Radio map prediction method and device integrating physical equations and deep learning

Abstract

This invention discloses a radio map prediction method and apparatus that integrates physical equations and deep learning, belonging to the field of communication technology. The method includes: inputting an environmental map of the environment to be tested and base station location information into a trained singularity map prediction network to obtain a singularity map of the environment to be tested; wherein the singularity map prediction network is trained based on sample singularity maps, and the sample singularity maps are calculated according to the Helmholtz equation; inputting the singularity map, environmental map, and base station location information into the trained radio map prediction network to obtain a radio map of the environment to be tested. This invention has low computational complexity, wide applicability, and good prediction accuracy.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically relating to a radio map prediction method and apparatus that integrates physical equations and deep learning. Background Technology

[0002] Driven by the growing demand for intelligence and proactive optimization in sixth-generation (6G) networks, wireless communication is shifting towards an environment-aware paradigm, making the construction of accurate radio maps (RMs) to provide location-specific wireless channel characteristics crucial. Current work on radio map prediction primarily utilizes traditional methods and data-driven approaches.

[0003] Traditional methods for electromagnetic computation are based on geometric programming or numerical solutions, such as ray tracing, the finite element method, and the finite-difference time-domain method. These methods rely on accurate numerical solutions to physical models of electromagnetic wave propagation, typically requiring detailed geometric information and complex mathematical models to simulate electromagnetic wave reflection, refraction, and scattering. Therefore, the computational complexity of these methods increases dramatically with environmental complexity, especially in urban environments with numerous obstacles and reflective surfaces, where computation times can be extremely long. Furthermore, because they are based on static environmental models, they struggle to handle dynamically changing factors.

[0004] Data-driven methods typically employ neural networks, such as RadioUNet, Generative Adversarial Networks (GANs), or the more recent Radio Diffusion Model (RadioDiff). These methods construct radio maps by analyzing vast amounts of data, learning complex radio signal propagation patterns and generating high-resolution radio maps, thus reducing reliance on physical models. While this approach eliminates the need for physical environment modeling, data-driven methods often treat radio signal propagation as a black box process, ignoring the physical laws governing electromagnetic wave propagation. This can lead to models failing to generalize to new environments or scenarios. Although their prediction efficiency is high, ignoring physical laws during prediction makes it difficult to model electromagnetic singularities caused by multipath effects, resulting in insufficient prediction accuracy.

[0005] Therefore, traditional electromagnetic calculation methods are difficult to apply due to their high computational complexity. Current neural network methods cannot effectively capture electromagnetic singularities caused by multipath effects (such as abrupt changes in path loss), resulting in insufficient reconstruction accuracy. Summary of the Invention

[0006] This invention provides a radio map prediction method and apparatus that integrates physical equations and deep learning, which can solve the problems of current radio map prediction methods being either too computationally complex and have a narrow range of applications, or have poor prediction accuracy.

[0007] In a first aspect, embodiments of the present invention provide a radio map prediction method that integrates physical equations and deep learning, the method comprising:

[0008] The environment map of the test environment and the base station location information are input into the trained singularity map prediction network to obtain the singularity map of the test environment.

[0009] The singular point map prediction network is trained based on sample singular point maps, which are calculated based on the Helmholtz equation and sample radio maps.

[0010] The singularity map, the environment map, and the base station location information are input into a trained radio map prediction network to obtain a radio map of the environment to be tested.

[0011] Secondly, embodiments of the present invention provide a radio map prediction device that integrates physical equations and deep learning, comprising:

[0012] The singular point map prediction unit is used to input the environmental map of the environment to be tested and the base station location information into the trained singular point map prediction network to obtain the singular point map of the environment to be tested.

[0013] The singular point map prediction network is trained based on sample singular point maps, which are calculated based on the Helmholtz equation and sample radio maps.

[0014] A radio map prediction unit is used to input the singularity map, the environment map, and the base station location information into a trained radio map prediction network to obtain a radio map of the environment to be tested.

