Edge network digital twin application migration and evolution method based on non-stationary online learning

Abstract

The application discloses an edge network digital twin application migration and evolution method based on non-stationary online learning and belongs to the technical field of communication network resource management and edge computing. The application is suitable for digital twin application deployment and service request processing under end-edge-cloud cooperation. The method is based on non-stationary online learning, dynamically migrates and continuously evolves the digital twin application in the system to adapt to the mobility of physical entities and the continuous change of states. With the aim of maximizing the long-term average weighted service quality of the digital twin application under the premise of meeting the system cost constraint, the method comprises adopting a non-stationary slot machine learning assisted online joint optimization algorithm to determine the service priority of each type of service request in the digital twin application, the migration position of the digital twin application, the experience knowledge type for personalized service capability improvement, and the ability record fusion type and cache position for diversified service capability maintenance.

Description

Technical Field

[0001] This invention belongs to the field of communication network resource management and edge computing technology, specifically involving the deployment of digital twin applications in an end-edge-cloud collaborative network architecture, and particularly a method for the migration and evolution of edge network digital twin applications based on non-stationary online learning. Background Technology

[0002] A digital twin is a high-fidelity, dedicated virtual model of a physical entity (such as a vehicle in intelligent transportation or a patient in smart healthcare). It establishes and maintains a precise one-to-one mapping and synchronization between the physical and digital spaces. A digital twin is not merely a passive data mirror; it is expected to be an active application, providing service request processing services to its corresponding physical entity. These service requests typically require complex reasoning and decision-making capabilities to achieve a high level of service quality. Therefore, digital twins should incorporate advanced intelligent technologies, such as deep neural networks and large-scale language models, to meet the diverse service needs of the physical entity.

[0003] Edge-cloud collaboration offers a promising paradigm for the low-cost, timely deployment of digital twin applications. Under this paradigm, digital twin applications can be dynamically deployed across different edge servers through migration mechanisms, based on the potential mobility and access switching of physical entities, while relying on real-time data collected from user terminals and cloud centers for support. Although some existing research has considered the deployment of digital twin applications at the network edge, several issues remain unresolved, primarily including the following: 1) Unlike traditional service applications that are typically pre-configured and have unchanging service capabilities, digital twin applications, as virtual counterparts of physical entities, must continuously evolve once the state of their corresponding physical entities changes due to internal or external factors. Otherwise, the effectiveness of the digital twin will be reduced, rendering it ineffective or even causing misleading effects. For example, if a patient's digital twin model is not updated in a timely manner, any diagnosis based on that model could lead to incorrect prescriptions or dangerous delays in critical care.

[0004] 2) While some pioneering work has addressed similar issues, most studies have viewed digital twin applications as dedicated service providers with single functions, primarily focusing on personalization. However, in practical applications, a digital twin application often faces a variety of complex service requests from its corresponding physical entity. These requests typically arrive randomly and each has different performance requirements. Therefore, digital twin applications not only need to continuously evolve to improve their personalized service capabilities but also must maintain stable and diverse service capabilities. Similarly, in the medical field, digital twin applications need to simultaneously provide multiple medical services, such as remote physiological monitoring, risk prediction and assessment, and customized diagnostic testing, and dynamically adjust the priority of various services based on the patient's specific condition.

[0005] To address the aforementioned issues, it is necessary to determine the target edge servers for the dynamic migration of digital twin applications and the subsequent service capability evolution strategy for these applications. Specifically, to enhance the personalized service capabilities of each digital twin application, the experiential knowledge accumulated in handling specific types of service requests should be used as input for adaptive optimization. This experiential knowledge includes both historical training data from the cloud center (i.e., offline experience) and the latest state data from its corresponding physical entity (i.e., newly injected context information). Simultaneously, to maintain the diverse service capabilities of each digital twin application, it is necessary to build, record, and select capability records formed in handling various types of service requests at appropriate times, and integrate these records into the evolution process of the digital twin application. These capability records are typically cached or stored on designated edge servers, each characterizing the current processing capability for a specific type of service request. Clearly, all of the above processes require joint optimization. However, achieving this goal is challenging for the following reasons.

