Multi-height three-dimensional gravity and gradient joint inversion method based on physical information neural network

Abstract

The invention provides a multi-height three-dimensional gravity and gradient joint inversion method based on a physical information neural network, and the method comprises the steps: building a forward neural network and an inversion neural network based on the physical information neural network; pre-training an inversion neural network on the synthetic data set; wherein the synthetic data set comprises multiple pairs of synthetic data, and each pair of synthetic data comprises original three-dimensional gravity anomaly data and real three-dimensional density data; constructing a closed-loop network based on the forward neural network and the pre-trained inversion neural network; and carrying out iterative training on the closed-loop network on given to-be-solved data to obtain an inversion neural network meeting requirements. According to the scheme of the invention, under the condition of introducing limited cost increase, abundant vertical resolution is provided.

Description

Technical Field

[0001] The present invention relates to the field of geophysical inversion imaging technology, and in particular to a multi-height three-dimensional gravity and its gradient joint inversion based on physical information neural network. Background Art

[0002] Gravity inversion is an important, non-destructive geophysical exploration method. Due to the gravitational force, objects on the surface are subject to the gravitational force of the earth (i.e., gravity). The uneven distribution of materials with different densities underground will cause anomalies in the surface gravity field. Gravity inversion estimates the density distribution of underground materials through the gravity field information detected on the surface. Gravity inversion is widely used in many research fields such as geological structure research, mineral exploration, and engineering environment research.

[0003] Three-dimensional gravity inversion is the solution from two-dimensional gravity field observation data to three-dimensional density data. It is an ill-posed problem with a non-unique solution space. Currently, the more mature gravity inversion algorithms include traditional methods such as Newton's method, conjugate gradient method, least squares method, and machine learning algorithms such as simulated annealing algorithm, particle swarm algorithm, ant colony algorithm, and genetic algorithm. Traditional algorithms have fast solution speed and low accuracy, while machine learning algorithms have high accuracy but slow solution speed. Balancing speed and accuracy is an important problem facing gravity inversion. Another problem that gravity inversion needs to solve is the problem of multiple solutions, which requires full use of prior knowledge from domain experts or related data.

[0004] In recent years, deep learning methods have developed rapidly, and a large number of deep learning algorithms have successfully promoted the solution of image-related pathological problems such as super-resolution and deblurring. Treating the inverted matrix data as an image can improve the quality of the inversion results from the perspective of image super-resolution. A more direct method is to directly use a deep learning algorithm to implement gravity inversion, and the solution can be quickly obtained during the reasoning process. However, this method relies on high-quality training data and cannot adjust the inversion results based on prior knowledge.

[0005] The lack of training data is the main obstacle to the application of deep learning technology in fields such as geophysics and medical imaging. The current main solution is to synthesize training data based on expert knowledge and apply it to actual data after training. This method can alleviate the data problem to a certain extent, but it is affected by the difference between synthetic data and actual data, and its effect is limited. In order to make deep learning technology free from dependence on data, a large number of scholars are committed to studying self-supervised learning technology. Self-supervised learning technology has been applied to image quality restoration tasks such as super-resolution, and has achieved natural image super-resolution quickly, flexibly and accurately.

[0006] In some exemplary techniques, a self-supervised algorithm based on a closed-loop network is used to achieve three-dimensional gravity inversion, and self-supervised gravity inversion (SSGI) is proposed accordingly. The forward problem has a unique solution space. This method constrains the inversion process through a known forward process, builds a neural network to respectively implement the inversion process and the forward process, and constrains the inversion process through the inversion-forward closed loop process. The closed-loop network is a self-supervised algorithm and does not require additional training data. Since the goal of gravity inversion is to solve the three-dimensional underground density distribution from the two-dimensional surface gravity anomaly, this problem is a highly ill-conditioned problem with dimensionality enhancement. SSGI introduces vertical vectors from logging or other inversion methods to solve the problem of insufficient vertical resolution. However, such reference vectors will cause the cost of gravity inversion to increase significantly.

[0007] Therefore, how to provide rich vertical resolution without significantly increasing the cost of gravity inversion has become a problem that needs to be solved urgently. Summary of the invention

[0008] The present invention provides a multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network, which is used to solve the defect that vertical resolution and gravity inversion cost cannot be taken into account at the same time, and to provide rich vertical resolution with a small increase in cost.

[0009] The present invention provides a multi-height three-dimensional gravity and its gradient joint inversion method based on a physical information neural network, comprising: building a forward neural network based on the physical information neural network; building an inversion neural network based on the physical information neural network; pre-training the inversion neural network on a synthetic data set; wherein the synthetic data set includes multiple pairs of synthetic data, each pair of synthetic data includes original three-dimensional gravity anomaly data and real three-dimensional density data; building a closed-loop network based on the forward neural network and the pre-trained inversion neural network; iteratively training the closed-loop network on given data to be solved to obtain an inversion neural network that meets the requirements.

[0010] According to a multi-height three-dimensional gravity and its gradient joint inversion method based on a physical information neural network provided by the present invention, the inversion neural network is built based on the physical information neural network, including: building the inversion neural network through a three-dimensional preprocessing module, a two-dimensional encoder, a two-dimensional decoder and a three-dimensional post-processing module.

[0011] According to a multi-height three-dimensional gravity and its gradient joint inversion method based on a physical information neural network provided by the present invention, the physical information neural network is based on which a forward neural network is constructed, including: determining a first expression of the original three-dimensional gravity field about three-dimensional density information according to the universal gravitation formula; determining a second expression of the three-dimensional gravity anomaly gradient about three-dimensional density data according to the first expression; and constructing the forward neural network according to the first expression and the second expression.