[0015] The beneficial effects of this invention compared to existing technologies are as follows: The method provided by this invention first predicts a singularity map, and then generates a radio map under the guidance of the singularity map. Since these electromagnetic singularities are caused by complex multipath effects, they can affect the characteristics of the wireless channel and produce drastic spatial changes. This is key information that traditional data-driven methods find difficult to capture accurately. Therefore, the method provided by this invention can improve the prediction accuracy of the radio map. Furthermore, this invention uses a sample singularity map calculated based on the Helmholtz equation to train the singularity map prediction network, instead of directly embedding partial differential equation (PDE) constraints in the loss function. This allows the physical law of the Helmholtz equation to be explicitly integrated into the learning process of the neural network, effectively guiding the learning of the singularity map prediction network and accurately extracting electromagnetic singularities. Attached Figure Description

[0016] Figure 1 A flowchart illustrating the implementation of a training method for a singularity map prediction network and a radio map prediction network provided in an embodiment of the present invention;

[0017] Figure 2 A flowchart illustrating a predictive radio map provided in an embodiment of the present invention;

[0018] Figure 3 This is a schematic diagram of a process for generating a sample singularity map according to an embodiment of the present invention;

[0019] Figure 4 A flowchart illustrating the implementation of a radio map prediction method that integrates physical equations and deep learning, provided in an embodiment of the present invention.

[0020] Figure 5 A schematic diagram of the structure of a radio map prediction device that integrates physical equations and deep learning, provided for an embodiment of the present invention;

[0021] Figure 6 A comparative schematic diagram of radio maps predicted by different methods provided in an embodiment of the present invention;

[0022] Figure 7 A comparative schematic diagram showing radio maps predicted by another different method provided in an embodiment of the present invention. Detailed Implementation

[0023] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0024] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0025] It should also be understood that the term “and / or” as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0026] As used in this specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if [described condition or event] is detected" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once [described condition or event] is detected," or "in response to detection of [described condition or event]."

[0027] Furthermore, in the description of this invention and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0028] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of the invention include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0029] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0030] The method provided in this embodiment of the invention can be applied to electronic devices such as mobile terminals, personal laptops, and supercomputers. This embodiment of the invention does not impose any restrictions on the specific type of electronic device.

[0031] Example 1

[0032] Figure 1 The diagram illustrates a training method for a singularity map prediction network and a radio map prediction network provided by an embodiment of the present invention. As an example and not a limitation, the method may include steps S101-S107, which are described below.

[0033] S101, input the sample environment map and sample base station location information of round t into the singular point map prediction network after round t iteration to obtain the prediction result of the singular point map prediction network in round t.

[0034] In one example, the sample environment map can be a binary matrix used to describe the distribution of static obstacles.

[0035] For example, see Figure 2 Sample environment map 201. Sample environment map It can be represented as ,in This represents the size of the sample environment map. If a matrix element at a certain location is 1, it indicates that there is an obstacle at that location that completely blocks electromagnetic waves (internal path loss is 0). If a matrix element at a certain location is 0, it indicates that there is no obstacle at that location.

[0036] Sample base station location information refers to the location information of base stations used as samples. In one example, base station location information can be defined by triples to describe the location and altitude of the base station.

[0037] For example, base station location information It can be represented as ,in For base station height, , These represent the coordinates of the base station on the horizontal and vertical axes, respectively.

[0038] In one example, see Figure 2 In the example 202, the prediction result of the singularity map prediction network in round t can be a predicted singularity map. This singularity map can also be a binary matrix, where the elements can be 0 or 1; 0 indicates that this is not an electromagnetic singularity, and 1 indicates that this is an electromagnetic singularity.

[0039] S102, input the sample environment map of round t, the sample base station location information, and the prediction results of the singular point map prediction network of round t into the radio map prediction network after round t iteration, and obtain the prediction results of the radio map prediction network of round t.

[0040] For example, see Figure 2 In the singularity map prediction network (see...) Figure 2 202) Based on the sample environment map (see Figure 2 The sample base station location information (not shown here) is used to generate a predicted singularity map (see 201). Figure 2 After step 203), the inputs and outputs of the singularity map prediction network can be fed together into the radio map prediction network (see [reference]). Figure 2 In 204), the predicted radio map was obtained (see [reference]). Figure 2 (205 in the middle).

[0041] S103. Based on the prediction results of the singular point map prediction network in round t and the sample singular point map, determine the t-th loss value of the singular point map prediction network.

[0042] In one possible implementation, the sample singularity map can be calculated based on the Helmholtz equation.

[0043] For example, see Figure 3 It can be based on the discretized Helmholtz equations, according to the sample radio map (see...). Figure 3 301) calculation Map (see map) Figure 3 (302 in the middle), then filter In the map The region was used to obtain a sample singularity map (see [reference]). Figure 3 (303 in the middle).

