Electromagnetic field calculation method, device and equipment based on physical constraint neural network

Abstract

The application provides an electromagnetic field calculation method, device and equipment based on a physically constrained neural network. Applied to the field of electromagnetic field calculation, the method comprises: a distribution range, physical parameters and a background signal source of a model of an electromagnetic field to be calculated can be acquired; a model constraint condition and a physical constraint condition are determined according to the distribution range, the physical parameters and the background signal source; sampling data of the model are input into a preset neural network model for calculating an electromagnetic field to obtain an electromagnetic field of the model. The method of the application constrains the neural network through the physical law of electromagnetic field change, and only the model range of the electromagnetic field to be calculated needs to be determined when the electromagnetic field is calculated, without a large amount of known data as data driving, so that the calculation efficiency of the electromagnetic field is improved.

Description

Technical Field

[0001] This application relates to the field of electromagnetic field calculation, and in particular to an electromagnetic field calculation method, apparatus and device based on a physically constrained neural network. Background Technology

[0002] Electromagnetic field calculation is an important tool for studying electromagnetic phenomena. Traditional electromagnetic field calculations often employ the finite difference method, finite element method, and boundary element method, which are computationally intensive and complex. With the rapid development of neural network technology, neural network-based electromagnetic field calculation methods have attracted considerable attention, as they have significant application value in addressing problems related to electromagnetic radiation, electromagnetic interference, and electromagnetic shielding.

[0003] In related technologies, neural networks, as data-driven electromagnetic field calculation models, require a large amount of data for network training to construct a mapping relationship between known and unknown data. However, this method is limited by the size and quality of the database, and its over-reliance on known data leads to low computational efficiency for electromagnetic fields. Summary of the Invention

[0004] This application provides an electromagnetic field calculation method, apparatus, and device based on a physical constraint neural network, which can improve the calculation efficiency of electromagnetic fields.

[0005] In a first aspect, this application provides an electromagnetic field calculation method based on a physically constrained neural network, comprising:

[0006] Obtain the distribution range, physical parameters, and background signal sources of the model of the electromagnetic field to be calculated;

[0007] Based on the distribution range, physical parameters, and background signal sources, determine the model constraints and physical constraints;

[0008] The sampled data of the model is input into a preset neural network model for calculating the electromagnetic field to obtain the electromagnetic field of the model; wherein, the neural network model adopts a loss function constructed according to the model constraints and the physical constraints, and the sampled data includes the three-dimensional coordinate data of multiple sampling points of the model sampled according to preset rules.

[0009] In one possible implementation, determining the model constraints and physical constraints based on the distribution range, physical parameters, and background signal source includes:

[0010] Based on the distribution range, the physical parameters, the background signal source, the electromagnetic field unique theorem, and Maxwell's equations, determine the model characteristics and physical conditions for calculating the electromagnetic field.

[0011] The model constraints are constructed based on the model characteristics, and the physical constraints are constructed based on the boundary conditions of the electromagnetic field and the physical conditions.

[0012] In one possible implementation, the loss function is:

[0013]

[0014] in,

[0015] as well as,

[0016]

[0017] MES represents mean squared error, loss represents the difference between the model prediction and the true value, i represents current intensity, ω represents angular frequency, μ0 represents free magnetic permeability, σ0 represents background complex conductivity, σ represents complex conductivity, and E s E represents the scattering field, E0 represents the background field, and loss represents the difference between the model prediction and the true value. m (m=x,y,z) represents the electric field generated by magnetic dipoles in different directions, and k represents the proportionality constant of the electric field strength.

[0018] In one possible implementation, obtaining the distribution range, physical parameters, and background signal source of the model of the electromagnetic field to be calculated includes:

[0019] A three-dimensional coordinate system is created with the center point of the model as the origin, and the distribution range of the model is obtained according to the shape and size of the model;

[0020] The physical parameters of the model are obtained by acquiring the background stratum size, background stratum resistivity, fixed anomaly size, fixed anomaly resistivity, instrument transmission signal frequency, source distance, and distance between the instrument midpoint and the anomaly center.

[0021] The background signal source is obtained by applying a background field to the model to perform equivalent processing on the signal source.

[0022] In one possible implementation, the method further includes:

[0023] Sampling is performed on the model by extracting multiple sampling points inside the model and multiple sampling points at the boundary of the model, and obtaining the three-dimensional coordinate data of all sampling points in a three-dimensional space centered on the center point of the model, thus obtaining the sampling data.

[0024] In one possible implementation, the step of inputting the sampled data of the model into a preset neural network model for calculating the electromagnetic field to obtain the electromagnetic field of the model includes:

[0025] The sampled data is input into the neural network model for electromagnetic field calculation. During the calculation process, the Adam stochastic algorithm and the L-BFGS-B gradient algorithm are used to optimize the neural network to obtain the electromagnetic field of the model.