[0012] According to a multi-height three-dimensional gravity and its gradient joint inversion method based on a physical information neural network provided by the present invention, the inversion neural network is pre-trained on a synthetic data set, including: performing iterative pre-training processing on the inversion neural network on the synthetic data set until the performance of the inversion neural network on the synthetic data set reaches a predetermined standard or the number of iterations is completed; wherein the iterative pre-training processing includes: taking the original three-dimensional gravity anomaly data as input, performing forward propagation through the inversion neural network, and outputting predicted three-dimensional density data; calculating a first loss function based on the predicted three-dimensional density data and the real three-dimensional density data in the synthetic data set; performing a back propagation algorithm on the inversion neural network based on the first loss function to calculate a first parameter gradient; using an Adam optimizer to update the network parameters of the inversion neural network based on the first parameter gradient; and gradually reducing the learning rate as the number of iterations increases.

[0013] According to a multi-height three-dimensional gravity and its gradient joint inversion method based on a physical information neural network provided by the present invention, the closed-loop network is iteratively trained on given data to be solved, including: using the original three-dimensional gravity field and a given energy distribution curve as input, performing forward propagation through an inversion neural network, and outputting predicted three-dimensional density information and predicted three-dimensional density data; using the predicted three-dimensional density information and predicted three-dimensional density data output by the inversion neural network as inputs of a forward neural network, and calculating a reconstructed gravity field; calculating a second loss function based on the original three-dimensional gravity field and the reconstructed three-dimensional gravity field; performing back propagation on the forward neural network and the inversion neural network based on the second loss function, and calculating a second parameter gradient; using an Adam optimizer to update the network parameters of the inversion neural network based on the second parameter gradient; and gradually reducing the learning rate as the number of iterations increases.

[0014] According to a multi-height three-dimensional gravity and its gradient joint inversion method based on a physical information neural network provided by the present invention, before pre-training the inversion neural network on a synthetic data set, the method also includes: applying a synthetic data method to randomly synthesize a plurality of real three-dimensional density data; based on the plurality of real three-dimensional density data, generating a plurality of original three-dimensional gravity anomaly data through a forward neural network; wherein the plurality of original three-dimensional gravity anomaly data correspond one-to-one to the plurality of real three-dimensional density data; and according to the corresponding relationship, combining the plurality of original three-dimensional gravity anomaly data and the plurality of real three-dimensional density data into a plurality of pairs of synthetic data to obtain the synthetic data set.

[0015] The present invention also provides a multi-height three-dimensional gravity and its gradient joint inversion device based on a physical information neural network, comprising: a building module, used to build a forward neural network and an inversion neural network based on the physical information neural network; a pre-training module, used to pre-train the inversion neural network on a synthetic data set; wherein the synthetic data set includes multiple pairs of synthetic data, each pair of synthetic data includes original three-dimensional gravity anomaly data and real three-dimensional density data; a processing module, used to construct a closed-loop network based on the forward neural network and the pre-trained inversion neural network; on given data to be solved, the closed-loop network is iteratively trained to obtain an inversion neural network that meets the requirements.

[0016] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements any of the above-mentioned methods for joint inversion of multi-height three-dimensional gravity and its gradient based on a physical information neural network.

[0017] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for joint inversion of multi-height three-dimensional gravity and its gradient based on a physical information neural network as described in any one of the above is implemented.

[0018] The present invention also provides a computer program product, comprising a computer program, which, when executed by a processor, implements any of the above-mentioned methods for joint inversion of multi-height three-dimensional gravity and its gradient based on a physical information neural network.

[0019] The multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network provided by the present invention realizes self-supervised learning of the inversion process through a forward process with known parameters and unique solution space. Compared with the existing gravity inversion algorithm based on deep learning, the solution of the present invention does not rely on training data and has no risk of overfitting. It provides rich vertical resolution with limited cost increase. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the present invention or 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 some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0021] Figure 1 It is a flow chart of the method for joint inversion of multi-height three-dimensional gravity and its gradient based on physical information neural network provided by the present invention.

[0022] Figure 2 It is a schematic diagram of the inversion neural network provided by the present invention.

[0023] Figure 3 It is a schematic diagram of an encoder in an inversion neural network provided by the present invention.

[0024] Figure 4 It is a schematic diagram of a decoder in an inversion neural network provided by the present invention.

[0025] Figure 5 It is a schematic diagram of the attention fusion module provided by the present invention.

[0026] Figure 6 It is a schematic diagram of the cross-scale feature fusion model provided by the present invention.

[0027] Figure 7 It is a schematic diagram of the principle of the multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network provided by the present invention.

[0028] Figure 8 It is a schematic diagram of the effect provided by the present invention.

[0029] Fig. 9 It is a structural schematic diagram of a multi-height three-dimensional gravity and its gradient joint inversion device based on a physical information neural network provided by the present invention.

[0030] Fig.10 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0032] Combine the following Figure 1-Figure 8 The invention describes the multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network.

[0033] Figure 1 : is a flow chart of a method for joint inversion of multi-height three-dimensional gravity and its gradient based on physical information neural network provided by the present invention, such as Figure 1 As shown, the method includes the following steps 101 to 104.

[0034] Step 101: Build a forward neural network based on the physical information neural network.

[0035] Among them, Physics-Informed Neural Networks (PINN) is a machine learning model that combines deep learning and physics knowledge. Unlike traditional data-driven neural networks, PINNs use physical laws to guide the model during the learning process, thereby improving the model's generalization ability.

