Radio map prediction method and device fusing physical equation and deep learning

Abstract

The invention discloses a radio map prediction method and device fusing a physical equation and deep learning, and belongs to the technical field of communication, and the method comprises the steps: inputting an environment map of a to-be-detected environment and the position information of a base station into a trained singular point map prediction network, and obtaining a singular point map of the to-be-detected environment; wherein the singular point map prediction network is trained according to a sample singular point map, and the sample singular point map is calculated according to a Helmholtz equation; and inputting the singular point map, the environment map and the base station position information into the trained radio map prediction network to obtain a radio map of the environment to be measured. The method is low in calculation complexity, wide in application range and good in prediction precision.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of communication, and particularly relates to a radio map prediction method and device fusing physical equations and deep learning. BACKGROUND

[0002] Driven by the growing demand for intelligence and proactive optimization of the sixth generation (6G) network, wireless communication is shifting towards an environment perception paradigm, making it essential to construct accurate radio maps (RM) to provide wireless channel characteristics at specific locations. In current radio map prediction work, traditional methods and data-driven methods are mainly used for prediction.

[0003] Traditional methods are electromagnetic calculation methods based on geometric programming or numerical solution, such as ray tracing, finite element method, and finite difference time domain method, etc. This method relies on accurate numerical solution of the physical model of electromagnetic wave propagation, usually requires detailed geometric environment information, and uses complex mathematical models to simulate the reflection, refraction and scattering of electromagnetic waves. Therefore, the computational complexity of these methods increases dramatically with the complexity of the environment, especially in urban environments with a large number of obstacles and reflective surfaces, the calculation time can be very long; at the same time, since it is based on a static environment model for calculation, it is difficult to handle dynamic changes.

[0004] Data-driven methods generally use neural networks such as RadioUNet, generative adversarial network (GAN) or the latest radio diffusion model (Radio Diffusion Model, RadioDiff). This method constructs a radio map by analyzing a large amount of data, which can learn complex radio signal propagation patterns from it and generate high-resolution radio maps to reduce dependence on physical models. Although this method eliminates the dependence on physical environment modeling, data-driven methods generally treat radio signal propagation as a black box process, ignoring the physical laws of electromagnetic wave propagation, which may result in the model failing to generalize to new environments or scenarios. Although the prediction efficiency is high, the physical laws are ignored in the prediction process, and it is difficult to model electromagnetic singular points caused by multipath effects, resulting in insufficient prediction accuracy.

[0005] Therefore, traditional electromagnetic calculation methods are difficult to apply due to high computational complexity. Current neural network methods cannot effectively capture electromagnetic singular points (such as path loss mutations) caused by multipath effects, resulting in insufficient reconstruction accuracy. SUMMARY

[0006] The embodiment of the present application provides a radio map prediction method and device fusing a physical equation and deep learning, and can solve the problems that current radio map prediction methods have high calculation complexity, narrow application range, or poor prediction accuracy.

[0007] In a first aspect, the embodiment of the present application provides a radio map prediction method fusing a physical equation and deep learning, and the method comprises the following steps: inputting an environment map and base station position information of a to-be-tested environment into a trained singular point map prediction network to obtain a singular point map of the to-be-tested environment; The singular point map prediction network is trained according to a sample singular point map, and the sample singular point map is calculated according to a sample radio map based on a Helmholtz equation. inputting the singular point 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.

[0008] In a second aspect, the embodiment of the present application provides a radio map prediction device fusing a physical equation and deep learning, and the device comprises the following units: a singular point map prediction unit, configured to input an environment map and base station position information of a to-be-tested environment into a trained singular point map prediction network to obtain a singular point map of the to-be-tested environment; The singular point map prediction network is trained according to a sample singular point map, and the sample singular point map is calculated according to a sample radio map based on a Helmholtz equation. a radio map prediction unit, configured to input the singular point 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.

