Aero-electromagnetic forward modeling method and medium based on physical information neural network
A neural network-based method for airborne electromagnetic simulation addresses computational bottlenecks by solving Maxwell's equations directly, providing fast and accurate determination of electric and magnetic fields without grid-based methods.
Patent Information
- Application Number
- CN202411376952.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-30
- Publication Date
- 2024-12-10
- Estimated Expiration
- 2044-09-30
AI Technical Summary
Traditional three-dimensional frequency-domain airborne electromagnetic forward simulation methods are computationally intensive due to their dependence on grid division and basis function selection, especially when dealing with complex geometric bodies, leading to slow calculation speeds.
An approach using a physical information-based neural network to solve Maxwell's equations, incorporating boundary and internal electric field values, trained with a loss function to determine secondary electric and magnetic fields without the need for traditional grid-based methods.
Enables fast and accurate three-dimensional forward simulation by reducing computational complexity and eliminating the need for fine grid divisions, allowing for efficient processing of complex geometric anomalies.
Smart Images
Figure CN118884546B_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of geophysical exploration technology, and in particular to an airborne electromagnetic forward modeling method and medium based on a physical information neural network. Background Art
[0002] Airborne electromagnetic method is a geophysical method that uses an airborne electromagnetic system (i.e., electromagnetic exploration equipment mounted on an aircraft platform) to detect underground targets. It is divided into two categories: frequency domain and time domain. Since this method uses an aircraft as a carrier, its emission source is constantly moving. Therefore, in the three-dimensional forward and inversion calculations of airborne electromagnetics, the equations formed by each source need to be solved.
[0003] Traditional frequency-domain airborne electromagnetic three-dimensional forward numerical simulation methods mainly include: integral equation method, finite difference method, finite element method, finite volume method and spectral element method. All of the above methods are based on Maxwell equations theory, discretize the solution area, and establish the weak form of the electromagnetic field by selecting different grids and basis functions to solve the equation group.
[0004] Among them, the above-mentioned traditional numerical methods need to use high-order basis functions or fine grid division to achieve the purpose of accurate characterization for areas containing complex geometric bodies (i.e., geometric bodies composed of various materials in the target detection area), which will undoubtedly greatly increase the amount of calculation required to solve the system of equations, thereby slowing down the calculation speed. Therefore, in view of the serious dependence of traditional three-dimensional frequency domain airborne electromagnetic forward simulation on grid division, basis function selection, and numerical solution methods, it is urgent to design a new solution method to get rid of the dependence on the above process. Summary of the invention
[0005] The purpose of this application is to provide an airborne electromagnetic forward modeling method and medium based on a physical information neural network, using a new physical information neural network to complete a frequency domain airborne electromagnetic three-dimensional forward modeling and determine the secondary magnetic field value of the target airborne electromagnetic measuring point.
[0006] To achieve the above objectives, the embodiments of the present application provide the following solutions.
[0007] In a first aspect, the present application provides an airborne electromagnetic forward modeling method based on a physical information neural network, the airborne electromagnetic forward modeling method based on a physical information neural network comprising: determining a three-dimensional stereo model of an airborne electromagnetic exploration area; delineating a plurality of airborne electromagnetic measuring points based on the three-dimensional stereo model; the airborne electromagnetic measuring points comprising: boundary measuring points and model internal measuring points; obtaining the three-dimensional coordinates of all airborne electromagnetic measuring points and setting the secondary electric field values of the boundary measuring points; constructing a physical information neural network; the physical information neural network comprising: an input layer, a hidden layer for adding physical information, and an output layer; the physical information comprises a derivation of Maxwell's equations; using the three-dimensional coordinates of different airborne electromagnetic measuring points, the secondary electric field values of the boundary measuring points, and the airborne electromagnetic system parameters The physical information neural network is trained and optimized with the minimum mean square error of the loss function as the goal; the airborne electromagnetic system parameters at least include the frequency of the airborne electromagnetic system in the frequency domain; the loss function is determined based on the real and imaginary losses of the secondary electric field at the boundary measuring point, and the real and imaginary losses of the secondary electric field control function at the internal measuring point of the model; the three-dimensional coordinates of the target airborne electromagnetic measuring point are input into the optimized physical information neural network for frequency domain airborne electromagnetic three-dimensional forward simulation to obtain the secondary electric field value of the target airborne electromagnetic measuring point; based on the secondary electric field value of the target airborne electromagnetic measuring point, the secondary electric field is converted into a secondary magnetic field using Faraday's law of electromagnetic induction to obtain the secondary magnetic field value of the target airborne electromagnetic measuring point.