[0006] a. The migration and evolution of digital twin applications are highly coupled, making sequential optimization impossible. Specifically, the migration location of a digital twin application affects the resource conditions available for its subsequent capability evolution; conversely, the costs associated with long-term evolution should also be considered during application migration. Furthermore, since the corresponding physical entity may experience uncertain access switching due to random movement, and its state may continuously evolve due to unpredictable changes in service preferences, all related decisions must be made dynamically over time. Overall, these time-varying decisions involve both deploying digital twin applications across different edge servers through migration mechanisms and leveraging edge-cloud collaboration for knowledge selection and capability record management to achieve continuous evolution of the digital twin application's service capabilities, while simultaneously maintaining personalized and diversified service capabilities. Clearly, an online optimization method is urgently needed to support this dynamic migration and continuous evolution framework.

[0007] b. The evolution of digital twin applications involves two interrelated aspects: enhancing personalized service capabilities and maintaining diversified service capabilities. Constrained by the limited scale of applications, improving the personalized service capabilities of digital twin applications often inevitably weakens their diversified service capabilities; conversely, overemphasizing diversified service capabilities will also limit personalized service capabilities to some extent. Therefore, it is necessary to achieve a flexible balance between the two by carefully adjusting the service priorities of digital twin applications when handling different types of service requests, thereby driving the continuous evolution of digital twin applications on demand. However, these service priorities depend not only on the uncertain changes in the subjective preferences of the physical entity but also on the objective service quality performance generated by the digital twin application during the decision-making process, and there is no clear analytical relationship between the two. Furthermore, even if the above two factors are known, service priorities are still difficult to obtain directly because they are essentially implicit control variables and cannot be obtained through traditional learning algorithms. This necessitates an advanced online learning algorithm that can operate under implicit decision feedback conditions and is compatible with online optimization methods. Summary of the Invention

[0008] Purpose of the invention: To address the shortcomings of existing technologies mentioned in the background section regarding the migration and evolution of digital twin applications in edge networks, this invention provides a method for the migration and evolution of digital twin applications in edge networks based on non-stationary online learning.

[0009] Technical Solution: A method for migration and evolution of edge network digital twin applications based on non-stationary online learning. This method is based on non-stationary online learning, oriented towards physical entity-digital twin pairs, and aims to maximize the long-term system-level average weighted service quality while satisfying system cost constraints. It dynamically migrates and continuously evolves the capabilities of digital twin applications within the system. The method is characterized by: constructing a non-stationary online learning-assisted online joint optimization algorithm, which, at each time step, jointly optimizes the service priority of each type of service request in the digital twin application, the migration location of the digital twin application, the type of experience knowledge used for personalized service capability enhancement, and the capability record fusion type and cache location used for maintaining diversified service capabilities. The method includes the following steps: (1) For edge computing systems, a system model for the migration and continuous evolution of digital twin applications is constructed under the end-edge-cloud network architecture. This system model includes several physical entity-digital twin application pairs, edge servers and central cloud. (2) Calculate the costs of the system model at each time step, including the migration and transmission costs of digital twin applications between edge servers, the transmission costs of downloading and uploading experience knowledge, the computational costs of the evolution of digital twin application capabilities, and the transmission costs of caching capability records. (3) Optimize the dynamic application migration and continuous capability evolution of digital twin applications in the system model. The mathematical representation of this optimization process is as follows:

[0010] in, This represents the decisions made at all time steps. This indicates the service priority of each type of service request in a digital twin application. This indicates the service quality for the corresponding type of service request. This represents the total number of time steps. The total number of physical entity-digital twin application pairs. Total number of service request types; (4) Solve the optimization problem in step (3), including: Define deployment cost queue To describe the extent to which system costs deviate from the budget threshold; The original problem is decomposed into multiple instantaneous problems with single time steps using the Lyapunov optimization method for solution; For the instantaneous problem within each time step, it is decoupled into two coupled sub-problems: the first sub-problem includes decisions on digital twin application migration and capability record caching, and the second sub-problem includes decisions on service priority, types of acquired experience knowledge, and types of aggregated capability records. For the first subproblem, a method based on the McCormick envelope is used to solve it; For the second subproblem, a nonstationary combinatorial multi-armed slot machine algorithm is used to learn the optimal decision. Within each time step, the McCormick envelope-based method and the non-stationary combinatorial multi-armed slot machine algorithm are executed alternately until convergence.

[0011] Beneficial effects: Compared with the prior art, the substantial progress and significant effects of the present invention are as follows: (1) This invention takes into account the random mobility of physical entities and the diverse and time-varying service requirements, and realizes the dynamic migration of digital twin applications on edge servers, as well as the continuous capability evolution that includes both the improvement of personalized service capabilities and the maintenance of diversified service capabilities, so as to ensure the high service quality and low system cost of digital twin applications.

[0012] (2) The method described in this invention comprehensively weighs the service quality and service cost of digital twin applications, and takes into account influencing factors, including the service priority of each type of service request in digital twin applications, the migration location of digital twin applications, the type of experience knowledge used to improve personalized service capabilities, and the type of capability record fusion and cache location used to maintain diversified service capabilities. (3) By analyzing the characteristics of the problem studied in this invention, a non-stationary online learning-assisted online optimization algorithm was designed to solve the optimization decision. First, the Lyapunov decomposition method was used to decompose the long-term optimization problem into a series of instantaneous optimization problems, and then further decomposed them into two interrelated subproblems. Then, the two subproblems were solved alternately using the McCormick envelope-based method and the non-stationary combined multi-armed slot machine algorithm until convergence. Finally, the service quality of the digital twin application was maximized and the system cost was minimized. Attached Figure Description

[0013] Figure 1 This is a system model diagram of digital twin application migration and evolution under the terminal-edge-cloud architecture in the embodiment; Figure 2 is a comparison chart of the long-term average quality of service and system cost of the embodiment and the prior art under different numbers of physical entities. Detailed Implementation

[0014] To illustrate the technical solutions disclosed in this invention in detail, further explanation will be provided below with reference to the accompanying drawings and specific embodiments.

[0015] Considering the high interaction costs between digital twin applications and physical entities due to high-speed movement of physical entities when processing service requests from physical entities, and the personalized and diversified needs faced by digital twin applications when handling dynamically changing service requests from their corresponding physical entities, this invention provides a method for dynamically migrating and evolving the capabilities of digital twin applications at the edge. Specifically, this method deploys a dedicated digital twin application for each physical entity at the network edge to provide various types of complex services. On the one hand, due to the mobility of physical entities, their corresponding digital twin applications will dynamically migrate between edge servers. On the other hand, because the state of physical entities is constantly changing and digital twin applications need to handle various types of service requests, their corresponding digital twin applications continuously evolve by acquiring experience and knowledge from the central cloud and physical entities, and by fusing cached capability records, thereby simultaneously improving personalized service capabilities and maintaining diversified service capabilities.

[0016] This invention provides a method for the migration and evolution of edge network digital twin applications based on non-stationary online learning. Based on the method described in this invention, we propose an online joint optimization mechanism assisted by non-stationary online learning. This mechanism maximizes the long-term average service quality of the digital twin application while meeting strict system cost constraints, and considers system uncertainties (i.e., the mobility and continuous changes in the state of physical entities). Unlike existing technologies, this method considers the need for a dynamic balance between enhancing personalized service capabilities and maintaining diversified service capabilities in digital twin applications. Specifically, the method includes constructing an online joint optimization scheme to determine the service priority of each type of service request in the digital twin application, the migration location of the digital twin application, the type of experience knowledge used for enhancing personalized service capabilities, and the capability record fusion type and cache location used for maintaining diversified service capabilities, thereby ensuring high-quality task processing and controlling the long-term total system cost.

