Electromagnetic detection data efficient three-dimensional inversion method based on operator learning

Abstract

The invention discloses an electromagnetic detection data efficient three-dimensional inversion method based on operator learning, and belongs to the technical field of geophysical inversion, and the method comprises the steps: constructing an operator learning data set which comprises a plurality of electromagnetic forward modeling models and forward modeling responses of the electromagnetic forward modeling models; performing aviation electromagnetic frequency domain forward calculation training based on the operator learning data set by using a DeepONet network to obtain a trained aviation electromagnetic three-dimensional forward operator; inputting the initial uniform half-space model, replacing a generator with an aviation electromagnetic three-dimensional positive operator, and constructing a WGAN network by taking a KAN network as a discriminator to carry out aviation electromagnetic three-dimensional inversion; training is carried out based on the loss function and the data fitting difference convergence condition to update the KAN network and the uniform half-space model, and finally the updated uniform half-space model is obtained to serve as an inversion result. According to the method, more efficient and accurate three-dimensional aviation electromagnetic inversion can be realized, and the method is more suitable for geophysical inversion application under complex data distribution.

Description

Technical Field

[0001] The present invention belongs to the technical field of geophysical inversion, and in particular relates to an efficient three-dimensional inversion method for electromagnetic detection data based on operator learning. Background Art

[0002] With the acceleration of industrialization and urbanization, the contradiction between supply and demand of mineral resources, which are the basic guarantee for the development of the national economy, has become increasingly prominent. Airborne Electromagnetic (AEM) methods are widely used in mineral exploration, oil and gas, environmental engineering, groundwater exploration, disaster prediction and marine surveys because they can carry detection systems on flying platforms to quickly realize large-scale data collection. However, after years of exploration, the degree of mineral resource exploration in areas with excellent geological conditions has reached saturation. The current difficulties in mineral exploration are concentrated in areas with complex geological structures, especially in remote areas with rugged terrain and difficult to reach by humans. Ground exploration in these areas faces challenges such as difficult construction, high safety risks and long exploration cycles. There is an urgent need to develop airborne geophysical technology to achieve efficient and accurate detection.

[0003] Currently, airborne electromagnetic data interpretation primarily relies on one-dimensional inversion methods, with two- and three-dimensional inversion interpretations only used for detailed interpretation in select survey areas. This technological landscape is primarily constrained by two factors: first, the high temporal and spatial resolution of airborne electromagnetic systems generates massive amounts of data, leading to a dramatic increase in the computational load for inversion; second, as the model dimension increases, the non-uniqueness of the inversion problem increases exponentially, leading to a sharp increase in computational costs. However, real underground geological bodies generally exhibit three-dimensional inhomogeneous characteristics, and the traditional layered medium assumption often produces significant errors in structurally complex areas. In comparison, three-dimensional inversion technology can accurately simulate undulating terrain and irregular ore bodies, significantly improving imaging resolution and the reliability of geological interpretation, making it an ideal development direction for airborne electromagnetic data interpretation.

[0004] Efficient airborne electromagnetic three-dimensional forward modeling technology is the foundation for the practical application of three-dimensional inversion. Currently, commonly used airborne electromagnetic three-dimensional numerical simulation methods mainly include the integral equation method, finite difference method, finite volume method, and finite element method. Combined with acceleration technologies such as local grid, "moving footprint" and direct solution, these methods have been widely used for airborne electromagnetic three-dimensional numerical simulation of complex models. However, these conventional numerical simulation methods all require mesh discretization or numerical approximation of the model, and then construct and solve a large system of equations based on the governing equations. The computational efficiency is significantly affected by factors such as model scale, solver performance, and the number of emitters, and their use requires high computing resources. Due to the huge amount of airborne electromagnetic data, these mainstream three-dimensional forward modeling methods have low computational efficiency, which restricts the promotion and application of three-dimensional inversion technology in the detailed interpretation of airborne electromagnetic field data.

