GNN-PINN coupled multi-lane heterogeneous traffic joint modeling method and system

Abstract

The invention discloses a multi-lane heterogeneous traffic joint modeling method and system based on a GNN-PINN coupling architecture. The method comprises the following steps: constructing a space-time dynamic graph coding lane changing rule through a GNN, embedding a traffic flow physical constraint through a PINN, and solving a source item; according to the method, CAV behaviors are described by using improved IDM in the mid-microscopic view, an LWR equation subjected to GNN lane change flow correction is solved by using PINN in the macro view, GNN and PINN closed-loop optimization is realized by combining a double-path back propagation mechanism, and a model is optimized based on a residual loss function fusing physical loss, data driving items and boundary constraints. The system comprises a dynamic graph topology module, a GNN coding module, a PINN solving module and the like, the multi-lane traffic dynamic description precision can be improved, the multi-scale characteristic is considered, real-time simulation is supported, and the system is suitable for heterogeneous traffic modeling.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent transportation, in particular to a multi-lane heterogeneous traffic joint modeling method and system based on GNN-PINN coupling architecture. BACKGROUND

[0002] There are many technical bottlenecks in the field of existing multi-lane heterogeneous traffic modeling: traditional traffic modeling methods are difficult to consider multi-scale characteristics, micro models (such as classic IDM) can describe individual vehicle behavior, but have high computational complexity and are difficult to extend to macro traffic flow analysis; macro models (such as LWR equations) can describe the overall evolution of traffic flow, but cannot accurately reflect multi-lane dynamics due to the neglect of lane changing and other micro interactions.

[0003] At the same time, in the heterogeneous traffic environment (traditional vehicles and intelligent connected vehicles CAV coexist), the V2X communication capability of CAV makes its behavior pattern significantly different from traditional vehicles, and the existing model is not suitable for the intelligent lane changing and following behavior of CAV, and cannot reflect its characteristics of optimizing decision-making through real-time information.

[0004] In addition, multi-lane lane changing behavior has a significant impact on macro traffic flow, but existing models have weak dynamic encoding ability for lane changing rules, and lack coupling mechanisms for the relationship between lane changing flow and macro flow density, resulting in limited fitting accuracy of macro models to actual traffic. In addition, physical models and data-driven models are fragmented: pure physical models rely on strict assumptions and have poor generalization; pure data-driven models easily ignore traffic flow conservation and other physical constraints, resulting in prediction results that do not conform to actual laws. At the same time, existing systems lack real-time performance in large-scale multi-lane scenarios, and the simulation step length cannot meet the engineering needs of traffic control, real-time decision-making, etc., restricting the practical application value of the model. SUMMARY

[0005] The purpose of the present application is to provide a GNN-PINN coupled multi-lane heterogeneous traffic joint modeling method and system to solve the problems in the background art.

[0006] The present application is achieved by the following technical solutions: A GNN-PINN coupled multi-lane heterogeneous traffic joint modeling method, comprising the following steps: S1. Dynamic graph construction and lane changing rule encoding: a dynamic graph topology module is used to detect multi-lane vehicle clusters in real time based on a DBSCAN clustering algorithm, generate node connection relationships of the graph structure, and use a graph neural network to construct a spatiotemporal dynamic graph as: , where the nodes represent lane traffic state vectors, the lane distance and lane changing conflict probability are used to dynamically generate an edge weight matrix, and a graph attention network is used to learn the lane changing rule to obtain the predicted lane changing flow; S2. Physical constraint embedding and source term solving: embedding the traffic flow conservation equation constraint with the physical information neural network, solving the residual of the conservation equation through automatic differentiation technology, and constructing the residual loss function; S3. Multi-scale traffic modeling: using the improved intelligent driver model (IDM) to describe the intelligent and connected vehicle (CAV) behavior at the mesoscopic and microscopic level; and implicitly solving the LWR equation at the macroscopic level through the physical information neural network, and the flow-density relationship of the LWR equation is dynamically corrected by the lane-changing flow predicted by the graph neural network; S4. Closed-loop collaborative optimization: constructing a double-back propagation mechanism: inputting the lane-changing flow of the graph neural network as the source term boundary condition of the physical information neural network; at the same time, feeding back the velocity gradient ∂u / ∂x calculated by the physical information neural network to the edge weight update module of the graph neural network, and dynamically adjusting the edge weight matrix; through iterative optimization, the collaborative training of the graph neural network and the physical information neural network is realized; S5. Model optimization: optimizing the physical information neural network based on the residual loss function.