[0017] Furthermore, combined Figure 1 The implementation process of the method described in this invention is explained in detail below: Step 1: Build an edge-cloud network architecture that enables the migration and evolution of digital twin applications, and construct a mathematical model for the system.

[0018] This step will provide a mathematical analysis of the practical problems addressed by the migration and evolution methods for edge network digital twin applications based on non-stationary online learning.

[0019] Based on practical application scenarios, the digital twin application migration and evolution system based on an edge-cloud collaborative architecture consists of a central cloud, M edge servers, and N mobile physical entities and their dedicated digital twin applications. The central cloud acts as a global controller and knowledge base, storing general model training data. The edge servers are distributed at the network edge close to users, providing computing, communication, and caching resources. Each physical entity continuously generates multiple types (with a total of K types) of complex task requests, which are then executed by the dedicated digital twin application deployed on the edge server. Due to the random movement patterns of physical entities, their corresponding digital twin applications need to dynamically migrate between different edge servers. More importantly, to cope with the time-varying states of physical entities, the digital twin applications must continuously evolve their capabilities. On the one hand, by downloading general training data from the central cloud and uploading real-time state data (collectively referred to as experiential knowledge) from physical entities, the personalized service capabilities for handling specific service requests are improved. On the other hand, by caching and integrating capability records of different types of service requests on the edge servers, the diversified service capabilities for handling other types of service requests are maintained.

[0020] In the aforementioned digital twin application migration and evolution system, the migration and transmission cost of digital twin applications between edge servers... The expression is as follows:

[0021] The transmission cost of downloading experience and knowledge The expression is as follows:

[0022] Transmission cost of uploading experience and knowledge The expression is as follows:

[0023] The computational cost of the evolution of digital twin application capabilities The expression is as follows:

[0024] Capability record cache transmission cost The expression is as follows:

[0025] in, This indicates the transmission rate between edge servers. This represents the transmission cost per unit time for the edge server. This indicates the size of the downloaded experience and knowledge data. This indicates the transmission rate from the central cloud to the edge server. This represents the transmission cost per unit time of the central cloud. This indicates the size of the uploaded experience and knowledge data. This represents the transmission cost per unit of time for a physical entity. This represents the total amount of experiential knowledge data used to evolve digital twin application capabilities. The training rounds in the computational process representing the evolution of digital twin application capabilities. This indicates the CPU processing speed of the edge server. Indicates the effective switched capacitor of the edge server. This indicates the number of CPU cycles required for an edge server to process a unit of data.

[0026] Furthermore, the quality of service for each type of service request in digital twin applications The piecewise evolution expression is as follows: when , At this time, personalized service capabilities are improved. ; when , At this time, the ability decreases: ; when , At this time, diversified service capabilities are maintained. ; in, and These respectively represent the service quality degradation caused by the improved service capabilities of other types of service requests, and the service quality restored while maintaining diversified service capabilities. This indicates the current parameter values ​​for the digital twin application. This indicates a parameter value that is suitable for handling a certain type of service request. This indicates the importance of the parameter value in handling a certain type of service request.

[0027] Next, we mathematically model the long-run average weighted quality of service (SQS) problem of the digital twin application under the system cost constraint, and the mathematical expression is:

[0028] in, This indicates the service priority of each type of service request in a digital twin application. This indicates the service quality for the corresponding type of service request. Represents the decision at all time steps: ; The constraints are as follows:

[0029] in, Indicates migration decision, This indicates the type of experiential knowledge acquired for decision-making. The ability to record the type of decision indicates the fusion capability. The ability to record cache decisions, Indicates service priority decision, It is the amount of data used in digital twin applications. It is the ability to record the amount of data. This is the maximum cache space limit for edge servers. It is a preference for physical entity services. It is the total system cost. It is the system cost budget threshold; Step 2: Problem Solving.