[0005] Three-dimensional airborne electromagnetic inversion can be categorized by search method: gradient-based optimization inversion and global optimization inversion. Global optimization inversion does not rely on an initial model, but requires extensive searches of the computational space, resulting in long computational times and being more suitable for low-dimensional problems. Gradient-based inversion algorithms are computationally efficient but are sensitive to the initial model and prone to local minima. To overcome the limitations of traditional methods, machine learning techniques, particularly deep learning networks, have shown great potential in geophysics, offering new approaches to solving these problems. Machine learning methods can be broadly categorized into three main groups: data-driven, physics-driven, and operator learning, and these methods are often used in a cross-functional manner. Data-driven neural networks achieve fast computational speeds after training with large sample sets, but they face challenges such as overfitting and limited generalization. Physics-driven neural networks implement constraints by incorporating physical equations, but require retraining for each calculation, reducing computational efficiency. Generative adversarial networks (GANs) suffer from pattern collapse and training instability. WGANs, as a variant, improve data fitting quality. Operator learning methods extend neural network mapping to infinite-dimensional function spaces. A typical network, DeepONet, combines branch networks with a backbone network, capable of learning complex mapping relationships. However, these methods suffer from drawbacks such as requiring high-dimensional datasets and insufficient generalization. FNO, which utilizes Fourier transforms to efficiently handle physical problems with global dependencies, struggles with non-periodic data. Therefore, further algorithm optimization is needed to achieve efficient and accurate inversion of complex geology. Summary of the Invention

[0006] In view of the above, the purpose of the present invention is to provide an efficient three-dimensional inversion method for electromagnetic detection data based on operator learning. By combining the advantages of operator learning and generative adversarial networks, the Branch-Trunk structure of DeepONet is used to extract local features, and a large number of training sets are used as an airborne electromagnetic three-dimensional forward operator to replace the generator of WGAN to quickly and accurately calculate the forward data. At the same time, the KAN network is used as a discriminator to evaluate the authenticity of the generated model. It can learn complex data distributions and measure the difference between observed data and predicted data through loss functions and data fitting errors. It is more suitable for geophysical inversion applications, and ultimately achieves more efficient and accurate three-dimensional airborne electromagnetic inversion.

[0007] To achieve the above-mentioned purpose, the present invention provides the following technical solutions: In a first aspect, an embodiment of the present invention provides an efficient three-dimensional inversion method for electromagnetic detection data based on operator learning, comprising the following steps: Construct an operator learning dataset including several electromagnetic forward models and their forward responses; The DeepONet network is used to train the airborne electromagnetic frequency domain forward modeling based on the operator learning dataset to obtain the trained airborne electromagnetic three-dimensional forward modeling operator. The initial uniform half-space model is input to replace the generator with the airborne electromagnetic 3D forward operator and the KAN network is used as the discriminator to construct the WGAN network for airborne electromagnetic 3D inversion. Training is performed based on the loss function and the data fitting error convergence condition to update the KAN network and the uniform half-space model, and finally the updated uniform half-space model is obtained as the inversion result.

[0008] Preferably, the constructing of an operator learning data set including several electromagnetic forward models and their forward responses comprises: The Gaussian random field method is used to generate several electromagnetic forward models, and the forward response values at different altitudes and frequencies are calculated based on the electromagnetic forward models. The generated electromagnetic forward models and their corresponding forward response values are compiled into an operator learning dataset and divided into a training set and a test set for airborne electromagnetic three-dimensional forward operator training.

[0009] Preferably, the method of using the DeepONet network to perform airborne electromagnetic frequency domain forward modeling training based on an operator learning data set to obtain a trained airborne electromagnetic three-dimensional forward modeling operator includes: Based on the dual network architecture consisting of a branch network and a backbone network in the DeepONet network, airborne electromagnetic frequency domain forward modeling is performed. The branch network is used to process the discretized input electromagnetic forward model data, while the backbone network processes the query parameters. The predicted response data output by the two networks is fused through the inner product operation. An approximate expression of the operator is constructed, and the absolute error between the predicted response data and the actual forward response in the operator learning dataset is used as the loss function. The operator is trained until the error is less than the set threshold, so that the operator has the ability to replace the actual airborne electromagnetic 3D forward modeling. The operator is then used as the trained airborne electromagnetic 3D forward modeling operator.

[0010] Preferably, the step of inputting the initial uniform half-space model to replace the generator with an airborne electromagnetic three-dimensional forward operator and constructing a WGAN network using a KAN network as a discriminator to perform airborne electromagnetic three-dimensional inversion comprises: The airborne electromagnetic three-dimensional forward operator replaces the generator, and the KAN network is used as the discriminator to construct a WGAN network. The initial uniform half-space model as the inversion starting point is input into the WGAN network for airborne electromagnetic three-dimensional inversion. The initial uniform half-space model is calculated using the airborne electromagnetic three-dimensional forward operator to obtain predicted data, and the predicted data and the actual observation data are discriminated through the KAN network.

