A method and system for modeling swarm intelligence emergence based on physical information neural networks

Abstract

This invention provides a method and system for swarm intelligence emergence modeling based on physical information neural networks, belonging to the fields of computer science and robotics. Firstly, by embedding partial differential equations as hard constraints into the neural network training process, this invention ensures that the model output strictly conforms to physical laws, avoiding policy behaviors that violate physical common sense, thus fundamentally improving the interpretability and engineering reliability of the system. Secondly, physical modeling provides prior information on system evolution, effectively reducing the dependence on large-scale training data, making it particularly suitable for practical application scenarios where data acquisition is difficult or the environment is complex, and enabling efficient training under limited sample conditions. Finally, the optimization process is guided by physical constraints, significantly reducing ineffective exploration and fluctuations during training, enabling the model to quickly converge to a high-quality policy solution, improving overall training efficiency and task achievement speed.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computer science and robotics, and particularly relates to a swarm intelligence emergence modeling method and system based on a physical information neural network. BACKGROUND

[0002] Swarm robot system, as an important representative of multi-agent system, is widely used in disaster rescue, regional monitoring, target search, collaborative transportation and other scenarios. Such systems rely on the local perception and collaborative decision-making ability between multiple individuals, thus forming efficient emergent behavior to complete complex global tasks.

[0003] In order to realize effective training and control of group behavior, it is usually necessary to accurately model the dynamic interaction between individuals and the environment in current research. Partial differential equations (PDEs) as a mathematical tool for describing local interaction rules in continuous space are widely used to model typical behaviors such as aggregation, dispersion, formation, obstacle avoidance, random walk, etc. in swarm robots. By introducing parameter constraints related to control, partial differential equations can effectively describe the physical limitations and evolution process of group behavior, providing explicit structural prior for training.

[0004] At the same time, deep reinforcement learning (DRL) as a rapidly developing intelligent control method in recent years has shown significant potential in multi-agent behavior learning. The basic idea is to extract environmental state features through deep neural networks, and combine them with reward mechanisms in reinforcement learning to guide each robot to continuously optimize its strategy according to task requirements, thus making appropriate behavior decisions in different environmental and task contexts.

[0005] However, existing methods usually separate the modeling of partial differential equations and the training of deep learning, making it difficult to directly embed physical prior constraints during neural network training, resulting in slow strategy convergence speed, insufficient physical consistency, poor behavior transfer ability and other problems. Especially in the context of complex environment and frequent task changes, traditional methods are difficult to guarantee the explainability and stability of learned behavior. SUMMARY

[0006] To address the problems in the existing technologies, this invention provides a method and system for modeling swarm intelligence emergence based on physical information neural networks. First, this invention utilizes partial differential equations to express the physical constraints of swarm intelligence robot behavior, establishing a physical constraint model of swarm behavior. This enables reinforcement learning to possess structured priors, significantly improving training sample efficiency and policy generalization ability. Second, it integrates the physical constraint model of swarm behavior with deep neural networks, overcoming the lack of physical interpretation and constraint control in traditional black-box reinforcement learning, and accelerating the policy convergence process. Finally, it completes the swarm behavior training model in a virtual simulation environment and then completes the swarm intelligence model training on an actual simulation platform, reducing training costs and improving the feasibility of system deployment, demonstrating good behavioral accuracy, environmental adaptability, and task completion ability. To achieve the above objectives, the technical solution is as follows:

[0007] On the one hand, this invention provides a method for modeling swarm intelligence emergence based on physical information neural networks, the method comprising:

[0008] S1. Based on the dynamic evolution process of the swarm robot system, a physical constraint model of the swarm behavior is established through partial differential equations.

[0009] S2. Based on the physical constraint model of the group behavior, a group behavior training model is obtained by training a single environment through a physical information neural network.

[0010] S3. Based on the group behavior training model, train it through an interactive environment to obtain the group intelligence model.

[0011] Optionally, the physical constraint model for the group behavior includes: a composite density field model;

[0012] The composite density field model consists of the target guiding potential field, the sensor detection potential field, the group cooperation potential field, and the task-related constraint potential field.