[0008] Optionally, the Maxwell equations are derived as follows.
[0009] .
[0010] In the formula, is the curl operator, is the secondary electric field value of the airborne electromagnetic measuring point, , , Represents the airborne electromagnetic measurement points x , y , z The secondary electric field value in the direction, is the value of the secondary electric field in the source term, is the angular frequency, f is the frequency of the airborne electromagnetic system in the frequency domain, is the abnormal conductivity, is the earth's electrical conductivity, is the background field conductivity, is the magnetic permeability in vacuum, is the dielectric constant, For the interior of the three-dimensional model, is the boundary of the three-dimensional model, i Is an imaginary unit.
[0011] Optionally, the loss function is as follows.
[0012] .
[0013] In the formula, is the total secondary electric field loss at the airborne electromagnetic measuring point, is the number of boundary measurement points, is the number of measurement points inside the model, is the three-dimensional coordinate of the boundary measurement point, is the three-dimensional coordinate of the measuring point inside the model, The first k The real part of the secondary electric field at the boundary measurement point, The first step of the neural network to input physical information k The real part of the secondary electric field at the boundary measurement point, The first k The imaginary part of the secondary electric field at each boundary point, The first step of the neural network to input physical information k The imaginary part of the secondary electric field at each boundary point, For the j The real part of the secondary electric field control function of each internal measurement point of the model, For the j The imaginary part of the secondary electric field control function of each measuring point inside the model.
[0014] Optionally, the real part and the imaginary part of the secondary electric field control function for any airborne electromagnetic measurement point satisfy the following relationship.
[0015] .
[0016] .
[0017] .
[0018] .
[0019] .
[0020] .
[0021] .
[0022] In the formula, is the real part of the secondary electric field control function of the airborne electromagnetic measurement point, , , Represents the airborne electromagnetic measurement pointsx , y , z The real part of the direction quadratic electric field control function, is the imaginary part of the secondary electric field control function of the airborne electromagnetic measurement point, , , Represents the airborne electromagnetic measurement points x , y , z The imaginary part of the direction quadratic electric field control function, is the real part of the secondary electric field at the airborne electromagnetic measuring point, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The real part in the direction, is the imaginary part of the secondary electric field at the airborne electromagnetic measuring point, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The imaginary part of the direction, The real part of the secondary electric field in the source term, , , They represent the secondary electric field in the source term x , y , z The real part in the direction, The imaginary part of the secondary electric field in the source term, , , They represent the secondary electric field in the source term x , y , z The imaginary part of the direction, , , Represents the airborne electromagnetic measurement points x , y , z The secondary electric field value in the direction, , Respectively exist y , z The second-order partial derivative in the direction, , Respectively exist y , z The second-order partial derivative in the direction, , Respectively exist x , z The second-order partial derivative in the direction, , Respectively exist x , z The second-order partial derivative in the direction, , Respectively exist x , y The second-order partial derivative in the direction, , Respectively exist x , y The second-order partial derivative in the direction, is the angular frequency, is the magnetic permeability in vacuum, is the dielectric constant, is the earth's electrical conductivity, is the abnormal conductivity, is the three-dimensional coordinate of the airborne electromagnetic measurement point, for The real part of the secondary electric field in the coordinates, for The imaginary part of the secondary electric field in coordinates.