[0026] Secondly, this application provides an electromagnetic field calculation device based on a physically constrained neural network, comprising:

[0027] The first processing module is used to obtain the distribution range, physical parameters, and background signal sources of the model of the electromagnetic field to be calculated;

[0028] The second processing module is used to determine the model constraints and physical constraints based on the distribution range, physical parameters and background signal source.

[0029] The third processing module is used to input the sampled data of the model into a preset neural network model for calculating the electromagnetic field to obtain the electromagnetic field of the model; wherein, the neural network model adopts a loss function constructed according to the model constraints and the physical constraints, and the sampled data includes the three-dimensional coordinate data of multiple sampling points of the model sampled according to preset rules.

[0030] In one possible implementation, the second processing module is specifically used for:

[0031] Based on the distribution range, the physical parameters, the background signal source, the electromagnetic field unique theorem, and Maxwell's equations, determine the model characteristics and physical conditions for calculating the electromagnetic field.

[0032] The model constraints are constructed based on the model characteristics, and the physical constraints are constructed based on the boundary conditions of the electromagnetic field and the physical conditions.

[0033] In one possible implementation, the loss function is:

[0034]

[0035] in,

[0036] as well as,

[0037]

[0038] MES represents mean squared error, loss represents the difference between the model prediction and the true value, i represents current intensity, ω represents angular frequency, μ0 represents free magnetic permeability, σ0 represents background complex conductivity, σ represents complex conductivity, and E s E represents the scattering field, E0 represents the background field, and loss represents the difference between the model prediction and the true value. m (m=x,y,z) represents the electric field generated by magnetic dipoles in different directions, and k represents the proportionality constant of the electric field strength.

[0039] In one possible implementation, the first processing module is specifically used for:

[0040] A three-dimensional coordinate system is created with the center point of the model as the origin, and the distribution range of the model is obtained according to the shape and size of the model;

[0041] The physical parameters of the model are obtained by acquiring the background stratum size, background stratum resistivity, fixed anomaly size, fixed anomaly resistivity, instrument transmission signal frequency, source distance, and distance between the instrument midpoint and the anomaly center.

[0042] The background signal source is obtained by applying a background field to the model to perform equivalent processing on the signal source.

[0043] In one possible implementation, the apparatus further includes a fourth processing module, the fourth processing module being used for:

[0044] Sampling is performed on the model by extracting multiple sampling points inside the model and multiple sampling points at the boundary of the model, and obtaining the three-dimensional coordinate data of all sampling points in a three-dimensional space centered on the center point of the model, thus obtaining the sampling data.

[0045] In one possible implementation, the third processing module is specifically used for:

[0046] The sampled data is input into the neural network model for electromagnetic field calculation. During the calculation process, the Adam stochastic algorithm and the L-BFGS-B gradient algorithm are used to optimize the neural network to obtain the electromagnetic field of the model.

[0047] Thirdly, this application provides an electronic device, including: a processor, a memory, and an interaction interface;

[0048] The memory stores computer-executed instructions;

[0049] The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any of the first aspects.

[0050] Fourthly, this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processing unit, are used to implement the method described in any of the first aspects.

[0051] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processing unit, implements the method shown in any of the first aspects.

[0052] This application provides a method, apparatus, and device for electromagnetic field calculation based on a physically constrained neural network. This method involves acquiring the distribution range, physical parameters, and background signal sources of a model of the electromagnetic field to be calculated. Based on these parameters, the model constraints and physical constraints are determined. The sampled data from the model is then input into a pre-defined neural network model for electromagnetic field calculation to obtain the electromagnetic field. In this process, by defining the model constraints and physical constraints, a large amount of known data is not required as a data driver. Only the range of the electromagnetic field to be calculated needs to be clearly defined, and the electromagnetic field can be obtained through neural network calculation, thereby improving the computational efficiency of electromagnetic field calculation. Attached Figure Description

[0053] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0054] Figure 1 A schematic diagram illustrating the application scenarios provided in the embodiments of this application;

[0055] Figure 2 A flowchart illustrating an electromagnetic field calculation method based on a physically constrained neural network, provided in an embodiment of this application;

[0056] Figure 3 A schematic diagram of a model space distribution provided for an embodiment of this application;

[0057] Figure 4 A schematic diagram of a model of an electromagnetic field to be calculated, provided for an embodiment of this application;

[0058] Figure 5 A flowchart illustrating another electromagnetic field calculation method based on a physically constrained neural network provided in this application embodiment;

[0059] Figure 6 A schematic diagram illustrating the relationship between training error and the number of iterations, provided for an embodiment of this application;

[0060] Figure 7 A schematic diagram of an electromagnetic field slice provided in an embodiment of this application;

[0061] Figure 8 A flowchart of an electromagnetic field calculation process is provided for an embodiment of this application;

[0062] Figure 9 A schematic diagram of the structure of an electromagnetic field calculation device based on a physically constrained neural network provided in an embodiment of this application;

[0063] Figure 10 A schematic diagram of another electromagnetic field calculation device based on a physically constrained neural network provided in this application embodiment;

[0064] Figure 11 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0065] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0066] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0067] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0068] Figure 1 This is a schematic diagram illustrating an application scenario provided in an embodiment of this application. Please refer to [link / reference]. Figure 1 The constraints for calculating the electromagnetic field can be determined by the distribution range of the electromagnetic field, its physical parameters, and the background signal source. Based on the distribution range of the electromagnetic field, multiple sampling data points are acquired within the electromagnetic field, and these data points are input into a neural network model. Combined with the determined constraints of the electromagnetic field, the magnitude of the electromagnetic field is calculated.

