U-type factorization Fourier neural operator for oil exploration

Abstract

The invention relates to the technical field of oil exploration, in particular to a U-shaped factorization Fourier neural operator for oil exploration. The system comprises a conversion module, and a lifting operator lifts an input function to a potential space through a linear full-connection network; the U-Net neural network module is used for acquiring high-frequency information; the operator layer module enters a Fourier neural operator layer to learn low-frequency information; and a projection operator is projected back to a physical space through a linear full-connection network. According to the technical scheme, the U-shaped factorization Fourier neural operator can effectively reduce the influence of lost high-frequency information on the solving precision, the difficulty of learning the partial differential equation by the U-shaped factorization Fourier neural operator is reduced, the partial differential equation solver is a core component of petroleum industry software, and the cost is reduced. The assembly is integrated into petroleum industry software and is a key technology for increasing storage and production, improving the recovery efficiency and optimizing the production process.

Description

Technical Field

[0001] The invention relates to the technical field of oil exploration, in particular to a U-type factorized Fourier neural operator used for oil exploration. Background Art

[0002] Partial differential equations have a wide range of applications in science and engineering, especially in problems involving practical applications, such as oil exploration, natural gas exploration, atmospheric circulation simulation, and population dynamics modeling. Traditional methods for solving a specific partial differential equation (PDE) include the finite element method and the finite difference method. These numerical methods will result in different solution accuracy and time due to different degrees of mesh division. The finer the mesh division, the higher the solution accuracy, and the corresponding cost in solution time is also higher. Therefore, traditional solvers need to make a trade-off between solution time and solution accuracy.

[0003] With the development of deep learning, relevant researchers have proposed to use deep learning methods to replace traditional methods, and use data-driven machine learning methods to solve partial differential equations using observed data. Deep learning methods can learn natural laws from a large amount of data and thus obtain solutions to partial differential equations; neural operators, as a new type of data-driven model for solving partial differential equations in recent years, can learn nonlinear mappings between infinite-dimensional spaces, and achieve gridless learning by generating a set of neural network parameters that can be shared with different discretizations. In other words, neural operators are a gridless, infinite-dimensional method that has discretization invariance and does not require knowledge of underlying partial differential equations; graph neural operators use random The finite-rank neural operator uses the fast Fourier transform to process the irregular grids; the multi-level graph neural operator uses the multi-scale decomposition of the kernel through the fast multi-level method to achieve the linear complexity of the calculation; the low-rank neural operator directly forces the kernel to be in the form of tensor product to reduce the computational complexity, which is equivalent to directly parameterizing the finite-rank operator; the Fourier neural operator uses the fast Fourier transform to put the operator learning process in the Fourier domain, which greatly improves the solution time and solution accuracy. In addition, the multi-wavelet-based operator learning processes irregular grids by using wavelet basis. Inspired by the classical spectral method, the latent spectral model is proposed based on the attention mechanism to solve high-dimensional problems. As a relatively mature neural operator, the Fourier neural operator has derived many variants. The U-type neural operator combines the U-type structure of U-Net with the Fourier neural operator, which is a U-type memory enhancement architecture; the irregular grid is converted into a latent uniform grid using the geometric Fourier transform, so that the neural operator can process irregular grids.

[0004] The Fourier Neural Operator (FNO) learns operators in the frequency domain through fast Fourier transform. The emergence of the Fourier Neural Operator fills the performance gap between pure machine learning methods and numerical solvers. The Factorized Fourier Neural Operator (F-FNO) introduces dimensional decomposition, which further accelerates the solution time. However, after the spatial domain is transformed into the frequency domain using the fast Fourier transform, the high-frequency information in the features is lost due to the existence of the truncation coefficient, and the resulting errors will accumulate during the forward and back propagation processes, causing unpredictable impacts on the solution accuracy. Summary of the invention

[0005] In order to solve the problem that traditional numerical methods are slow in solving partial differential equations and have low solution accuracy, which in turn leads to low efficiency in the actual process of oil resource exploration and development, the present invention provides a U-type factorization Fourier neural operator for oil exploration. The U-type factorization Fourier neural operator can effectively reduce the influence of lost high-frequency information on the solution accuracy, and reduce the difficulty of the U-type factorization Fourier neural operator to learn partial differential equations, thereby solving partial differential equations more accurately and quickly, improving the reliability of oil industry software, and reducing the cost for the actual exploration and development of oil resources.