[0036] As an example, the PINN model is usually composed of a deep neural network, which is characterized by the addition of physical information items to the loss function, that is, the physical laws followed. When training the model, it is necessary not only to minimize the data error, but also to minimize the physical information error to ensure that the prediction results comply with the laws of physics.

[0037] In this embodiment, a forward neural network is constructed based on a physical information neural network. The forward neural network is used to implement a three-dimensional forward calculation process, that is, to calculate three-dimensional gravity anomaly data based on three-dimensional density data. In practical applications, the parameters of each neuron of the forward neural network are calculated using the universal gravitational formula.

[0038] As an example, in one implementation, the above step 101 includes: According to the universal gravitation formula, determine the first expression of the original three-dimensional gravity field with respect to the three-dimensional density information; Determine a second expression of the three-dimensional gravity anomaly gradient with respect to the three-dimensional density data according to the first expression; According to the first expression and the second expression, a forward neural network is constructed.

[0039] In practical applications, the forward neural network implements matrix multiplication through neurons to achieve the forward process. The basis of the forward process is the universal gravitational formula, which is as follows: (1)

[0040] in, is the gravitational coefficient, are the masses of the two objects, and are the distance and gravity between the two. In reality, objects on the surface are affected by the gravity of the earth, which is the combined force of the earth's gravity and the inertial centrifugal force caused by the earth's rotation. Due to the uneven density distribution of underground materials, the gravitational effects on the surface are different.

[0041] As an example, the underground three-dimensional space is gridded into several regions, the number of regions is recorded as n, and the gravitational force on each surface observation point is the resultant force of these n regions, which can be expressed as: (2)

[0042] in, is the mass of the observer, For the underground The mass of each region. It can be understood that when the volume of each region is known, the mass of each region is determined by the density of each region. is the distance from the region to the observer.

[0043] Furthermore, take the component of gravity perpendicular to the surface: (3)

[0044] in, is the distance from the area to the surface. In practical applications, multiple observation points are collected on the surface to form an observation point matrix to obtain gravity field data.

[0045] The gravity forward modeling process is the process of solving the underground density information shown in formula (3) to obtain gravity field data. It can be generalized to obtain the first expression of the original three-dimensional gravity field for three-dimensional density information: (4)

[0046] in, is the underground three-dimensional density information, including the Related items. is the forward modeling matrix, which contains the remaining terms in formula (3). is the forward solution, i.e. the observed gravity field. The forward processing based on neural network can be realized by using a neural network composed of neurons to implement the matrix multiplication operation shown in formula (4).

[0047] In the present invention, gravity anomaly data are collected at different heights to perform three-dimensional gravity inversion. Gravity anomaly data and their gradients from different heights can provide rich vertical resolution at a small additional cost.

[0048] Specifically, the forward neural network in this embodiment can also realize gravity gradient forward modeling. Gravity gradient forward modeling is to obtain the three-dimensional gravity anomaly gradient on the ground from the three-dimensional density underground. The second expression is: (5)

[0049] in, is the three-dimensional gravity anomaly gradient on the ground obtained by forward modeling, It represents the forward modeling of gravity anomaly. The forward modeling of gravity gradient can also be realized by using neural network. By using the neural network composed of neurons to realize formula (5), the forward modeling of gravity gradient can be realized.

[0050] Step 102: Building an inversion neural network based on the physical information neural network.

[0051] Specifically, the inversion process is the gravity field observed on the surface Solving for underground density information process, i.e. The inversion problem is an ill-posed problem with a non-unique solution space, so a deep learning network is used to fit the process. In this embodiment, the inversion neural network is used to implement a three-dimensional inversion calculation process, that is, to calculate three-dimensional density data based on three-dimensional gravity anomaly data.

[0052] In a possible implementation, the above step 102 includes: An inversion neural network is built through a three-dimensional preprocessing module, a two-dimensional encoder, a two-dimensional decoder and a three-dimensional post-processing module.

[0053] Specifically, Figure 2 is a schematic diagram of the inversion neural network provided by the present invention. The inversion process is as follows Figure 2 As shown in the figure, firstly, 3D convolution and 3D residual connection blocks are used to preprocess the 3D gravity anomaly data. Then, the channel dimension C and the height (depth) dimension D are merged to convert the feature map into 2D features, perform 2D encoding and decoding, and then convert it to the 3D refiner for post-processing to obtain 3D density data. Considering batch processing and multi-channel, the above three-dimensional feature size is [B, C, D, H, W], and the two-dimensional feature size is [B, CD, H, W].

[0054] Among them, B is the batch size, which refers to the number of samples processed at a time. When training a neural network, the data is usually divided into multiple batches to improve computational efficiency and stability. Among them, C is the channel dimension, which is usually used to represent the different feature dimensions of the data. Among them, D is the depth, which refers to the dimension of the data in the direction perpendicular to the image plane. Among them, H is the height, which refers to the size of the data in the vertical direction, usually expressed in the number of pixels or voxels. W is the width, which refers to the size of the data in the horizontal direction, also expressed in the number of pixels or voxels.

[0055] Figure 3 Schematic diagram of the encoder in the inversion neural network provided by the present invention, such as Figure 3 As shown in the figure, the encoder consists of four jumper blocks, and its input is 3D gravity anomaly data and 3D gravity anomaly gradient. The encoder outputs feature maps of four sizes, with C channels and a size ratio of 8:4:2:1. The largest feature map size is consistent with the input gravity field size. Three downsampling operations are performed in the encoder, and the downsampling method is a convolutional layer with a stride of 2.