[0013] Optionally, the target guides the potential field, including:

[0014]

[0015] In the formula: ρ target β represents the target guiding potential field. t dx represents the target field attenuation coefficient, dy represents the difference in horizontal coordinates between the swarm robot and the target position, and dy represents the difference in vertical coordinates between the swarm robot and the target position.

[0016] Optionally, the sensor detects a potential field, including:

[0017]

[0018] In the formula: ρ sensor α represents the potential field detected by the sensor.s β represents the sensor field intensity coefficient, ∈ represents the zero constant, d represents the distance from the sensor to the obstacle, and β represents the distance from the sensor to the obstacle. s θ represents the angle sensitivity coefficient, and θ represents the deviation angle between the target direction and the current orientation of the swarm robot.

[0019] Optionally, the group's cooperative potential field includes:

[0020]

[0021] In the formula: ρ group The d represents the collaborative potential field of the group, N represents the number of swarm intelligence robots in the system, and d represents the number of swarm intelligence robots in the system. i α represents the Euclidean distance between the current swarm intelligence robot and the i-th swarm intelligence robot. g β represents the intensity coefficient of the density field. g The decay rate coefficient of the density field is represented by r0, and the ideal spacing between the swarm robots is represented by r0.

[0022] Optionally, in S2, based on the physical constraint model of the group behavior, a group behavior training model is obtained by training a physical information neural network in a single environment, including:

[0023] S21. Based on the physical constraint model of the group's behavior, obtain the forward propagation function of the neural network through the physical information neural network;

[0024] S22. Based on the forward propagation function of the neural network, the residual terms of the physical constraint model are obtained through multi-constraint residual calculation.

[0025] S23. Based on the residual terms of the physical constraint model, establish a loss function and obtain the weights of the loss terms by combining the AdamW optimizer with learning rate decay.

[0026] S24. Load the weights of the loss term into the physical information neural network to obtain the group behavior training model.

[0027] Optionally, in S3, based on the group behavior training model, a crowd intelligence model is obtained through training in an interactive environment, including:

[0028] S31. Load the group behavior training model into the swarm intelligence robot to obtain the initially trained swarm intelligence robot;

[0029] S32. Based on the multi-source perception devices of the initially trained swarm intelligence robot, collect data and train it to obtain the model's experience pool.

[0030] S33. Based on the experience pool of the model, obtain a batch of samples and update the policy to obtain the crowd intelligence model.

[0031] On the other hand, the present invention provides a swarm intelligence emergence modeling system based on a physical information neural network, which is applied to a swarm intelligence emergence modeling method based on a physical information neural network. The system includes:

[0032] The physical model building module is used to establish a physical constraint model of the group behavior based on the dynamic evolution process of the swarm robot system through partial differential equations.

[0033] The training model building module is used to train a group behavior training model in a single environment based on the physical constraint model of the group behavior through a physical information neural network.

[0034] The crowd intelligence model building module is used to train a model based on the behavior of the group. The model is trained through an interactive environment to obtain the crowd intelligence model.

[0035] Compared with the prior art, the technical solution of the present invention has at least the following beneficial effects:

[0036] The above-mentioned approach firstly ensures that the model output strictly conforms to physical laws by embedding partial differential equations as hard constraints into the neural network training process, thus avoiding policy behaviors that violate physical common sense and fundamentally improving the interpretability and engineering reliability of the system. Secondly, physical modeling provides prior information on the system's evolution, effectively reducing the dependence on large-scale training data, and is particularly suitable for practical application scenarios where data acquisition is difficult or the environment is complex, enabling efficient training under limited sample conditions. Thirdly, the optimization process is guided by physical constraints, significantly reducing ineffective exploration and fluctuations in the training process, enabling the model to quickly converge to a high-quality policy solution, thereby improving overall training efficiency and task completion speed. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of an embodiment of the crowd intelligence emergence modeling method based on physical information neural networks of the present invention;

[0039] Figure 2 This is a flowchart illustrating the process of obtaining a group behavior training model in an embodiment of the crowd intelligence emergence modeling method based on physical information neural networks of the present invention.