[0006] In order to solve the above problems, the following technical solutions are provided:

[0007] The U-factored Fourier neural operator for oil exploration of the present invention comprises:

[0008] The transformation module elevates the input function to the latent space through a linear fully connected network;

[0009] U-Net neural network module, used to obtain high-frequency information, adopts encoder and decoder structures, performs downsampling operation in the encoder and doubles the number of feature channels, and performs upsampling operation in the decoder and halves the number of feature channels. Each downsampling has a jump connection with the corresponding upsampling to supplement information;

[0010] In the operator layer module, the tanh function is used for pre-activation processing, the Gaussian low-pass filter is used to enhance the low-frequency information, and the high-frequency information obtained by the U-Net neural network module is combined to enter the Fourier neural operator layer to learn the low-frequency information; the application is iterated; in each enhanced operator layer, there is

[0011]

[0012] Among them, v0 represents the output from the previous layer, represents a linear transformation, represents the integral operator kernel with Fourier transform, represents the Gaussian kernel generated by the Gaussian function, Θ represents the pre-activation function, σ represents the activation function, and v1(x) is the output function promoted to the latent space;

[0013] The projection module projects v1(x) back to the physical space through a linear fully connected network.

[0014] Through the above scheme, the U-type factorization Fourier neural operator is used as a method for solving partial differential equations, which improves the accuracy of solving partial differential equations and greatly reduces the solution time. It is integrated into the petroleum industry software, which can quickly and accurately detect the relevant physical parameters of underground oil and gas reservoirs, and then formulate mining plans to achieve efficient development; through the operator layer module, pre-activation processing is performed through the tanh function, and a Gaussian low-pass filter is introduced to enhance the low-frequency information in the frequency domain. On the basis of improving numerical stability, the U-type factorization Fourier neural operator is easier to learn the physical knowledge contained in the laws of nature, reducing the difficulty of the U-type factorization Fourier neural operator to learn partial differential equations.

[0015] The calculation process of the conversion module is:

[0016] v0(x)=P(a(x))

[0017] Among them, P is the lifting operator, a(x) is the input function, v0(x) is the input function lifted to the latent space, and the lifting operator P is used to project the equation information from the physical space to the latent space for learning by the artificial intelligence model.

[0018] The encoder downsamples the grid, which can reduce computational cost and capture global information; the decoder upsamples the grid to restore a high-resolution grid.

[0019] The jump connection is used to realize data transmission between layers. The specific operation of the jump connection is to directly transfer the output data of a certain operator layer to a certain subsequent layer, thereby realizing information supplementation.

[0020] The Gaussian low-pass filter is a filter based on a Gaussian function, which is used for image processing and signal processing. The Gaussian low-pass filter is mainly used to smooth images, remove noise or blur images. The two-dimensional Gaussian function used to generate the Gaussian kernel can be described as:

[0021]

[0022] Among them, σ ， is the standard deviation, and its size is related to the degree of convergence of the Gaussian kernel. The smaller the value, the more concentrated the weight of the Gaussian kernel, and the larger the value, the more dispersed the weight of the Gaussian kernel; x and y are the coordinates of the distance from the center of the filter.

[0023] The operator layer of the application iteration: G1→G2→…G i →G i+1 …→G M ,

[0024] Among them, G i It represents the i-th operator layer, and there is a skip connection between the i-th layer and the Mi layer.

[0025] The calculation process of the projection module is:

[0026] u(x)=Q(v1(x))

[0027] Among them, Q is the projection operator, v1(x) is the enhanced operator layer, and u(x) is the output function projected back to the physical space.

[0028] The above solution has the following advantages:

[0029] 1. The present invention adopts U-type factorization Fourier neural operator as a method for solving partial differential equations, which improves the accuracy of solving partial differential equations and greatly reduces the solution time. It is integrated into the oil industry software, which can quickly and accurately detect the relevant physical parameters of underground oil and gas reservoirs, and then formulate mining plans to achieve efficient development;

[0030] 2. Through the operator layer module, pre-activation processing is performed through the tanh function, and a Gaussian low-pass filter is introduced to enhance the low-frequency information in the frequency domain. On the basis of improving numerical stability, the U-type factorization Fourier neural operator is easier to learn the physical knowledge contained in the laws of nature, and the difficulty of the U-type factorization Fourier neural operator to learn partial differential equations is reduced. As an artificial intelligence solver, the amount of training data is crucial. The oil field data retained in actual oil field production can be used as training data to further improve the accuracy of the solver. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0032] Figure 1 The architecture diagram of the U-factorized Fourier neural operator;