[0044] Therefore, the sample singularity map The following formula can be satisfied:

[0045] ,

[0046] in, This represents a binary matrix containing information about all pixels in the entire sample singularity map. Location of sample singularities in the map The value at this location indicates the position. Is this a singularity? (abbreviated as) The position is calculated using the discretized Helmholtz equation. The electromagnetic singularity value at that location.

[0047] Specifically, the sample singularity map, sample radio map, sample environment map, and the environment map, singularity map, and radio map of the environment under test are all maps of the same size. Each pixel on the map corresponds to a location area in the actual environment. A positive integer less than or equal to the map's horizontal dimension. It is a positive integer less than or equal to the vertical dimension of the map.

[0048] For example, electromagnetic singularities (EMS) are caused by complex electromagnetic wave interactions (such as multipath interference) and manifest as abrupt changes in wireless channel characteristics (such as path loss and angle of arrival), which can directly affect communication performance.

[0049] Specifically, the sample radio map can be targeted at discretized... The grid is constructed for specific geographic regions, with each grid cell being small enough to ensure constant path loss within its cells, allowing the sample radio maps to be processed through the path loss matrix. This indicates. Therefore, , Both can be less than or equal to Positive integers.

[0050] In one example, the discretized Helmholtz equation can be expressed by the following formula:

[0051] ,

[0052] in, It is the Laplace operator. express The sum of the second-order partial derivatives, Indicates the location in the sample radio map Electromagnetic wave intensity at that location Let be the area size of each pixel in the sample singularity map. Location in the sample radio map Electromagnetic wave intensity at that location Location in the sample radio map Electromagnetic wave intensity at that location Location in the sample radio map Electromagnetic wave intensity at that location Location in the sample radio map The electromagnetic wave intensity at that location.

[0053] For example, in calculating via discretized Helmholtz equations Dirichlet boundary conditions also need to be applied: ;in, The values ​​of the sample radio map at the boundary points. It is the set of all boundary points.

[0054] For example, the loss value of a singularity map prediction network can be calculated using the following loss function:

[0055] ,

[0056] in, This represents the loss value of the singularity map prediction network. The dimensions of the singularity map and the sample environment map. For singularity map prediction networks, the location is predicted. The prediction results at that location.

[0057] Traditional physical information neural networks (RMs) typically enhance the Helmholtz equation constraints by adding a loss term to the loss function, such as adding a partial differential term calculated by the Helmholtz equation after the binary cross-entropy. However, extensive experiments have shown that RM reconstruction involves highly discontinuous spatial features (such as abrupt changes in path loss), and directly applying PDE constraints can lead to overly smooth prediction results, resulting in the loss of crucial details.

[0058] Therefore, this invention uses a sample singular point map calculated based on the discretized Helmholtz equation to train the singular point map prediction network, instead of directly embedding PDE constraints. This allows the Helmholtz equation to be integrated as a physical constraint into the network training process, achieving a balance between physical laws and data-driven approaches.

[0059] S104. Based on the prediction results of the radio map prediction network in round t and the sample radio maps, determine the t-th loss value of the radio map prediction network.

[0060] In one example, the t-th loss value of the radio map prediction network can be calculated using the following loss function:

[0061] ,

[0062] in, This represents the loss value of the radio map prediction network. For radio map prediction networks in location The prediction results at the location, Indicates the location in the sample radio map The electromagnetic wave intensity at that location.

[0063] S105, update the network parameters of the singular point map prediction network and the radio map prediction network according to the t-th loss value of the singular point map prediction network and the t-th loss value of the radio map prediction network, respectively, to obtain the singular point map prediction network and the radio map prediction network after the (t+1)-th iteration.

[0064] In one example, the singularity map prediction network can be updated based on the t-th loss value of the singularity map prediction network using the backpropagation algorithm. The network parameters are used to obtain the singularity map prediction network after the (t+1)th iteration; the radio map prediction network is updated based on the t-th loss value of the radio map prediction network. The network parameters are used to obtain the radio map prediction network after the (t+1)th iteration.

[0065] For example, the training objectives of these two networks can be expressed as:

[0066]

[0067] in, Indicates by , The overall network Network parameters, This represents the predicted radio map. Represents a sample radio map, The actual value of the radio map; The training objective is to minimize and Differences between . Indicates will , Input overall network After that, you can get .

[0068] S106, Determine whether the preset convergence conditions are met.

[0069] In one example, if the preset convergence condition is met, the following step S107 can be performed.

[0070] For example, the preset convergence condition can be that t is greater than or equal to the maximum number of training iterations. The accuracy rate is greater than the minimum accuracy threshold, etc.