[0007] Further, the construction of the space-time dynamic graph in S1 is , wherein: The node represents the traffic state vector of lane i, and the node feature includes the CAV penetration rate and the average speed. The edge weight matrix is dynamically generated by the lane distance and the lane-changing conflict probability . The lane-changing rule is learned by the graph attention network , wherein: represents the probability weight of changing from lane i to lane j; represents the lane-changing decision function learned by the graph neural network; represents the average speed of lane i and lane j; represents the distance between lane i and lane j.

[0008] Further, the CAV acceleration calculation formula of the improved IDM model in S3 is , wherein: represents the maximum acceleration capability of the vehicle under ideal conditions, u is the actual driving speed of the vehicle, is the ideal cruise speed that the CAV expects to achieve, is the expected distance, represents the actual distance between the current vehicle and the preceding vehicle, which is optimized in real time by V2X communication.

[0009] Further, the dynamic correction of the flow-density relationship in S3 refers to: The lane-changing flow predicted by the graph neural network is input as a correction parameter into the LWR equation, so that the macroscopic traffic flow model can respond to the influence of lane-changing behavior on the overall flow in real time.

[0010] Further, in the closed-loop optimization process of the double-back propagation mechanism in S4: The lane-changing flow, traffic state vector and edge weight matrix output by the graph neural network are input as boundary conditions into the physical information neural network; The speed gradient calculated by the physical information neural network is fed back to the edge weight update module of the GNN to dynamically adjust the edge weight matrix; Through iterative optimization, the collaborative training of the graph neural network and the physical information neural network is realized.

[0011] Further, the expression of the residual loss function in S5 is , wherein: is the physical differential equation loss, and the data-driven term is the boundary constraint term fused with NGSIM trajectory data is the flow continuity of the forced ramp area, and the weights of each part are balanced through hyperparameters α, β and γ.

[0012] Further, a GNN-PINN coupled multi-lane heterogeneous traffic joint modeling system comprises: Dynamic graph topology module: based on the DBSCAN clustering algorithm, real-time detection of multi-lane vehicle clusters is performed to generate node connection relationships of the graph structure, which is output to the GNN encoding module; GNN encoding module: receiving the output of the dynamic graph topology module, constructing a spatio-temporal dynamic graph, learning lane-changing rules between lanes through a graph attention network, and outputting lane-changing flow to the PINN solving module and the hybrid solver module; PINN solving module: embedding traffic flow conservation equation constraints, receiving the lane-changing flow, traffic state vector and edge weight matrix output by the GNN encoding module as source term boundary conditions, solving the source term of the conservation equation through automatic differentiation technology and constructing a residual loss, outputting the speed gradient ∂u / ∂x to the hybrid solver module, and outputting the modified macroscopic LWR equation solving result to the heterogeneous traffic modeling module; Heterogeneous traffic modeling module: calling the improved IDM model to describe the micro-behavior of CAV, receiving the macroscopic LWR equation result output by the PINN solving module, and realizing multi-scale traffic joint modeling; Hybrid solver module: receiving the output of the GNN encoding module and the speed gradient ∂u / ∂x of the PINN solving module, realizing double-back propagation closed-loop optimization of the GNN and the PINN, and dynamically adjusting the edge weight matrix of the GNN; The physical constraint module: the GPU acceleration calculation is realized by using the JAX framework, supports real-time simulation step of ≤0.1s, and outputs real-time results of multi-lane heterogeneous traffic modeling.