[0033] Figure 2 Schematic diagram before and after Gaussian low-pass filter processing;

[0034] Figure 3 is the ground truth plot of the airfoil equation;

[0035] Figure 4 This is the prediction result diagram of the FNO model of the airfoil equation;

[0036] Figure 5 This is the prediction result diagram of the LSM model of the airfoil equation;

[0037] Figure 6 It is a prediction result diagram of the UFFNO model of the airfoil equation in the present invention;

[0038] Figure 7 is the absolute error diagram of the FNO model of the airfoil equation;

[0039] Figure 8 is the absolute error plot of the LSM model for the airfoil equation;

[0040] Fig. 9 is the absolute error diagram of the UFFNO model of the airfoil equation in the present invention;

[0041] Fig.10 is the ground truth map of the elastic equation;

[0042] Fig.11 The prediction results of the FNO model and LSM model for the elastic equation are shown in Figure 2.

[0043] Fig.12 This is a diagram of the prediction results of the UFFNO model of the elastic equation in the present invention;

[0044] Fig.13 is the absolute error diagram of the FNO model and LSM model of the elastic equation;

[0045] Fig.14 is the absolute error diagram of the UFFNO model of the elastic equation in the present invention;

[0046] Fig.15 is the ground truth map of the plasticity equation;

[0047] Fig.16 The prediction results of the FNO model and LSM model of the plasticity equation are shown in the figure;

[0048] Fig.17 It is a prediction result diagram of the UFFNO model of the plasticity equation in the present invention;

[0049] Fig.18 is the absolute error diagram of the FNO model and LSM model of the plasticity equation;

[0050] Fig.19 is the absolute error diagram of the UFFNO model of the plasticity equation in the present invention;

[0051] Fig. 20 is the ground truth map of the pipeline equation;

[0052] Fig.21The prediction results of the FNO model and LSM model for the pipeline equation are shown in Figure 2.

[0053] Fig. 22 It is a prediction result diagram of the UFFNO model of the pipeline equation in the present invention;

[0054] Fig.23 The absolute error diagram of the FNO model and the LSM model for the pipeline equation;

[0055] Fig.24 is the absolute error diagram of the UFFNO model of the pipeline equation in the present invention;

[0056] Fig.25 The performance of each model at different resolutions;

[0057] Fig.26 is the ground truth map of the Darcy flow equation;

[0058] Fig. 27 The prediction results of the FNO model and LSM model of the Darcy flow equation are shown in Figure 2.

[0059] Fig.28 It is a prediction result diagram of the UFFNO model of the Darcy flow equation in the present invention;

[0060] Fig.29 The absolute error diagram of the FNO model and the LSM model for the Darcy flow equation;

[0061] Fig.30 is the absolute error diagram of the UFFNO model of the Darcy flow equation in the present invention;

[0062] Fig.31 is the ground truth plot for the Navier-Stokes equations;

[0063] Fig.32 It is a prediction result diagram of the UFFNO model of the Navier-Stokes equations in the present invention;

[0064] Fig.33 It is the absolute error diagram of the UFFNO model of the Navier-Stokes equations in the present invention. DETAILED DESCRIPTION

[0065] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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.

[0066] In a specific embodiment, if Figure 1As shown, the U-type factorization Fourier neural operator for oil exploration of the present invention includes:

[0067] In the transformation module, the lifting operator P lifts the input function to the latent space through a linear fully connected network. The lifting operator P is used to project the equation information from the physical space to the latent space for the artificial intelligence model to learn. The specific calculation process is as follows:

[0068] v0(x)=P(a(x))

[0069] Where P is the lifting operator, a(x) is the input function, and v0(x) is the input function lifted to the latent space.

[0070] The U-Net neural network module is used to obtain high-frequency information. It adopts an encoder structure and a decoder structure. The encoder performs downsampling operations and doubles the number of feature channels. The encoder downsamples the grid to reduce computational costs and capture global information. The decoder performs upsampling operations and halves the number of feature channels. The decoder upsamples the grid to restore a high-resolution grid. Each downsample has a jump connection with the corresponding upsample. The jump connection is used to realize data transmission between layers. The output data of a certain operator layer is directly transferred to a subsequent layer to supplement information.