[0071] In another example, if the preset convergence condition is not met, t can be set to t+1, and the next round of training can begin from step S101.

[0072] S107, the singular point map prediction network after the (t+1)th iteration and the radio map prediction network after the (t+1)th iteration are respectively output as the trained singular point map prediction network and the trained radio map prediction network.

[0073] According to the training method provided by the present invention, the singular point map prediction network is trained by using a sample singular point map calculated based on the discretized Helmholtz equation, rather than directly embedding PDE constraints. This allows the Helmholtz equation to be integrated as a physical constraint into the network training process, achieving a balance between physical laws and data-driven approaches, thereby improving the prediction accuracy of the radio map prediction network.

[0074] Example 2

[0075] Figure 4 The diagram illustrates a flowchart of a radio map prediction method integrating physical equations and deep learning, provided by an embodiment of the present invention. As an example and not a limitation, the method may include steps S401-S402. The steps are described below.

[0076] S401, input the environment map of the environment to be tested and the base station location information into the trained singularity map prediction network to obtain the singularity map of the environment to be tested.

[0077] For example, similar to the sample environment map and sample base station location information, the environment map and base station location information of the environment under test can be represented by a binary matrix. and triplet express.

[0078] S402, input the singularity map, environment map and base station location information into the trained radio map prediction network to obtain the radio map of the environment to be tested.

[0079] For example, see Figure 2 After obtaining the singularity map, the input and output of the singularity map prediction network can be fed into the radio map prediction network to obtain the final result (i.e., the radio map of the environment under test).

[0080] Specifically, both the singularity map prediction network and the radio map prediction network used here can be trained using the training methods described above.

[0081] This invention first predicts a singularity map, and then generates a radio map guided by the singularity map. Since these electromagnetic singularities are caused by complex multipath effects, they can significantly alter the spatial characteristics of the wireless channel, providing crucial information that traditional data-driven methods struggle to capture accurately. Therefore, this method improves the prediction accuracy of the radio map. Furthermore, this invention trains the singularity map prediction network using sample singularity maps calculated based on the Helmholtz equation, rather than directly embedding PDE constraints into the loss function. This explicitly integrates the physical laws of the Helmholtz equation into the neural network's learning process, effectively guiding the network's learning and accurately extracting electromagnetic singularities. In addition, using a neural network-based data-driven method for radio map prediction, instead of a traditional static model, reduces computational complexity and improves prediction efficiency. Moreover, when the operating environment changes, only environmental and base station information needs to be re-acquired and input; there is no need to remodel based on specific environments, improving the method's applicability. This meets the future demands of 6G networks for high speed, large connection count, low latency, and high service quality.

[0082] Example 3

[0083] Figure 5 The diagram shown illustrates the structure of a radio map prediction device integrating physical equations and deep learning, provided by an embodiment of the present invention. As an example and not a limitation, the device may include a singularity map prediction unit 510 and a radio map prediction unit 520.

[0084] For example, the singularity map prediction unit 510 is used to input the environment map of the test environment and the base station location information into the trained singularity map prediction network to obtain the singularity map of the test environment; wherein, the singularity map prediction network is trained based on the sample environment map, sample base station location information and sample singularity map, and the sample singularity map is calculated based on the Helmholtz equation; the radio map prediction unit 520 is used to input the singularity map, environment map and base station location information into the trained radio map prediction network to obtain the radio map of the test environment.

[0085] In one example, the sample singularity map can satisfy the following formula:

[0086] ,

[0087] in, Location of sample singularities in the map The value at this location indicates the position. Is this a singularity? The position is calculated using the discretized Helmholtz equations. The electromagnetic singularity value at that location.

[0088] In one example, the discretized Helmholtz equation can satisfy the following formula:

[0089] ,

[0090] in, It is the Laplace operator. express The sum of the second-order partial derivatives, Indicates the location in the sample radio map Electromagnetic wave intensity at that location Let be the area size of each pixel in the sample singularity map. Location in the sample radio map Electromagnetic wave intensity at that location Location in the sample radio map Electromagnetic wave intensity at that location Location in the sample radio map Electromagnetic wave intensity at that location Location in the sample radio map The electromagnetic wave intensity at that location.

[0091] In one example, the loss function used by the singularity map prediction network during training can satisfy the following formula:

[0092] ,

[0093] in, This represents the loss value of the singularity map prediction network. The dimensions of the singularity map and the sample environment map. For singularity map prediction networks, the location is predicted. The prediction results at that location.