[0013] The present application has the beneficial effects of: 1. Realize the deep collaborative optimization of GNN and PINN, and significantly improve the accuracy of the model in describing the multi-lane traffic dynamics. By constructing a double-way back propagation mechanism, the lane changing flow, traffic state vector and edge weight matrix output by GNN are used as the source term boundary condition of PINN, which provides accurate input for the solution of macroscopic traffic flow physical constraints; at the same time, the speed gradient calculated by PINN is fed back to the edge weight update module of GNN, and the edge weight matrix is dynamically adjusted to adapt to the real-time traffic changes. This closed-loop iteration process links the learning of lane changing rules by GNN and the solution of physical laws such as LWR equation by PINN, effectively reduces the error accumulation when a single model is trained independently, and makes the model not only accurately capture the dynamic characteristics of lane changing behavior between lanes, but also accurately reflect the evolution law of macroscopic traffic flow, greatly improving the fitting accuracy of the whole dynamics of multi-lane heterogeneous traffic system.

[0014] 2. Fusion of multi-scale modeling advantages, taking into account the accurate description of mesoscopic vehicle behavior and macroscopic traffic flow characteristics. At the mesoscopic level, the improved IDM model optimizes the expected distance in real time through V2X communication, accurately describes the following, acceleration and deceleration behaviors of intelligent and connected vehicles (CAV), and fully reflects the intelligent decision-making characteristics of CAV under information interaction; at the macro level, the LWR equation corrected by GNN lane changing flow is implicitly solved by PINN, so that the flow-density relationship of macroscopic traffic flow can respond to the lane changing behavior between lanes in real time. This multi-scale coupling design breaks through the limitations of single-scale models - it not only avoids the shortcomings of micro-models in describing macroscopic traffic flow evolution, but also solves the defects of traditional macro-models in ignoring individual vehicle dynamic interaction, realizes the coherent description from individual vehicle behavior to overall traffic flow characteristics, and is more in line with the complex nature of multi-lane heterogeneous traffic system.

[0015] 3. The design of the residual loss function and system architecture ensures the reliability and engineering practicality of the model. The residual loss function integrates physical differential equation loss (ensuring compliance with traffic flow conservation laws), data-driven terms (integrating NGSIM trajectory data to improve experimental fitting ability), and boundary constraint terms (forcing traffic flow continuity in ramp areas). By balancing the weights of each component through hyperparameters, it effectively avoids biases caused by excessive reliance on data or physical assumptions, thus improving generalization ability in complex scenarios. Simultaneously, the system uses DBSCAN clustering in the dynamic graph topology module to generate vehicle cluster node relationships in real time, ensuring real-time matching between input data and traffic conditions. The physical constraint module utilizes the JAX framework for GPU acceleration, supporting real-time simulation step sizes of ≤0.1s. This ensures both the timeliness of model input and meets the real-time requirements of traffic management, simulation, and other engineering applications, achieving a good balance between theoretical reliability and practical application value. Attached Figure Description

[0016] Figure 1 This is a logical schematic diagram of the present invention. Detailed Implementation

[0017] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0018] See the example. Figure 1 : A joint modeling method for multi-lane heterogeneous traffic coupled with GNN-PINN includes the following steps: S1. Dynamic Graph Construction and Lane Changing Rule Encoding: A dynamic graph topology module is used to detect multi-lane vehicle clusters in real time based on the DBSCAN clustering algorithm, generating node connections in a graph structure; a spatiotemporal dynamic graph is constructed using a graph neural network as follows: The system uses nodes to represent lane traffic state vectors (including CAV penetration rate and average speed), dynamically generates edge weight matrices based on lane spacing and lane change conflict probability, and then learns lane change rules through a graph attention network to obtain the predicted lane change flow. S2. Physical constraint embedding and source term solution: The physical information neural network is used to embed the traffic flow conservation equation constraints, and the residuals in the conservation equation are solved by automatic differentiation technology, and the residual loss function is constructed. S3. Multi-scale traffic modeling: At the micro to meso level, an improved intelligent driver model is used to describe the behavior of intelligent connected vehicles; at the macro level, the LWR equation is implicitly solved through a physical information neural network, and the flow density relationship of the LWR equation is dynamically corrected by the lane-changing flow predicted by the graph neural network. S4. Closed-loop collaborative optimization: Construct a double back propagation mechanism: take the lane-changing flow of the graph neural network as the source term boundary condition input of the physical information neural network; at the same time, feedback the velocity gradient calculated by the physical information neural network to the edge weight update module of the graph neural network, dynamically adjust the edge weight matrix; through iterative optimization, realize the collaborative training of the graph neural network and the physical information neural network; S5. Model optimization: optimize the physical information neural network based on the residual loss function.