[0023] Optionally, the hidden layer for adding physical information includes multiple layers of neurons; the information transmission between neurons in each layer satisfies the following relationship.
[0024] .
[0025] In the formula, and Indicates n - Two neurons in layer 1, Indicates n A neuron in a layer, n >1, X is the variable in the activation function, is the first weight, is the second weight, is the bias, e The natural index.
[0026] Optionally, the calculation formula for the secondary electric field value is as follows.
[0027] .
[0028] In the formula, is the secondary electric field value of the airborne electromagnetic measuring point, , , Represents the airborne electromagnetic measurement points x , y , z The secondary electric field value in the direction, i is an imaginary unit, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The real part in the direction, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The imaginary part of the direction.
[0029] Optionally, a calculation formula for the secondary magnetic field value is as follows.
[0030] .
[0031] In the formula, is the secondary magnetic field value of the airborne electromagnetic measuring point, , , Represents the airborne electromagnetic measurement points x , y , z The secondary magnetic field value of the direction, is the angular frequency, is the magnetic permeability in vacuum, , , Represents the airborne electromagnetic measurement points x , y , z The secondary electric field value in the direction.
[0032] Optionally, the hidden layer that adds physical information selects L-BFGS-B algorithm or Adam algorithm as an optimizer for optimizing the gradient of the loss function.
[0033] In a second aspect, the present application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aeronautical electromagnetic forward modeling method based on a physical information neural network.
[0034] According to the specific embodiments provided by the present application, the present application discloses the following technical effects: the present application adds the derivation of Maxwell's equations as physical information to the hidden layer of the neural network, and completes the frequency domain airborne electromagnetic three-dimensional forward simulation by approximating the solution of the derivation of Maxwell's equations. At the same time, the present application determines the loss function based on the real and imaginary losses of the secondary electric field at the boundary measuring points, as well as the real and imaginary losses of the secondary electric field control function of the internal measuring points of the model, and continuously optimizes the parameters of the physical information neural network through the back propagation mechanism of the neural network to minimize the loss function. In addition, the optimized physical information neural network of the present application does not need to add other constraints, because the secondary electric field values of the boundary measuring points are given in the input layer as boundary conditions, and physical information is added in the hidden layer as a priori conditions. Therefore, the present application can use a brand-new physical information neural network to complete the frequency domain airborne electromagnetic three-dimensional forward simulation and determine the secondary magnetic field value of the target airborne electromagnetic measuring point. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.
[0036] Figure 1 A flowchart of an airborne electromagnetic forward modeling method based on a physical information neural network provided in an embodiment of the present application.
[0037] Figure 2 A structural hierarchical diagram of the physical information neural network provided in an embodiment of the present application.
[0038] Figure 3 An internal relationship diagram of the physical information neural network provided in an embodiment of the present application.
[0039] Figure 4 A diagram of the information transmission relationship between the various layers of neurons provided in the embodiment of the present application.
[0040] Figure 5 A diagram of the training process of the physical information neural network provided in an embodiment of the present application. DETAILED DESCRIPTION
[0041] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.
[0042] The purpose of this application is to provide an airborne electromagnetic forward modeling method and medium based on a physical information neural network, using a new physical information neural network to complete a frequency domain airborne electromagnetic three-dimensional forward modeling and determine the secondary magnetic field value of the target airborne electromagnetic measuring point.
[0043] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.
[0044] like Figure 1 As shown, this embodiment provides an airborne electromagnetic forward modeling method based on physical information neural network, which is specifically as follows.
[0045] Step S1: Determine a three-dimensional model of the airborne electromagnetic survey area.
[0046] In this embodiment, the three-dimensional stereo model of the airborne electromagnetic exploration area includes an underground exploration area model and a ground space area model.