[0071] The operator layer module uses the tanh function for pre-activation processing, the Gaussian low-pass filter enhances the low-frequency information, and combines the high-frequency information obtained by the U-Net neural network module to enter the Fourier neural operator layer to learn the low-frequency information. The integral kernel in the Fourier space follows the original setting of the factorized Fourier neural operator. The original setting of the factorized Fourier neural operator is: The original Fourier neural operator architecture is driven by the kernel formula of the solution of the linear partial differential equation using the Green function, and an iterative method for mapping from the input function space to the output function space is proposed:

[0072]

[0073] in Indicates compound, is a lifting operator that lifts the input function into the latent space, is the lth nonlinear operator, is a projection operator that maps the latent space back to the physical space. Each operator layer can be expressed as

[0074]

[0075] Among them, σ represents the activation function, represents a linear transformation, is the integral operator kernel with Fourier transform,

[0076]

[0077] in, is the weight matrix in the Fourier domain, FFT and IFFT represent fast Fourier transform and inverse fast Fourier transform, respectively.

[0078] The factorization Fourier neural operator introduces the idea of ​​dimensional decomposition and transforms the above formula into:

[0079]

[0080] Each dimension is processed separately and then the features are summed.

[0081] like Figure 2 As shown in the figure, the Gaussian low-pass filter is a filter based on the Gaussian function, which is used in image processing and signal processing. It is mainly used to smooth images, remove noise or blur images. The two-dimensional Gaussian function used to generate the Gaussian kernel can be described as:

[0082]

[0083] Among them, σ' is the standard deviation, and its size is related to the degree of aggregation of the Gaussian kernel. The smaller the value, the more concentrated the weight of the Gaussian kernel, and the larger the value, the more dispersed the weight of the Gaussian kernel; x and y are the coordinates of the distance from the center of the filter.

[0084] Perform application iteration, the operator layer of application iteration: G1→G2→…G i →G i+1 …→G M ,

[0085] Among them, G i represents the i-th operator layer, and there is a skip connection between the i-th layer and the Mi layer;

[0086] In each enhanced operator layer, there are

[0087]

[0088] Among them, v0 represents the output from the previous layer, represents a linear transformation, represents the integral operator kernel with Fourier transform, represents the Gaussian kernel generated by the Gaussian function, Θ represents the pre-activation function, σ represents the activation function, and v1(x) is the output function promoted to the latent space.

[0089] Projection module, the projection operator Q projects v1(x) back to the physical space through a linear fully connected network. The specific calculation process is:

[0090] u(x)=Q(v1(x))

[0091] Among them, Q is the projection operator, v1(x) is the enhanced operator layer, and u(x) is the output function projected back to the physical space.

[0092] 1. If Figures 3 to 24 As shown in Table 1, the U-factorized Fourier neural operator (U-FFNO) is experimentally evaluated by partial differential equations in solids and fluids.

[0093] Table 1 Summary of experimental datasets

[0094] form Benchmarks Input Format Dimensions solid Elasticity-G Regular grid 2D solid Plasticity Structured Grid 3D fluid Navier-Stokes Regular grid 3D fluid Darcy Regular grid 2D fluid Airfoils Structured Grid 2D fluid Pipe Structured Grid 2D

[0095] Benchmark: Solid equations include elasticity and plasticity equations, where elasticity-G is obtained by interpolating the input format of the point cloud; fluid equations include Navier-Stokes equations, Darcy flow equations, airfoil equations, and pipe equations. The airfoil equations and pipe equations are both controlled by the Navier-Stokes equations, and the difference lies in the different boundary conditions.

[0096] Baselines: A comprehensive comparison of U-factorized Fourier neural operators is conducted, involving nine different benchmarks, including U-Net (2015) proposed for visual tasks and DeepONet (2021), FNO (2021), U-FNO (2021), WMT (2021), SNO (2022), U-NO (2022), F-FNO (2023), LSM (2023) proposed for partial differential equations, and all of the above baselines are proposed for regular grids or structured grids.

[0097] All experiments were conducted on a single Nvidia GeForce RTX 3090 24GB GPU (python 3.8, torch1.10, CUDA 11.3). Except for the pre-activation operation, all non-linear activation functions used the Gelu activation function. The training process used the Adam optimizer with L2 loss and 500 iterations of training. The initial learning rate was 10-4. Due to memory limitations, the batch size was set to 10 in the plasticity equation and 20 in the other equations. As shown in Table 2, all settings follow the settings of FNO and geo-FNO. The input and output tensors are given in the form of (space, variable, time), and " / " indicates the absence of this dimension. Among them, PDEs, tasks, inputs, and outputs are physical information, and the training set size, test set size, input tensors, and output tensors are data information.