[0069] In related technologies, neural networks, as electromagnetic field calculation models based on data-driven models, require a large amount of data on known electromagnetic field magnitudes for network training to construct the relationship between known and unknown electromagnetic field magnitudes. However, this method is limited by the scale and quality of known electromagnetic field data, and its over-reliance on known data leads to low computational efficiency for electromagnetic fields.

[0070] In this embodiment, the distribution range, physical parameters, and background signal sources of the model of the electromagnetic field to be calculated can be obtained. Based on the distribution range, physical parameters, and background signal sources, model constraints and physical constraints are determined. The sampled data of the model is then input into a preset neural network model for calculating the electromagnetic field to obtain the electromagnetic field. In the above process, by determining the model constraints and physical constraints, a large amount of known data is not required as data-driven processing; only the model range of the electromagnetic field to be calculated needs to be clearly defined, thereby improving the computational efficiency of the electromagnetic field.

[0071] The technical solutions shown in this application will now be described in detail through specific embodiments. It should be noted that the following embodiments may exist independently or in combination with each other; for identical or similar content, the description will not be repeated in different embodiments.

[0072] Figure 2 This is a flowchart illustrating an electromagnetic field calculation method based on a physically constrained neural network, provided as an embodiment of this application. Please refer to... Figure 2 The method may include:

[0073] S101. Obtain the distribution range, physical parameters, and background signal source of the electromagnetic field model to be calculated.

[0074] The execution subject of this application embodiment can be an electronic device or an electromagnetic field calculation device based on a physically constrained neural network installed in an electronic device. The electromagnetic field calculation device based on a physically constrained neural network can be implemented through software or a combination of software and hardware. For ease of understanding, the following description uses an electronic device as the execution subject.

[0075] In this step, a reference coordinate system can be constructed within the model of the electromagnetic field to be calculated to obtain the distribution range of the model. The model of the electromagnetic field to be calculated can contain multiple physical parameters and can have corresponding background signal sources. Here, the model distribution range refers to the spatial location of the model of the electromagnetic field to be calculated.

[0076] Since directly applying a signal source to the model of the electromagnetic field to be calculated will cause the electromagnetic field near the source point to be singular, it is necessary to perform equivalent processing on the signal source by applying a background field, thereby forming a background signal source.

[0077] Below, in conjunction with Figure 3 This section describes the distribution range of the model and its location in space.

[0078] Figure 3 This is a schematic diagram of a model space distribution provided in an embodiment of this application. Please refer to... Figure 3 If the electromagnetic field to be calculated is a three-dimensional model, a three-dimensional coordinate system can be constructed at the center point of the three-dimensional model space, i.e., the geometric center. Then the position distribution range of the three-dimensional model in the three-dimensional coordinate system can be used as the distribution range of the model.

[0079] Optionally, the model of the electromagnetic field to be calculated can have different material characteristics and include multiple physical parameters. For example, the model of the electromagnetic field to be calculated can include the size and resistivity of the background strata, the frequency and source distance of the instrument's transmitted (T) and received (R) signals, the size and resistivity of the anomalous body, etc.

[0080] Figure 4 This is a schematic diagram of a model for calculating an electromagnetic field, provided as an embodiment of this application. Please refer to [link / reference]. Figure 4 The electromagnetic field to be calculated is a three-dimensional model. The background stratum is a homogeneous medium with a size of 40m*40m*40m. The fixed anomaly has a size of 4m*15m*15m. The resistivity of the background stratum is R0 = 1Ω·m, and the resistivity of the anomaly is R1 = 10Ω·m. The midpoint of the instrument and the center of the anomaly are on the same straight line and are 5m apart.

[0081] Optionally, the instrument can be a three-component sensor, with at least one transmitting antenna and at least one receiving antenna. The antenna used to radiate radio waves is called the transmitting antenna, and the antenna used to receive radio waves is called the receiving antenna. For example, the transmitting and receiving signals of the three-component sensor can have a frequency of 400 kHz and a source distance of 2 m.

[0082] In one specific implementation, the signal source can be equivalently processed by applying a background field, and the electric field at any point can be regarded as the sum of the scattered field and the background field.

[0083] S102. Determine the model constraints and physical constraints based on the distribution range, physical parameters, and background signal sources.

[0084] After obtaining the distribution range, physical parameters, and background signal sources of the model of the electromagnetic field to be calculated, the model characteristics and physical conditions for calculating the electromagnetic field can be determined based on the distribution range, physical parameters, background signal sources, the electromagnetic field unique theorem, and Maxwell's equations. Model constraints are then constructed based on the model characteristics, and physical constraints are constructed based on the boundary conditions and physical conditions of the electromagnetic field.