[0019] Further, the construction of the space-time dynamic graph in S1 is , wherein: The node characterizes the traffic state vector of lane i, and the node feature includes CAV penetration rate and average speed; The edge weight matrix is dynamically generated by lane distance and lane-changing conflict probability ; The lane-changing rule is learned by the graph attention network , wherein: represents the probability weight of changing from lane i to lane j; represents the lane-changing decision function learned by the graph neural network; represents the average speed of lane i and lane j; represents the distance between lane i and lane j.

[0020] By representing the key traffic state of the lane through the node, dynamically reflecting the lane distance and lane-changing conflict probability through the edge weight matrix, and learning the lane-changing rule through GAT, the dynamic characteristics of lane-changing behavior between multiple lanes can be accurately captured. This design allows the model to adapt to changes in traffic flow in real time, improves the accuracy of lane-changing rule coding, and lays a reliable graph structure foundation for the coupling of subsequent macro and mesoscopic models.

[0021] Further, the CAV acceleration calculation formula of the improved IDM model in S3 is , wherein: represents the maximum acceleration ability of the vehicle under ideal conditions, is the actual driving speed of the vehicle, is the ideal cruise speed expected to be reached by the CAV, is the expected distance, which is optimized in real time by V2X communication, represents the actual distance between the current vehicle and the preceding vehicle.

[0022] In the improved CAV acceleration calculation formula of the IDM model, the parameters cover the ideal maximum acceleration of the vehicle, the actual driving speed, the expected cruising speed, the expected distance optimized in real time through V2X communication, and the actual distance between the current vehicle and the front vehicle. Through real-time optimization of the expected distance through V2X communication, the acceleration calculation of the CAV is more in line with the vehicle interaction characteristics in the intelligent network environment, and can more accurately describe the micro behavior of the CAV in the following scene. Further, the dynamic correction of the traffic density relationship in S3 refers to: The lane-changing flow predicted by the GNN is input as a correction parameter into the LWR equation to adjust the traffic density relationship of the macroscopic traffic flow in real time.

[0023] Since the lane-changing behavior in a multi-lane environment can significantly affect the macroscopic traffic flow characteristics, by introducing the lane-changing flow as a dynamic parameter, the LWR equation can more accurately reflect the change rule of the macroscopic traffic flow in a multi-lane scene, and enhance the adaptability of the macroscopic model to the actual traffic.

[0024] Further, the closed-loop optimization process of the double-back propagation mechanism in S4 includes: The lane-changing flow output by the GNN is input as a source term into the physical information neural network; The velocity gradient calculated by the physical information neural network is fed back to the edge weight update module of the GNN to dynamically adjust the edge weight matrix; Through iterative optimization, the GNN and the physical information neural network are trained cooperatively.

[0025] The lane-changing flow output by the GNN is input as a boundary condition into the physical information neural network, and the velocity gradient calculated by the physical information neural network is fed back to the edge weight update module of the GNN to dynamically adjust the edge weight matrix. Through iterative optimization, the GNN and the physical information neural network are trained cooperatively, so that the learning of the lane-changing rules by the GNN and the solving of the physical equation by the physical information neural network are linked, and the two are calibrated with each other in the training process, improving the consistency and accuracy of the entire model.

[0026] Further, the expression of the residual loss function in S5 is , wherein: is the physical differential equation loss, the data-driven term is the boundary constraint term fused with the NGSIM trajectory data is the traffic continuity of the forced ramp area, and a, b, are weight hyperparameters.

[0027] The residual loss function f combines a physical differential equation loss, a data-driven term (fusing NGSIM trajectory data), and a boundary constraint term (forcing the flow continuity in ramp regions), and adjusts the weights of each part through hyperparameters a, b, The physical differential equation loss ensures that the model conforms to the physical laws of traffic flow, the data-driven term improves the fitting ability of the model using measured trajectory data, and the boundary constraint term guarantees the flow continuity in key regions such as ramps. The combination of the three makes the model balanced between theoretical rationality and actual adaptability. By adjusting the weights of each part through hyperparameters, the risk of overfitting can be reduced, and the reliability and generalization ability in complex traffic scenarios can be improved.

