A multi-cluster aerial computing method and system based on a deep unfolded graph neural network

Abstract

The application discloses a kind of multi-cluster air computing method and system based on depth unfolding graph neural network, belong to air computing technical field in wireless network, first, define the aggregation center node in heterogeneous graph neural network, wireless device node and the edge of connecting two kinds of nodes;Second, the multi-cluster control calculation optimization problem needing to be solved is decomposed into the neural network solving module of unfolding structure.Following, design feature extraction and feature embedding method in neural network solving module;Then design heterogeneous graph neural network encoder to aggregate features, and the variable to be optimized is mapped to the aggregated features by the designed multilayer perceptron decoder;Finally, the parameter sharing strategy of the whole network and the learning method of neural network are designed, the neural network is trained, and a general model is obtained.The scheme of the application is superior to the existing optimization scheme in terms of calculation rate, and the solving speed is greatly improved, and has very strong generalization ability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of air computation (AirComp) in wireless networks, and particularly relates to a multi-cluster air computation method and system based on a deep unfolding graph neural network. BACKGROUND

[0002] Due to the unique way of data processing, air computation (AirComp) shows great potential in multiple scenarios, such as perception data fusion, control information aggregation and federated learning, covering a variety of cyber-physical system applications. Therefore, it is crucial to extend the existing single-task air computation to multi-cluster air computation in order to support concurrent computing instances of different services. From the networking perspective, this can be modeled as a multi-cluster air computation architecture, each cluster being associated with an independent aggregation center. Under this architecture, different types of tasks, such as temperature measurement, fire monitoring and neural network learning, can be performed simultaneously. However, the coexistence of multiple clusters brings the problem of interference, which becomes a major challenge because it affects the data aggregation within each cluster and further hinders the scalability of more diverse data. Therefore, in addition to the problem of transmission-reception coordination in traditional air computation scenarios, effective interference management is needed to achieve efficient multi-cluster air computation.

[0003] In addition, the principle of air computation requires joint optimization at the sending and receiving ends to achieve effective computation. Therefore, it is essential to efficiently and accurately determine the transmission-reception strategy. However, from the optimization perspective, this problem usually requires multiple iterations to reach a certain stable point strategy, which may not be the optimal solution and is time-consuming. At the same time, machine learning technology achieves fast execution through well-trained neural networks, but pure data-driven methods may lack sufficient adaptability in changing environments. In this context, unfolding learning technology, which combines knowledge-driven and data-driven design, becomes an attractive solution. Under the guidance of theoretical derivation, unfolding technology produces a problem-oriented iterative-inspired neural network architecture. Therefore, unfolding learning can efficiently explain the problem structure through fast-executable neural networks, improving adaptability and scalability.

[0004] Meanwhile, for a multi-cluster aerial computing system, the strategy decision of a cluster will affect the strategies of other clusters. From the perspective of learning, graph neural networks (GNNs) are particularly suitable for solving such problems due to their natural suitability for graph-structured data. Under the framework of graph neural networks, the transmission and reception behaviors in multi-cluster aerial computing can be embedded as the features of graph elements, and the mutual influence between different clusters can also be implanted into the graph structure. In addition, the permutation equivalence property in graph neural networks facilitates generalization to networks of arbitrary size. Therefore, the use of graph neural networks in the unfolded learning architecture provides an effective tool for solving multi-cluster aerial computing problems, enabling well-trained neural networks to provide effective computing strategies and adapt to dynamic network environments. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a multi-cluster aerial computing method and system based on a deep unfolded graph neural network to solve the technical problems of the difficulty of traditional optimization methods to adapt to flexible wireless environments and low solving efficiency in a multi-cluster aerial computing scenario.

[0006] The application adopts the following technical solutions:

[0007] A multi-cluster aerial computing method based on a deep unfolded graph neural network comprises the following steps:

[0008] S1, defining an aggregation center node, a wireless device node and an edge connecting the two nodes in a heterogeneous graph neural network;

[0009] S2, based on the aggregation center node, the wireless device node and the edge connecting the two nodes defined in step S1, decomposing a multi-cluster control computing optimization problem to be solved into an unfolded neural network solving module;

[0010] S3, designing a feature extraction method in the neural network solving module obtained in step S2 to obtain key features that determine the output of the current solving module from the input channel information and the transmission factor output by the previous solving module;

[0011] S4, designing a feature embedding method for the neural network to embed the key features obtained in step S3, and mapping low-dimensional features to high-dimensional features;

[0012] S5, designing a graph neural network encoder based on the key features embedded in step S4, and defining a method for generating and aggregating messages in the graph neural network;

[0013] S6, designing a multi-layer perceptron as a decoder to decode the output of the graph neural network obtained in step S5 into variables to be optimized;

[0014] S7. Design a parameter sharing strategy and learning method for graph neural networks. Train the graph neural network to obtain a model with good generalization ability. Pass the channel information of the network in the new scenario as input to the model and output the transmission factor of each wireless device and the receiving beam of each aggregation center to improve the multi-cluster air computing rate.

[0015] Preferably, in step S1, the over-the-air computing service coverage area includes N clusters, each cluster performing different over-the-air computing tasks, and the set of all clusters is defined as... ={1, 2, ..., K}; each cluster is equipped with an aggregation center at its center;

[0016] For a given cluster k, containing A wireless device, using This represents the nth wireless device in the cluster. ={1, 2, ..., } represents the set of all wireless devices.

[0017] wireless devices The maximum transmission power is expressed as The k-th aggregation center is equipped with One antenna, used Indicates wireless device The channel to the k-th aggregation center;

[0018] When l equals k Indicates a communication channel; otherwise, it indicates an interference channel.

[0019] wireless devices The transfer factor is The receiving beamforming at the aggregation center is ;

[0020] Define all reflective end devices as Node1={ }, Let represent the first type of node in the first type of graph; define the aggregation center of all receivers as Node2={k}. , representing the second type of node in the graph;

[0021] The channel between the first type of node and the second type of node is defined as the edge connecting the two types of nodes: Edge = { }, .