[0047] Step S2: Delineate a plurality of airborne electromagnetic measurement points based on the three-dimensional model; the airborne electromagnetic measurement points include: boundary measurement points and model internal measurement points.
[0048] In this embodiment, after the three-dimensional coordinates of the airborne electromagnetic measurement points are graphically represented, a three-dimensional hexahedral model (i.e., the three-dimensional solid model mentioned above) is obtained. N Aerial electromagnetic measurement points, including the edge of the hexahedral model Boundary points and The internal measurement points of the model, namely N=N u +N f .
[0049] Step S3: Obtain the three-dimensional coordinates of all airborne electromagnetic measurement points and set the secondary electric field values of the boundary measurement points.
[0050] In this embodiment, the secondary electric field value at the boundary measurement point is expressed as , is the real part of the secondary electric field at the boundary point, is the imaginary part of the secondary electric field at the boundary measuring point. In this embodiment, the secondary electric field value of the boundary measuring point is set to 0, and the set secondary electric field value of the boundary measuring point is input into the neural network as a priori boundary conditions.
[0051] Step S4: construct a physical information neural network; the physical information neural network includes: an input layer, a hidden layer for adding physical information, and an output layer; the physical information includes a derivation of Maxwell's equations.
[0052] like Figure 2 As shown, in this embodiment, the physical information neural network is divided into an input layer, a hidden layer and an output layer. The function of the input layer is to input the data required in the hidden layer, and the input data includes: N The three-dimensional coordinates of the airborne electromagnetic measurement points The secondary electric field value at the boundary measurement point is expressed as , and aviation electromagnetic system parameters (transmitting altitude, receiving altitude, frequency, etc. of aviation electromagnetic system in frequency domain).
[0053] The purpose of the hidden layer is to abstract the features of the input data and present its more abstract features from another dimension. The hidden layer contains information transmission between neurons and uses activation functions, biases, and weights to obtain the loss function. Figure 3 As shown, the hidden layer has a total of n ( n >1) layer neurons (one neuron represents the real and imaginary parts of the secondary electric field of an airborne electromagnetic measurement point), use the input parameters as the training parameters of the physical information neural network, add the activation function, bias and weight to the connection between each neuron, and obtain the values of neurons in different layers in turn, and then determine the value of the loss function. When the loss function meets the requirements, the secondary electric field value of the airborne electromagnetic measurement point is output ; When the loss function does not meet the requirements, the back propagation mechanism of the physical information neural network is used to update the values of weights and biases until the loss function meets the requirements.
[0054] like Figure 4 As shown in the figure, the activation function in the hidden layer transmits information between layers by combining with neurons, converting the output information of the neurons in the previous layer and inputting it into the neurons in the next layer. n -1 layer of neurons can calculate the n The neurons in the first layer n Layer of neurons With n -1 layer of neurons , The following relationship is satisfied.
[0055] .
[0056] In the formula, X is the variable in the activation function, is the first weight, is the second weight, is the bias, eis the natural index. By analogy, the calculation process between multiple layers of neurons can be completed, and the calculation process of back propagation is the same as that of forward propagation, which is to calculate the information of the previous layer of neurons based on the information of the latter layer of neurons.
[0057] Furthermore, in order to realize the frequency domain airborne electromagnetic three-dimensional forward simulation, this embodiment adds the Maxwell equation derivation as physical information into the hidden layer. Starting from the Maxwell total field equation, in order to avoid the field source singularity, the Maxwell total field is separated into the primary electric field and the secondary electric field, and the full space analytical solution (that is, the resistivity of the three-dimensional model is assigned to 10 6 Ω·m is used for calculation) as the source term, and the secondary electric field (double curl) control equation and boundary conditions are determined, that is, the derivation of Maxwell's equations in this embodiment, which are specifically as follows.
[0058] .