[0085] The unique law of electromagnetic fields states that the solution that satisfies the Poisson equation or the Laplace equation and all given boundary conditions is unique.

[0086] Maxwell's equations are four fundamental equations describing the relationship between electromagnetic fields and electric charges. They are Gauss's law, Faraday's law, Ampere's law, and Maxwell-Henry's law.

[0087] Model constraints refer to the conditions that satisfy the characteristics of the model. Model constraints can be constructed based on the spatial structure and electromagnetic properties of the model. For example, model constraints can be constructed based on the size, resistivity and distribution range of the background strata of the model.

[0088] Physical constraints refer to the physical constraints that satisfy the unique law of electromagnetic fields and Maxwell's equations.

[0089] S103. Input the sampled data of the model into the preset neural network model for calculating the electromagnetic field to obtain the electromagnetic field of the model.

[0090] After acquiring multiple sampling data points, these data points can be input into a pre-defined electromagnetic field neural network model for calculation, yielding the electromagnetic field of the model to be calculated. The neural network model employs a loss function constructed based on model constraints and physical constraints. The sampling data includes the three-dimensional coordinates of multiple sampling points sampled according to pre-defined rules.

[0091] A loss function is used to evaluate the degree to which a model's predictions differ from the actual values. A better loss function generally indicates better model performance. Different models typically use different loss functions.

[0092] A neural network model consists of an input layer, hidden layers, and an output layer. Hidden layers can be multiple, and neural networks with multiple hidden layers are also known as deep neural networks. Each layer of a neural network has several neurons, and the neurons in each layer are fully interconnected. Each neuron receives the output value of the neuron in the previous layer as its input value, processes it, and then outputs it to the neuron in the next layer. Finally, the neurons in the output layer output the predicted result value.

[0093] In one specific implementation, a simultaneous analysis of the Maxwell equations in the frequency domain reveals that:

[0094]

[0095] In equation (1), Let E represent the gradient operator, i represent the electric field intensity, ω represent the angular frequency, μ0 represent the free magnetic permeability, σ represent the complex conductivity, and J represent the gradient operator. i This represents the current density.

[0096] If the signal source is processed equivalently by applying a background field, then equation (1) can be derived as follows:

[0097]

[0098] In equation (2), E s Let E0 represent the scattering field and E0 represent the background field. The expression for the background field is:

[0099]

[0100] In equation (3), σ0 represents the background complex conductivity. Subtracting equations (2) and (3) eliminates J. i Equation (4) is derived:

[0101]

[0102] In one specific implementation, the background field can be treated as an equivalent source term and applied to every point in the solution domain of the model of the electromagnetic field to be calculated, thus yielding an analytical expression for the background signal source:

[0103]

[0104]

[0105]

[0106] In equations (5-7), E m (m = x, y, z) represents the electric field generated by magnetic dipoles in different directions; k represents the proportionality constant of the electric field strength; r 2 =x 2 +y 2 +z 2 .

[0107] According to the uniqueness theorem of electromagnetic fields, the loss function can be divided into two parts, including the Poisson equation and the boundary conditions. The expression for the Poisson equation can be expanded and rearranged from equation (4) to obtain the electromagnetic constraint expressions shown in equations (8-10):

[0108]

[0109]

[0110]

[0111] In equations (8-10), loss represents the difference between the model's prediction and the actual value.

[0112] The electromagnetic constraints shown in equations (8-10) can be used to make the predicted electromagnetic field satisfy the physical constraint of Maxwell's equations.

[0113] After obtaining the electromagnetic constraints, appropriate boundary conditions can be applied to determine the unique electromagnetic field. In electrical logging problems, since the signal is constantly attenuating, the electric field at the boundary can be approximated as zero when the formation model is sufficiently large. Therefore, equivalent boundary conditions can be set at the boundary, and the corresponding boundary constraint expressions are as follows:

[0114]

[0115] In equation (11), where E b Let x, y, and z represent the electric field values ​​at the boundary. Therefore, the loss function can be obtained as:

[0116]

[0117] In Equation (12), MSE (Mean square error) is a measure that reflects the degree of difference between the estimator and the estimated quantity, and is widely used in tasks such as linear regression and multiple linear regression.

[0118] Optionally, the preset rules can be to divide the interior of the model of the electromagnetic field to be calculated into small grid-like cubes, and to divide the boundary of the model of the electromagnetic field to be calculated. For example, the interior of the model of the electromagnetic field to be calculated can be divided into small grid-like cubes, each cube being 0.2m*0.2m*0.2m in size, with the geometric center point of the small cube as the sampling point; alternatively, the boundary of the model of the electromagnetic field to be calculated can be divided, with each division occurring every 0.2m, and the center point of each line segment at the boundary being the sampling point, which includes the three-dimensional coordinate data of each sampling point.