[0009] Compared with the prior art, the embodiment of the present application has the beneficial effects that: the method provided by the present application first predicts a singular point map, and then generates a radio map under the guidance of the singular point map. Since these electromagnetic singular points are caused by complex multipath effects, they can affect the characteristics of the wireless channel to produce dramatic spatial changes, which are key information that is difficult for traditional data-driven methods to accurately capture. Therefore, the prediction accuracy of the radio map can be improved by the method provided by the present application. Moreover, the singular point map prediction network is trained using the sample singular point map calculated based on the Helmholtz equation, rather than directly embedding the partial differential equation (PDE) constraint in the loss function. This can explicitly incorporate the physical law of the Helmholtz equation into the learning process of the neural network, effectively guiding the learning of the singular point map prediction network and accurately extracting electromagnetic singular points. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 An implementation flowchart of a singular point map prediction network and a training method of a radio map prediction network provided by the embodiment of the present application is shown in the following figure: Figure 2 A flowchart of predicting a radio map provided by the embodiment of the present application is shown in the following figure: Figure 3 A flowchart of generating a sample singular point map provided by the embodiment of the present application is shown in the following figure: Figure 4 An implementation flowchart of a radio map prediction method that fuses physical equations and deep learning provided by the embodiment of the present application is shown in the following figure: Figure 5 A structure diagram of a radio map prediction device that fuses physical equations and deep learning provided by the embodiment of the present application is shown in the following figure: Figure 6 A comparison diagram of radio maps predicted by different methods provided by the embodiment of the present application is shown in the following figure: Figure 7 Another comparison diagram of radio maps predicted by different methods provided by the embodiment of the present application is shown in the following figure. DETAILED DESCRIPTION

[0011] In the following description, specific details are set forth such as particular system configurations, techniques, etc., in order to provide a thorough understanding of the embodiments of the present application. However, it should be apparent to those skilled in the art that the present application can be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.

[0012] It will be understood that the term "includes", "comprises", "comprising", "includes... but not limited to" or "comprising but not limited to", when used in the specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0013] It will be further understood that the term "and / or", "or" as used in the specification and in the claims, if and when used, means "one or the other", but also "both".

[0014] As used in the specification and the appended claims, the term "if can be construed to mean "when" or "upon" or "in response to determining" or "in response to detecting" depending on the context. Similarly, the phrase "if it is determined" or "if [a described condition or event] is detected" can be construed to mean "upon determining" or "in response to determining" or "upon detecting [the described condition or event]" or "in response to detecting [the described condition or event]" depending on the context.

[0015] In addition, the terms "first", "second", "third", etc. as used in the description of the specification and the appended claims are only used to distinguish descriptions and cannot be understood as indicating or implying relative importance.

[0016] Reference in the specification to "one embodiment" or "some embodiments" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the application. The appearances of the phrases "in one embodiment", "in some embodiments", "in other embodiments", "in additional embodiments", etc. in various places in the specification are not necessarily all referring to the same embodiment, although it can be so in some cases. The terms "including", "comprising", "having" and variations thereof mean "including but not limited to", unless expressly specified otherwise.

[0017] The application will be further described below in conjunction with specific embodiments, but the embodiments of the application are not limited thereto.

[0018] The method provided by the embodiments of the application can be applied to electronic devices such as mobile terminals, personal notebook computers, supercomputers, etc. The embodiments of the application do not make any limitation on the specific type of electronic devices.

[0019] Embodiment 1 Figure 1The flowchart shown is an implementation flow of a method for training a singularity map prediction network and a radio map prediction network according to an embodiment of the present invention. As an example and not a limitation, the method may include steps S101-S107, each of which is described below.

[0020] S101: Input the sample environment map and sample base station location information of the tth round into the singular point map prediction network after the tth round of iteration to obtain the prediction result of the singular point map prediction network in the tth round.

[0021] In an example, the sample environment map may be a binary matrix used to describe the distribution of static obstacles.

[0022] For example, see Figure 2 Sample environment map in 201. Sample environment map It can be expressed as ,in is the size of the sample environment map. If the matrix element corresponding to a certain position is 1, it means that there is an obstacle that completely blocks the electromagnetic wave at that position (the internal path loss is 0). If the matrix element corresponding to a certain position is 0, it means that there is no obstacle at that position.

[0023] The sample base station location information refers to the base station location information used as a sample. In an example, the base station location information may be defined by a triplet, which is used to describe the location and height of the base station.

[0024] For example, base station location information It can be expressed as ,in is the base station height, 、 Represent the coordinates of the base station on the horizontal axis and vertical axis respectively.

[0025] In one example, see Figure 2 In 202, the prediction result of the singular point map prediction network in round t may be a predicted singular point map. The singular point map may also be a binary matrix, wherein the elements may be 0 or 1; 0 indicates that the location is not an electromagnetic singular point, and 1 indicates that the location is an electromagnetic singular point.

[0026] S102: Input the sample environment map of the tth round, the sample base station location information, and the prediction result of the singular point map prediction network of the tth round into the radio map prediction network after the tth round of iteration to obtain the prediction result of the radio map prediction network of the tth round.