[0011] Preferably, the loss function is expressed as: , in, represents the loss function, denotes the parameters of the initial uniform half-space model, represents the parameters of the KAN network, represents the KAN network, represents the observation data, represents the airborne electromagnetic three-dimensional forward operator, represents the initial uniform half-space model, represents the weight of the gradient penalty term, , yes A random number in the range, represents the gradient of the KAN network relative to the input, represents the L2 norm.

[0012] Preferably, the data fitting error convergence condition is expressed as: , in, Indicates a poor fit to the data. represents the predicted data output by the airborne electromagnetic three-dimensional forward operator, represents the observation data, represents the L2 norm, when The inversion is stopped when the iteration number is less than the preset convergence threshold.

[0013] Preferably, when training and updating the KAN network and the uniform half-space model, in each iterative step, first, the uniform half-space model parameters are fixed and the KAN network is trained, the predicted data and the corresponding observed data are input, the loss function is calculated and the KAN network parameters are updated, then, the KAN network parameters are fixed and the uniform half-space model is trained, the predicted data is input into the updated KAN network, the loss function value is calculated, and the uniform half-space model parameters are updated by gradient backpropagation, the above steps are repeated until the convergence condition is reached, and the final updated uniform half-space model is used as the inversion result.

[0014] In a second aspect, an embodiment of the present invention provides an efficient three-dimensional inversion device for electromagnetic detection data based on operator learning, which is implemented using the above-mentioned efficient three-dimensional inversion method for electromagnetic detection data based on operator learning, and includes: a data set construction module, a forward operator training module, an inversion network construction module, and an inversion training update module; The data set construction module is used to construct an operator learning data set including a plurality of electromagnetic forward modeling models and their forward responses; The forward operator training module is used to perform airborne electromagnetic frequency domain forward calculation training based on the operator learning data set using the DeepONet network to obtain a trained airborne electromagnetic three-dimensional forward operator; The inversion network construction module is used to input the initial uniform half-space model, replace the generator with the airborne electromagnetic three-dimensional forward operator, and construct the WGAN network using the KAN network as the discriminator to perform airborne electromagnetic three-dimensional inversion; The inversion training update module is used to perform training based on the loss function and the data fitting error convergence condition to update the KAN network and the uniform half-space model, and finally obtain the updated uniform half-space model as the inversion result.

[0015] In a third aspect, an embodiment of the present invention provides an electronic device comprising a memory and one or more processors, wherein the memory is used to store a computer program, and the processor is used to implement the above-mentioned efficient three-dimensional inversion method of electromagnetic detection data based on operator learning when executing the computer program.

[0016] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a computer, the above-mentioned efficient three-dimensional inversion method of electromagnetic detection data based on operator learning is implemented.

[0017] Compared with the prior art, the present invention has the following beneficial effects: (1) Based on the WGAN network framework, the present invention uses the DeepONet network trained on the operator learning dataset to replace the traditional airborne electromagnetic 3D forward modeling. At the same time, the KAN network is used as the discriminator to construct the WGAN network for inversion. By using DeepONet to calculate the forward modeling data, the forward modeling speed is significantly improved, and large-scale electromagnetic detection data can be quickly processed, providing an efficient data foundation for inversion. At the same time, training based on the loss function and the data fitting error convergence condition can solve the minimum-maximum competitive learning problem, effectively update the model, and improve the accuracy of the inversion.