[0119] For example, according to preset rules, N values ​​are taken within the model of the electromagnetic field to be calculated. a =1000 sampling points, M is taken at the boundary. b =100 sampling points, resulting in a total of 1100 sampling data points. Each sampling point is composed of three-dimensional coordinate data corresponding to the X, Y, and Z directions. The 1100 sampling data points are input into a preset neural network model for calculating the electromagnetic field to obtain the electromagnetic field of the model to be calculated.

[0120] In this embodiment, the distribution range, physical parameters, and background signal sources of the model for calculating the electromagnetic field can be obtained. Based on the distribution range, physical parameters, and background signal sources, model constraints and physical constraints are determined. The sampled data of the model is then input into a preset neural network model for calculating the electromagnetic field to obtain the electromagnetic field of the model. In the above process, by determining the model constraints and physical constraints, a large amount of known data is not required as a data driver. Only the range of the model for calculating the electromagnetic field needs to be clearly defined, and the electromagnetic field of the model can be obtained through calculation by the neural network model, thereby improving the computational efficiency of the electromagnetic field.

[0121] Below, in Figure 2 Based on the illustrated embodiments, combined with Figure 5 The electromagnetic field calculation method based on the physical constraint neural network described above will be explained in detail.

[0122] Figure 5 This is a flowchart illustrating another electromagnetic field calculation method based on a physically constrained neural network, provided as an embodiment of this application. Please refer to... Figure 5 The method may include:

[0123] S201. Create a three-dimensional coordinate system with the center point of the model as the origin, and obtain the distribution range of the model according to its shape and size.

[0124] In this step, the model distribution range of the electromagnetic field to be calculated can be determined by combining the shape and size of the electromagnetic field model with a three-dimensional coordinate system created within the model.

[0125] For example, if the model of the electromagnetic field to be calculated is a three-dimensional model, the origin of the three-dimensional coordinate system can be set at the geometric center of the three-dimensional model. With the user facing the three-dimensional model, the X-axis can be drawn to the right of the origin of the three-dimensional coordinate system, the Z-axis can be drawn upward from the origin of the three-dimensional coordinate system, and the Y-axis can be drawn from the origin of the three-dimensional coordinate system towards the user. This will allow us to obtain the distribution range of the model.

[0126] S202. Obtain the background stratum size, background stratum resistivity, fixed anomaly size, fixed anomaly resistivity, instrument transmission signal frequency, source distance, and distance between the instrument midpoint and the anomaly center in the model to form the physical parameters of the model.

[0127] When obtaining the model distribution range of the electromagnetic field to be calculated, the model can contain multiple physical parameters. These multiple physical parameters may include the size of the background strata, the resistivity of the background strata, the size of the fixed anomaly, the resistivity of the fixed anomaly, the frequency of the instrument's transmitted signal, the source distance, and the distance between the instrument's midpoint and the center of the anomaly.

[0128] For example, the model of the electromagnetic field to be calculated is a three-dimensional model. The background stratum is a homogeneous medium with a size of 50m*50m*50m and a resistivity of R0 = 1Ω·m. The fixed anomaly has a size of 5m*15m*15m and a resistivity of R1 = 10Ω·m. The instrument is a three-component inductor with a transmission and reception frequency of 400kHz and a source distance of 2m. The midpoint of the instrument and the center of the anomaly are on the same straight line and are 5m apart.

[0129] S203. The background signal source is obtained by applying a background field to the model to perform equivalent processing on the signal source.

[0130] In electromagnetic wave logging technology, the current density only exists at the source point. If a point source signal is directly applied, it will cause the electromagnetic field near the source point to be singular. Therefore, the signal source can be equivalently processed by applying a background field. The electric field at any point can be regarded as the sum of the scattered field and the background field, which constitutes the background signal source.

[0131] S204. Determine the model constraints and physical constraints based on the distribution range, physical parameters, and background signal sources.

[0132] It should be noted that the specific execution process of step S204 can be found in the specific execution process of step S102, and will not be repeated here.

[0133] S205. Sampling is performed on the model. Multiple sampling points are extracted inside the model and multiple sampling points are extracted at the boundary of the model. The three-dimensional coordinate data of all sampling points in the three-dimensional space centered on the center point of the model are obtained to obtain the sampling data.

[0134] In this step, sampling can be performed on the model to be calculated to obtain all sampling points. These sampling points include multiple sampling points extracted from within the model and multiple sampling points extracted from the model's boundaries. Specifically, the interior of the model can be divided into multiple grid-like small cubes, where the spatial coordinates of each small cube can be represented by the coordinates of its geometric center. The edges of the model's boundaries can be divided into multiple small line segments, where the coordinates of the midpoint of each line segment represent its spatial coordinates. The Latin hypercube algorithm is used to extract sampling data from the model, extracting multiple sampling points both inside and at the model's boundaries. Each sampling point contains the three-dimensional coordinates of its center point in three-dimensional space. These multiple sampling points, extracted from both the interior and boundary areas, together constitute the sampling data for the model to be calculated.