[0027] For example, see Figure 2 , in the singularity map prediction network (see Figure 2 202) according to the sample environment map (seeFigure 2 201 in), sample base station location information (not shown here) generates a predicted singular point map (see Figure 2 203 in ), the input and output of the singularity map prediction network can be input together into the radio map prediction network (see Figure 2 204), the predicted radio map is obtained (see Figure 2 205 in ).

[0028] S103: Determine the tth loss value of the singular point map prediction network based on the prediction result of the tth round of the singular point map prediction network and the sample singular point map.

[0029] In one possible implementation, the sample singular point map may be calculated according to the Helmholtz equation.

[0030] For example, see Figure 3 , can be based on the discretized Helmholtz equation, according to the sample radio map (see Figure 3 301) calculation Map (see Figure 3 302 in ), and then filter On the map The region of the sample singular point map is obtained (see Figure 3 303 in the ).

[0031] Therefore, the sample singularity map The following formula can be satisfied: , in, Represents a binary matrix including all pixel information of the entire sample singular point map, is the position of the sample singular point map The value at, indicating the position Is it a singular point? (abbreviated as ) is the position calculated by discretizing the Helmholtz equation The electromagnetic singularity value at .

[0032] Specifically, the sample singular point map, sample radio map, sample environment map, and the environment map, singular point map, and radio map of the environment to be tested are all maps of the same size. Each pixel on the map corresponds to a location area in the actual environment. is a positive integer less than or equal to the horizontal size of the map. A positive integer that is less than or equal to the vertical size of the map.

[0033] Exemplarily, electromagnetic singularities (EMS) are caused by complex electromagnetic wave interactions (e.g., multipath interference), which manifest as abrupt changes in wireless channel characteristics (e.g., path loss, angle of arrival) and can directly affect communication performance.

[0034] In particular, the sample radio map can be constructed for a specific geographical area discretized into grid, each grid cell being small enough to ensure that the path loss is constant inside it, so that the sample radio map can be represented by a path loss matrix Therefore, , may be positive integers less than or equal to .

[0035] In one example, the discretized Helmholtz equation can be expressed by 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 singular 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.

[0036] Exemplarily, Dirichlet boundary conditions also need to be imposed when calculating by the discretized Helmholtz equation: wherein is the value of the sample radio map at the boundary point, is the set of all boundary points.

[0037] Exemplarily, the loss value of the singular map prediction network can be calculated by the following loss function: , wherein denotes the loss value of the singular map prediction network, a size of the singularity map and the sample environment map, a prediction result of the singularity map prediction network at the position .

[0038] Traditional physical information neural networks generally enhance the Helmholtz equation constraint by adding a loss term in the loss function, for example, adding a partial differential term calculated by the Helmholtz equation after the binary cross-entropy. However, through a large number of experiments, it is found that: the RM reconstruction involves highly discontinuous spatial features (such as path loss mutations), and directly imposing PDE constraints will cause the prediction result to be too smooth, losing key details.

[0039] Therefore, the present application uses a sample singularity map calculated based on a discretized Helmholtz equation to train the singularity map prediction network, rather than directly embedding PDE constraints, which can integrate the Helmholtz equation as a physical constraint into the training process of the network, achieving a balance between physical laws and data-driven.

[0040] S104, determining a tth loss value of the radio map prediction network according to the prediction result of the tth round of the radio map prediction network and the sample radio map.

[0041] In one example, the tth loss value of the radio map prediction network can be calculated by the following loss function: , wherein, represents a loss value of the radio map prediction network, a prediction result of the radio map prediction network at the position , represents an electromagnetic wave intensity at the position in the sample radio map.

[0042] S105, updating network parameters of the singularity map prediction network and the radio map prediction network according to the tth loss value of the singularity map prediction network and the tth loss value of the radio map prediction network respectively, to obtain the singularity map prediction network after the t+1th iteration and the radio map prediction network after the t+1th iteration.

[0043] In one example, the network parameters of the singularity map prediction network may be updated according to the tth loss value of the singularity map prediction network based on a backpropagation algorithm, to obtain the singularity map prediction network after the t+1th iteration; and the network parameters of the radio map prediction network may be updated according to the tth loss value of the radio map prediction network, to obtain the radio map prediction network after the t+1th iteration.