[0056] Figure 4 Schematic diagram of the decoder in the inversion neural network provided by the present invention, such as Figure 4 As shown, the decoder receives feature maps of four sizes from the encoder, with the skip block as the basic unit for feature extraction. Figure 5 It is a schematic diagram of the attention fusion module provided by the present invention. Figure 6 is a schematic diagram of the cross-scale feature fusion model provided by the present invention. The decoder uses Figure 5 The attention fusion module shown fuses the feature maps from the encoder and the upsampled feature maps. The decoder contains four feature propagation channels, processing feature maps of four sizes, using Figure 6 The cross-scale feature fusion module shown implements cross-scale feature fusion.

[0057] Furthermore, the 3D refiner transforms the 2D feature map of size [B, C, H, W] (B and C are batch parameters and number of channels, respectively, and H and W are two dimensions of the feature map) output by the decoder into a 3D feature map of size [B, C, D, H, W]. After processing using the 3D jumper block, two density data are obtained, corresponding to the gravity inversion results and gravity anomaly inversion results, respectively.

[0058] Step 103: pre-train the inversion neural network on the synthetic data set.

[0059] The synthetic data set includes multiple pairs of synthetic data, and each pair of synthetic data includes original three-dimensional gravity anomaly data and real three-dimensional density data.

[0060] Specifically, for the process of obtaining the synthetic data set, as an example, in a possible implementation, before the above step 103, the above multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network further includes: The synthetic data method is applied to randomly synthesize multiple real three-dimensional density data.

[0061] Based on multiple real three-dimensional density data, multiple original three-dimensional gravity anomaly data are generated through a forward neural network; wherein the multiple original three-dimensional gravity anomaly data correspond one-to-one to the multiple real three-dimensional density data.

[0062] According to the corresponding relationship, multiple original three-dimensional gravity anomaly data and multiple real three-dimensional density data are combined into multiple pairs of synthetic data to obtain a synthetic data set.

[0063] Specifically, for the process of pre-training the inversion neural network, as an example, in a possible implementation, the above step 103 includes: On the synthetic data set, an iterative pre-training process is performed on the inversion neural network until the performance of the inversion neural network on the synthetic data set reaches a predetermined standard or the number of iterations is completed; wherein the iterative pre-training process includes: taking the original three-dimensional gravity anomaly data as input, forward propagating through the inversion neural network, and outputting predicted three-dimensional density data; calculating a first loss function based on the predicted three-dimensional density data and the real three-dimensional density data in the synthetic data set; performing a back propagation algorithm on the inversion neural network based on the first loss function, and calculating a first parameter gradient; using an Adam optimizer, updating the network parameters of the inversion neural network based on the first parameter gradient; and gradually reducing the learning rate as the number of iterations increases.

[0064] As an example, the expression of the first loss function is as follows: (6)

[0065] in For the inversion neural network, Represents its parameters, They are the density data corresponding to gravity inversion and the density data corresponding to gravity anomaly inversion, respectively. is a norm loss, is the weight parameter. is the cross gradient loss, which is expressed as follows: (7)

[0066] Optionally, the first loss function may be a mean absolute error (MAE) between the predicted three-dimensional density data and the actual three-dimensional density data.

[0067] Step 104: construct a closed-loop network based on the forward neural network and the pre-trained inversion neural network, and iteratively train the closed-loop network on given data to be solved to obtain an inversion neural network that meets the requirements.

[0068] As an example, for the process of iterative training of a closed-loop network, in a possible implementation manner, the iterative training of the closed-loop network on given data to be solved includes: Using the original three-dimensional gravity field and the given energy distribution curve as input, forward propagation is performed through the inversion neural network to output predicted three-dimensional density information and predicted three-dimensional density data.

[0069] Furthermore, the predicted three-dimensional density information and the predicted three-dimensional density data output by the inversion neural network are used as inputs of the forward neural network to calculate and obtain the reconstructed gravity field.

[0070] Furthermore, a second loss function is calculated based on the original three-dimensional gravity field and the reconstructed three-dimensional gravity field.

[0071] Further, according to the second loss function, back propagation is performed on the forward neural network and the inversion neural network to calculate the second parameter gradient.

[0072] Furthermore, an Adam optimizer is used to update the network parameters of the inversion neural network according to the second parameter gradient.

[0073] Furthermore, the learning rate is gradually reduced as the number of iterations increases.

[0074] Specifically, the second loss function expression in the closed-loop training stage is as follows: (8)

[0075] in, and They are the detected gravity anomaly and gravity gradient anomaly, , and They are the joint inversion, gravity forward modeling and gravity gradient forward modeling processes, is the regularization constraint of the inversion result.

[0076] Optionally, the second loss function may also be the mean absolute error (MAE) between the reconstructed gravity field and the original gravity field.

[0077] Figure 7 The figure is a schematic diagram of the principle of the multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network provided by the present invention. Figure 7 The process of iterative training of the closed-loop network is described in detail.

[0078] Specifically, the original gravity field and the given energy distribution curve are used as inputs of the inversion neural network. The original gravity field data is the gravity value observed on the surface, while the energy distribution curve may refer to a certain energy characteristic or density distribution related to the underground structure. The inversion neural network processes the input gravity field and energy distribution and outputs density data, which reflects the spatial distribution of underground materials.

[0079] Furthermore, the density data output by the inversion neural network is input into the forward neural network, and the forward neural network calculates the reconstructed gravity field based on the density data through physical formulas or numerical methods.

[0080] Furthermore, the mean absolute error (MAE) between the original gravity field and the reconstructed gravity field is calculated. This is an indicator to measure the performance of the model and is used to evaluate how close the reconstructed gravity field is to the actual observation data.