[0040] Figure 3 This is a flowchart illustrating the process of obtaining a swarm intelligence model in an embodiment of the swarm intelligence emergence modeling method based on physical information neural networks of the present invention;

[0041] Figure 4 This is a system block diagram of an embodiment of the crowd intelligence emergence modeling system based on physical information neural networks of the present invention. Detailed Implementation

[0042] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0043] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0044] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0045] like Figure 1 The flowchart shown is an embodiment of the crowd intelligence emergence modeling method based on a physical information neural network of the present invention. The present invention provides a crowd intelligence emergence modeling method based on a physical information neural network, which is implemented by a crowd intelligence emergence modeling system based on a physical information neural network. The method includes:

[0046] S1. Based on the dynamic evolution process of the swarm robot system, a physical constraint model of the swarm behavior is established through partial differential equations.

[0047] Specifically, the physical constraint model of the group behavior includes: a composite density field model;

[0048] The composite density field model consists of the target guiding potential field, the sensor detection potential field, the group cooperation potential field, and the task-related constraint potential field.

[0049] Specifically, the target guides the potential field, including:

[0050]

[0051] In the formula: ρ target β represents the target guiding potential field. t dx represents the target field attenuation coefficient, dy represents the difference in horizontal coordinates between the swarm robot and the target position, and dy represents the difference in vertical coordinates between the swarm robot and the target position.

[0052] Furthermore, corresponding to the gravitational effect at the target point, a Gaussian decay field is used. The closer to the target, the higher the potential field value (the gradient points towards the target). The gradient calculation methods are formulas (4) and (5):

[0053]

[0054] Specifically, the sensor detects the potential field, including:

[0055]

[0056] In the formula: ρ sensor α represents the potential field detected by the sensor. s β represents the sensor field intensity coefficient, ∈ represents the zero constant, d represents the distance from the sensor to the obstacle, and β represents the distance from the sensor to the obstacle. s θ represents the angle sensitivity coefficient, and θ represents the deviation angle between the target direction and the current orientation of the swarm robot.

[0057] Furthermore, it is activated only when an obstacle is detected, taking into account both distance and angle factors; the closer to the obstacle, the higher the potential field value.

[0058] The deviation angle θ between the target direction and the current orientation of the swarm robot is calculated using formulas (6) and (7).

[0059] θ=φ target -ψ(6)

[0060] φ target =atan2(y target -y robot ,x target -x robot (7)

[0061] In the formula: ψ represents the current orientation of the swarm robot, atan2(y,x) represents a mathematical function for calculating the azimuth angle (polar angle), and y target The ordinate of the target point, x target The x-coordinate of the target point, y robot The vertical axis representing the swarm intelligence robot, x robot The horizontal axis represents the collective intelligence robot.

[0062] The gradient calculation methods are Equations (8), (9), and (10):

[0063]

[0064] It should be noted that the negative value in the vertical axis direction is determined by both the directionality of the derivative and the definition of the coordinate system, ensuring that the direction of the repulsive force points to the safe region. This needs to be adjusted accordingly based on the specific task requirements.

[0065] Specifically, the collaborative potential field of this group includes:

[0066]

[0067] In the formula: ρ group The d represents the collaborative potential field of the group, N represents the number of swarm intelligence robots in the system, and d represents the number of swarm intelligence robots in the system. i α represents the Euclidean distance between the current swarm intelligence robot and the i-th swarm intelligence robot. g β represents the intensity coefficient of the density field. g The decay rate coefficient of the density field is represented by r0, and the ideal spacing between the swarm robots is represented by r0.

[0068] Specifically, the task is subject to additional constraints, including handling moving obstacles and preventing swarm robots from venturing out of safe areas.

[0069] The swarm intelligence robot calculates the direction of the resultant force using gradient descent to determine its speed and direction of motion. It also optimizes the parameters based on the weights of each potential field to avoid getting trapped in local minima or oscillations.