[0059] In the formula, is the curl operator, , , Represents the airborne electromagnetic measurement points x , y , z The secondary electric field value in the direction, is the value of the secondary electric field in the source term, is the angular frequency, f is the frequency of the airborne electromagnetic system in the frequency domain, is the abnormal conductivity, is the earth's electrical conductivity, is the background field conductivity, is the magnetic permeability in vacuum, is the dielectric constant, For the interior of the three-dimensional model, is the boundary of the three-dimensional model, i Is an imaginary unit.
[0060] make , , , , e x , e y , e z The secondary electric field x , y , z The unit vector of the direction. Decomposition and The decomposition method is the same, that is, , , By specifically expanding the Maxwell equations in this embodiment in the above manner, the real part and imaginary part of the secondary electric field control function of the airborne electromagnetic measurement point can be obtained, as shown below.
[0061] .
[0062] .
[0063] .
[0064] .
[0065] .
[0066] .
[0067] .
[0068] In the formula, is the real part of the secondary electric field control function of the airborne electromagnetic measurement point, , , Represents the airborne electromagnetic measurement points x , y , z The real part of the direction quadratic electric field control function, is the imaginary part of the secondary electric field control function of the airborne electromagnetic measurement point, , , Represents the airborne electromagnetic measurement points x , y , z The imaginary part of the direction quadratic electric field control function, is the real part of the secondary electric field at the airborne electromagnetic measuring point, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The real part in the direction, is the imaginary part of the secondary electric field at the airborne electromagnetic measuring point, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The imaginary part of the direction, The real part of the secondary electric field in the source term, , , They represent the secondary electric field in the source termx , y , z The real part in the direction, The imaginary part of the secondary electric field in the source term, , , They represent the secondary electric field in the source term x , y , z The imaginary part of the direction.
[0069] , Respectively exist y , z The second-order partial derivative in the direction, , Respectively exist y , z The second-order partial derivative in the direction, , Respectively exist x , z The second-order partial derivative in the direction, , Respectively exist x , z The second-order partial derivative in the direction, , Respectively exist x , y The second-order partial derivative in the direction, , Respectively exist x , y Second-order partial derivative in direction.
[0070] , Respectively represent the boundary measurement points on the left and right sides of the three-dimensional model. , They represent the front and back boundary points in the three-dimensional model respectively. , They represent the boundary points at the bottom and top of the three-dimensional model respectively. for The real part of the secondary electric field in the coordinates, for The imaginary part of the secondary electric field in coordinates.
[0071] Since this embodiment adds the derivation of Maxwell's equations as physical information into the hidden layer, in order to effectively train and optimize the physical information neural network, this embodiment determines the loss function of the physical information neural network based on the real and imaginary losses of the secondary electric field at the boundary measurement points, and the real and imaginary losses of the secondary electric field control function at the internal measurement points of the model, as shown below.
[0072] .
[0073] In the formula, is the total secondary electric field loss at the airborne electromagnetic measuring point, is the three-dimensional coordinate of the boundary measurement point, is the three-dimensional coordinate of the measuring point inside the model, The first k The real part of the secondary electric field at the boundary measurement point, The first step of the neural network to input physical information k The real part of the secondary electric field at the boundary measurement point, The first k The imaginary part of the secondary electric field at each boundary point, The first step of the neural network to input physical information k The imaginary part of the secondary electric field at each boundary point, For the j The real part of the secondary electric field control function of each internal measurement point of the model, For the j The imaginary part of the secondary electric field control function of each measuring point inside the model.
[0074] Step S5: Taking the three-dimensional coordinates of different airborne electromagnetic measurement points, the secondary electric field values of the boundary measurement points and the airborne electromagnetic system parameters as input, the physical information neural network is trained and optimized with the minimum mean square error of the loss function as the goal.