[0094] In one example, the loss function used by the radio map prediction network during training can satisfy the following formula:

[0095] ,

[0096] in, This represents the loss value of the radio map prediction network. For radio map prediction networks in location The prediction results at the location, Indicates the location in the sample radio map The electromagnetic wave intensity at that location.

[0097] The device provided by this invention first predicts a singularity map, and then generates a radio map under the guidance of the singularity map. Since these electromagnetic singularities are caused by complex multipath effects, they can affect the characteristics of the wireless channel and produce drastic spatial changes. This is key information that traditional data-driven methods find difficult to capture accurately, thus improving the prediction accuracy of the radio map. Furthermore, this invention uses sample singularity maps calculated based on the Helmholtz equation to train the singularity map prediction network, instead of directly embedding PDE constraints in the loss function. This allows the physical law of the Helmholtz equation to be explicitly integrated into the learning process of the neural network, effectively guiding the learning of the singularity map prediction network and accurately extracting electromagnetic singularities.

[0098] To better illustrate the beneficial effects of the present invention, the following simulation experiments were conducted:

[0099] For example, the method provided by this invention can be evaluated using the RadioMapSeer dataset in a simulation experiment. This dataset includes 700 radio maps containing detailed geographic information, such as building layouts, and 80 transmitter locations and their corresponding real-world data. These maps vary in complexity, with each scenario containing 50 to 150 buildings. In the experiment, the dataset can be divided into 500 training maps and 200 test maps, ensuring no overlap in terrain information to prevent data leakage. The transmitter's transmit power is set to 23 dBm, and the carrier frequency is fixed at 5.9 GHz.

[0100] Specifically, widely used metrics such as normalized mean square error (MSE) and root mean square error (RMSE) can be used for evaluation. To better capture the fine-grained spatial variations crucial for wireless channel reconstruction, additional evaluation metrics can be used, such as the Structural Similarity Index (SSIM) and Peak Signal-to-Noise Ratio (PSNR). SSIM measures the preservation of structural details, while PSNR assesses the fidelity of reconstructed features, particularly the accuracy of edge signals for path loss variations, which is essential for modeling abrupt changes in path loss caused by multipath effects.

[0101] Meanwhile, all experiments were run on NVIDIA Tesla A40 GPUs. Methods trained using PDE physical loss were labeled "w / PDE", while methods not using PDE physical loss were labeled "w / oPDE".

[0102] Table 1

[0103]

[0104] Table 2

[0105]

[0106] Tables 1 and 2 above show the evaluation results of different methods. Compared with methods based on convolutional neural networks (RadioUNet), generative adversarial networks (RME-GAN), the Mamba architecture (UVM-Net), and state-of-the-art (SOTA) methods based on diffusion models (RadioDiff), it can be seen that the present invention achieves the best performance on all evaluation metrics, surpassing traditional deep learning methods.

[0107] Specifically, referring to the evaluation results in the Dominant Path Model (DPM) scenario shown in Table 1, it can be seen that the present invention achieves nearly twice the improvement in NMSE index compared to the RadioDiff method, which indicates that the physical information-guided singularity extraction strategy has significant advantages in radio map construction tasks.

[0108] Specifically, referring to the evaluation results in the Intelligent Ray Tracing (IRT) scenario shown in Table 2, it can be seen that, regardless of the method, the performance of the model actually decreases after training with PDE physical loss.

[0109] Table 3 Training time for different methods

[0110]

[0111] For example, Table 3 above shows the inference time for different methods. It can be seen that the computational efficiency of the present invention is extremely high, only 1 / 30th that of the RadioDiff method, which proves that the present invention has extremely high scalability and practicality.

[0112] Figure 6 The diagram shown is a comparison of radio maps predicted by different methods according to an embodiment of the present invention.

[0113] See Figure 6 As can be seen, in single-path scenarios, because this invention more effectively captures electromagnetic singularity features, the predicted radio map is clearer and more detailed. Especially... Figure 6 The area of ​​rapidly changing path loss, highlighted in red, is where traditional data-driven methods have failed to capture this information. However, this invention can accurately locate electromagnetic singularities and effectively model fine-grained changes, resulting in superior reconstruction performance.

[0114] Figure 7 The diagram shown is a comparison of radio maps predicted by another different method provided in an embodiment of the present invention.