[0018] (2) In terms of application convenience, the inversion process does not require labeled data, eliminating the tedious data labeling process and reducing the cost of data acquisition. It also does not require network pre-training, making it more versatile and flexible, with strong generalization capabilities. In addition, the inversion time is greatly shortened, the computational efficiency is significantly improved, and the inversion results can be quickly obtained, meeting the timeliness requirements of actual engineering. Experimental verification shows that the forward response value is quickly calculated based on the airborne electromagnetic three-dimensional forward operator and embedded in the WGAN. The whole method can be run efficiently in Python. Compared with the traditional Gauss-Newton inversion, the computational time is reduced by nearly 87%, and any airborne electromagnetic three-dimensional model can be efficiently inverted. This provides a new inversion method for future airborne electromagnetic three-dimensional data inversion and provides strong support for applications in the field of electromagnetic detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0020] Figure 1 1 is a flow chart of an efficient three-dimensional inversion method for electromagnetic detection data based on operator learning provided by an embodiment of the present invention; Figure 2 Schematic diagram of the WGAN network structure and training process provided by an embodiment of the present invention; Figure 3 Schematic diagram of the internal structure of the MLP and KAN networks provided by an embodiment of the present invention; Figure 4 Schematic diagram of data distribution of W distance and L2 norm provided by an embodiment of the present invention; Figure 5 Schematic diagram of a theoretical plate-like body model and inversion results provided by an embodiment of the present invention; Figure 6 It is a structural schematic diagram of an efficient three-dimensional inversion device for electromagnetic detection data based on operator learning provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0022] The inventive concept of this invention is to address the time-consuming nature of existing airborne electromagnetic 3D inversion and the limited generalization of data-driven machine learning-based inversion methods. This invention provides an efficient 3D inversion method for electromagnetic exploration data based on operator learning. By constructing an operator learning dataset containing an electromagnetic forward model and its forward response, and training airborne electromagnetic frequency-domain forward modeling using a DeepONet network, an efficient airborne electromagnetic 3D forward modeling operator is derived. This operator replaces traditional forward modeling and is combined with a KAN network to construct a WGAN network framework. This achieves airborne electromagnetic 3D inversion without relying on labeled data or network pre-training, improving inversion speed while enhancing the model's generalization capability, providing a higher-quality and more efficient technical solution for the field of electromagnetic exploration.

[0023] like Figure 1 As shown, the embodiment provides an efficient three-dimensional inversion method for electromagnetic detection data based on operator learning, comprising the following steps: S1, construct an operator learning dataset including several electromagnetic forward models and their forward responses.

[0024] The generation of training datasets is an important part of supervised learning, which requires two key conditions: (1) creating a sufficient number of training samples to effectively enable the neural network to learn the input-output mapping relationship; (2) ensuring that the training samples are both representative and diverse, providing the network with strong generalization capabilities.

[0025] In the embodiment, in order to achieve this diversity, the Gaussian Random Field (GRF) method is used to generate several electromagnetic forward models. The GRF method uses simple assumptions and two parameters to capture the key macroscopic features of the target information, which is sufficient to characterize the basic properties of many naturally occurring structures. A total of 30,000 models are generated to construct the dataset, and the mesh size of each model is 48×48×20. The random process of each point defined above is , define the model grid points: , Among them, the index , Represents the grid point coordinate value. From this, the covariance matrix between any two points is constructed: , in, represents the variance, Represents the length scale. Perform Cholesky decomposition on the covariance matrix: , in, represents a lower triangular matrix, the superscript Generates a random vector that satisfies the standard normal distribution. , so the sample That is, the calculation formula of the electromagnetic forward model is: , in, Represents the mean function, which defines the expected value of the random process at each point.

[0026] Based on the generated electromagnetic forward models, the forward response values at different heights and frequencies are calculated using the forward code. The traditional AEM frequency domain forward calculation starts from Maxwell's equations and assumes that the time harmonic factor is , the double curl equation of the secondary electric field is expressed as: , in, represents the gradient operator, Indicates abnormal field, represents the background field, represents the wave number, represents the magnetic permeability of the medium, represents the conductivity, represents the angular frequency, represents the wave number of the background field. The governing equation (5) is solved using the finite difference (FD) method on a staggered grid. This method produces electric field values along any grid edge, which can be interpolated to calculate the electric field at the receiver location, and then the magnetic field is calculated using Faraday's law. The above process can be simplified to: , in, represents the forward operator, represents the model resistivity structure, Indicates frequency, Indicates the measurement point location, The data corresponds to the forward response data. The model data generated by the Gaussian random field and the forward response data corresponding to the model calculated using formula (6) are combined to finally complete the construction of the operator learning data set. It is divided into a training set and a test set for the subsequent airborne electromagnetic three-dimensional forward operator training.

[0027] S2, using the DeepONet network to perform airborne electromagnetic frequency domain forward modeling training based on the operator learning data set to obtain a trained airborne electromagnetic three-dimensional forward modeling operator.