[0075] In this embodiment, the hidden layer of the physical information neural network can select the L-BFGS-B algorithm or the Adam algorithm as the optimizer for optimizing the gradient of the loss function. The L-BFGS-B algorithm is a method for minimizing the loss function of variables in the L-BFGS minimization process. z (i.e., the real and imaginary parts of the secondary electric field at the airborne electromagnetic measurement point) impose constraints, namely z min < z < z max , z max and z minRespectively represent the maximum and minimum boundaries of the variables. The L-BFGS-B algorithm is an extension of the mature L-BFGS algorithm, adding the function of processing simple boundaries on the model. It draws on the idea of the trust region method, while maintaining the L-BFGS update of the Hessian matrix and the linear search algorithm. In actual calculations, three different stopping criteria are required to control the calculation. First, when the maximum number of iterations is reached, the iteration terminates; second, when the attenuation of the objective function is small enough, the iteration terminates; third, when the norm of the projected gradient is small enough, the iteration terminates. The Adam algorithm, also known as adaptive moment estimation, is an optimization algorithm for finding the global optimal point. The first-order moment estimate and second-order moment estimate of the gradient of each network parameter are dynamically adjusted according to the loss function. The advantage of this algorithm is that after bias correction, the learning rate of each iteration has a certain range, which makes the network parameters relatively stable, not easy to fall into the local optimum, and the calculation speed is fast.
[0076] like Figure 5 As shown in the figure, first, the input data is used to construct the input layer of the physical information neural network; secondly, the input data and the neurons containing physical information are forward transmitted, and the loss function is used for constraint, and the loss function optimization algorithm and optimizer are used to optimize it, that is, each layer of neurons is back-propagated, and the network parameters such as weights and biases are continuously updated; finally, the secondary electric field value of the airborne electromagnetic measuring point is calculated using the optimized network parameters.
[0077] Step S6: input the three-dimensional coordinates of the target airborne electromagnetic measuring point into the trained and optimized physical information neural network to perform frequency domain airborne electromagnetic three-dimensional forward simulation to obtain the secondary electric field value of the target airborne electromagnetic measuring point.
[0078] In this embodiment, the formula used by the physical information neural network to calculate the secondary electric field value of the airborne electromagnetic measurement point is as follows.
[0079] .
[0080] In the formula, i Is an imaginary unit.
[0081] Step S7: Based on the secondary electric field value of the target airborne electromagnetic measuring point, the secondary electric field is converted into a secondary magnetic field using Faraday's law of electromagnetic induction to obtain the secondary magnetic field value of the target airborne electromagnetic measuring point.
[0082] In this embodiment, the calculation formula of the secondary magnetic field value is as follows.
[0083] .
[0084] In the formula, is the secondary magnetic field value of the airborne electromagnetic measuring point, , , Represents the airborne electromagnetic measurement points x , y , z The secondary magnetic field value of the direction, express exist y The partial derivative in the direction, express exist z The partial derivative in the direction, express exist z The partial derivative in the direction, express exist x The partial derivative in the direction, express exist x The partial derivative in the direction, express exist y Partial derivatives in the direction.
[0085] In summary, the aero-electromagnetic forward modeling method based on physical information neural network provided in this application mainly has the following advantages.
[0086] 1) The traditional frequency domain airborne electromagnetic 3D forward modeling method is based on meshing, basis function selection and numerical solution. However, there are technical bottlenecks in the accuracy and speed of complex geometric balance calculations, which hinders the large-scale practical application of this technology. This application breaks the traditional thinking mode and uses nonlinear functions (i.e., the above f u and f v ) infinitely approximates the solution of the Maxwell equations to obtain a solution that satisfies the conditions to achieve forward simulation. For the multi-source problem of airborne electromagnetic measurement points, the traditional method needs to recalculate the right-hand side of the Maxwell equations to solve the equations, while this application only needs to convert the source data, i.e. , , , , , As part of the input layer. Therefore, the successful construction of the physical information neural network in this application is an innovative application of deep learning methods in the field of aeronautical electromagnetic simulation.