[0070] S2. Based on the physical constraint model of the group behavior, a group behavior training model is obtained by training a single environment through a physical information neural network.

[0071] Specifically, such as Figure 2 The flowchart shown in this embodiment of the swarm intelligence emergence modeling method based on physical information neural networks of the present invention obtains a group behavior training model. The training process of this group behavior training model is implemented based on a virtual simulation platform, specifically including: 1. The experimental environment is constructed using simulation platforms such as Ubuntu operating system and Webots, supporting parallel deployment of multiple agents and task simulation; 2. Data interaction relies on the communication mechanism of the ROS2 system, adopting three interaction methods: Topic, Service, and Action, to realize real-time transmission and processing of agent state information, sensor data, and control commands; 3. The four types of physical potential fields (target guidance potential field, sensor detection potential field, group cooperation potential field, and task-related constraint potential field) constructed in the PDE model are embedded in the neural network during training. Each type of potential field corresponds to an independent loss component, and the weight ratio is dynamically adjusted in combination with task progress or environmental feedback to achieve the function that can be dominated by different physical potential fields in different environments. As the network training progresses, the influence weight of the physical potential field on the network will be adjusted accordingly. In S2, based on the physical constraint model of the group behavior, the group behavior training model is obtained by training a single environment through a physical information neural network, including:

[0072] S21. Based on the physical constraint model of the group's behavior, obtain the forward propagation function of the neural network through the physical information neural network;

[0073] Furthermore, the total density field is defined as the superposition of four components:

[0074] ρ tota l(u,t)=ρtarget (u,t)+ρ sensor (u,t)+ρ group (u,t)+ρ ot her(u,t)

[0075] (ρ target ,ρ sensor ,ρ group ,ρ other )=f(u;θ)(11)

[0076] f is the forward propagation function of the neural network, θ is the learnable parameter of the neural network, where u represents the input of the neural network, including the combined form of data from time, spatial coordinates, infrared sensors, distance sensors, and Immu, etc., and ρ other The task-related constraint potential field is represented as follows:

[0077] u(t)=[t,x,y,sensor1(t),sensor2(t),sensor3(t)…sensor n (t)] (12)

[0078] Each component is generated by a separate branch of the neural network:

[0079]

[0080] Where W is the weight matrix in the neural network, z is the shared feature layer, and σ is the tanh activation function.

[0081] z=σ(W shared ·[u,t]) (14)

[0082] S22. Based on the forward propagation function of the neural network, the residual terms of the physical constraint model are obtained through multi-constraint residual calculation.

[0083] Furthermore, the residual terms for the four types of PDE constraints are:

[0084]

[0085] Where v is the velocity field of the agent, and Q is the source term.

[0086] S23. Based on the residual terms of the physical constraint model, establish a loss function and obtain the weights of the loss terms by combining the AdamW optimizer with learning rate decay.

[0087] Furthermore, the loss function is a metric that measures the difference between the neural network output and the actual physical constraints. The loss function consists of two parts: data loss and physical loss (i.e., the residuals of the partial differential equations).

[0088] Data item loss:

[0089]

[0090] in, It is the network prediction value, ρ total (u,t) is the actual value.

[0091] Physical loss:

[0092]

[0093] Combining data item loss and physical loss, the final loss function is:

[0094]

[0095] It is the weight of the physical loss term, which controls the balance between physical constraints and data fitting.

[0096] Initialize network parameters θ, and use the AdamW optimizer combined with learning rate decay:

[0097]

[0098] Where, θ k Let η represent the model parameters at the k-th iteration, η be the initial learning rate, and α be the model parameters at the k-th iteration. k It is the learning rate decay factor, used to implement learning rate scheduling. This is the corrected second-order moment estimate, used for adaptively adjusting the learning rate of the parameters, where ∈ is the parameter to prevent division by zero. It is a loss function The gradient with respect to the parameter θ.

[0099]

[0100] pass Increase the strength of physical constraints in stages.