[0098] Table 2 Detailed information of experimental data

[0099]

[0100]

[0101] The U-factorized Fourier neural operator shows advanced performance on all six datasets covered, with an average relative gain of 14.5%. The main results of each experiment are shown in Table 3:

[0102] Table 3 Performance comparison of 9 benchmarks on 6 datasets

[0103]

[0104] The performance of each benchmark is compared on six datasets, with MSE as the evaluation metric. The smaller the MSE, the better the performance. The best result of each dataset is in bold, the second best result is underlined, and the percentage in the last row indicates the proportion of the relative error reduction of the best result relative to the second best result.

[0105] 2. U-type factorization Fourier neural operator analysis:

[0106] Ablation experiment: In order to prove the effectiveness of each component in the model without loss of generality, a detailed ablation experiment was conducted using the Darcy flow equation and the hyperelastic equation as examples. Key components were removed one by one, including the U-Net neural network, the pre-activated tanh function, and the Gaussian low-pass filter. When a component was removed, the other experimental settings remained unchanged. The experimental results are shown in Table 4:

[0107] Table 4 Results of ablation experiments using elastic equation and Darcy flow equation as examples

[0108] design Evaluation Metrics Elasticity Evaluation Metrics Darcy Removing UNet 0.0440 0.0055 Remove the Gaussian low-pass filter 0.0397 0.0044 Removing tanh 0.0399 0.0043 Ours 0.0396 0.0042

[0109] Through ablation experiments, it is found that all components in the U-shaped factorization Fourier neural operator are crucial for solving partial differential equations. The lack of any one of them will lead to a decrease in solution accuracy. In addition, increasing the number of operator layers and the number of jump connections sometimes improves the solution accuracy. The setting of six operator layer iterations and two jump connections is selected.

[0110] Performance at different resolutions: Figures 25 to 30 As shown in FIG. 5 , experiments were conducted at different resolutions on the Darcy flow benchmark. The Darcy flow benchmark was set to four resolutions, namely s=85, 141, 211, and 421, where s represents the input function a(x) and the output function u(x) discretized into s*s grids. The data sets of s=85, 141, and 211 were obtained by downsampling the data set of resolution s=421. The experimental results are shown in Table 5:

[0111] Table 5 Comparison of prediction errors of various models at different resolutions of Darcy flow equation

[0112]

[0113]

[0114] Performance of the same equation under different parameters: Figure 31 to Figure 33 As shown, experiments were conducted on the Navier-Stokes equation with different parameters, and the viscosity coefficient was expanded to v = 1e-3, v = 1e-4, and v = 1e-5. The flow conditions after 50 time steps, 30 time steps, and 20 time steps were predicted respectively. The smaller the viscosity coefficient, the more chaotic the flow. The experimental results are shown in Table 6:

[0115] Table 6 Prediction error under different viscosity coefficients in Navier-Stokes equation

[0116] Model v=1e-3 v=1e-4 v=1e-4 v=1e-5 Model T＝50 T＝30 T＝30 T＝20 Model N＝1000 N＝1000 N＝9800 N＝1000 FNO 0.0129 0.1564 0.0810 0.1556 F-FNO 0.0235 0.1996 0.1248 0.1772 LSM 0.0274 0.1981 0.1101 0.1535 U-FFNO(Ours) 0.0122 0.1795 0.0753 0.1479

[0117] It can be seen from the above table that when the viscosity coefficient is v=1e-3 and v=1e-5, the prediction error of the U-factorized Fourier neural operator reaches an excellent level, with an improvement of 5.4% and 3.6% respectively compared with the suboptimal benchmark. When the viscosity coefficient v=1e-4, when there is sufficient data (N=9800), a lower error can be achieved, which is a 7% improvement compared with the suboptimal benchmark.