[0135] The Latin hypercube algorithm is a multidimensional random sampling method. Essentially, it divides each dimension into several equal regions, and then randomly selects a point within each region for sampling.

[0136] For example, using the Latin hypercube calculation, a total of N values ​​are taken within the model of the electromagnetic field to be calculated. a =100,000 sampling points, M is taken at the boundary. b =900 sampling points, resulting in a total of 100,900 sampling points. Within the model, the 3D coordinate data of these sampling points can be: N1(0.1, 0.1, 0.1), N2(0.2, 0.2, 0.2), ..., N 100000 (-24.9, -24.9, -24.9). At the model boundary, the 3D coordinate data of the sampling points can be: M1(25, 0.1, 25), M2(25, 25, 0.1), ..., M 900 (0.1, 25, 25).

[0137] S206. Input the sampled data into the neural network model to calculate the electromagnetic field. During the calculation process, the Adam (adaptive moment estimation) stochastic algorithm and the L-BFGS-B (Limited memory-Broyden Fletcher Goldfarb Shanno-Bound) gradient algorithm are used to optimize the neural network to obtain the electromagnetic field of the model.

[0138] Within the model of the electromagnetic field to be calculated, N a Each sampling point, and boundary M b When the sampling data consists of sampling points, the sampling points can be input into the neural network model for electromagnetic field calculation. During the calculation process, the Adam random algorithm and the L-BFGS-B gradient algorithm are used to optimize the neural network to obtain the electromagnetic field of the model.

[0139] The Adam stochastic algorithm is a deep learning optimization algorithm based on gradient descent. It combines momentum and adaptive learning rate methods to adaptively adjust the learning rate of each parameter during training, achieving faster and more accurate convergence. Because of its adaptive learning rate, it is widely used in the training of neural networks, making the training process smoother.

[0140] The L-BFGS-B gradient algorithm is an algorithm for unconstrained nonlinear optimization problems. It is mainly used to solve large-scale optimization problems and has a faster convergence speed and lower storage space consumption compared to other algorithms.

[0141] Optionally, when optimizing the neural network using the Adam random algorithm and the L-BFGS-B gradient algorithm, the Adam random algorithm can be used for the first N (N≥1) iterations to perform large-scale and rapid optimization of the simulation, quickly reducing training errors. Subsequently, in the N+1th iteration, the gradient algorithm (L-BFGS-B) is used for faster and more accurate solutions, gradually improving computational accuracy. Here, N can be the iteration number segmentation value. For example, when optimizing the neural network using the Adam random algorithm and the L-BFGS-B gradient algorithm, if the iteration number segmentation value is selected as 0, 1000, 3000, and 5000 respectively, the prediction errors of the combined optimization of the Adam random algorithm and the L-BFGS-B gradient algorithm can be shown in Table 1.

[0142] Table 1

[0143] Training time 78.09s 86.25s 95.09s 107.16s Prediction error 4.38％ 2.45％ 1.38％ 1.18％

[0144] It should be noted that when the iteration number segmentation value N is 0, 1000, 3000, or 5000, the relationship between training error and the number of iterations can be as follows: Figure 6 As shown.

[0145] Figure 6 This diagram illustrates the relationship between training error and the number of iterations, as provided in an embodiment of this application. (Refer to Table 1 and...) Figure 6 It can be observed that when N=0, i.e., when only gradient algorithm is used for training, the L-BFGS-B gradient algorithm has high training efficiency but poor accuracy. As the number of iterations and the segmentation value N increase, the Adam random algorithm can effectively improve training accuracy by performing a global search of the solution space, but it will increase the training time.

[0146] For example, 100,900 sampling points are input into a neural network model for electromagnetic field calculation. During the calculation process, the Adam stochastic algorithm and the L-BFGS-B gradient algorithm are used to optimize the neural network. After comprehensively considering the training time and training error, N=30,000 is selected as the selection criterion for the optimization algorithm. The electromagnetic field of the model is determined by the minimum value of the loss function.

[0147] Figure 7 This is a schematic diagram of an electromagnetic field slice provided in an embodiment of this application. Please refer to [link / reference]. Figure 7 In the electromagnetic field calculation results, slices of the three planes xoy, xoz, and yoz are taken respectively. The electromagnetic field of the model can be obtained by extracting sampling data from the model of the electromagnetic field to be calculated and inputting it into the preset neural network model for calculating the electromagnetic field. Combined with the model constraints and physical constraints, the electromagnetic field of the model can be obtained.