[0101] S24. Load the weights of the loss term into the physical information neural network to obtain the group behavior training model.

[0102] S3. Based on the group behavior training model, train it through an interactive environment to obtain the group intelligence model.

[0103] Specifically, such as Figure 3 The flowchart shown in this embodiment of the crowd intelligence emergence modeling method based on physical information neural networks of the present invention illustrates the process of obtaining a crowd intelligence model. In step S3, the crowd intelligence model is obtained by training the model based on the group behavior training model through an interactive environment, including:

[0104] S31. Load the group behavior training model into the swarm intelligence robot to obtain the initially trained swarm intelligence robot;

[0105] Furthermore, in order to accurately characterize the behavioral features of swarm robots in multi-task scenarios, it is necessary to establish a swarm behavior training model that covers multiple factors such as kinematics, dynamics, sensor accuracy, environmental disturbances, and system stability.

[0106] After the system starts, it will automatically complete the following operations: initialize the model and network parameter storage path; start the monitoring module to obtain global task data; construct the simulation world (e.g., based on Webots); and automatically generate multiple intelligent agents for subsequent learning tasks.

[0107] S32. Based on the multi-source perception devices of the initially trained swarm intelligence robot, collect data and train it to obtain the model's experience pool.

[0108] Furthermore, the system utilizes the Topic, Service, and Action communication mechanisms in ROS2 to facilitate data interaction between the supervisory module, the agent, and the simulation environment. The agent uses multi-source sensing devices such as infrared sensors, distance sensors, IMUs, gyroscopes, and wheel speedometers to collect data on the task environment's status. The supervisory module is responsible for summarizing and coordinating various data to ensure the stable progress of the training process. The collected data includes, but is not limited to: agent speed, position, sensor output values, and relative distances between agents.

[0109] Each training iteration must complete the following processes: initialize the training data structure and policy parameters; update the RNN state (including the hidden state of each agent and the commentator state); obtain the current action and its probability distribution based on exploration and sampling methods; execute the action and record the environmental feedback, collect the next state and reward; and store the complete data sequence generated in this round into the model's experience pool.

[0110] S33. Based on the experience pool of the model, obtain a batch of samples and update the policy to obtain the crowd intelligence model.

[0111] Furthermore, batch samples are retrieved from the model's experience pool and formatted into data structures supported by the deep learning framework (such as Torch tensors). Policy updates consist of two parts:

[0112] Policy network optimization: The importance sampling weights are calculated by the probability ratio of the new and old policies, a bi-objective function based on the clipping policy is constructed, and the minimum value is taken as the negative of the final policy loss function value;

[0113] Value network optimization: Construct a loss function using the mean squared error (MSE) between the current state estimate and the target value, and update the parameters through backpropagation and gradient pruning.

[0114] During training, an entropy regularization term is introduced to penalize actions, thereby suppressing overly deterministic behavior and improving the exploratory and robust nature of the strategy.

[0115] After training, the system will automatically save the network structure and its parameters to a preset path to obtain the swarm intelligence model.

[0116] like Figure 4 The diagram shown is a system block diagram of an embodiment of the swarm intelligence emergence modeling system based on a physical information neural network of the present invention. The present invention provides a swarm intelligence emergence modeling system based on a physical information neural network, which is applied to a swarm intelligence emergence modeling method based on a physical information neural network. The system includes: a physical model building module, a training model building module, and a swarm intelligence model building module. Specifically,

[0117] The physical model building module is used to establish a physical constraint model of the group behavior based on the dynamic evolution process of the swarm robot system through partial differential equations.

[0118] The training model building module is used to train a group behavior training model in a single environment based on the physical constraint model of the group behavior through a physical information neural network.

[0119] The crowd intelligence model building module is used to train a model based on the behavior of the group. The model is trained through an interactive environment to obtain the crowd intelligence model.