[0030] Based on the original optimization problem in step 1, we first define a deployment cost queue to reflect the total system cost of the digital twin application at each time step relative to a long-term budget threshold. The deviation of the queue. The evolution of the queue over time can be represented as:

[0031] Next, based on the Lyapunov optimization framework, the satisfaction of long-run system cost constraints is transformed into a queue of guaranteed deployment costs. The original long-term optimization problem can be transformed into an instantaneous subproblem that is solved independently at each time step t by introducing a drift penalty term, with the objective of minimizing the following terms:

[0032] Where V is a Lyapunov control parameter used to balance the cost of the control system with maximizing the system-level weighted quality of service.

[0033] Furthermore, since the transformed instantaneous problem contains complex discrete variable couplings and bilinear terms, direct solution is extremely difficult. Therefore, this invention decouples it into two related sub-problems for alternating solution: For decisions involving migration of digital twin applications And capability record caching decision The first subproblem, whose objective function extracts the cost terms associated with these two decisions, is expressed as follows:

[0034] The constraints are as follows:

[0035] For the bilinear term in the first subproblem The process employs a McCormick envelope-based approach. Specifically, this includes: processing discrete transfer decisions... And capability record caching decision Relaxation as a continuous variable and Then, auxiliary variables are introduced. And add the following McCormick envelope constraint:

[0036] Finally, after obtaining fractional solutions by solving the linearized convex optimization problem using the existing solver, the solutions are restored to integer solutions that satisfy the physical constraints.

[0037] Decisions involving the type of acquired experiential knowledge Integration capabilities record type decision and service priority decision The second subproblem is expressed as follows:

[0038] The constraints are as follows:

[0039] Due to service priority Essentially, it is an implicit control parameter that cannot be directly calculated analytically. This invention employs a non-stationary combined multi-armed slot machine learning algorithm to infer implicit priorities and learn the optimal decision, specifically including: First, construct the superarm set. The acquired experience knowledge type decision and the fusion capability record type decision are paired and recombined into a single superarm to reduce the decision search space; Then, an adaptive confidence upper bound mechanism is used to determine service priority, as shown in the following expression:

[0040] in, Indicates the number of rounds in which the execution alternates. Indicates the cumulative number of selections; Finally, based on the sampling probability distribution The optimal superarm is selected using the following expression:

[0041] in, This represents the learning rate of the superarm. , The indicator function is used to indicate whether the superarm was selected in the previous round. This represents the learning rate of the superarm.

[0042] Within each time step, the McCormick envelope algorithm and the non-stationary combinatorial multi-armed slot machine learning algorithm are executed alternately until convergence, thereby outputting the optimal decision for the current time step.

[0043] Experimental setup: Simulate a certain An edge-cloud collaborative network system within a square area, which includes... One edge server and There are 10 physical entities. The movement trajectory characteristics of these physical entities and the deployment locations of the edge servers are constructed based on real-world scene datasets. All key simulation parameters of the system are detailed in Table 1. Specifically, the relevant parameters for the migration and continuous update mechanism of digital twin applications are set with reference to the medical image segmentation task scenario in medical and health twin applications; the network configuration parameters of the system are set with reference to existing typical network environments.

[0044] Table 1. Experimental parameters

[0045] Comparison method: To verify the superiority of the method proposed in this invention in optimizing long-term average weighted service quality, this experiment simulated the following benchmark scheme for comparative analysis: Comparison Method 1 (GST Method): This method optimizes all decision variables through a greedy strategy at each time step to maximize the service quality of processing various types of service requests, but completely ignores long-term system cost constraints.

[0046] Comparison Method 2 (SIO Method): This method uses the particle swarm optimization algorithm to determine all decision variables, aiming to achieve a balance between the service quality and system cost of various types of service requests at each time step.