[0022] Preferably, in step S2, the airborne computation problem is expanded into multiple cascaded neural network computation modules. For module j, the current channel information is input { } and the transmission factor output by the previous module , output the optimized transmission factor ;

[0023] The solving module is packaged as an optimizer of the transmission factor, and internally includes an optimal receiving beam submodule, an optimal transmission factor phase submodule, and a transmission factor modulus optimization submodule. The optimal receiving beam submodule is in a cascaded structure with the optimal transmission factor phase submodule and the transmission factor modulus optimization submodule, and the optimal transmission factor phase submodule and the transmission factor modulus optimization submodule are in a parallel structure. Finally, the optimized complex transmission factor is formed by combination.

[0024] Preferably, the cascaded multiple neural network calculation modules are specifically:

[0025]

[0026] wherein, is the entire network channel information, is the learnable parameter of the neural network, is the receiving beam of the aggregation center k, is the receiving beamforming optimization submodule, is the input transmission factor of the jth solving module, is the nth wireless device of the lth cluster, is the aggregation center set, is the phase of the output transmission factor of the jth solving module, is the transmission factor phase optimization submodule, is the channel from the device to the aggregation center k, is the nth device of the kth cluster, is the wireless device set of the kth cluster, is the modulus of the output transmission factor of the jth solving module, is the transmission factor phase submodule, is the output transmission factor of the jth solving module, is the wireless device set of the lth cluster.

[0027] Preferably, in step S3, the feature extraction of the wireless device node in the heterogeneous graph neural network adopts the following scheme:

[0028]

[0029] wherein, is the feature of the wireless device input into the jth solving module, and each item in the bracket represents a wireless device the old transmission factor of the corresponding aggregation center, the equivalent channel of the corresponding aggregation center, the interference channel of other aggregation centers, the received power of the corresponding aggregation center, the interference power of other aggregation centers;

[0030] The feature extraction of the aggregation center node in the heterogeneous graph neural network adopts a similar scheme:

[0031]

[0032] wherein, is the feature of the aggregation center k input into the jth solving module, and each item in the brackets represents the old mean square error of the aggregation center k, the equivalent interference channel received by the aggregation center from the effective device and, the interference channel received by the aggregation center from the interference device and, the effective power received by the aggregation center and, and the interference power received by the aggregation center and.

[0033] Preferably, in step S4, the device node and the embedding operation of the aggregation center node k are represented as:

[0034]

[0035]

[0036] wherein, and respectively represent the features of the embedded wireless device and the aggregation center k, the embedding layer is a single-layer neural network, and a tanh function is used as an activation function, is a device feature embedding neural network, is a device feature embedding neural network parameter, is an aggregation center feature embedding neural network parameter, is the embedded feature output by the aggregation center k through the embedding layer, is the embedded feature output by the device through the feature embedding layer.

[0037] Preferably, in step S5, the encoder is composed of I-layer information transmission, each layer of the encoder includes, the information transmission includes message generation, aggregation and combination, constitutes a linear layer in cascade, for message aggregation, each node aggregates the features of other types of nodes through a weighted sum, that is, the device node aggregates the features of the aggregation center node, and the node combines the previous features and the obtained aggregated message through a linear layer with a layer normalization function, and this process is represented as ; the coefficient is introduced into the information transmission mechanism in the encoder of the heterogeneous graph neural network, the information transmission is defined to enable information transmission between different types of nodes, and information transmission is not performed between nodes of the same type.

[0038] Preferably, in step S6, the decoder is represented as:

[0039]

[0040] wherein, denotes the decoding operation, is the neural network parameter, adopts the SELU function as the activation function of the input layer and the hidden layer, and the output activation function uses Sigmoid.

[0041] Preferably, in step S7, the loss function is:

[0042]

[0043] wherein, denotes the averaging operation on the channel random variable denotes the averaging operation on the channel random variable denotes the over-the-air computation rate function, denotes the unfolded heterogeneous graph neural network generating the transmission strategy, denotes the channel condition sample.

[0044] In a second aspect, an embodiment of the present application provides a multi-cluster over-the-air computation system based on a deep unfolded graph neural network, comprising:

[0045] a node module defining an aggregation center node, a wireless device node and an edge connecting the two nodes in the heterogeneous graph neural network; decomposing a multi-cluster control computation optimization problem to be solved into an unfolded neural network solving module;

[0046] an embedding module, a feature extraction method in the designed neural network solving module, obtaining key features determining the output of the current solving module from the input channel information and the transmission factor output by the last solving module, designing a feature embedding method of the neural network, embedding the obtained key features, and mapping low-dimensional features to high-dimensional features;

[0047] an encoding module, designing a graph neural network encoder based on the embedded key features, defining a method of message generation and message aggregation in the graph neural network;

[0048] a decoding module, designing a multilayer perceptron as a decoder to decode the output of the graph neural network into variables to be optimized;

[0049] a computing module, designing a graph neural network parameter sharing strategy and a learning method of the graph neural network, training the graph neural network to obtain a model with good generalization ability, inputting the channel information of the network in a new scenario into the model, outputting the transmission factor of each wireless device and the receiving beam of each aggregation center, and achieving the improvement of the multi-cluster over-the-air computation rate.

[0050] In a third aspect, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the above method for multi-cluster aerial computing based on a deep unfolded graph neural network when executing the computer program.

[0051] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium including a computer program, and the computer program implements the steps of the above method for multi-cluster aerial computing based on a deep unfolded graph neural network when executed by a processor.

[0052] In a fifth aspect, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the above method for multi-cluster aerial computing based on a deep unfolded graph neural network when executing the computer program.

[0053] In a sixth aspect, an embodiment of the present application provides an electronic device including a computer program, and the computer program implements the steps of the above method for multi-cluster aerial computing based on a deep unfolded graph neural network when executed by the electronic device.

[0054] Compared with the prior art, the present application has at least the following beneficial effects:

[0055] A method for multi-cluster aerial computing based on a deep unfolded graph neural network, through an unfolding learning method, significantly improves the aerial computing rate under different clusters, devices, and antenna numbers, especially in a multi-cluster and high interference scenario. Compared with a traditional optimization method (such as alternating optimization), the present application effectively avoids the problem of falling into a suboptimal solution in a large-scale scenario. Thanks to the introduction of a heterogeneous graph neural network structure, the present application has strong generalization ability and can maintain good performance in untrained scenarios, especially in a strong interference condition, through effective feature extraction to achieve better performance. This feature is particularly significant when the number of clusters and devices changes, indicating its adaptability in complex network environments. Compared with the large number of iterative calculations of the traditional optimization method, the unfolding learning method realizes nearly instantaneous calculation output through a neural network, greatly improving the operation efficiency. In addition, the present application also adopts a progressive learning and parameter sharing strategy, further optimizing the training efficiency and reducing the memory and computing resource consumption. Through the reasonable design of multiple receiving antennas, the receiving ability and interference suppression effect of the aggregation center are improved, especially when the number of antennas is large, the receiving beamforming degree of freedom is enhanced, and a high aerial computing rate is achieved. In the traditional optimization method, limited by the suboptimal solution problem, the interference suppression effect is not as good as the present application.