[0081] Furthermore, the calculation results of MAE can be used to iteratively optimize the inverse neural network. If the MAE is large, it indicates that the inverse neural network needs further adjustment. In practical applications, by adjusting model parameters or improving algorithms, the MAE can be reduced and the prediction accuracy of the model can be improved.

[0082] It is understandable that the MAE calculation during the iterative training of the closed-loop network provides a self-supervised learning mechanism, where the model guides the training process through its own predictions, reducing the reliance on external labeled data. Through self-supervised learning, the closed-loop network can adapt to new data and be effectively trained without a large amount of labeled data.

[0083] In practical applications, in order to verify the effectiveness of the multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network provided by the present invention, the method proposed by the present invention is applied to a certain observed gravity field to demonstrate the processing effect of the closed-loop self-supervised network model in the present invention. Specifically, the inversion neural network and the forward neural network are implemented in Python3.5 language, the framework is Pytorch, and the operating system used is Linux. The machine configuration is: CPU model: Intel(R) Core(TM) i9-10900X CPU @ 3.70GHz; memory size: 64G; GPU model: GeForce RTX2080Ti.

[0084] The underground density bodies in the training data and test data are sampled at intervals of 100m in the horizontal direction and 100m in the depth direction; the ground gravity anomalies are sampled at intervals of 100m in the horizontal direction and 200m in the height direction. The parameters in the loss function (Formula 5) are , the initial learning rate of the network is 0.0001. The data used for pre-training is composed of 30k sets of data, including 20k training sets, 2k validation sets, and 8k test sets. The pre-training process iterates 200 times on all training data, and the learning rate is decayed to 50% of the current learning rate after the 50th, 100th, and 150th iterations. In transfer learning, the target data is iterated 3000 times, and the learning rate is decayed to 50% of the current learning rate at the 1000th, 2000th, and 2500th iterations, respectively.

[0085] Figure 8 It is a schematic diagram of the effect provided by the present invention. Figure 8 (a) is the original surface gravity anomaly data, Figure 8 (b) is the surface gravity anomaly reconstructed by SSGI closed-loop processing. Figure 8 (c) is the surface gravity anomaly reconstructed by closed-loop processing of this method. Figure 8 (d) is the density data obtained by SSGI processing (inversion result), Figure 8 (e) is the density data obtained by the method. In terms of visual perception, the closed-loop processing result is consistent with the original gravity field data, and no additional logging data is required. The present invention achieves better results by using fewer parameters without the need for logging data.

[0086] In the multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network provided in this embodiment, first, a forward neural network and an inversion neural network are built based on the physical information neural network; then, the inversion neural network is pre-trained on a synthetic data set; then, a closed-loop network is constructed based on the forward neural network and the pre-trained inversion neural network; finally, the closed-loop network is iteratively trained on given data to be solved to obtain an inversion neural network that meets the requirements. The scheme of this embodiment realizes self-supervised learning of the inversion process through a forward process with known parameters and a unique solution space. Compared with the existing gravity inversion algorithm based on deep learning, the scheme of the present invention does not rely on training data, has no risk of overfitting, and provides rich vertical resolution with limited cost increase.

[0087] The multi-height three-dimensional gravity and its gradient joint inversion device based on physical information neural network provided by the present invention is described below. The multi-height three-dimensional gravity and its gradient joint inversion device based on physical information neural network described below and the multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network described above can be referenced to each other.

[0088] Fig. 9 Schematic diagram of the structure of the multi-height three-dimensional gravity and its gradient joint inversion device based on physical information neural network provided by the present invention. Fig. 9As shown, the device includes: a building module 91, a pre-training module 92 and a processing module 93.

[0089] The above-mentioned building module 91 is used to build a forward neural network based on the physical information neural network.

[0090] Among them, the Physical Information Neural Network (PINN) is a machine learning model that combines deep learning and physics knowledge. Unlike traditional data-driven neural networks, PINNs use physical laws to guide the model during the learning process, thereby improving the model's generalization ability.

[0091] As an example, the PINN model is usually composed of a deep neural network, which is characterized by the addition of physical information items to the loss function, that is, the physical laws followed. When training the model, it is necessary not only to minimize the data error, but also to minimize the physical information error to ensure that the prediction results comply with the laws of physics.

[0092] In this embodiment, a forward neural network is constructed based on a physical information neural network. The forward neural network is used to implement a three-dimensional forward calculation process, that is, to calculate three-dimensional gravity anomaly data based on three-dimensional density data. In practical applications, the parameters of each neuron of the forward neural network are calculated using the universal gravitational formula.

[0093] As an example, in one implementation, the building module 91 is specifically used for: According to the universal gravitation formula, determine the first expression of the original three-dimensional gravity field with respect to the three-dimensional density information; Determine a second expression of the three-dimensional gravity anomaly gradient with respect to the three-dimensional density data according to the first expression; According to the first expression and the second expression, a forward neural network is constructed.

[0094] In practical applications, the forward neural network implements matrix multiplication through neurons to achieve the forward process. The basis of the forward process is the universal gravitational formula, which is as follows: (1)

[0095] in, is the gravitational coefficient, are the masses of the two objects, and are the distance and gravity between the two. In reality, objects on the surface are affected by the gravity of the earth, which is the combined force of the earth's gravity and the inertial centrifugal force caused by the earth's rotation. Due to the uneven density distribution of underground materials, the gravitational effects on the surface are different.

[0096] As an example, the underground three-dimensional space is gridded into several regions, the number of regions is recorded as n, and the gravitational force on each surface observation point is the resultant force of these n regions, which can be expressed as: (2)

[0097] in, is the mass of the observer, For the underground The mass of each region. It can be understood that when the volume of each region is known, the mass of each region is determined by the density of each region. is the distance from the region to the observer.