[0044] Exemplarily, the training objectives of the two networks can be represented as:

[0045] wherein, represents the whole network composed of , network parameters of the whole network , represents the predicted radio map, represents the sample radio map, is the true value of the radio map; represents that the training objective is to minimize the difference between . . represents that after , inputting the whole network , the can be obtained.

[0046] S106, determining whether the preset convergence condition is met.

[0047] In one example, if the preset convergence condition is met, the following step S107 can be performed.

[0048] Exemplarily, the preset convergence condition can be that t is greater than or equal to the maximum number of training times, the accuracy is greater than the minimum accuracy threshold, and the like.

[0049] 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 be performed from step S101.

[0050] S107, outputting the singular point map prediction network after the t+1th iteration and the radio map prediction network after the t+1th iteration as the trained singular point map prediction network and the trained radio map prediction network, respectively.

[0051] According to the training method provided by the present application, the singular point map prediction network is trained by the sample singular point map calculated according to the discretized Helmholtz equation, rather than directly embedding the PDE constraint, which can integrate the Helmholtz equation as a physical constraint into the training process of the network, realize the balance between physical law and data-driven, and thus improve the prediction accuracy of the radio map prediction network.

[0052] Embodiment 2 Figure 4An implementation flowchart of a radio map prediction method fusing physical equations and deep learning provided by an embodiment of the present application is shown. As an example but not limitation, the method can include steps S401-S402. Each step is explained below.

[0053] S401, input the environment map and base station position information of the to-be-tested environment into the trained singularity point map prediction network to obtain a singularity point map of the to-be-tested environment.

[0054] Exemplarily, the environment map and base station position information of the to-be-tested environment can be represented by binary matrixes and triplets respectively, same as the sample environment map and sample base station position information.

[0055] S402, input the singularity point map, environment map and base station position information into the trained radio map prediction network to obtain a radio map of the to-be-tested environment.

[0056] Exemplarily, referring to Figure 2 , after obtaining the singularity point map, the input and output of the singularity point map prediction network can be input into the radio map prediction network together to obtain the final result (i.e. the radio map of the to-be-tested environment).

[0057] Specifically, the singularity point map prediction network and the radio map prediction network used here can both be trained by the above training method.

[0058] The present application first predicts a singularity point map, and then generates a radio map under the guidance of the singularity point map. Since these electromagnetic singularities are caused by complex multipath effects and can affect the characteristics of wireless channels to produce dramatic spatial changes, they are key information that is difficult for traditional data-driven methods to accurately capture. Therefore, by this method, the prediction accuracy of the radio map can be improved. Moreover, the present application uses sample singularity point maps calculated based on the Helmholtz equation to train the singularity point map prediction network, rather than directly embedding PDE constraints in the loss function, which can explicitly incorporate the physical law of the Helmholtz equation into the learning process of the neural network, effectively guiding the learning of the singularity point map prediction network and accurately extracting electromagnetic singularities. In addition, using a data-driven method based on a neural network to predict a radio map, rather than a traditional static model, can reduce computational complexity and improve prediction efficiency. Moreover, when the use environment changes, only the environment information and base station information need to be reacquired and input, without the need for specific re-modeling according to the environment, which can improve the applicability of the method and meet the demand of future 6G networks for high speed, large connection number, low delay and high service quality.

[0059] Embodiment 3 Figure 5Fig. 1 shows a structural schematic diagram of a radio map prediction device for fusing physical equations and deep learning according to an embodiment of the present application. By way of example and not limitation, the device can include a singular point map prediction unit 510 and a radio map prediction unit 520.

[0060] The singular point map prediction unit 510 is configured to input an environment map of a to-be-tested environment and base station position information into a trained singular point map prediction network to obtain a singular point map of the to-be-tested environment. The singular point map prediction network is trained according to a sample environment map, sample base station position information, and a sample singular point map, and the sample singular point map is calculated according to a Helmholtz equation. The radio map prediction unit 520 is configured to input the singular point 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.

[0061] In one example, the sample singular point map can satisfy the following formula: , wherein, is a value of a position in the sample singular point map, and represents whether the position is a singular point, is an electromagnetic singular point value of the position calculated by discretizing the Helmholtz equation.

[0062] In one example, the discretized Helmholtz equation can satisfy the following formula: , wherein, is a Laplace operator, represents a sum of second-order partial derivatives of , represents an electromagnetic wave intensity of a position in a sample radio map, is an area size of each pixel in the sample singular point map, represents an electromagnetic wave intensity of a position in the sample radio map, represents an electromagnetic wave intensity of a position in the sample radio map, represents an electromagnetic wave intensity of a position in the sample radio map, represents an electromagnetic wave intensity of a position in the sample radio map.