[0056] Further, the use of the heterogeneous graph neural network conforms to the architecture of the multi-cluster air computing system, the multi-cluster air computing system has two different nodes of wireless devices and aggregation centers, the two different nodes are associated through a channel, and the two different nodes in the heterogeneous graph neural network represent the wireless devices and the aggregation centers respectively, and the edges connecting the heterogeneous nodes represent the channel.

[0057] Further, the neural network structure required for directly solving the original problem is relatively complex, a large number of samples are required for training, and it is easy to fall into a local optimal solution. The decomposition of the problem into an expansion structure is equivalent to the neural network outputting a better solution based on the suboptimal solution output by the input, the required function is relatively simple, and the design of sharing parameters by each module can realize the reuse of a training sample, and the distribution of the training sample is more diverse, and it is not easy to fall into a local optimal solution.

[0058] Further, the number of wireless devices and aggregation centers in the network is large, and the aggregation center adopts a multi-antenna design, so the channel feature dimension is high, and a lot of information redundancy is also contained, which is not conducive to the training of the neural network. The design of the feature extraction method can perform some equivalent processing on the channel, reduce the channel feature dimension, and extract the key features in the channel that affect the performance index, so that the subsequent training is more targeted.

[0059] Further, in order to achieve strong generalization ability, a single device and a single aggregation center are required as input, and the representation of the overall features of the network is lacking. Here, the extracted features are embedded, and the low-dimensional features are mapped to high-dimensional features. The high-dimensional features are equivalent to containers, providing a basis for subsequent aggregation of the overall features of the network using the graph neural network.

[0060] Further, the embedded features of each wireless device are aggregated into the aggregation center, and then the embedded features of the aggregation center are aggregated into each wireless device. Through multiple back-and-forth operations, each aggregation center and each wireless device can obtain the overall features of the network, which is beneficial to the joint optimization of the overall network.

[0061] Further, the multi-layer perceptron is used as a decoder to map the aggregated features of each device to obtain the transmission power allocation of each wireless device required by the multi-cluster air computing system.

[0062] Further, each solving module has the same function, and sharing parameters for each solving module can effectively reduce the number of parameters required by the model, so that the model is easier to train. At the same time, the input of each module can be used as a training sample to expand the training evolution, so that the model is more stable and reliable and is not easy to overfit.

[0063] It can be understood that the beneficial effects of the above-mentioned second aspect to the sixth aspect can be referred to the related description in the first aspect, which will not be repeated here.

[0064] In summary, the aerial computing rate performance of the present application is superior, the generalization ability is strong, the training efficiency is high, and the computing cost is low, and the best interference suppression effect is realized through the designed model.

[0065] The technical solutions of the present application will be further described in detail below by means of the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0066] Figure 1 The flowchart of the present application is shown in the figure;

[0067] Figure 2 The heterogeneous graph neural network structure diagram of the present application is shown in the figure;

[0068] Figure 3 The relationship diagram of the weighted sum and the computing rate changing with the number of clusters in the network is shown in the figure;

[0069] Figure 4 The comparison diagram of the consumption time of the present application and other solutions is shown in the figure;

[0070] Figure 5 The schematic diagram of the computer device provided by an embodiment of the present application is shown in the figure;

[0071] Figure 6 The block diagram of a chip provided by an embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0072] The technical solutions in the embodiments of the present application will be described clearly and completely below by combining the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0073] In the description of the present application, it should be understood that the terms “include” and “contain” indicate the existence of described features, whole, steps, operations, elements and / or components, but do not exclude the existence or addition of one or more other features, whole, steps, operations, elements, components and / or sets thereof.

[0074] It should also be understood that the terms used in the specification of the present application are only for the purpose of describing specific embodiments and do not intend to limit the present application. As used in the specification and the appended claims of the present application, unless otherwise clearly indicated by the context, the singular forms “a”, “an” and “the” are intended to include the plural forms.

[0075] It should be further understood that the term "and / or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items, and that the term "at least one of' as used herein means "one, two, three, four, or more" and that the term "one or more of as used herein means "one, two, three, four, or more". It should be further understood that the term "comprises" as used herein is not intended to exclude the presence of terms other than those recited in the list of recited elements, and that the term "comprising" as used herein is not intended to exclude the presence or addition of one or more other elements or integers. It should be further understood that the term "coupled" as used herein means the joined, attached, connected, or linked in a direct or indirect way, and that the terms "coupled" and "connected" as used herein are used in the sense of being joined together and are not necessarily intended to exclude the presence of an intermediate member between the joined members.

[0076] It should be understood that, although the terms first, second, third, etc. can be used herein to describe various ranges or elements, these ranges or elements should not be limited by these terms. These terms are only used to distinguish one range or element from another. For example, a first range could be termed a second range without departing from the scope of the embodiments.

[0077] Depending on the context, the word "if' as used herein can be interpreted to mean "when" or "while" or "in response to the determination" or "in response to the occurrence." Similarly, the phrase "if it is determined" or "if [a stated condition or event] is detected" can be interpreted to mean "upon the determination" or "upon the occurrence" or "in response to the determination" or "in response to the occurrence" of [the stated condition or event].

[0078] Various structural diagrams according to the disclosed embodiments of the present application are shown in the accompanying drawings. These diagrams are not drawn to scale, in which certain details are shown in a somewhat exaggerated manner for the purpose of clarity and understanding, and certain details can be omitted. The shapes of various regions, layers, and the relative size and positional relationship between them shown in the drawings are only exemplary, and in actuality, they can deviate due to manufacturing tolerances or technical limitations, and a person skilled in the art can additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0079] The present application provides a multi-cluster air computing method based on deep unfolding graph neural network. First, the aggregation center node, wireless device node and edge connecting the two nodes in the heterogeneous graph neural network are defined. Second, the multi-cluster control computing optimization problem to be solved is decomposed into an unfolding structure neural network solving module. Then, the feature extraction and feature embedding method in the neural network solving module is designed. Then the designed heterogeneous graph neural network encoder aggregates the features, and the aggregated features are mapped to the variables to be optimized through the designed multilayer perceptron decoder. Finally, the parameter sharing strategy of the whole network and the learning method of the neural network are designed, the neural network is trained, and a general model is obtained. The scheme of the present application is superior to the existing optimization scheme in terms of calculation rate, and the solving speed is greatly improved, and has strong generalization ability.