[0148] In this embodiment, a three-dimensional coordinate system is created with the center point of the model as the origin. The distribution range of the model is obtained based on its shape and size. The physical parameters of the model are formed by obtaining the background stratum size, background stratum resistivity, fixed anomaly size, fixed anomaly resistivity, instrument transmission signal frequency, source distance, and the distance between the instrument midpoint and the anomaly center. The signal source is equivalently processed by applying a background field to the model to obtain the background signal source. Based on the distribution range, physical parameters, and background signal source, model constraints and physical constraints are determined. Sampling is performed on the model, with multiple sampling points extracted inside the model and multiple sampling points extracted at the model boundaries. The three-dimensional coordinate data of all sampling points in the three-dimensional space centered on the model's center point are obtained to obtain the sampling data. The sampling data is input into a neural network model for electromagnetic field calculation. During the calculation process, the Adam random algorithm and the L-BFGS-B gradient algorithm are used to optimize the neural network to obtain the electromagnetic field of the model. In the above process, by determining the model constraints and physical constraints, and by using optimization algorithms to optimize the neural network, when calculating the electromagnetic field, it is only necessary to clarify the model range of the electromagnetic field to be calculated. The electromagnetic field of the model can be obtained through the neural network model, thereby improving the calculation efficiency of the electromagnetic field.

[0149] To further understand the electromagnetic field calculation method based on physical constraint neural networks, the electromagnetic field calculation process involved will be further explained.

[0150] Figure 8 A flowchart illustrating an electromagnetic field calculation process provided in this application embodiment. Please refer to [link / reference]. Figure 8 By clearly defining the distribution range, physical parameters, and background signal sources of the model to be calculated, the distribution range can include the solution space of the model to be calculated. Sampling points are determined using sampling methods, and multiple sampling points are extracted from the model of the electromagnetic field to be calculated to form sampling data. The extracted sampling data is used as the input of the neural network to analyze the physical laws that the electromagnetic field to be calculated needs to satisfy, construct the loss function of the neural network, and input the sampling data into the neural network to obtain the electromagnetic field that satisfies the model constraints and physical constraints, i.e., the electromagnetic field to be calculated.

[0151] It should be noted that the specific execution process of the electromagnetic field calculation process provided in this application embodiment can be found in the electromagnetic field calculation method based on physical constraint neural network provided in the above embodiment.

[0152] Figure 9 This is a schematic diagram of an electromagnetic field calculation device based on a physically constrained neural network, provided as an embodiment of this application. Please refer to... Figure 9 An electromagnetic field calculation device 10 based on a physical constraint neural network includes:

[0153] The first processing module 11 is used to obtain the distribution range, physical parameters and background signal source of the model of the electromagnetic field to be calculated;

[0154] The second processing module 12 is used to determine the model constraints and physical constraints based on the distribution range, physical parameters and background signal sources.

[0155] The third processing module 13 is used to input the sampled data of the model into a preset neural network model for calculating the electromagnetic field to obtain the electromagnetic field of the model; wherein, the neural network model adopts a loss function constructed according to the model constraints and physical constraints, and the sampled data includes the three-dimensional coordinate data of multiple sampling points of the model sampled according to preset rules.

[0156] The electromagnetic field calculation device based on a physical constraint neural network provided in this application can execute the technical solutions shown in the above embodiments. Its implementation principle and beneficial effects are similar and will not be repeated here.

[0157] In one possible implementation, the second processing module 12 is specifically used for:

[0158] Based on the distribution range, physical parameters, background signal source, electromagnetic field unique theorem, and Maxwell's equations, the model characteristics and physical conditions for calculating the electromagnetic field are determined.

[0159] Model constraints are constructed based on model characteristics, and physical constraints are constructed based on the boundary conditions of the electromagnetic field and physical conditions.

[0160] In one possible implementation, the loss function is:

[0161]

[0162] in,

[0163] as well as,

[0164]

[0165] MES represents mean squared error, loss represents the difference between the model prediction and the true value, i represents current intensity, ω represents angular frequency, μ0 represents free permeability, σ0 represents background complex conductivity, σ represents complex conductivity, and E s E represents the scattering field, E0 represents the background field, and loss represents the difference between the model prediction and the true value. m (m=x,y,z) represents the electric field generated by magnetic dipoles in different directions, and k represents the proportionality constant of the electric field strength.

[0166] In one possible implementation, the first processing module 11 is specifically used for:

[0167] Create a three-dimensional coordinate system with the center point of the model as the origin, and obtain the distribution range of the model according to its shape and size;

[0168] The physical parameters of the model are obtained by acquiring the background stratum size, background stratum resistivity, fixed anomaly size, fixed anomaly resistivity, instrument transmission signal frequency, source distance, and distance between the instrument midpoint and the anomaly center.

[0169] The background signal source is obtained by applying a background field to the model to perform equivalent processing on the signal source.

[0170] Figure 10 This is a schematic diagram of another electromagnetic field calculation device based on a physically constrained neural network, provided as an embodiment of this application. Figure 9 Based on the illustrated embodiments, please refer to Figure 10 The electromagnetic field calculation device 10 based on a physical constraint neural network further includes: a fourth processing module 14, which is used for:

[0171] Sampling is performed on the model by extracting multiple sampling points inside the model and multiple sampling points at the boundary of the model. The three-dimensional coordinate data of all sampling points in the three-dimensional space centered on the center point of the model are obtained to obtain the sampling data.