[0063] In one example, a loss function used by the singular point map prediction network during training can satisfy the following formula: , wherein, denotes the loss value of the singularity map prediction network, is the size of the singularity map and the sample environment map, is the prediction result of the singularity map prediction network at the position .

[0064] In one example, the loss function used by the radio map prediction network during training can satisfy the following formula: , wherein, denotes the loss value of the radio map prediction network, is the prediction result of the radio map prediction network at the position , denotes the electromagnetic wave intensity at the position in the sample radio map.

[0065] The device provided by the present application can improve the prediction accuracy of the radio map by first predicting the singularity map and then generating the 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 dramatic spatial changes, which are key information that traditional data-driven methods cannot accurately capture. Therefore, the prediction accuracy of the radio map can be improved. Moreover, the singularity map prediction network is trained using the sample singularity map calculated based on the Helmholtz equation, rather than directly embedding PDE constraints in the loss function. This can explicitly incorporate 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.

[0066] In order to better illustrate the beneficial effects of the present application, the following simulation experiments are performed: Illustratively, in the simulation experiment, the RadioMapSeer dataset can be used to evaluate the method provided by the present application. The dataset includes 700 radio maps containing detailed geographic information such as building layout, as well as 80 transmitter locations and their corresponding true data. The complexity of these maps varies, with each scene containing 50 to 150 buildings. In the experiment, the dataset can be divided into 500 training maps and 200 test maps, ensuring that there is no overlap between the terrain information to prevent data leakage. The transmitter's transmission power is set to 23dBm, and the carrier frequency is fixed at 5.9GHz.

[0067] Specifically, the widely used indicators of normalized mean square error and root mean square error can be used for evaluation. In order to better capture the fine-grained spatial variation which is crucial in the process of wireless channel reconstruction, the structural similarity index (SSIM) and the peak signal-to-noise ratio (PSNR) can also be used as additional evaluation indicators. SSIM can be used to measure the preservation of structural details, while PSNR can evaluate the fidelity of reconstructed features, especially the edge signal accuracy of path loss changes, which is crucial for modeling the path loss abrupt changes caused by multipath effects.

[0068] At the same time, all experiments are run on an NVIDIA Tesla A40 GPU. The method trained with PDE physical loss is marked as “w / PDE”, and the method without PDE physical loss is marked as “w / oPDE”.

[0069] Table 1

[0070] Table 2

[0071] The above Tables 1 and 2 show the evaluation results of different methods. Compared with the method based on convolutional neural network (RadioUNet), the method based on generative adversarial network (RME-GAN), the method based on Mamba architecture (UVM-Net) and the latest cutting-edge technology (State Of The Art, SOTA) method based on diffusion model (RadioDiff); it can be seen that the present application achieves the best performance in all evaluation indicators, surpassing traditional deep learning methods.

[0072] Specifically, referring to the evaluation results shown in Table 1 in the dominant path model (DPM) scenario, it can be seen that compared with the RadioDiff method, the present application achieves nearly twice the improvement in the NMSE indicator, which indicates that the singularity extraction strategy guided by physical information has a significant advantage in the task of radio map construction.

[0073] Specifically, referring to the evaluation results shown in Table 2 in the intelligent ray tracing (IRT) scenario, it can be seen that after training with PDE physical loss, the performance of the model of any method will decrease.

[0074] Table 3 Training time of different methods

[0075] Exemplarily, Table 3 shown above shows the inference time of different methods. It can be seen that the calculation efficiency of the present application is extremely high, only 1 / 30 of the RadioDiff method, which proves that the present application has extremely high scalability and practicability.

[0076] Figure 6 A comparison diagram of radio maps predicted by different methods provided by an embodiment of the present application is shown.

[0077] Referring to Figure 6 It can be seen that in a single path scenario, because the present application more effectively captures electromagnetic singularity features, the predicted radio map is clearer and more detailed. Especially in the area of sharp change in path loss boxed by the red box in Figure 6 The traditional data-driven method fails to successfully capture this information, while the present application can accurately locate electromagnetic singularities and effectively model fine-grained changes, and its reconstruction effect is more outstanding.

[0078] Figure 7 A comparison diagram of radio maps predicted by another different method provided by an embodiment of the present application is shown.