[0080] Please refer to Figure 1 The application discloses a multi-cluster aerial computing method based on a deep unfolded graph neural network, and comprises the following steps:

[0081] S1, define the aggregation center node in the heterogeneous graph neural network, the wireless device node and the edge connecting the two nodes;

[0082] Please refer to Figure 2 Considering an aerial computing service coverage area, the entire area is composed of N clusters, and different aerial computing computing tasks are performed, and the set of all clusters is defined as ={1, 2,..., K}. Each cluster is equipped with an aggregation center (FC).

[0083] For a given cluster k, which contains wireless devices, the nth wireless device in the cluster is denoted as , and the set of all wireless devices is denoted as ={1, 2,..., K}.

[0084] The maximum transmission power of the wireless device is denoted as ; the kth FC is equipped with antennas, and the channel from the wireless device to the kth FC is denoted as .

[0085] When l is equal to k, denotes a communication channel; otherwise, it denotes an interference channel. The transmission factor of the wireless device is denoted as , and the receive beamforming of the FC is denoted as .

[0086] All reflection end devices in the network are defined as Node1={ }, , the first type of node in the first graph is denoted as Node1={1, 2,..., K}, , the second type of node in the graph is denoted as Node2={k}, , the channel between the first type of node and the second type of node is defined as the edge connecting the two types of nodes Edge={ }, .

[0087] S2, decompose the multi-cluster control computing optimization problem to be solved into an unfolded neural network solving module;

[0088] The aerial computing problem is unfolded into a plurality of neural network computing modules in cascade. For module j, the current channel information is inputted and the transmission factor output by the previous module , output the optimized transmission factor The solving module is encapsulated as an optimizer for transmission factors, which is internally composed of three sub-modules, namely the optimal receiving beam sub-module, the optimal transmission factor phase sub-module, and the transmission factor modulus optimization sub-module. The optimal receiving beam and the other two sub-modules adopt a cascaded structure, while the optimal transmission factor phase and the transmission factor modulus optimization sub-module adopt a parallel structure. Finally, the two modules are combined to form an optimized complex transmission factor, which can be expressed in the following mathematical form:

[0089]

[0090] wherein, represents all channel information of the entire network, represents the learnable parameters of the neural network.

[0091] The jth solving module can be abstracted as:

[0092]

[0093] S3, design a feature extraction method in the neural network solving module, to obtain key features that determine the output of the current solving module from the input channel information and the transmission factor output by the previous solving module;

[0094] For the transmission factor modulus optimization sub-module in step S2, key features reflecting the current graph neural network node are extracted from the current channel information , the optimal receiving beam , and the output transmission factor of the previous solving module The feature extraction of the wireless device node in the heterogeneous graph neural network adopts the following scheme:

[0095]

[0096] wherein, each item in the brackets represents the old transmission factor of the wireless device , the equivalent channel of the corresponding aggregation center, the interference channel to other aggregation centers, the received power of the corresponding aggregation center, and the interference power to other aggregation centers.

[0097] The feature extraction of the aggregation center node in the heterogeneous graph neural network adopts a similar scheme:

[0098]

[0099] wherein each item in the bracket represents the old mean square error of the aggregation center k, the equivalent interference channel received by the aggregation center from the effective device, the interference channel received by the aggregation center from the interference device, the effective power received by the aggregation center, and the interference power received by the aggregation center.

[0100] S4, a feature embedding method of the neural network is designed to map low-dimensional features to high-dimensional features, so that subsequent other node features can be aggregated together;

[0101] The features defined in step S3 are embedded and mapped to high-dimensional vectors. Nodes of the same type share one neural network for embedding, respectively denoted as and denote the embedding functions of the device node and the aggregation center node, and the above two embedding functions are neural networks, and the parameters are defined as and .

[0102] Therefore, the embedding operation of the device node and the aggregation center node k is represented as:

[0103]

[0104]

[0105] wherein, and respectively represent the features of the wireless device and the aggregation center k after embedding, and the embedding layer is a single-layer neural network using the tanh function as the activation function.

[0106] S5, a graph neural network encoder is designed to define the message generation and message aggregation method in the graph neural network;

[0107] The heterogeneous graph neural network encoder processes the embedding features of the nodes by using the information transmission mechanism, so that the features can be fully aggregated to represent the network characteristics, which enables each node in the network to have the information of the whole network. The encoder is composed of I layers of information transmission, and each layer of the encoder includes, the information transmission includes message generation, aggregation and combination, and these operations constitute a cascaded linear layer, wherein the operation of the i-th layer is represented as:

[0108]

[0109]

[0110] wherein, and respectively represent the information transmission related to the node features of the device and the aggregation center, and is the shared neural network parameter generated by the information generation of the device and aggregation center of the i-th layer encoder in the j-th module.

[0111] Then, for message aggregation, each node aggregates the features of other types of nodes by weighted sum, i.e., device nodes aggregate the features of center nodes, where the weight coefficient is defined as:

[0112]

[0113] Finally, the node combines the previous features and the obtained aggregated message by a linear layer with layer normalization function, which is represented as .

[0114] The information passing mechanism proposed in the heterogeneous graph neural network encoder has two special designs. First, by introducing the coefficient , the aggregation result is positively enhanced in the expected signal and negatively affected in the interference. Second, the information passing is defined so that the information is passed between different types of nodes, and the information passing between the same type of nodes is not performed, but the information of the same type of nodes is indirectly obtained in the process of multiple information passing of different types of nodes, which matches the physical model of communication.

[0115] S6, design a multi-layer perceptron as a decoder to decode the output of the graph neural network into the variables to be optimized;

[0116] A multi-layer perceptron (MLP) decoder is used to interpret the output features of the heterogeneous graph neural network encoding as the expected modulus of the transmission factor of each device.