[0028] In the embodiment, a dual network architecture consisting of a branch network and a trunk network in the DeepONet network is used for forward modeling in the airborne electromagnetic frequency domain. Based on the approximation ability and flexibility of the dual network structure, it performs well in solving partial differential equations (PDEs). The input of DeepONet is processed by these two networks, both of which have a multi-layer neural network architecture, where the branch network processes the electromagnetic forward model data of the discretized input, while the trunk network processes the spatial coordinates or other related parameters. The outputs of the two networks are then combined using an inner product operation to obtain the predicted response data to fully capture the basic characteristics and transformations of the input data. This method effectively simulates the forward operator and solves the corresponding partial differential equations. DeepONet is particularly suitable for handling complex geometric and nonlinear problems, making it an ideal choice for training data sets with different input and output dimensions. As shown in Equation (7), the DeepONet architecture can be expressed in a more intuitive format, that is, , in, represents the airborne electromagnetic three-dimensional forward modeling, and the forward operator in formula (6) Has the same function, Represents the forward response data in the data set , represents the operator, Represents an operator for any input function and input The output value of , that is, the predicted response data. Represents the input function, used to discrete input model data .Will Expanded to: , in, ,index , It represents any number greater than 0. Represents the activation function. When the absolute value of the difference between the predicted response data and the true response data is less than any positive number When Can replace airborne electromagnetic 3D forward modeling , and the operator As a trained airborne electromagnetic three-dimensional forward operator.

[0029] S3, the initial uniform half-space model is input to replace the generator with the airborne electromagnetic three-dimensional forward operator and the KAN network is used as the discriminator to construct the WGAN network for airborne electromagnetic three-dimensional inversion.

[0030] In the embodiment, Figure 2 As shown, the airborne electromagnetic three-dimensional forward operator replaces the generator, and the KAN network is used as the discriminator to construct a WGAN network. The initial uniform half-space model as the inversion starting point is input into the WGAN network to perform airborne electromagnetic three-dimensional inversion. The initial uniform half-space model is calculated by the airborne electromagnetic three-dimensional forward operator to obtain predicted data, and the predicted data and the actual observation data are discriminated by the KAN network.

[0031] like Figure 3 The figure shows the network structure of the multi-layer perceptron MLP and KAN. The multi-layer perceptron (MLP) is based on the universal approximation theorem and uses linear transformation of each node plus nonlinear activation function to approximate any function. It is a basic component of the current deep learning model. Figure 3 in 、 、 Represent the weight parameters of each layer, 、 、 Represents the bias term of each layer. However, MLP has poor interpretability, cannot learn complex relational data relationships, and has serious forgetting problems. For Kolmogorov-Arnold Networks (KAN), each layer is composed of multiple spline functions weighted and combined into a multidimensional space, and each weight parameter is replaced by a one-dimensional function. It truly realizes the splitting of a high-dimensional function into multiple learnable one-dimensional functions, which has stronger interpretability. Figure 3 in 、 、 Represents the learnable activation function for each layer. Using a spline function as an activation function allows the network to locally adjust weights when learning new knowledge without completely overwriting previous knowledge. Because airborne electromagnetic 3D data exhibits complex functional relationships, KAN is chosen as the discriminator for fitting in this paper.

[0032] S4, training is performed based on the loss function and the data fitting error convergence condition to update the KAN network and the uniform half-space model, and finally the updated uniform half-space model is obtained as the inversion result.

[0033] In probability theory and statistics, Wasserstein distance (W distance) is a method to measure the difference between two probability distributions. It describes the transformation of one distribution into another with minimal cost. Figure 4 The L2 norm and W distance values between two different distribution data are presented intuitively. Dataset 1, Dataset 2 and Dataset 3 are randomly generated sample arrays, each containing 1000 elements, with a mean of 0 and variances of 1, 1 and 6 respectively. For Dataset 1 and Dataset 2, the corresponding L2 norm and W distance values are 45.14 and 0.05 respectively; for Dataset 1 and Dataset 3, the corresponding L2 norm and W distance values are 45.13 and 1.12 respectively. For the two pairs of data with different distributions, the value of the L2 norm has hardly changed, but the value of the W distance differs by nearly 22 times, which shows that the W distance can better capture the differences between different arrays. Therefore, the present invention considers selecting the W distance to quantify the differences between different response data.