[0120] This invention provides a method and system for modeling swarm intelligence emergence based on physical information neural networks. First, it utilizes partial differential equations to express the physical constraints of swarm intelligence robot behavior, establishing a physical constraint model of group behavior. This enables reinforcement learning to possess structured priors, significantly improving training sample efficiency and policy generalization ability. Second, it integrates the physical constraint model of group behavior with deep neural networks, overcoming the lack of physical interpretation and constraint control in traditional black-box reinforcement learning, thus accelerating the policy convergence process. Finally, it completes the training of the swarm behavior model in a virtual simulation environment and then completes the training of the swarm intelligence model on an actual simulation platform, reducing training costs and improving the feasibility of system deployment. The invention demonstrates good behavioral accuracy, environmental adaptability, and task completion ability.

[0121] It is understood that the present invention has been described through the above embodiments and should not be construed as limiting the implementation and scope of the present invention. Those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the present invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A physical information neural network based crowd intelligence emergent modeling method, characterized in that, The method comprises: S1, according to the dynamic evolution process of the swarm robot system, a physical constraint model of group behavior is established by means of partial differential equation; S2, according to the physical constraint model of group behavior, a single environment is trained by means of physical information neural network to obtain a group behavior training model; S3, according to the group behavior training model, an interactive environment is trained to obtain a swarm intelligence model; The physical constraint model of group behavior comprises a composite density field model; The composite density field model is composed of a target guiding potential field, a sensor detection potential field, a group cooperation potential field and a task additional constraint potential field; The target guiding potential field comprises: （1） In the formula: represents a target guiding potential field, represents a target field attenuation coefficient, dx represents a horizontal coordinate difference between the swarm intelligence robot and the target position, and dy represents a vertical coordinate difference between the swarm intelligence robot and the target position. The sensor detection potential field comprises: （2） In the formula: represents the potential field detected by the sensor, represents the field intensity coefficient of the sensor, represents the prevention zero constant, represents the distance from the sensor to the obstacle, represents the angle sensitivity coefficient, represents the deviation angle between the target direction and the current direction of the swarm robot. The group cooperation potential field comprises: （3） In the formula: represents a group cooperation potential field, represents the number of group intelligent robots in the system, represents the Euclidean distance between the current group intelligent robot and the ith group intelligent robot, represents the intensity coefficient of the density field, represents the attenuation rate coefficient of the density field, represents the ideal distance between group intelligent robots.

2. The physical information neural network based swarm emergence modeling method according to claim 1, wherein, In S2, according to the physical constraint model of group behavior, a single environment is trained by means of physical information neural network to obtain a group behavior training model, which comprises: S21, according to the physical constraint model of group behavior, a forward propagation function of neural network is obtained by means of physical information neural network; S22, according to the forward propagation function of neural network, a residual term of physical constraint model is obtained by means of multi-constraint residual calculation; S23, according to the residual term of physical constraint model, a loss function is established and a weight of loss term is obtained by means of AdamW optimizer combined with learning rate decay; S24, the weight of loss term is loaded into the physical information neural network to obtain a group behavior training model. 3.The physical information neural network based swarm emergence modeling method according to claim 1, wherein, In S3, according to the group behavior training model, an interactive environment is trained to obtain a swarm intelligence model, which comprises: S31, the group behavior training model is loaded into the swarm robot to obtain an initially trained swarm robot; S32, according to the multi-source perception device of the initially trained swarm robot, data is collected and trained to obtain an experience pool of model; S33, according to the experience pool of model, batch samples are obtained and strategy is updated to obtain a swarm intelligence model.

4. A physical information neural network based crowd intelligence emergent modeling system for implementing the physical information neural network based crowd intelligence emergent modeling method according to any one of claims 1-3, characterized in that, The system comprises: A physical model establishing module is configured to establish a physical constraint model of group behavior by means of partial differential equation according to the dynamic evolution process of the swarm robot system; A training model establishing module is configured to train a single environment by means of physical information neural network according to the physical constraint model of group behavior to obtain a group behavior training model; A swarm intelligence model establishing module is configured to train an interactive environment according to the group behavior training model to obtain a swarm intelligence model.

Images