[0118] Zero-sample super-resolution: The Fourier neural operator parameterizes the kernel integral operator and truncates the Fourier series, which has discretization invariance. Specifically, the neural operator can be trained at a lower resolution and then solve the high-resolution problem without the need for high-resolution data training. Taking the Darcy flow equation as an example, the experimental results of the Fourier neural operator and the U-factorized Fourier neural operator are shown in Table 7:

[0119] Table 7 Prediction errors of FNO and U-FFNO trained and evaluated at different resolutions

[0120]

[0121]

[0122] The results show that the U-factorized Fourier neural operator also has discretization invariance. Compared with the Fourier neural operator, the prediction effect at different resolutions on the Darcy flow dataset is improved to a certain extent, especially when the training resolution is s=85 and s=421. When the evaluation resolution is expanded to higher or lower, the average relative error is reduced by about 9.1% and 12.7%, respectively. However, the performance of the U-factorized Fourier neural operator at medium resolution is not stable.

[0123] In summary, the U-shaped factorization Fourier neural operator as a method for solving partial differential equations has improved accuracy. The U-shaped factorization Fourier neural operator can effectively reduce the impact of lost high-frequency information on the solution accuracy; the U-shaped factorization Fourier neural operator has demonstrated advanced levels on six challenging partial differential equation data sets, with an average gain of 14.5%; integrating the neural operator solver into the petroleum industry software can improve the versatility and solution efficiency of the software, and can adapt to the exploration and development of oil and gas fields in various complex situations.

Claims

1. U-factorized Fourier neural operator for oil exploration, characterized by: include: The transformation module elevates the input function to the latent space through a linear fully connected network; U-Net neural network module, used to obtain high-frequency information, adopts encoder and decoder structures, performs downsampling operation in the encoder and doubles the number of feature channels, and performs upsampling operation in the decoder and halves the number of feature channels. Each downsampling has a jump connection with the corresponding upsampling to supplement information; In the operator layer module, the tanh function is used for pre-activation processing, the Gaussian low-pass filter is used to enhance the low-frequency information, and the high-frequency information obtained by the U-Net neural network module is combined to enter the Fourier neural operator layer to learn the low-frequency information; the application is iterated; in each enhanced operator layer, there is Among them, v0 represents the output from the previous layer, represents a linear transformation, represents the integral operator kernel with Fourier transform, represents the Gaussian kernel generated by the Gaussian function, Θ represents the pre-activation function, σ represents the activation function, and v1(x) is the output function promoted to the latent space; The projection module projects v1(x) back to the physical space through a linear fully connected network.

2. The U-factorized Fourier neural operator for oil exploration according to claim 1, characterized in that: The calculation process of the conversion module is: v0(x)=P(a(x)) Where P is the lifting operator, a(x) is the input function, and v0(x) is the input function lifted to the latent space.

3. The U-factorized Fourier neural operator for oil exploration according to claim 2, characterized in that: The lifting operator P is used to project equation information from the physical space into the latent space for learning by the artificial intelligence model.

4. The U-factorized Fourier neural operator for oil exploration according to claim 1, characterized in that: The encoder downsamples the grid, which can reduce computational cost and capture global information; the decoder upsamples the grid to restore a high-resolution grid.

5. The U-factorized Fourier neural operator for oil exploration according to claim 1, characterized in that: The jump connection is used to realize data transmission between layers. The specific operation of the jump connection is to directly transfer the output data of a certain operator layer to a certain subsequent layer, thereby realizing information supplementation.

6. The U-factorized Fourier neural operator for oil exploration according to claim 1, characterized in that: The Gaussian low-pass filter is a filter based on a Gaussian function and is used for image processing and signal processing.

7. The U-factorized Fourier neural operator for oil exploration according to claim 6, characterized in that: The Gaussian low-pass filter is mainly used to smooth images, remove noise or blur images. The two-dimensional Gaussian function used to generate the Gaussian kernel can be described as: Among them, σ ， is the standard deviation, and its size is related to the degree of convergence of the Gaussian kernel. The smaller the value, the more concentrated the weight of the Gaussian kernel, and the larger the value, the more dispersed the weight of the Gaussian kernel; x and y are the coordinates of the distance from the center of the filter.

8. The U-factorized Fourier neural operator for oil exploration according to claim 1, characterized in that: The calculation process of the application iteration is: Apply iterative operator layers: G1→G2→…G i →G i+1 …→G M , Among them, G i It represents the i-th operator layer, and there is a skip connection between the i-th layer and the Mi layer.

9. The U-factorized Fourier neural operator for oil exploration according to claim 1, characterized in that: The calculation process of the projection module is: u(x)=Q(v1(x)) Among them, Q is the projection operator, v1(x) is the enhanced operator layer, and u(x) is the output function projected back to the physical space.

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