[0117] Specifically, the decoder is represented as:

[0118]

[0119] where, represents the decoding operation, is the neural network parameter.

[0120] In addition, the SELU function is used as the activation function of the input layer and the hidden layer, while the output activation function uses Sigmoid, which is further scaled to the interval , corresponding to the range of the modulus of the transmission factor.

[0121] S7, design the whole network parameter sharing strategy and the learning method of the neural network, train the neural network, and obtain a model with good generalization ability.

[0122] For the above-mentioned expanded heterogeneous graph neural network, we need to train the network parameters to maximize the weighted sum of the air computing rate.

[0123] Therefore, the loss function is defined as:

[0124]

[0125] where, represents the distribution of the collected channel conditions.

[0126] With unsupervised learning, given the channel condition samples , the heterogeneous graph neural network is expanded to generate the transmission strategy , so as to train to obtain the highest average weighted and over-the-air computing rate, that is, to minimize the loss function. The neural network training is performed by using the stochastic gradient descent method, and the calculation in the real number field significantly simplifies the training process.

[0127] In addition, in order to improve the training efficiency and performance, a progressive learning and parameter sharing strategy is adopted. Since in the initial stage of training, the function is located in the linear region, the gradient is sparse, and it is difficult to train, therefore, the progressive learning technology is adopted, and the training is divided into two stages, wherein in the first stage, the is relaxed to .

[0128] Therefore, when the first stage of training is completed and some good parameters with differential loss are obtained, in the second stage, the is restored to further enhance the training.

[0129] In addition, the learning rate adopts an exponential decay schedule, which allows a larger step size when training in the initial stage, and a more delicate step size when approaching the optimum, so as to achieve better convergence.

[0130] In addition, for the proposed J-layer learning architecture, a parameter sharing strategy is adopted, so that the blocks in the first half share the same parameters, and the remaining blocks also share the same parameters. In this way, the number of model parameters is significantly reduced, and the training process is completed in a more memory and calculation saving manner.

[0131] Those skilled in the art can understand that various aspects of the present application can be implemented as a system, a method or a program product. Therefore, various aspects of the present application can be embodied as a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or an implementation combining hardware and software aspects, which can be collectively referred to as "circuitry", "module" or "platform" here.

[0132] In still another embodiment of the present application, a multi-cluster aerial computing system based on a deep unfolded graph neural network is provided, which can be used to implement the multi-cluster aerial computing method based on a deep unfolded graph neural network described above. Specifically, the multi-cluster aerial computing system based on a deep unfolded graph neural network includes a node module, an embedding module, an encoding module, a decoding module, and a computing module.

[0133] The node module defines the aggregation center node, the wireless device node, and the edge connecting the two nodes in the heterogeneous graph neural network, and decomposes the multi-cluster control computing optimization problem to be solved into an unfolded neural network solving module.

[0134] The embedding module designs a feature extraction method in the obtained neural network solving module, obtains key features that determine the output of the current solving module from the input channel information and the transmission factor output by the previous solving module, designs a feature embedding method for the neural network, and embeds the obtained key features to map low-dimensional features to high-dimensional features.

[0135] The encoding module designs a graph neural network encoder based on the embedded key features, and defines a method for generating and aggregating messages in the graph neural network.

[0136] The decoding module designs a multi-layer perceptron as a decoder to decode the output of the graph neural network into variables to be optimized.

[0137] The computing module designs a graph neural network parameter sharing strategy and a learning method for the graph neural network, trains the graph neural network to obtain a model with good generalization ability, inputs the channel information of the network in a new scenario into the model, outputs the transmission factor of each wireless device and the receiving beam of each aggregation center, and realizes the improvement of the multi-cluster aerial computing rate.

[0138] In another embodiment of the present application, a terminal device is provided, which comprises a processor and a memory, the memory being configured to store a computer program, the computer program comprising program instructions, and the processor being configured to execute the program instructions stored in the computer storage medium. The processor can be a central processing unit (CPU), and can also be other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, and are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions to implement a corresponding method flow or a corresponding function; the processor in the embodiments of the present application can be used for the operation of the multi-cluster aerial computing method based on the deep unfolded graph neural network, including:

[0139] Defining the aggregation center node, the wireless device node and the edge connecting the two nodes in the heterogeneous graph neural network; decomposing the multi-cluster control computing optimization problem to be solved into an unfolded neural network solving module; designing a feature extraction method in the neural network solving module to obtain key features determining the output of the current solving module from the input channel information and the transmission factor output by the previous solving module; designing a feature embedding method of the neural network to embed the obtained key features and map the low-dimensional features to high-dimensional features; designing a graph neural network encoder based on the embedded key features, defining the message generation and message aggregation method in the graph neural network; designing a multilayer perceptron as a decoder to decode the output of the obtained graph neural network into the variables to be optimized; designing a graph neural network parameter sharing strategy and a graph neural network learning method to train the graph neural network and obtain a model with good generalization ability, input the channel information of the network in a new scenario into the model, output the transmission factor of each wireless device and the receiving beam of each aggregation center, and realize the improvement of the multi-cluster aerial computing rate.

[0140] Please refer to Figure 5, the terminal device is a computer device, the computer device 60 of this embodiment includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61, and the computer program 63, when executed by the processor 61, implements the method of multi-cluster aerial computing based on a deep unfolded graph neural network in the embodiment. To avoid repetition, details are not repeated here. Alternatively, the computer program 63, when executed by the processor 61, implements the functions of each model / unit in the system of multi-cluster aerial computing based on a deep unfolded graph neural network in the embodiment. To avoid repetition, details are not repeated here.

[0141] The computer device 60 can be a desktop computer, a notebook computer, a palm computer, a cloud server, and the like. The computer device 60 can include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art can understand that the computer device 60 can include more or fewer components, or combine certain components, or include different components, for example, the computer device can also include an input / output device, a network access device, a bus, and the like. Figure 5 The computer device 60 is only an example and does not constitute a limitation on the computer device 60, and can include more or fewer components than the diagram, or combine certain components, or different components, for example, the computer device can also include an input / output device, a network access device, a bus, and the like.

[0142] The processor 61 can be a central processing unit (CPU), and can also be other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, and the like. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor.

[0143] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or a memory of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, and the like.