[0079] Referring to Figure 7 It can be seen that in the IRT scenario, the present application still has the best prediction effect. This is sufficient to prove that the present application not only has good prediction accuracy in a single path scenario, but also maintains its excellence in a multi-path rich environment, making it a powerful tool for 6G wireless network optimization.

[0080] Therefore, the method provided by the present application can improve the prediction accuracy of the radio map by first predicting a singularity point map and then generating a radio map under the guidance of the singularity point map. Moreover, the present application uses a sample singularity point map calculated based on the Helmholtz equation to train the singularity point map prediction network, rather than directly embedding the PDE constraint in the loss function, which can explicitly incorporate the physical law of the Helmholtz equation into the learning process of the neural network, effectively guiding the learning of the singularity point map prediction network and accurately extracting electromagnetic singularities. In addition, the data-driven method based on the neural network is used to predict the radio map, rather than the traditional static model, which can reduce the calculation complexity and improve the prediction efficiency. Moreover, when the use environment is changed, only the environment information and base station information need to be reacquired and input, without the need for specific re-modeling according to the environment, which can improve the applicability of the method. It meets the demand of future 6G networks for high speed, large connection number, low delay and high service quality.

[0081] In the above embodiments, the description of each embodiment has its own focus, and the parts not described or recorded in detail in a certain embodiment can be referred to the relevant description of other embodiments.

Claims

1. A radio map prediction method integrating physical equations and deep learning, characterized in that: include: Inputting 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; wherein the singular point map prediction network is trained based on a sample singular point map, and the sample singular point map is calculated based on a sample radio map based on the Helmholtz equation; The singular point 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.

2. The method according to claim 1, characterized in that The sample singular point map satisfies the following formula: ， in, is the position of the sample singular point map The value at, indicating the position Is it a singular point? is the position calculated by discretizing the Helmholtz equation The electromagnetic singularity value at .

3. The method according to claim 2, characterized in that The discretized Helmholtz equation satisfies the following formula: ， in, is the Laplace operator, express The sum of the second-order partial derivatives of Represents the location in the sample radio map The electromagnetic wave intensity at is the area of ​​each pixel in the sample singular point map, The location in the sample radio map The electromagnetic wave intensity at The location in the sample radio map The electromagnetic wave intensity at The location in the sample radio map The electromagnetic wave intensity at The location in the sample radio map The electromagnetic wave intensity at .

4. The method according to claim 2, characterized in that The loss function used in the training of the singularity map prediction network satisfies the following formula: ， in, represents the loss value of the singularity map prediction network, is the size of the singularity map and sample environment map, For the singular point map prediction network at location The prediction results at .

5. The method according to claim 4, characterized in that The loss function used in the training of the radio map prediction network satisfies the following formula: ， in, represents the loss value of the radio map prediction network, For the radio map, predict the network at the location The prediction results at Represents the location in the sample radio map The electromagnetic wave intensity at .

6. A radio map prediction device integrating physical equations and deep learning, characterized in that: include: a singular point map prediction unit, configured to input an environment map of the environment to be tested and base station location information into a trained singular point map prediction network to obtain a singular point map of the environment to be tested; wherein the singular point map prediction network is trained based on a sample singular point map, and the sample singular point map is calculated based on a sample radio map based on the Helmholtz equation; A radio map prediction unit is configured to input the singular point 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.

7. The device according to claim 6, characterized in that The sample singular point map satisfies the following formula: ， in, is the position of the sample singular point map The value at, indicating the position Is it a singular point? is the position calculated by discretizing the Helmholtz equation The electromagnetic singularity value at .

8. The device according to claim 7, characterized in that The discretized Helmholtz equation satisfies the following formula: ， in, is the Laplace operator, express The sum of the second-order partial derivatives of Represents the location in the sample radio map The electromagnetic wave intensity at is the area of ​​each pixel in the sample singular point map, The location in the sample radio map The electromagnetic wave intensity at The location in the sample radio map The electromagnetic wave intensity at The location in the sample radio map The electromagnetic wave intensity at The location in the sample radio map The electromagnetic wave intensity at .

9. The device according to claim 7, characterized in that The loss function used in the training of the singularity map prediction network satisfies the following formula: ， in, represents the loss value of the singularity map prediction network, is the size of the singularity map and sample environment map, For the singular point map prediction network at location The prediction results at .

10. The device according to claim 9, characterized in that The loss function used in the training of the radio map prediction network satisfies the following formula: ， in, represents the loss value of the radio map prediction network, For the radio map, predict the network at the location The prediction results at Represents the location in the sample radio map The electromagnetic wave intensity at .

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