[0098] Furthermore, take the component of gravity perpendicular to the surface: (3)

[0099] in, is the distance from the area to the surface. In practical applications, multiple observation points are collected on the surface to form an observation point matrix to obtain gravity field data.

[0100] The gravity forward modeling process is the process of solving the underground density information shown in formula (3) to obtain gravity field data. It can be generalized to obtain the first expression of the original three-dimensional gravity field for three-dimensional density information: (4)

[0101] in, is the underground density information, including the The relevant items, i.e. . is the forward matrix, which contains the remaining items in formula (3), namely . is the forward solution, i.e. the observed gravity field. The forward processing based on neural network can be realized by using a neural network composed of neurons to implement the matrix multiplication operation shown in formula (4).

[0102] In the present invention, gravity anomaly data are collected at different heights to perform three-dimensional gravity inversion. Gravity anomaly data and their gradients from different heights can provide rich vertical resolution at a small additional cost.

[0103] Specifically, the forward neural network in this embodiment can also realize gravity gradient forward modeling. Gravity gradient forward modeling is to obtain the three-dimensional gravity anomaly gradient on the ground from the three-dimensional density underground. The second expression is: (5)

[0104] in, is the three-dimensional gravity anomaly gradient on the ground obtained by forward modeling, It represents the forward modeling of gravity anomaly. The forward modeling of gravity gradient can also be realized by using neural network. By using the neural network composed of neurons to realize formula (5), the forward modeling of gravity gradient can be realized.

[0105] The above-mentioned building module 91 is also used to build an inversion neural network based on the physical information neural network.

[0106] Specifically, the inversion process is the gravity field observed on the surface Solving for underground density information process, that is The inversion problem is an ill-posed problem with a non-unique solution space, so a deep learning network is used to fit the process. In this embodiment, the inversion neural network is used to implement a three-dimensional inversion calculation process, that is, to calculate three-dimensional density data based on three-dimensional gravity anomaly data.

[0107] In a possible implementation, the building module 91 is specifically used to build an inversion neural network through a three-dimensional pre-processing module, a two-dimensional encoder, a two-dimensional decoder and a three-dimensional post-processing module.

[0108] Specifically, the inversion process is as follows: Figure 2 As shown in the figure, firstly, 3D convolution and 3D residual connection blocks are used to preprocess the 3D gravity anomaly data. Then, the channel dimension C and the height (depth) dimension D are merged to convert the feature map into 2D features, perform 2D encoding and decoding, and then convert it to the 3D refiner for post-processing to obtain 3D density data. Considering batch processing and multi-channel, the above three-dimensional feature size is [B, C, D, H, W], and the two-dimensional feature size is [B, CD, H, W].

[0109] Among them, B is the batch size, which refers to the number of samples processed at a time. When training a neural network, the data is usually divided into multiple batches to improve computational efficiency and stability. Among them, C is the channel dimension, which is usually used to represent the different feature dimensions of the data. Among them, D is the depth, which refers to the dimension of the data in the direction perpendicular to the image plane. Among them, H is the height, which refers to the size of the data in the vertical direction, usually expressed in the number of pixels or voxels. W is the width, which refers to the size of the data in the horizontal direction, also expressed in the number of pixels or voxels.

[0110] like Figure 3As shown in the figure, the encoder consists of four jumper blocks, and its input is 3D gravity anomaly data and 3D gravity anomaly gradient. The encoder outputs feature maps of four sizes, with C channels and a size ratio of 8:4:2:1. The largest feature map size is consistent with the input gravity field size. Three downsampling operations are performed in the encoder, and the downsampling method is a convolutional layer with a stride of 2.

[0111] like Figure 4 As shown in Figure 2, the decoder receives feature maps of four sizes from the encoder and uses the jump block as the basic unit for feature extraction. Figure 5 The attention fusion module shown fuses the feature maps from the encoder and the upsampled feature maps. The decoder contains four feature propagation channels, processing feature maps of four sizes, using Figure 6 The cross-scale feature fusion module shown implements cross-scale feature fusion.

[0112] Furthermore, the 3D refiner transforms the 2D feature map of size [B, C, H, W] (B and C are batch parameters and number of channels, respectively, and H and W are two dimensions of the feature map) output by the decoder into a 3D feature map of size [B, C, D, H, W]. After processing using the 3D jumper block, two density data are obtained, corresponding to the gravity inversion results and gravity anomaly inversion results, respectively.

[0113] The pre-training module 92 is used to pre-train the inversion neural network on the synthetic data set.

[0114] The synthetic data set includes multiple pairs of synthetic data, and each pair of synthetic data includes original three-dimensional gravity anomaly data and real three-dimensional density data.

[0115] Specifically, for the process of obtaining the synthetic data set, as an example, in a possible implementation, the multi-height three-dimensional gravity and its gradient joint inversion device based on physical information neural network further includes a synthesis module for: The synthetic data method is applied to randomly synthesize multiple real three-dimensional density data.

[0116] Based on multiple real three-dimensional density data, multiple original three-dimensional gravity anomaly data are generated through a forward neural network; wherein the multiple original three-dimensional gravity anomaly data correspond one-to-one to the multiple real three-dimensional density data.

[0117] According to the corresponding relationship, multiple original three-dimensional gravity anomaly data and multiple real three-dimensional density data are combined into multiple pairs of synthetic data to obtain a synthetic data set.