[0144] Further, the memory 62 can include both an internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0145] Referring to Figure 6 The terminal device is a chip, and the chip 600 of the embodiment includes one or more processors 622 and a memory 632 for storing computer programs executable by the processor 622. The computer programs stored in the memory 632 can include one or more modules each corresponding to a set of instructions. In addition, the processor 622 can be configured to execute the computer programs to perform the multi-cluster aerial computing method based on the deep unfolding graph neural network described above.

[0146] In addition, the chip 600 can further include a power supply component 626 configured to perform power management of the chip 600 and a communication component 650 configured to implement communication of the chip 600, such as wired or wireless communication. In addition, the chip 600 can further include an input / output interface 658. The chip 600 can operate based on an operating system stored in the memory 632.

[0147] In another embodiment of the present application, the present application also provides a storage medium, specifically a computer readable storage medium, which is a memory device in a terminal device and is used to store programs and data. It can be understood that the computer readable storage medium herein can include an internal storage medium in the terminal device, and of course can also include an expansion storage medium supported by the terminal device. The computer readable storage medium provides a storage space, and the storage space stores an operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by a processor are also stored in the storage space, and the instructions can be one or more computer programs. It should be noted that the computer readable storage medium herein can be a high-speed RAM memory or a non-volatile memory such as at least one disk memory.

[0148] The one or more instructions stored in the computer readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the multi-cluster aerial computing method based on the deep unfolding graph neural network in the above embodiments; the one or more instructions stored in the computer readable storage medium are loaded and executed by the processor as follows:

[0149] The aggregation center node, the wireless device node and the edge connecting the two nodes in the heterogeneous graph neural network are defined, a multi-cluster control computation optimization problem to be solved is decomposed into an unfolded neural network solving module, a feature extraction method in the neural network solving module is designed to obtain key features determining the output of the current solving module from the input channel information and the transmission factor output by the previous solving module, a feature embedding method of the neural network is designed to embed the obtained key features and map the low-dimensional features to high-dimensional features, a graph neural network encoder is designed based on the embedded key features, a message generation and message aggregation method in the graph neural network is defined, a multilayer perceptron is designed as a decoder to decode the output of the obtained graph neural network into variables to be optimized, a graph neural network parameter sharing strategy and a learning method of the graph neural network are designed, the graph neural network is trained to obtain a model with good generalization ability, channel information of the network in a new scenario is input into the model, transmission factors of each wireless device and receiving beams of each aggregation center are output, and the multi-cluster air computing rate is improved.

[0150] To make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work belong to the scope of protection of the present application.

[0151] Please refer to Figure 3 , a diagram showing the relationship between the system weighted sum and the computation rate with the number of clusters in the network is given.

[0152] The present application shows the results of the air computing rate changing with the number of clusters under different schemes. Overall, the air computing rate increases with the increase of the number of clusters, but gradually tends to saturation. Especially when the number of clusters exceeds 4, the rate of the adaptive transmission and the maximum power transmission scheme decreases instead. In contrast, the learning scheme of the present application achieves better performance than the traditional alternating optimization scheme in the 5-cluster training scenario. In addition, when the number of clusters is larger, the scheme of the present application has strong generalization ability, and its performance advantage is more obvious. The reason is that the traditional optimization method can only achieve a suboptimal solution, which is more significant when the number of clusters increases and the interference increases; while the learning method of the present application can extract the feature representation of the air computing network, bringing performance improvement. The expanded multi-layer perception scheme has limited performance due to the lack of design for feature aggregation of different types of nodes.

[0153] Please refer to Figure 4 , which gives the comparison chart of the time consumed by the scheme of the present application and other schemes.

[0154] Generally speaking, the alternating optimization method needs a large number of iterations, while the adaptive power and maximum power scheme is almost a closed-form solution, and the learning-based method can be quickly executed. We show the average running time of the alternating optimization scheme in 5000 random deployments, and the total running time of the remaining schemes under the same settings. The results show that the neural network can almost output instantaneously, which is much more efficient than iterative optimization. It can be seen that the expanded learning of the present application has a significant performance advantage and is further enhanced by fine-tuning.

[0155] In summary, the multi-cluster air computing method and system based on deep expanded graph neural network of the present application have better performance than traditional methods. In addition, the structure based on heterogeneous graph neural network gives strong generalization ability, which can adapt to different network scenarios, and the learned interference management ability significantly improves the performance of air computing.

[0156] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above functional units and modules is exemplified, and in actual application, the above functions can be completed by different functional units and modules according to needs, that is, the internal structure of the device is divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated in one processing unit, or each unit can be physically present separately, or two or more units can be integrated in one unit. The above integrated unit can be realized in the form of hardware or software function unit. In addition, the specific names of each functional unit and module are only for easy distinction, and do not limit the protection scope of the present application. The specific working process of the units and modules in the above system can refer to the corresponding process in the foregoing method embodiments, which will not be repeated here.

[0157] In the above embodiments, the description of each embodiment has its own focus, and the parts not described or recorded in a certain embodiment can be referred to the relevant description of other embodiments.

[0158] Those skilled in the art can understand that the units and algorithm steps of each example described in combination with the embodiments disclosed in the present application can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software mode depends on the specific application and design constraints of the technical solution. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0159] In the embodiments provided by the present application, it should be understood that the disclosed apparatus / terminal and method can be implemented in other ways. For example, the apparatus / terminal embodiments described above are merely schematic, for example, the division of the modules or units is only a logical function division, and actual implementation can have another division manner, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the displayed or discussed each other can be indirect coupling or communication connection through some interface, device or unit, which can be electrical, mechanical or other forms.

[0160] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, that is, they can be located in one place, or they can be distributed on a plurality of network units. According to actual needs, part or all of the units can be selected to achieve the purpose of the embodiment.

[0161] In addition, each functional unit in each embodiment of the present application can be integrated in one processing unit, or each unit can be physically present separately, or two or more units can be integrated in one unit. The integrated unit can be realized in the form of hardware or in the form of a software functional unit.