[0047] Comparison Method 3 (FPL Method): This method adopts an optimization process similar to that of the method in this invention, that is, to maximize the service quality of each type of service request under the premise of satisfying long-term system cost constraints; its core difference is that this method uses an algorithm based on perturbation following the leader to determine the type of acquired experience knowledge, the type of ability record fusion, and the service priority, rather than using the online learning process designed in this invention.

[0048] Instructions for setting test indicators: Long-term average weighted quality of service (SQSA): This is calculated by averaging the weighted sum of the SQSA of all digital twin applications handling various types of service requests and their corresponding service priorities over time. This metric reflects the overall processing efficiency of digital twin applications on complex, time-varying service requests from physical entities within a non-stationary online learning framework, through personalized capability enhancement and diversified capability maintenance.

[0049] Total system cost: This includes the migration and transmission costs of digital twin applications between edge servers, the transmission costs of downloading and uploading experience knowledge, the computational costs of evolving digital twin application capabilities, and the transmission costs of caching capability records. This metric reflects the comprehensive resource overhead consumed by the system in supporting the dynamic migration and continuous evolution of digital twin applications under the edge-cloud collaborative architecture, and is used to evaluate the cost control capability of the method while meeting long-term budget thresholds.

[0050] Based on the experimental results in Figure 2, further analysis of the metrics is presented below. The experiments compared the long-term average weighted quality of service (SHS), SIO, FPL, and the method of this invention in handling various service requests, as well as the resulting system costs, under varying physical entity-digital twin application pairs N. From Figure 2(a), we can see that this method exhibits the best performance in terms of SHS under different numbers of physical entities. From Figure 2(b), we can observe that this method also has the lowest system cost under different numbers of physical entities. The core reasons are as follows: Unlike the GST method, which only maximizes short-term service quality, the method of this invention can dynamically adjust the importance of these two evaluation indicators based on the deployment cost queue and Lyapunov control parameters, thereby achieving an optimal balance between long-term average weighted service quality and system cost. Compared to the SIO method, which uses particle swarm optimization to handle complex non-convex optimization problems to obtain suboptimal solutions, the method of this invention first decouples the original problem into two subproblems, and then alternately solves them using a method based on McCormick envelope and a method based on non-stationary combinatorial multi-armed slot machine algorithm, significantly reducing the overall computational complexity while achieving better solution results. Compared to the FPL method, which obtains decisions by simply applying a perturbation to the actual cumulative loss, the method of this invention calculates the sampling probability distribution of each superarm based on a carefully designed learning rate and estimated cumulative loss, thereby providing a better selection mechanism for decisions such as service priority and experience knowledge type.

Claims

1. A method for migrating and evolving digital twin applications in edge networks based on non-stationary online learning, wherein the method is based on non-stationary online learning, is oriented towards physical entity-digital twin pairs, and aims to maximize the long-term system-level average weighted quality of service while satisfying system cost constraints, and dynamically migrates and continuously evolves the capabilities of digital twin applications in the system, characterized in that: This method includes constructing an online joint optimization algorithm for non-stationary slot machine learning assistance, which jointly optimizes the service priority of each type of service request in the digital twin application, the migration position of the digital twin application, the type of experience knowledge for improving personalized service capabilities, and the capability record fusion type and cache position for maintaining diversified service capabilities in each time step; The method includes the following steps: (1) For edge computing systems, a system model for the migration and continuous evolution of digital twin applications is constructed under the end-edge-cloud network architecture. This system model includes several physical entity-digital twin application pairs, edge servers and central cloud. (2) Calculate the costs of the system model at each time step, including the migration and transmission costs of digital twin applications between edge servers, the transmission costs of downloading and uploading experience knowledge, the computational costs of the evolution of digital twin application capabilities, and the transmission costs of caching capability records. (3) Optimize the dynamic application migration and continuous capability evolution of digital twin applications in the system model. The mathematical representation of this optimization process is as follows: in, This represents the decisions made at all time steps. This indicates the service priority of each type of service request in a digital twin application. This indicates the service quality for the corresponding type of service request. This represents the total number of time steps. The total number of physical entity-digital twin application pairs. Total number of service request types; (4) Solve the optimization problem in step (3), including: Define deployment cost queue To describe the extent to which system costs deviate from the budget threshold; The original problem is decomposed into multiple instantaneous problems with single time steps using the Lyapunov optimization method for solution; For the instantaneous problem within each time step, it is decoupled into two coupled sub-problems: the first sub-problem includes decisions on digital twin application migration and capability record caching, and the second sub-problem includes decisions on service priority, types of acquired experience knowledge, and types of aggregated capability records. For the first subproblem, a method based on the McCormick envelope is used to solve it; For the second subproblem, a nonstationary combinatorial multi-armed slot machine algorithm is used to learn the optimal decision. Within each time step, the McCormick envelope-based method and the non-stationary combinatorial multi-armed slot machine algorithm are executed alternately until convergence.