[0028] Further, a GNN-PINN coupled multi-lane heterogeneous traffic joint modeling system includes: A dynamic graph topology module: based on the DBSCAN clustering algorithm, real-time detection of multi-lane vehicle clusters is performed, the node connection relationship of the graph structure is generated, and the output is output to the GNN encoding module; A GNN encoding module: receiving the output of the dynamic graph topology module, constructing a spatio-temporal dynamic graph, learning lane changing rules through a graph attention network, and outputting lane changing flow, traffic state vectors, and edge weight matrices to the PINN solving module and the hybrid solver module; A PINN solving module: embedding traffic flow conservation equation constraints, receiving lane changing flow, traffic state vectors, and edge weight matrices output by the GNN encoding module as source boundary conditions, solving the source term of the conservation equation through automatic differentiation technology and constructing a residual loss, and outputting the velocity gradient ∂u / ∂x to the hybrid solver module, while outputting the macroscopic LWR equation solving results to the heterogeneous traffic modeling module after modification; A heterogeneous traffic modeling module: calling the improved IDM model to describe the micro-behavior of CAV, receiving the macroscopic LWR equation results output by the PINN solving module, and realizing multi-scale traffic joint modeling; A hybrid solver module: receiving the output of the GNN encoding module and the velocity gradient ∂u / ∂x of the PINN solving module, realizing two-way backpropagation closed-loop optimization of GNN and PINN, and dynamically adjusting the edge weight matrix of GNN; A physical constraint module: using the JAX framework to realize GPU accelerated calculation, supporting real-time simulation step length less than or equal to 0.1s, and outputting real-time results of multi-lane heterogeneous traffic modeling.

[0029] The DBSCAN algorithm can effectively identify the clustering state of vehicles in traffic flow, and the division of vehicle clusters can accurately reflect the local dynamic characteristics of traffic flow. Mapping the relationship between clusters to node connection relationships provides a graph structure input for GNN that conforms to actual traffic distribution and allows the model to adapt to changes in traffic flow in real time, providing a reliable foundation for lane changing rule learning.

[0030] It can be understood that the above embodiments are only exemplary embodiments adopted for illustrating the principles of the present application / invention, and the present application / invention is not limited thereto. Various modifications and improvements can be made by those of ordinary skill in the art without departing from the spirit and essence of the present application / invention, and these modifications and improvements are also considered to be within the scope of protection of the present application / invention.

Claims

1. A GNN-PINN coupled multi-lane heterogeneous traffic joint modeling method, characterized in that, Comprising the following steps: S1. Dynamic graph construction and lane-changing rule coding: Through the dynamic graph topology module, the multi-lane vehicle cluster is detected in real time based on the DBSCAN clustering algorithm to generate the node connection relationship of the graph structure; the spatiotemporal dynamic graph is constructed by using the graph neural network, which is: The node represents the lane traffic state vector, the edge weight matrix is dynamically generated according to the lane distance and the lane-changing conflict probability, and the lane-changing rule is learned through the graph attention network to obtain the predicted lane-changing flow; S2. Physical constraint embedding and source term solving: embedding the traffic flow conservation equation constraint with the physical information neural network, solving the residual of the conservation equation through automatic differentiation technology, and constructing the residual loss function; S3. Multi-scale traffic modeling: using an improved intelligent driver model to describe the intelligent and connected vehicle behavior at the mesoscopic and microscopic levels; and implicitly solving the LWR equation through the physical information neural network at the macroscopic level, and dynamically correcting the flow-density relationship of the LWR equation by the lane-changing flow predicted by the graph neural network; S4. Closed-loop collaborative optimization: constructing a double-backpropagation mechanism: inputting the lane-changing flow of the graph neural network as the source term boundary condition of the physical information neural network; at the same time, feeding back the velocity gradient ∂u / ∂x calculated by the physical information neural network to the edge weight update module of the graph neural network to dynamically adjust the edge weight matrix; and achieving collaborative training of the graph neural network and the physical information neural network through iterative optimization; S5. Model optimization: optimizing the physical information neural network based on the residual loss function.