[0162] The integrated module / unit, if realized in the form of a software function unit and sold or used as an independent product, can be stored in a computer-readable storage medium. Based on such understanding, all or part of the processes in the above-mentioned embodiment methods can also be completed by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of each method embodiment when executed by a processor. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or some intermediate forms, etc. The computer-readable medium can include any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the computer-readable medium can include or exclude contents according to the requirements of legislation and patent practice in the jurisdiction, for example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0163] The present application is described with reference to flowcharts and / or block diagrams of methods, devices, and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in one or more flows and / or blocks Figure 1 The functions specified in one or more flows and / or blocks

[0164] These computer program instructions can also be stored in a computer-readable memory that can direct the computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including instruction devices that implement the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in one or more flows and / or blocks Figure 1 The functions specified in one or more flows and / or blocks

[0165] These computer program instructions can also be loaded into a computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable data processing devices to generate a computer implemented process, so that the instructions executed on the computer or other programmable data processing devices provide a process for implementing the flowchart Figure 1 one flow or a plurality of flows and / or the functions specified in the block Figure 1 one block or a plurality of blocks.

[0166] The above is only to illustrate the technical idea of the present application, and cannot limit the protection scope of the present application. Any modification made according to the technical idea of the present application on the basis of the technical scheme falls within the protection scope of the claims of the present application.

Claims

1. A multi-cluster aerial computing method based on a deep unfolded graph neural network, characterized in that, Comprising the following steps: S1, define the aggregation center node in the heterogeneous graph neural network, the wireless device node and the edge connecting the two nodes; S2, based on the aggregation center node, wireless device node and edge connecting the two nodes defined in step S1, decompose the multi-cluster control calculation optimization problem to be solved into an expanded neural network solving module, expand the air computing problem into a cascaded multiple neural network calculation module, for module j, input the current channel information } and the transmission factor output by the last module , output the optimized transmission factor ; The solving module is packaged as an optimizer for the transmission factor, which internally includes an optimal receiving beam submodule, an optimal transmission factor phase submodule and a transmission factor modulus optimization submodule, the optimal receiving beam submodule is in a cascaded structure with the optimal transmission factor phase submodule and the transmission factor modulus optimization submodule, the optimal transmission factor phase submodule and the transmission factor modulus optimization submodule are in a parallel structure, and finally combined to form an optimized complex transmission factor; S3, design a feature extraction method in the neural network solving module obtained in step S2, to obtain key features that determine the output of the current solving module from the input channel information and the transmission factor output by the previous solving module, and the feature extraction of the wireless device node in the heterogeneous graph neural network adopts the following scheme: wherein, the wireless device characterized by the terms in the brackets, respectively, representing the old transmission factor of the wireless device , the equivalent channel of the corresponding aggregation center, the interference channel to other aggregation centers, the received power of the corresponding aggregation center, and the interference power to other aggregation centers. The feature extraction of the aggregation center node in the heterogeneous graph neural network adopts a similar scheme: wherein, is the characteristic of the aggregation center k input to the jth solving module, wherein each item in the bracket represents the old mean square error of the aggregation center k, the equivalent interference channel sum from the effective device received by the aggregation center, the interference channel sum from the interference device received by the aggregation center, the effective power sum received by the aggregation center, and the interference power sum received by the aggregation center; S4, a feature embedding method of the neural network is designed, the key features obtained in step S3 are embedded, the low-dimensional features are mapped to high-dimensional features, and the device nodes and the embedding operation of the aggregation center node k is represented as: wherein, and respectively represent the features of the wireless devices and the aggregation center k after embedding, the embedding layer is a single-layer neural network, and a tanh function is used as an activation function, is a device feature embedding neural network, is a device feature embedding neural network parameter, is an aggregation center feature embedding neural network parameter, is an embedding feature output by the aggregation center k through the embedding layer, is a device output by the device through the feature embedding layer; S5, based on the key feature design figure neural network encoder embedded in step S4, define the method of message generation and message aggregation in graph neural network, the encoder is composed of I layer information transmission, each layer of the encoder includes, information transmission includes message generation, aggregation and combination, constitutes a cascade linear layer, for message aggregation, each node aggregates the features of other types of nodes through weighted sum, that is, device nodes aggregate the features of center nodes, nodes combine the previous features and the obtained aggregated messages through a linear layer with layer normalization function, this process is represented as ; introduce the coefficient in the information transmission mechanism proposed in the heterogeneous graph neural network encoder, define the information transmission, so that information is transmitted between different types of nodes, and information transmission is not performed between nodes of the same type; S6, design a multilayer perceptron as a decoder to decode the output of the graph neural network obtained in step S5 into variables to be optimized; S7, design a graph neural network parameter sharing strategy and a graph neural network learning method, train the graph neural network, obtain a model with good generalization ability, input the channel information of the network in a new scenario into the model, output the transmission factor of each wireless device and the receiving beam of each aggregation center, and realize the improvement of the multi-cluster air computing rate.

2. The deep unfolding graph neural network based multi-cluster aerial computing method according to claim 1, wherein, In step S1, the air computing service coverage area includes N clusters, the N clusters perform different air computing computing tasks, and the set of all clusters is defined as ={1, 2,..., K}; the center of each cluster is equipped with an aggregation center; For a given cluster k, containing A wireless device, using This represents the nth wireless device in the cluster. ={1, 2, ..., } represents the set of all wireless devices; Wireless device The maximum transmission power of the wireless device is denoted as The kth aggregation center is equipped with antennas, and denotes the channel from the wireless device to the kth aggregation center. when l is equal to k, denotes a communication channel; otherwise, it denotes an interference channel; Wireless device The transmission factor of , the receive beamforming of the aggregation center is ; Define all reflective end devices as Node1={ }, Let represent the first type of node in the first type of graph; define the aggregation center of all receivers as Node2={k}. , representing the second type of node in the graph; The channel between the first type of node and the second type of node is defined as the edge Edge={ }, .

3. The deep unfolding graph neural network based multi-cluster aerial computing method according to claim 1, wherein, The cascaded multiple neural network computing modules are specifically: wherein, is the channel information of the entire network, is the learnable parameter of the neural network, is the receive beam of the aggregation center k, is the receive beamforming optimization submodule, is the input transmission factor of the jth solving module, is the nth wireless device of the lth cluster, is the set of aggregation centers, is the phase of the output transmission factor of the jth solving module, is the transmission factor phase optimization submodule, is the device to the aggregation center k, is the nth device of the kth cluster, is the set of wireless devices of the kth cluster, is the output transmission factor module value of the jth solving module, is the transmission factor phase submodule, is the output transmission factor of the jth solving module, is the set of wireless devices of the lth cluster.