2. The method for migration and evolution of edge network digital twin applications based on non-stationary online learning according to claim 1, characterized in that: In step (2), the migration and transmission costs of digital twin applications between edge servers The expression is as follows: The transmission cost of downloading experience and knowledge The expression is as follows: Transmission cost of uploading experience and knowledge The expression is as follows: The computational cost of the evolution of digital twin application capabilities The expression is as follows: Capability record cache transmission cost The expression is as follows: In the formula, For the index of edge servers, Indicates the first The edge server and the first The transmission rate between edge servers Indicates the first The transmission cost per unit time for an edge server Indicates the first Service request type for download at each time step The size of the experiential knowledge data. Indicates from the central cloud to the first The transmission rate of each edge server This represents the transmission cost per unit time of the central cloud. Indicates the first The physical entity in the first The amount of experience and knowledge data uploaded at each time step Indicates the first The physical entity in the first The time step and the first Transmission rate between edge servers Indicates the first The transmission cost per physical entity per unit of time. Indicates the first The first digital twin application in the 1st The total amount of experiential knowledge data used for capability evolution at each time step Indicates the first The first digital twin application in the 1st The training round function in the computational process of capability evolution at each time step. Indicates the first CPU processing speed of an edge server Indicates the first Effective switching capacitors for each edge server Indicates the first The number of CPU cycles required for an edge server to process a unit of data.

3. The method for migration and evolution of edge network digital twin applications based on non-stationary online learning according to claim 1, characterized in that, Decision set at all time steps Specifically, it is expressed as follows: ； The constraints are as follows: in, Indicates the first The first digital twin application in the 1st The time step towards the first Migration decisions for individual edge servers Indicates the first The first digital twin application in the 1st The time step is for the first Decisions based on the type of experience knowledge obtained from service requests. Indicates the first The first digital twin application in the 1st The time step is for the first The capability record type decision for service requests Indicates the first The first digital twin application in the 1st The time step is for the first The capability record of the service request capability is cached to the first Caching decisions for edge servers No. The first digital twin application in the 1st Data volume per time step It is the first The first digital twin application in the 1st The time step is for the first The amount of data recorded for the capability of service requests. It is the first The maximum cache space limit for each edge server It is the first The physical entity in the first The time step for the first Service preferences for similar service requests It is a service priority mapping function. It is the first The physical entity-digital twin application for the first physical entity-digital twin application in ... Total system cost per time step It is the system cost budget threshold.

