the historical traffic flow sequence. The decoder generates the predicted traffic flow sequence based on the traffic flow-potential energy gradient relationship model from the predicted potential energy field sequence generates a predicted traffic flow sequence.

2. The spatio-temporal differential equation network for urban traffic prediction according to claim 1, wherein, The traffic flow and potential energy gradient relationship model is: where, is the graph gradient operator, the negative sign represents the direction of flow, is the traffic potential field of the whole road network, is the traffic potential of road network node i, and the flow of the whole road network is vector |ε| is the size of the edge set, which is the set of directed edges between two road network nodes.

3. The spatio-temporal differential equation network for urban traffic prediction of claim 1, wherein, Through the backward iteration algorithm, the logarithmic likelihood of the predicted traffic flow sequence is minimized as the target to train the framework.

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