[0118] Specifically, for the process of pre-training the inversion neural network, as an example, in a possible implementation, the pre-training module 92 is specifically used to: On the synthetic data set, an iterative pre-training process is performed on the inversion neural network until the performance of the inversion neural network on the synthetic data set reaches a predetermined standard or the number of iterations is completed; wherein the iterative pre-training process includes: taking the original three-dimensional gravity anomaly data as input, forward propagating through the inversion neural network, and outputting predicted three-dimensional density data; calculating a first loss function based on the predicted three-dimensional density data and the real three-dimensional density data in the synthetic data set; performing a back propagation algorithm on the inversion neural network based on the first loss function, and calculating a first parameter gradient; using an Adam optimizer, updating the network parameters of the inversion neural network based on the first parameter gradient; and gradually reducing the learning rate as the number of iterations increases.

[0119] As an example, the expression of the first loss function is as follows: (6)

[0120] in For the inversion neural network, Represents its parameters, They are the density data corresponding to gravity inversion and the density data corresponding to gravity anomaly inversion, respectively. is a norm loss, is the weight parameter. is the cross gradient loss, which is expressed as follows: (7)

[0121] Optionally, the first loss function may be a mean absolute error (MAE) between the predicted three-dimensional density data and the actual three-dimensional density data.

[0122] The processing module 93 is used to construct a closed-loop network based on the forward neural network and the pre-trained inverse neural network; iteratively train the closed-loop network on given data to be solved to obtain an inverse neural network that meets the requirements.

[0123] As an example, for the process of iterative training of the closed-loop network, in a possible implementation manner, the processing module 93 is used to iteratively train the closed-loop network on given data to be solved, specifically for: Using the original three-dimensional gravity field and the given energy distribution curve as input, forward propagation is performed through the inversion neural network to output predicted three-dimensional density information and predicted three-dimensional density data; The predicted three-dimensional density information and the predicted three-dimensional density data output by the inversion neural network are used as the input of the forward neural network to calculate and obtain the reconstructed gravity field; Calculating a second loss function according to the original three-dimensional gravity field and the reconstructed three-dimensional gravity field; According to the second loss function, back propagation is performed on the forward neural network and the inverse neural network to calculate the second parameter gradient; Using Adam optimizer, updating the network parameters of the inversion neural network according to the second parameter gradient; As the number of iterations increases, the learning rate is gradually reduced.

[0124] Specifically, the second loss function expression in the closed-loop training stage is as follows: (8)

[0125] in, and They are the detected gravity anomaly and gravity gradient anomaly, , and They are the joint inversion, gravity forward modeling and gravity gradient forward modeling processes, is the regularization constraint of the inversion result.

[0126] Optionally, the second loss function may also be the mean absolute error (MAE) between the reconstructed gravity field and the original gravity field.

[0127] Combination Figure 7 The process of iterative training of the closed-loop network is described in detail. Specifically, the original gravity field and the given energy distribution curve are used as inputs of the inversion neural network. The original gravity field data is the gravity value observed on the surface, and the energy distribution curve may refer to a certain energy characteristic or density distribution related to the underground structure. The inversion neural network processes and outputs density data based on the input gravity field and energy distribution. The density data reflects the spatial distribution of underground materials.

[0128] Furthermore, the density data output by the inversion neural network is input into the forward neural network, and the forward neural network calculates the reconstructed gravity field based on the density data through physical formulas or numerical methods.

[0129] Furthermore, the mean absolute error (MAE) between the original gravity field and the reconstructed gravity field is calculated. This is an indicator to measure the performance of the model and is used to evaluate how close the reconstructed gravity field is to the actual observation data.

[0130] Furthermore, the calculation results of MAE can be used to iteratively optimize the inverse neural network. If the MAE is large, it indicates that the inverse neural network needs further adjustment. In practical applications, by adjusting model parameters or improving algorithms, the MAE can be reduced and the prediction accuracy of the model can be improved.

[0131] It is understandable that the MAE calculation during the iterative training of the closed-loop network provides a self-supervised learning mechanism, where the model guides the training process through its own predictions, reducing the reliance on external labeled data. Through self-supervised learning, the closed-loop network can adapt to new data and be effectively trained without a large amount of labeled data.

[0132] In the multi-height three-dimensional gravity and its gradient joint inversion device based on physical information neural network provided by this embodiment, the building module builds the forward neural network and the inversion neural network based on the physical information neural network; the pre-training module pre-trains the inversion neural network on the synthetic data set; the processing module builds a closed-loop network based on the forward neural network and the pre-trained inversion neural network; the processing module iteratively trains the closed-loop network on the given data to be solved to obtain an inversion neural network that meets the requirements. The scheme of this embodiment realizes self-supervised learning of the inversion process through a forward process with known parameters and unique solution space. Compared with the existing gravity inversion algorithm based on deep learning, the scheme of the present invention does not rely on training data, has no risk of overfitting, and provides rich vertical resolution with limited cost increase.

[0133] Fig.10 is a schematic diagram of the structure of the electronic device provided by the present invention, such as Fig.10 As shown, the electronic device may include: a processor 1010, a communication interface 1020, a memory 1030 and a communication bus 1040, wherein the processor 1010, the communication interface 1020 and the memory 1030 communicate with each other through the communication bus 1040. The processor 1010 may call the logic instructions in the memory 1030 to execute a multi-height three-dimensional gravity and its gradient joint inversion method based on a physical information neural network, the method comprising: building a forward neural network and an inversion neural network based on a physical information neural network; pre-training the inversion neural network on a synthetic data set; wherein the synthetic data set comprises a plurality of pairs of synthetic data, each pair of synthetic data comprises original three-dimensional gravity anomaly data and real three-dimensional density data; constructing a closed-loop network based on the forward neural network and the pre-trained inversion neural network; iteratively training the closed-loop network on given data to be solved to obtain an inversion neural network that meets the requirements.