[0115] See Figure 7 As can be seen, this invention still exhibits the best prediction performance in IRT scenarios. This sufficiently demonstrates that this invention not only demonstrates good prediction accuracy in single-path scenarios but also maintains its excellence in multi-path environments, making it a powerful tool for optimizing 6G wireless networks.

[0116] Therefore, the method provided by this invention improves the prediction accuracy of radio maps by first predicting a singularity map and then generating a radio map guided by the singularity map. Furthermore, this invention trains the singularity map prediction network using sample singularity maps calculated based on the Helmholtz equation, rather than directly embedding PDE constraints into the loss function. This explicitly integrates the physical law of the Helmholtz equation into the learning process of the neural network, effectively guiding the learning of the singularity map prediction network and accurately extracting electromagnetic singularities. In addition, using a data-driven method based on neural networks to predict radio maps, instead of a traditional static model, reduces computational complexity and improves prediction efficiency. Moreover, when the usage environment changes, only environmental and base station information needs to be re-acquired and input; there is no need to remodel according to specific environments, improving the applicability of the method. This meets the future 6G network's requirements for high speed, large connection count, low latency, and high service quality.

[0117] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

Claims

1. A radio map prediction method fusing physical equations and deep learning, characterized in that, The method comprises: inputting an environment map of a to-be-tested environment and base station position information into a trained singularity map prediction network to obtain a singularity map of the to-be-tested environment; wherein the singularity map prediction network is trained according to a sample singularity map, and the sample singularity map is calculated according to a sample radio map based on a Helmholtz equation; inputting the singularity map, the environment map and the base station position information into a trained radio map prediction network to obtain a radio map of the to-be-tested environment; wherein the sample singularity map satisfies the following formula: ， wherein, is a value in the sample singularity map at a position represents whether the position is a singularity, is an electromagnetic singularity value at the position calculated by discretizing the Helmholtz equation; wherein the discretized Helmholtz equation satisfies the following formula: ， wherein, is the Laplacian operator, denotes the sum of the second order partial derivatives of denotes the electromagnetic wave intensity at position in the sample radio map, is the area size of each pixel in the sample singularity map, denotes the electromagnetic wave intensity at position in the sample radio map, denotes the electromagnetic wave intensity at position in the sample radio map, denotes the electromagnetic wave intensity at position in the sample radio map, denotes the electromagnetic wave intensity at position in the sample radio map; wherein a loss function used by the singularity map prediction network during training satisfies the following formula: ， wherein, represents a loss value of the anomaly map prediction network, is a size of the anomaly map and the sample environment map, is a prediction result of the anomaly map prediction network at a position . wherein a loss function used by the radio map prediction network during training satisfies the following formula: ， wherein, represents a loss value of a radio map prediction network, is a prediction result of the radio map prediction network at a location , represents an electromagnetic wave intensity at a location in the sample radio map. 2.A radio map prediction device that fuses a physical equation and deep learning, comprising: The method comprises: a singularity map prediction unit, configured to input an environment map of a to-be-tested environment and base station position information into a trained singularity map prediction network to obtain a singularity map of the to-be-tested environment; wherein the singularity map prediction network is trained according to a sample singularity map, and the sample singularity map is calculated according to a sample radio map based on a Helmholtz equation; a radio map prediction unit, configured to input the singularity map, the environment map and the base station position information into a trained radio map prediction network to obtain a radio map of the to-be-tested environment; wherein the sample singularity map satisfies the following formula: ， wherein, is a value in the sample singularity map at a position , indicating whether the position is a singularity, is an electromagnetic singularity value at the position calculated by discretizing the Helmholtz equation; wherein the discretized Helmholtz equation satisfies the following formula: ， wherein, is the Laplacian operator, denotes the sum of the second order partial derivatives of denotes the electromagnetic wave intensity at position in the sample radio map, is the area size of each pixel in the sample singularity map, denotes the electromagnetic wave intensity at position in the sample radio map, denotes the electromagnetic wave intensity at position in the sample radio map, denotes the electromagnetic wave intensity at position in the sample radio map, denotes the electromagnetic wave intensity at position in the sample radio map; wherein a loss function used by the singularity map prediction network during training satisfies the following formula: ， wherein, represents a loss value of the anomaly map prediction network, is a size of the anomaly map and the sample environment map, is a prediction result of the anomaly map prediction network at a position . wherein a loss function used by the radio map prediction network during training satisfies the following formula: ， wherein, represents a loss value of a radio map prediction network, is a prediction result of the radio map prediction network at a location , represents an electromagnetic wave intensity at a location in the sample radio map.

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