4. The deep unfolding graph neural network based multi-cluster aerial computing method according to claim 1, wherein, In step S6, the decoder is represented as: wherein, denotes a decoding operation, are neural network parameters, with a SELU function as activation function for the input layer and the hidden layers, and a Sigmoid for the output activation function.

5. The deep unfolding graph neural network based multi-cluster aerial computing method according to claim 1, wherein, In step S7, the loss function is: wherein, denotes a channel random variable averaged, denotes an over-the-air computation rate function, denotes an unrolled heterogeneous graph neural network generating a transmission policy, denotes a channel condition sample.

6. A multi-cluster aerial computing system based on deep unfolded graph neural networks, characterized in that, Comprising: A node module for defining the aggregation center node in the heterogeneous graph neural network, the wireless device node and the edge connecting the two nodes; The multi-cluster control computation optimization problem to be solved is decomposed into an unfolded structure neural network solving module, and an air computation problem is unfolded into a cascaded plurality of neural network computation modules. For a module j, input current channel information and a transmission factor output by a previous module , and output an optimized transmission factor ; The solving module is packaged as an optimizer for the transmission factor, which internally includes an optimal receiving beam submodule, an optimal transmission factor phase submodule and a transmission factor modulus optimization submodule, the optimal receiving beam submodule is in a cascaded structure with the optimal transmission factor phase submodule and the transmission factor modulus optimization submodule, the optimal transmission factor phase submodule and the transmission factor modulus optimization submodule are in a parallel structure, and finally combined to form an optimized complex transmission factor; An embedding module for designing a feature extraction method in the neural network solving module, to obtain key features that determine the output of the current solving module from the input channel information and the transmission factor output by the previous solving module, and the feature extraction of the wireless device node in the heterogeneous graph neural network adopts the following scheme: wherein, the wireless device is characterized by the quantities in the brackets, which represent, respectively, the old transmission factor of the wireless device , the equivalent channel to the corresponding aggregation center, the interference channel to other aggregation centers, the received power from the corresponding aggregation center, and the interference power from other aggregation centers. The feature extraction of the aggregation center node in the heterogeneous graph neural network adopts a similar scheme: wherein, The features of the aggregation center k input to the jth solving module, each item in the parentheses represents the old mean square error of the aggregation center k, the equivalent interference channel sum received by the aggregation center from the effective device, the interference channel sum received by the aggregation center from the interference device, the effective power sum received by the aggregation center, the interference power sum received by the aggregation center, the feature embedding method for designing the neural network, embedding the obtained key features, mapping low-dimensional features to high-dimensional features, device node The embedding operation of the aggregation center node k is represented as: wherein, and respectively represent the embedding of the wireless device and the aggregation center k features, the embedding layer is a single layer neural network using a tanh function as the activation function, is a device feature embedding neural network, is a device feature embedding neural network parameter, is an aggregation center feature embedding neural network parameter, is the embedding feature output by the aggregation center k through the embedding layer, is a device output by the feature embedding layer; The coding module is based on the embedded key feature design graph neural network encoder, defines the method of message generation and message aggregation in the graph neural network, and the encoder is composed of I layer information transmission, each layer of the encoder includes, the information transmission includes message generation, aggregation and combination, constitutes a cascaded linear layer, for message aggregation, each node aggregates the features of other types of nodes through weighted sum, that is, the device node aggregates the features of the center node, and the node combines the previous features and the obtained aggregated message through a linear layer with layer normalization function, and the process is represented as ; The coefficient is introduced in the information transmission mechanism proposed in the heterogeneous graph neural network encoder , the information transmission is defined to enable information transmission between different types of nodes, and the same type of nodes does not transmit information between them; A decoding module for designing a multilayer perceptron as a decoder to decode the output of the graph neural network into variables to be optimized; A computing module for designing a graph neural network parameter sharing strategy and a graph neural network learning method, training the graph neural network, obtaining a model with good generalization ability, inputting the channel information of the network in a new scenario into the model, outputting the transmission factor of each wireless device and the receiving beam of each aggregation center, and realizing the improvement of the multi-cluster air computing rate.

7. The deep unfolding graph neural network-based multi-cluster aerial computing system of claim 6, wherein, In step S1, the air computing service coverage area includes N clusters, the N clusters perform different air computing computing tasks, and the set of all clusters is defined as {1, 2,..., K}; the center of each cluster is equipped with an aggregation center; For a given cluster k, containing A wireless device, using This represents the nth wireless device in the cluster. ={1, 2, ..., } represents the set of all wireless devices; Wireless device The maximum transmission power of the wireless device is denoted as ; the kth aggregation center is equipped with antennas, and denotes the channel from the wireless device to the kth aggregation center. when l is equal to k, denotes a communication channel; otherwise, it denotes an interference channel; Wireless device The transmission factor of the wireless device is The receive beamforming of the aggregation center is ; Define all reflective end devices as Node1={ }, Let represent the first type of node in the first type of graph; define the aggregation center of all receivers as Node2={k}. , representing the second type of node in the graph; The channel between the first type of node and the second type of node is defined as the edge Edge={ }, .

8. The deep unfolding graph neural network-based multi-cluster aerial computing system of claim 6, wherein, The cascaded multiple neural network computing modules are specifically: wherein, is the channel information for the entire network, is the learnable parameter of the neural network, is the receive beam of the aggregation center k, is the receive beamforming optimization sub-module, is the input transmission factor of the jth solving module, is the nth wireless device of the lth cluster, is the set of aggregation centers, is the phase of the output transmission factor of the jth solving module, is the transmission factor phase optimization sub-module, is the device to the aggregation center k, is the nth device of the kth cluster, is the set of wireless devices of the kth cluster, is the output transmission factor modulus of the jth solving module, is the transmission factor phase sub-module, is the output transmission factor of the jth solving module, is the set of wireless devices of the lth cluster.

9. The deep unfolding graph neural network-based multi-cluster over-the-air computing system of claim 6, wherein, The decoder is represented as: wherein, denotes a decoding operation, are neural network parameters, with a SELU function as activation function for the input layer and the hidden layers, and a Sigmoid for the output activation function.

10. The deep unfolding graph neural network-based multi-cluster over-the-air computing system of claim 6, wherein, Loss function is: wherein, denotes a channel random variable averaged, denotes an over-the-air computation rate function, denotes an unrolled heterogeneous graph neural network generating a transmission policy, denotes a channel condition sample.

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