[0134] In addition, the logic instructions in the above-mentioned memory 1030 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[0135] On the other hand, the present invention also provides a computer program product, which includes a computer program, and the computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the multi-height three-dimensional gravity and its gradient joint inversion method based on the physical information neural network provided by the above-mentioned methods. The method includes: based on the physical information neural network, building a forward neural network and an inversion neural network; pre-training the inversion neural network on a synthetic data set; wherein the synthetic data set includes multiple pairs of synthetic data, each pair of synthetic data includes original three-dimensional gravity anomaly data and real three-dimensional density data; constructing a closed-loop network based on the forward neural network and the pre-trained inversion neural network; on given data to be solved, iteratively training the closed-loop network to obtain an inversion neural network that meets the requirements.

[0136] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the multi-height three-dimensional gravity and its gradient joint inversion method based on a physical information neural network provided by the above-mentioned methods, the method comprising: building a forward neural network and an inversion neural network based on a physical information neural network; pre-training the inversion neural network on a synthetic data set; wherein the synthetic data set comprises multiple pairs of synthetic data, each pair of synthetic data comprises original three-dimensional gravity anomaly data and real three-dimensional density data; constructing a closed-loop network based on the forward neural network and the pre-trained inversion neural network; iteratively training the closed-loop network on given data to be solved to obtain an inversion neural network that meets the requirements.

[0137] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0138] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0139] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network, characterized in that: include: Build a forward neural network based on physical information neural network; Build an inversion neural network based on physical information neural network; Pre-training the inversion neural network on a synthetic data set; wherein the synthetic data set includes multiple pairs of synthetic data, each pair of synthetic data includes original three-dimensional gravity anomaly data and real three-dimensional density data; Constructing a closed-loop network based on the forward neural network and the pre-trained inverse neural network; On given data to be solved, the closed-loop network is iteratively trained to obtain an inversion neural network that meets the requirements.

2. The multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network according to claim 1 is characterized in that: The physical information neural network is based on which an inversion neural network is constructed, comprising: The inversion neural network is constructed by means of a three-dimensional preprocessing module, a two-dimensional encoder, a two-dimensional decoder and a three-dimensional post-processing module.

3. The multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network according to claim 1 is characterized in that: The physical information neural network is based on which a forward neural network is constructed, including: According to the universal gravitation formula, determine the first expression of the original three-dimensional gravity field with respect to the three-dimensional density information; Determine a second expression of the three-dimensional gravity anomaly gradient with respect to the three-dimensional density data according to the first expression; According to the first expression and the second expression, the forward neural network is constructed.

4. The multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network according to claim 1 is characterized in that: The pre-training of the inversion neural network on the synthetic data set includes: On the synthetic data set, an iterative pre-training process is performed on the inversion neural network until the performance of the inversion neural network on the synthetic data set reaches a predetermined standard or the number of iterations is completed; wherein the iterative pre-training process includes: taking the original three-dimensional gravity anomaly data as input, performing forward propagation through the inversion neural network, and outputting predicted three-dimensional density data; calculating a first loss function based on the predicted three-dimensional density data and the real three-dimensional density data in the synthetic data set; performing a back propagation algorithm on the inversion neural network based on the first loss function to calculate a first parameter gradient; using an Adam optimizer to update the network parameters of the inversion neural network based on the first parameter gradient; and gradually reducing the learning rate as the number of iterations increases.

5. The multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network according to claim 1 is characterized in that: The iterative training of the closed-loop network on the given data to be solved includes: Using the original three-dimensional gravity field and the given energy distribution curve as input, forward propagation is performed through the inversion neural network to output predicted three-dimensional density information and predicted three-dimensional density data; The predicted three-dimensional density information and the predicted three-dimensional density data output by the inversion neural network are used as the input of the forward neural network to calculate and obtain the reconstructed gravity field; Calculating a second loss function according to the original three-dimensional gravity field and the reconstructed three-dimensional gravity field; According to the second loss function, back propagation is performed on the forward neural network and the inverse neural network to calculate the second parameter gradient; Using Adam optimizer, updating the network parameters of the inversion neural network according to the second parameter gradient; As the number of iterations increases, the learning rate is gradually reduced.

6. The multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network according to any one of claims 1 to 5, characterized in that: Before pre-training the inversion neural network on the synthetic data set, the method further includes: Apply the synthetic data method to randomly synthesize multiple real three-dimensional density data; Based on the multiple real three-dimensional density data, a plurality of original three-dimensional gravity anomaly data are generated through a forward neural network; wherein the multiple original three-dimensional gravity anomaly data correspond one to one to the multiple real three-dimensional density data; According to the corresponding relationship, the plurality of original three-dimensional gravity anomaly data and the plurality of real three-dimensional density data are combined into a plurality of pairs of synthetic data to obtain the synthetic data set.

7. A multi-height three-dimensional gravity and its gradient joint inversion device based on physical information neural network, characterized in that: include: Building modules for building forward neural networks and inverse neural networks based on physical information neural networks; A pre-training module, used for pre-training the inversion neural network on a synthetic data set; wherein the synthetic data set includes a plurality of pairs of synthetic data, each pair of synthetic data includes original three-dimensional gravity anomaly data and real three-dimensional density data; The processing module is used to construct a closed-loop network based on the forward neural network and the pre-trained inversion neural network; iteratively train the closed-loop network on given data to be solved to obtain an inversion neural network that meets the requirements.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network as described in any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, it implements the multi-height three-dimensional gravity and its gradient joint inversion method based on physical information neural network as described in any one of claims 1 to 6.

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