4. The method for migration and evolution of edge network digital twin applications based on non-stationary online learning according to claim 1 or 3, characterized in that: In step (3), the quality of service for each type of service request in the digital twin application. The expression is as follows: In the formula, This indicates that the improved service capabilities of other types of service requests have led to the [missing information]. The first digital twin application in the 1st The first time step processes the... Service quality is reduced by the decrease in the number of service requests. Indicates the first The first digital twin application in the 1st The first time step processes the... Quality of service restored while maintaining diverse service capabilities during service requests; The total number of parameter dimensions for digital twin applications. Indicates the first The first digital twin application in the 1st The first time step The current parameter value of the dimension. Indicates the first The first digital twin application in the 1st The first time step processes the... When requesting a service of the same type The adaptation parameter values ​​of the dimension, Indicates the first The first digital twin application in the 1st The first time step processes the... When requesting a service of the same type The importance of the dimension parameter values, The attenuation coefficient for service quality improvement For the first The first digital twin application in the 1st The time step is based on the first Training rounds for the total amount of experience and knowledge data of the class.

5. The method for migration and evolution of edge network digital twin applications based on non-stationary online learning according to claim 1, characterized in that: In step (4), the deployment cost queue is... The calculation expression for updating at each time step is as follows: In the formula, It is the first The physical entity-digital twin application for the first physical entity-digital twin application in ... The deployment cost queue value for each time step. No. The physical entity-digital twin application for the first physical entity-digital twin application in ... The deployment cost queue value for each time step.

6. The method for migration and evolution of edge network digital twin applications based on non-stationary online learning according to claim 1, characterized in that: In step (4), the expression for the first decoupled subproblem is as follows: The constraints are as follows: The expression for the second subproblem is as follows: The constraints are as follows: 。 7. The method for migration and evolution of edge network digital twin applications based on non-stationary online learning according to claim 1, characterized in that: In step (4), the first subproblem is solved using a method based on the McCormick envelope, specifically including: Discrete migration decisions And capability record caching decision Relaxation as a continuous variable and ; , ; Introducing auxiliary variables And add the following McCormick envelope constraint: in, For the first The physical entity-digital twin application for the first physical entity-digital twin application in ... Auxiliary variables for each time step; After obtaining fractional solutions by solving the linearized convex optimization problem using existing solvers, these fractional solutions are then converted back to integer solutions that satisfy the physical constraints to obtain the transfer decision. And capability record caching decision The optimal solution.

8. The method for migration and evolution of edge network digital twin applications based on non-stationary online learning according to claim 1, characterized in that: Step (4) employs a non-stationary combinatorial multi-armed slot machine algorithm to learn the optimal decision for the second subproblem, specifically including: (4.1) Constructing the superarm set The acquired experience knowledge type decision and the fusion capability record type decision are paired and recombined into a single superarm to reduce the decision search space; ； in, For the first The physical entity-digital twin application for the first physical entity-digital twin application in ... The first time step The decision index for selecting the type of experience knowledge corresponding to each superarm. For the first The physical entity-digital twin application for the first physical entity-digital twin application in ... The first time step The decision index for selecting the capability record type corresponding to each superarm. For the superarm's index set, For the superarm index; (4.2) An adaptive confidence upper bound mechanism is used to determine service priority, as shown in the following expression: in, Indicates the number of rounds in which the execution alternates. Indicates the first The physical entity-digital twin application for the first physical entity-digital twin application in ... The first time step Round processing The cumulative number of times a service type request is selected. Indicates the first The physical entity-digital twin application for the first physical entity-digital twin application in ... The first time step Round processing The loss value of the service request. The median value for service priority. This refers to the normalized service priority. (4.3) Based on sampling probability distribution The optimal superarm is selected using the following expression: in, Indicates the first The physical entity-digital twin application for the first physical entity-digital twin application in ... The first time step Rounds The learning rate of a superarm. For the index of the superarm, The update formula is: ， This is an indicator function that indicates whether the superarm was selected in the previous round. It takes the value 1 when the condition in parentheses is true, and 0 otherwise. Indicates the first The physical entity-digital twin application for the first physical entity-digital twin application in ... The first time step The overall loss value of the round, Indicates the first The physical entity-digital twin application for the first physical entity-digital twin application in ... The first time step Rounds The sampling probability of a superarm. This represents the learning rate of the superarm.

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