2. The GNN-PINN coupled multi-lane heterogeneous traffic joint modeling method according to claim 1, characterized in that, The constructed spatiotemporal dynamic graph in S1 is wherein: with node characterizing the traffic state vector of lane i, the node features include intelligent connected vehicle penetration rate and average speed; The edge weight matrix is dynamically generated based on the lane distance and the lane-changing conflict probability. The lane changing rule is learned by a graph attention network, wherein: represents a probability weight of changing from lane i to lane j; represents a lane changing decision function learned by a graph neural network; represents an average vehicle speed of lane i and lane j; represents a distance between lane i and lane j.

3. The GNN-PINN coupled multi-lane heterogeneous traffic joint modeling method according to claim 1, wherein, The intelligent networked vehicle acceleration calculation formula of the improved intelligent driver model in S3 is wherein: represents the maximum acceleration capability of the vehicle under ideal conditions, u is the actual driving speed of the vehicle, is the ideal cruise speed expected to be reached by the intelligent connected vehicle, is the expected distance, represents the actual distance between the current vehicle and the preceding vehicle, which is optimized in real time by V2X communication.

4. The GNN-PINN coupled multi-lane heterogeneous traffic joint modeling method according to claim 1, wherein, The dynamic correction of the flow-density relationship in S3 refers to: Inputting the lane-changing flow predicted by the graph neural network as a correction parameter into the LWR equation, so that the macroscopic traffic flow model can respond in real time to the influence of lane-changing behavior on the overall flow.

5. The GNN-PINN coupled multi-lane heterogeneous traffic joint modeling method according to claim 1, wherein, In the closed-loop optimization process of the double-backpropagation mechanism in S4: The lane-changing flow output by the graph neural network is input as a boundary condition into the physical information neural network; The speed gradient of the physical information neural network calculation is fed back to an edge weight updating module of the GNN to dynamically adjust the edge weight matrix ; Through iterative optimization, collaborative training of the graph neural network and the physical information neural network is achieved.

6. The GNN-PINN coupled multi-lane heterogeneous traffic joint modeling method according to claim 1, wherein, The expression of the residual loss function in S5 is wherein: is the physical differential equation loss, data-driven term is the fusion NGSIM trajectory data, boundary constraint term is the traffic continuity of forced ramp area, and the weights of each part are balanced by hyperparameters a, b, g.

7. A GNN-PINN coupled multi-lane heterogeneous traffic joint modeling system, characterized in that, It includes: Dynamic graph topology module: based on the DBSCAN clustering algorithm, real-time detection of multi-lane vehicle clusters is performed to generate node connection relationships of the graph structure, which is output to the GNN encoding module; GNN encoding module: receiving the output of the dynamic graph topology module, constructing a spatiotemporal dynamic graph, learning lane-changing rules between lanes through a graph attention network, and outputting lane-changing flow to the PINN solving module and the hybrid solver module; PINN solving module: embedding the traffic flow conservation equation constraint, receiving the lane-changing flow, traffic state vector, and edge weight matrix output by the GNN encoding module as source term boundary conditions, solving the conservation equation residual through automatic differentiation technology, and constructing a residual loss, outputting the velocity gradient ∂u / ∂x to the hybrid solver module, and outputting the corrected macroscopic LWR equation solution to the heterogeneous traffic modeling module; Heterogeneous traffic modeling module: calling the improved IDM model to describe the mesoscopic behavior of intelligent and connected vehicles, receiving the macroscopic LWR equation result output by the PINN solving module, and achieving multi-scale traffic joint modeling; Hybrid solver module: receiving the output of the GNN encoding module and the velocity gradient ∂u / ∂x of the PINN solving module, achieving double-backpropagation closed-loop optimization of GNN and PINN, and dynamically adjusting the edge weight matrix of GNN; Physical constraint module: using the JAX framework to realize GPU acceleration calculation, supporting real-time simulation step length ≤0.1s, and outputting real-time results of multi-lane heterogeneous traffic modeling.

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