[0087] 2) In the traditional frequency-domain airborne electromagnetic three-dimensional forward modeling method, grid division is used to describe complex geometric bodies. The more complex the anomaly, the finer the grid division, which leads to large computational complexity and long time consumption. The description of complex anomalies by physical information neural networks is based on the spatial distribution of training points, so any complex anomalies can be simulated. The three-dimensional spatial structure in the physical information neural network causes the number of internal training points to increase with the increase of dimension, which increases the computational time of the network in high-dimensional forward and inverse modeling. However, the reasonable selection of training points in this application combined with GPU technology can effectively solve the problem of computing speed and realize the fast calculation of frequency-domain airborne electromagnetic three-dimensional forward modeling.
[0088] In another embodiment, a computer-readable storage medium is provided, storing a computer program, which implements the steps in the above method embodiments when executed by a processor.
[0089] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).
[0090] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.
[0091] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.
[0092] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.
Claims
1. An aero-electromagnetic forward modeling method based on physical information neural network, characterized in that: The aero-electromagnetic forward modeling method based on physical information neural network includes: Determine the three-dimensional model of the airborne electromagnetic survey area; Delineating a plurality of airborne electromagnetic measurement points based on the three-dimensional model; the airborne electromagnetic measurement points include: boundary measurement points and model internal measurement points; Obtaining the three-dimensional coordinates of all airborne electromagnetic measuring points and setting the secondary electric field values of the boundary measuring points; Constructing a physical information neural network; the physical information neural network includes: an input layer, a hidden layer for adding physical information, and an output layer; the physical information includes a derivation of Maxwell's equations; The physical information neural network is trained and optimized with the three-dimensional coordinates of different airborne electromagnetic measuring points, the secondary electric field values of the boundary measuring points and the airborne electromagnetic system parameters as inputs, and the mean square error of the loss function is minimized as the goal; the airborne electromagnetic system parameters at least include the frequency of the airborne electromagnetic system in the frequency domain; the loss function is determined based on the real and imaginary losses of the secondary electric field of the boundary measuring points, and the real and imaginary losses of the secondary electric field control function of the internal measuring points of the model; Inputting the three-dimensional coordinates of the target airborne electromagnetic measuring point into the optimized physical information neural network to perform frequency domain airborne electromagnetic three-dimensional forward simulation to obtain the secondary electric field value of the target airborne electromagnetic measuring point; Based on the secondary electric field value of the target airborne electromagnetic measuring point, the secondary electric field is converted into a secondary magnetic field using Faraday's law of electromagnetic induction to obtain the secondary magnetic field value of the target airborne electromagnetic measuring point.
2. The aero-electromagnetic forward simulation method based on physical information neural network according to claim 1 is characterized in that: The Maxwell equations are derived as follows: ； In the formula, is the curl operator, is the secondary electric field value of the airborne electromagnetic measuring point, , , Represents the airborne electromagnetic measurement points x , y , z The secondary electric field value in the direction, is the value of the secondary electric field in the source term, is the angular frequency, f is the frequency of the airborne electromagnetic system in the frequency domain, is the abnormal conductivity, is the earth's electrical conductivity, is the background field conductivity, is the magnetic permeability in vacuum, is the dielectric constant, For the interior of the three-dimensional model, is the boundary of the three-dimensional model, i Is an imaginary unit.
3. The aero-electromagnetic forward simulation method based on physical information neural network according to claim 1 is characterized in that: The loss function is: ； In the formula, is the total secondary electric field loss at the airborne electromagnetic measuring point, is the number of boundary measurement points, is the number of measurement points inside the model, is the three-dimensional coordinate of the boundary measurement point, is the three-dimensional coordinate of the measuring point inside the model, The first k The real part of the secondary electric field at the boundary measurement point, The first k The real part of the secondary electric field at each boundary point, The first k The imaginary part of the secondary electric field at the boundary measurement point, The first step of the neural network to input physical information k The imaginary part of the secondary electric field at the boundary measurement point, For the j The real part of the secondary electric field control function of each internal measurement point of the model, For the j The imaginary part of the secondary electric field control function of each measuring point inside the model.