[0034] Furthermore, based on the Kantorovich-Rubinstein dual formula, the W distance can be converted into a more easily computable form and applied to the WGAN network. To satisfy the 1-Lipschitz constraint in the dual formula, WGAN uses two methods: weight clipping and gradient penalty. Weight clipping ensures that the W distance becomes computable in WGAN by clipping the gradient within a certain range. However, direct clipping may cause gradient vanishing or gradient exploding problems during the propagation process. Therefore, a gradient penalty mechanism is introduced. By adding this penalty term to the discriminator's loss function, these problems can be effectively alleviated. The loss function is: , in, and are two probability measures defined on the distribution space of observed data and predicted data, respectively. It is the probability measure of the sample space along the straight line between the sampled point pairs in the observed data and the predicted data distribution. Replacing the expected value with the empirical value, the loss function of the network in the embodiment of the present invention is: , in, represents the loss function, denotes the parameters of the initial uniform half-space model, represents the parameters of the KAN network, represents the KAN network, represents the observation data, represents the airborne electromagnetic three-dimensional forward operator, represents the initial uniform half-space model, represents the weight of the gradient penalty term, , yes A random number in the range, represents the gradient of the KAN network relative to the input, Denotes the L2 norm. The gradient penalty term plays a crucial role in WGANs. It improves training stability and the quality of generated samples by ensuring the 1-Lipschitz continuity of the discriminator. By adjusting the gradient penalty weight coefficient, the distribution of samples generated by the generator can be optimized while maintaining the performance of the discriminator.

[0035] In order to further control the training process and prevent overfitting, the data fitting error convergence condition is introduced in the embodiment, which is expressed as: , in, Indicates a poor fit to the data. represents the predicted data output by the airborne electromagnetic three-dimensional forward operator, represents the observation data, represents the L2 norm, when The inversion is stopped when the iteration number is less than the preset convergence threshold.

[0036] The specific training process is as follows: In each iteration step, first, the uniform half-space model parameters are fixed. And train the KAN network, input the predicted data and the corresponding observation data, calculate the loss function and update the KAN network parameters Then, the KAN network parameters are fixed And train the uniform half-space model, input the predicted data into the updated KAN network, calculate the loss function value, and update the uniform half-space model parameters through gradient backpropagation Repeat the above steps until the convergence condition is reached and the final updated uniform half-space model is As the inversion result.

[0037] To illustrate the effectiveness of the present invention, a specific experimental example is given. First, an operator learning data set is generated. Thirty thousand models are generated using a Gaussian random field. To meet the boundary conditions, the calculation area is divided into a core area and an extended area. The size of the core area is 480 meters × 480 meters × 532 meters, and it is discretized into 48 × 48 × 20 cells. Ten additional extended grids are added on both sides of the core area to ensure that the boundary conditions are met. The conductivity value of the core area is 10 -3 to 10 0 S / m. To predict the response at different altitudes, 12 flight altitudes were designed, ranging from 30 meters to 90 meters. A finite difference algorithm based on a staggered grid was used to calculate the magnetic field response of each model at five frequencies: 880 Hz, 980 Hz, 6606 Hz, 7001 Hz, and 34133 Hz.

[0038] The inversion process began with a theoretical plate model designed with a 100 × 100 × 20 grid, measuring 1000 × 1000 × 532 meters. The plate-like grid was 10 × 10 × 7, measuring 200 × 200 × 61 meters. Gaussian filtering was used to smooth the edges. Eleven survey lines were arranged symmetrically around the center of the model, with each line spaced 20 meters apart. Measurement points were evenly distributed, with each point spaced 20 meters apart. Figure 5 is the inversion result diagram, Figure 5 a) and b) are slices of the longitudinal and transverse centers of the real model (theoretical plate model). Figure 5 c) and d) are the vertical and horizontal center slices of the inversion results of the method provided in the embodiment of the present invention. Figure 5Figures e) and f) are longitudinal and transverse center slices of the inversion results using the traditional Gauss-Newton method. It can be seen that the method provided by the present invention provides more accurate results, closer to the true model. However, the longitudinal slices of the Gauss-Newton inversion results show a significant depression in the restored lower half of the anomaly, indicating poor performance.