[0172] In one possible implementation, the third processing module 13 is specifically used for:

[0173] The sampled data is input into the neural network model for electromagnetic field calculation. During the calculation process, the Adam stochastic algorithm and the L-BFGS-B gradient algorithm are used to optimize the neural network to obtain the electromagnetic field of the model.

[0174] The electromagnetic field calculation device based on a physical constraint neural network provided in this application can execute the technical solutions shown in the above embodiments. Its implementation principle and beneficial effects are similar and will not be repeated here.

[0175] Figure 11 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Please refer to... Figure 11 The electronic device 20 may include a processor 21, a memory 22, and an interface 24. Exemplarily, the processor 21, the memory 22, and the interface 24 are interconnected via a bus 23.

[0176] Memory 22 stores instructions executed by the computer;

[0177] The processor 21 executes computer execution instructions stored in the memory 22, causing the processor 21 to perform the method provided in the above method embodiments.

[0178] Accordingly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the methods of any of the above-described method embodiments.

[0179] Accordingly, embodiments of this application may also provide a computer program product, including a computer program, which, when executed by a processor, can implement the methods of any of the above method embodiments.

[0180] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0181] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations 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, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0182] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0183] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0184] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0185] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0186] Computer-readable media include both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0187] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0188] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for calculating electromagnetic fields based on physically constrained neural networks, characterized in that, include: Obtain the distribution range, physical parameters, and background signal sources of the model of the electromagnetic field to be calculated; Based on the distribution range, the physical parameters, the background signal source, the electromagnetic field unique theorem, and Maxwell's equations, determine the model characteristics and physical conditions for calculating the electromagnetic field. The model constraints are constructed based on the model characteristics, and the physical constraints are constructed based on the boundary conditions of the electromagnetic field and the physical conditions. The sampled data is input into the neural network model for electromagnetic field calculation. During the calculation, the Adam stochastic algorithm and the L-BFGS-B gradient algorithm are used to optimize the neural network to obtain the electromagnetic field of the model. The neural network model employs a loss function constructed based on the model constraints and physical constraints. The sampled data includes the three-dimensional coordinate data of multiple sampling points sampled from the model according to preset rules. The loss function is: ； in, , ,as well as, ； MSE represents the mean squared error, and loss represents the difference between the model's prediction and the true value. Represents current intensity. Represents angular frequency. Represents the vacuum permeability. Represents background complex conductivity. Represents complex conductivity. Represents the scattered field. Represents the background scene. This represents the difference between the model's predictions and the actual values. Represents the electric field generated by magnetic dipoles in different directions. The proportionality constant representing the electric field strength, Represents boundary conditions.

2. The method according to claim 1, characterized in that, The process of obtaining the distribution range, physical parameters, and background signal sources of the model of the electromagnetic field to be calculated includes: A three-dimensional coordinate system is created with the center point of the model as the origin, and the distribution range of the model is obtained according to the shape and size of the model; The physical parameters of the model are obtained by acquiring the background stratum size, background stratum resistivity, fixed anomaly size, fixed anomaly resistivity, instrument transmission signal frequency, source distance, and distance between the instrument midpoint and the anomaly center. The background signal source is obtained by applying a background field to the model to perform equivalent processing on the signal source.

3. The method according to claim 1 or 2, characterized in that, The method further includes: Sampling is performed on the model by extracting multiple sampling points inside the model and multiple sampling points at the boundary of the model, and obtaining the three-dimensional coordinate data of all sampling points in a three-dimensional space centered on the center point of the model, thus obtaining the sampling data.

4. An electromagnetic field calculation device based on a physically constrained neural network, characterized in that, include: The first processing module is used to obtain the distribution range, physical parameters, and background signal sources of the model of the electromagnetic field to be calculated; The second processing module is used to determine the model characteristics and physical conditions for calculating the electromagnetic field based on the distribution range, the physical parameters, the background signal source, the electromagnetic field unique theorem, and Maxwell's equations. The second processing module is further configured to construct the model constraints based on the model features, and to construct the physical constraints based on the boundary conditions of the electromagnetic field and the physical conditions; The third processing module is used to input the sampled data into the neural network model for electromagnetic field calculation, and to optimize the neural network using the Adam stochastic algorithm and the L-BFGS-B gradient algorithm during the calculation process to obtain the electromagnetic field of the model; wherein, the neural network model uses a loss function constructed based on the model constraints and the physical constraints, the sampled data includes the three-dimensional coordinate data of multiple sampling points of the model sampled according to preset rules, and the loss function is: ； in, , ,as well as, ； MSE represents the mean squared error, and loss represents the difference between the model's prediction and the true value. Represents current intensity. Represents angular frequency. Represents the vacuum permeability. Represents background complex conductivity. Represents complex conductivity. Represents the scattered field. Represents the background scene. This represents the difference between the model's predictions and the actual values. Represents the electric field generated by magnetic dipoles in different directions. The proportionality constant representing the electric field strength, Represents boundary conditions.

5. An electronic device, characterized in that, include: Processor, memory, and interaction interface; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1 to 3.

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