4. The aero-electromagnetic forward simulation method based on physical information neural network according to claim 3 is characterized in that: For any airborne electromagnetic measurement point, the real and imaginary parts of the secondary electric field control function satisfy the following relationship: ； ； ； ； ； ； ； In the formula, is the real part of the secondary electric field control function of the airborne electromagnetic measurement point, , , Represents the airborne electromagnetic measurement points x , y , z The real part of the direction quadratic electric field control function, is the imaginary part of the secondary electric field control function of the airborne electromagnetic measurement point, , , Represents the airborne electromagnetic measurement points x , y , z The imaginary part of the direction quadratic electric field control function, is the real part of the secondary electric field at the airborne electromagnetic measuring point, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The real part in the direction, is the imaginary part of the secondary electric field at the airborne electromagnetic measuring point, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The imaginary part of the direction, The real part of the secondary electric field in the source term, , , They represent the secondary electric field in the source term x , y , z The real part in the direction, The imaginary part of the secondary electric field in the source term, , , They represent the secondary electric field in the source term x , y , z The imaginary part of the direction; , , Represents the airborne electromagnetic measurement points x , y , z The secondary electric field value in the direction, , Respectively exist y , z The second-order partial derivative in the direction, , Respectively exist y , z The second-order partial derivative in the direction, , Respectively exist x , z The second-order partial derivative in the direction, , Respectively exist x , z The second-order partial derivative in the direction, , Respectively exist x , y The second-order partial derivative in the direction, , Respectively exist x , y The second-order partial derivative in the direction, is the angular frequency, is the magnetic permeability in vacuum, is the dielectric constant, is the earth's electrical conductivity, is the abnormal conductivity, is the three-dimensional coordinate of the airborne electromagnetic measurement point, for The real part of the secondary electric field in the coordinates, for The imaginary part of the secondary electric field in coordinates.
5. The aero-electromagnetic forward simulation method based on physical information neural network according to claim 1 is characterized in that: The hidden layer for adding physical information includes multiple layers of neurons; the information transmission between neurons in each layer satisfies the following relationship: ； In the formula, and Indicates n - Two neurons in layer 1, Indicates n A neuron in a layer, n >1, X is the variable in the activation function, is the first weight, is the second weight, is the bias, e The natural index.
6. The aero-electromagnetic forward simulation method based on physical information neural network according to claim 1 is characterized in that: The calculation formula of the secondary electric field value is: ； In the formula, is the secondary electric field value of the airborne electromagnetic measuring point, , , Represents the airborne electromagnetic measurement points x , y , z The secondary electric field value in the direction, i is an imaginary unit, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The real part in the direction, , , They represent the secondary electric field at the airborne electromagnetic measuring point x , y , z The imaginary part of the direction.
7. The aero-electromagnetic forward simulation method based on physical information neural network according to claim 1 is characterized in that: The calculation formula of the secondary magnetic field value is: ； In the formula, is the secondary magnetic field value of the airborne electromagnetic measuring point, , , Represents the airborne electromagnetic measurement points x , y , z The secondary magnetic field value of the direction, is the angular frequency, is the magnetic permeability in vacuum, , , Represents the airborne electromagnetic measurement points x , y , z The secondary electric field value in the direction.
8. The aero-electromagnetic forward simulation method based on physical information neural network according to claim 1 is characterized in that: The hidden layer adding physical information selects L-BFGS-B algorithm or Adam algorithm as the optimizer for optimizing the gradient of the loss function.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the aero-electromagnetic forward simulation method based on physical information neural network described in any one of claims 1 to 8 is implemented.