[0039] Table 1 Inversion iteration times and times of different methods for theoretical plate-like models

[0040] As shown in Table 1, the inversion time of the two methods is compared. The method provided by the embodiment of the present invention only takes 23.5 minutes, while the Gauss-Newton method takes 171.1 minutes. This proves that the efficient three-dimensional inversion method for electromagnetic detection data based on operator learning provided by the embodiment of the present invention is necessary and effective.

[0041] Based on the same inventive concept, Figure 6 As shown, an embodiment of the present invention further provides an efficient three-dimensional inversion device for electromagnetic detection data based on operator learning, including: a data set construction module 610, a forward operator training module 620, an inversion network construction module 630, and an inversion training update module 640.

[0042] The data set construction module 610 is used to construct an operator learning data set including a number of electromagnetic forward models and their forward responses.

[0043] The forward operator training module 620 is used to perform airborne electromagnetic frequency domain forward modeling training based on the operator learning data set using the DeepONet network to obtain a trained airborne electromagnetic three-dimensional forward operator.

[0044] The inversion network construction module 630 is used to input the initial uniform half-space model, replace the generator with the airborne electromagnetic three-dimensional forward operator, and construct a WGAN network using the KAN network as the discriminator to perform airborne electromagnetic three-dimensional inversion.

[0045] The inversion training update module 640 is used to perform training based on the loss function and the data fitting error convergence condition to update the KAN network and the uniform half-space model, and finally obtain the updated uniform half-space model as the inversion result.

[0046] Based on the same inventive concept, an embodiment of the present invention also provides an electronic device, including a memory and one or more processors, the memory is used to store a computer program, and the processor is used to implement the above-mentioned efficient three-dimensional inversion method of electromagnetic detection data based on operator learning when executing the computer program.

[0047] The electronic device provided in the embodiment, at the hardware level, includes not only a processor and memory, but also hardware required for other services such as an internal bus, a network interface, and memory. The memory is a non-volatile memory, and the processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to implement the efficient three-dimensional inversion method of electromagnetic detection data based on operator learning described in steps S1 to S4 above. Of course, in addition to software implementation, the present invention does not exclude other implementation methods, such as logic devices or a combination of software and hardware, etc., that is, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0048] Based on the same inventive concept, an embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a computer, the above-mentioned efficient three-dimensional inversion method of electromagnetic detection data based on operator learning is implemented.

[0049] In an embodiment, computer-readable storage media includes permanent and non-permanent, removable and non-removable media that can be used to store information by any method or technology. The information can be computer-readable instructions, data structures, program modules 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 technology, read-only compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device.

[0050] It should be noted that the efficient three-dimensional inversion device for electromagnetic detection data based on operator learning, electronic device and computer-readable storage medium provided in the above embodiments all belong to the same inventive concept as the efficient three-dimensional inversion method for electromagnetic detection data based on operator learning. The specific implementation process is detailed in the embodiment of the efficient three-dimensional inversion method for electromagnetic detection data based on operator learning, which will not be repeated here.

[0051] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An efficient three-dimensional inversion method for electromagnetic detection data based on operator learning, characterized in that: The following steps are involved: Construct an operator learning dataset including several electromagnetic forward models and their forward responses; The DeepONet network is used to train the airborne electromagnetic frequency domain forward modeling based on the operator learning dataset to obtain the trained airborne electromagnetic three-dimensional forward modeling operator. The initial uniform half-space model is input to replace the generator with the airborne electromagnetic 3D forward operator and the KAN network is used as the discriminator to construct the WGAN network for airborne electromagnetic 3D inversion. Training is performed based on the loss function and the data fitting error convergence condition to update the KAN network and the uniform half-space model, and finally the updated uniform half-space model is obtained as the inversion result.

2. The efficient three-dimensional inversion method for electromagnetic detection data based on operator learning according to claim 1 is characterized in that: The construction includes an operator learning data set of several electromagnetic forward models and their forward responses, including: The Gaussian random field method is used to generate several electromagnetic forward models, and the forward response values at different altitudes and frequencies are calculated based on the electromagnetic forward models. The generated electromagnetic forward models and their corresponding forward response values are compiled into an operator learning dataset and divided into a training set and a test set for airborne electromagnetic three-dimensional forward operator training.

3. The efficient three-dimensional inversion method for electromagnetic detection data based on operator learning according to claim 1 is characterized in that: The method of using the DeepONet network to perform airborne electromagnetic frequency domain forward modeling training based on an operator learning data set to obtain a trained airborne electromagnetic three-dimensional forward modeling operator includes: Based on the dual network architecture consisting of a branch network and a backbone network in the DeepONet network, airborne electromagnetic frequency domain forward modeling is performed. The branch network is used to process the discretized input electromagnetic forward model data, while the backbone network processes the query parameters. The predicted response data output by the two networks is fused through the inner product operation. An approximate expression of the operator is constructed, and the absolute error between the predicted response data and the actual forward response in the operator learning dataset is used as the loss function. The operator is trained until the error is less than the set threshold, so that the operator has the ability to replace the actual airborne electromagnetic 3D forward modeling. The operator is then used as the trained airborne electromagnetic 3D forward modeling operator.

4. The efficient three-dimensional inversion method for electromagnetic detection data based on operator learning according to claim 1 is characterized in that: The initial uniform half-space model is input, the airborne electromagnetic three-dimensional forward operator is used to replace the generator, and the KAN network is used as the discriminator to construct the WGAN network for airborne electromagnetic three-dimensional inversion, including: The airborne electromagnetic three-dimensional forward operator replaces the generator, and the KAN network is used as the discriminator to construct a WGAN network. The initial uniform half-space model as the inversion starting point is input into the WGAN network for airborne electromagnetic three-dimensional inversion. The initial uniform half-space model is calculated using the airborne electromagnetic three-dimensional forward operator to obtain predicted data, and the predicted data and the actual observation data are discriminated through the KAN network.

5. The efficient three-dimensional inversion method for electromagnetic detection data based on operator learning according to claim 1 is characterized in that: The loss function is expressed as: ， in, represents the loss function, denotes the parameters of the initial uniform half-space model, represents the parameters of the KAN network, represents the KAN network, represents the observation data, represents the airborne electromagnetic three-dimensional forward operator, represents the initial uniform half-space model, represents the weight of the gradient penalty term, , yes A random number in the range, represents the gradient of the KAN network relative to the input, represents the L2 norm.

6. The efficient three-dimensional inversion method for electromagnetic detection data based on operator learning according to claim 1 is characterized in that: The data fitting error convergence condition is expressed as: ， in, Indicates a poor fit to the data. represents the predicted data output by the airborne electromagnetic three-dimensional forward operator, represents the observation data, represents the L2 norm, when The inversion is stopped when the iteration number is less than the preset convergence threshold.

7. The efficient three-dimensional inversion method for electromagnetic detection data based on operator learning according to claim 1, characterized in that: When training and updating the KAN network and uniform half-space model, in each iterative step, first, the uniform half-space model parameters are fixed and the KAN network is trained, the predicted data and the corresponding observed data are input, the loss function is calculated and the KAN network parameters are updated. Subsequently, the KAN network parameters are fixed and the uniform half-space model is trained, the predicted data is input into the updated KAN network, the loss function value is calculated, and the uniform half-space model parameters are updated by gradient backpropagation. The above steps are repeated until the convergence condition is reached, and the final updated uniform half-space model is used as the inversion result.

8. An efficient three-dimensional inversion device for electromagnetic detection data based on operator learning, implemented using the efficient three-dimensional inversion method for electromagnetic detection data based on operator learning according to any one of claims 1 to 7, characterized in that: include: Dataset construction module, forward operator training module, inversion network construction module, and inversion training update module; The data set construction module is used to construct an operator learning data set including a plurality of electromagnetic forward modeling models and their forward responses; The forward operator training module is used to perform airborne electromagnetic frequency domain forward calculation training based on the operator learning data set using the DeepONet network to obtain a trained airborne electromagnetic three-dimensional forward operator; The inversion network construction module is used to input the initial uniform half-space model, replace the generator with the airborne electromagnetic three-dimensional forward operator, and construct the WGAN network using the KAN network as the discriminator to perform airborne electromagnetic three-dimensional inversion; The inversion training update module is used to perform training based on the loss function and the data fitting error convergence condition to update the KAN network and the uniform half-space model, and finally obtain the updated uniform half-space model as the inversion result.

9. An electronic device comprising a memory and one or more processors, wherein the memory is used to store a computer program, characterized in that: The processor is configured to implement the efficient three-dimensional inversion method for electromagnetic detection data based on operator learning as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a computer, the efficient three-dimensional inversion method for electromagnetic detection data based on operator learning as described in any one of claims 1 to 7 is implemented.

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