A method for identifying lithofacies structure of heterogeneous aquifers based on potential diffusion model
Through potential diffusion model and autoencoder technology, the lithologic structure of aquifer is directly extracted from the drilling data and head concentration data, solving the problems of large calculation volume and slow identification speed of traditional methods, and achieving fast and accurate aquifer structure inversion.
Patent Information
- Application Number
- CN202411813214.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-11
- Publication Date
- 2025-04-25
- Estimated Expiration
- 2044-12-11
AI Technical Summary
Traditional inversion methods are difficult to quickly and accurately capture the complex heterogeneity of the aquifer, with large calculations, slow convergence speed and sensitive to initial conditions.
Using a method based on the potential diffusion model, the lithologic structure of the aquifer is directly predicted through the variational autoencoder and the denoising diffusion probability model, drilling data, head and concentration observation data.
The spatial structure feature recognition of aquifers with low computational cost is achieved, and the lithologic structure of aquifers is rapidly and accurately inverted, reducing the dependence on groundwater flow and solute migration simulation.
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Figure CN119293567B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of inversion identification of lithologic structure of heterogeneous aquifers, and in particular relates to a method for identifying lithofacies structure of heterogeneous aquifers based on a potential diffusion model. Background Art
[0002] The complex structure of heterogeneous aquifers has a significant impact on the flow of groundwater and solute transport processes. Therefore, accurate characterization of the structure is of great significance for water resource protection, groundwater pollution prevention and control, and resource exploitation.
[0003] However, traditional inversion methods usually rely on numerical simulation and optimization algorithms, which face problems such as large computational complexity, slow convergence, and sensitivity to initial conditions, making it difficult to quickly and accurately capture the complex heterogeneity of aquifers.
[0004] In recent years, the potential diffusion model has shown great potential as a generative model in learning the distribution of complex spatial features. This method applies the potential diffusion model to the direct inversion of aquifer structure, combines the characteristics of the generative model, and identifies the spatial structural characteristics of the aquifer at a lower computational cost, providing a new generation of technical support for hydrogeological research and helping to promote the development of aquifer structure inversion technology. Summary of the invention
[0005] In order to solve the above technical problems, the present invention provides a method for identifying the lithofacies structure of a heterogeneous aquifer based on a potential diffusion model to solve the problems in the prior art. The technical solution adopted by the present invention is:
[0006] A method for identifying lithofacies structure of heterogeneous aquifers based on a potential diffusion model comprises the following steps:
[0007] Step 1: Obtain the prior distribution of borehole data and large-scale lithology and structural parameters of the aquifer, randomly generate lithology and structural samples of the aquifer, and normalize the data;
[0008] Step 2: Set initial and boundary conditions, use groundwater flow and solute transport simulation software to predict the concentration distribution field and hydraulic head distribution field at multiple times based on the different aquifer lithology structures obtained in step 1, obtain hydraulic head and concentration distribution field sample data, and normalize the data at the same time;
[0009] Step 3: Based on the aquifer lithology sample obtained in step 1, the variational autoencoder is trained to use low-dimensional latent random variables to represent the high-dimensional aquifer lithology;
[0010] Step 4: Input the aquifer lithology samples obtained in step 1 into the variational autoencoder trained in step 3 in sequence to obtain the corresponding low-dimensional latent random variable samples;
[0011] Step 5: Using the low-dimensional potential random variable samples obtained in step 4 as training data, and the head and concentration distribution field data corresponding to the lithological structure of each aquifer obtained in step 2 as image condition constraints, the denoised diffusion probability model under the image constraints is trained so that it can predict the corresponding denoised potential random variables based on the input low-dimensional potential random variables under the constraints of the head and concentration distribution fields;
[0012] Step 6: Based on the site water head and concentration observation data, use the interpolation method to obtain the water head and concentration distribution field and normalize them;
[0013] Step 7: Randomly generate a potential random variable, use the site water head and concentration distribution field obtained in step 6 as conditional constraints, and input them into the denoised diffusion probability model trained in step 5 to predict the corresponding denoised potential random variable;
[0014] Step 8: Input the denoised latent random variable predicted in step 7 into the variational autoencoder trained in step 3, denormalize the output result, and predict the lithology of the aquifer at the site.
[0015] Furthermore, step 1 uses exponential kriging simulation based on the analytical solution of transition probability to generate the lithology structure of the aquifer, and its analytical solution of transition probability is:
[0016] ;
[0017] In formula (1), yes The distance between the lithology i and the The probability of the lithology being j, is the volume fraction of lithology i, N is the number of lithology, is the Kronecker function, Is the lithology i The average extension length in the direction, .
[0018] Furthermore, the data normalization in step 1 and step 2 is to scale the data range to [-1, 1], where the normalization calculation formulas for lithology, hydraulic head and concentration distribution field parameters are:
[0019] ;
[0020] In formula (2): and Respectively represent the lithology, hydraulic head and concentration values before and after normalization at grid k, and Represent the minimum and maximum values of lithology, hydraulic head and concentration in all training samples, respectively.
[0021] Furthermore, the data normalization in step 6 is to scale the data range to [-1, 1], and the normalization formula used is formula (2).
[0022] Furthermore, the length and width of the potential random variable in step 4 are both 1 / 4 of the input lithological structure.
[0023] Furthermore, the loss function used in the variational autoencoder training in step 3 includes reconstruction loss and adversarial loss, and its expression is as follows:
[0024] ;
[0025] In formula (3), K represents the batch size. is the lithological structure of the ith input, is the lithological structure reconstructed by the variational autoencoder, is the predicted output of the discriminator for the reconstructed lithology structure, is the weight that controls the adversarial loss in the training of the generator in the variational autoencoder.
[0026] Furthermore, the denoising diffusion probability model training in step 5 uses the mean square error as the loss function, and its expression is as follows:
[0027] ;
[0028] In formula (4), K represents the batch size. is the predicted value of the underlying random variable by the denoised diffusion probability model, is the actual underlying random variable.
[0029] Furthermore, the learning rate of the training process of the variational autoencoder and the denoising diffusion probability model in step 5 uses a dynamic adjustment strategy, and the expression of the learning rate decay strategy is:
[0030] ;
[0031] In formula (5) represents the current learning rate, represents the updated learning rate, Represents the learning rate decay coefficient.
[0032] Furthermore, the denoising diffusion probability model in step 5 includes two stages, namely, a noise diffusion stage and a reverse denoising stage, when predicting potential random variables;
[0033] In the noise diffusion stage, a linear noise scheduler is used to gradually add noise to the potential random variables obtained in step 4. The noise scheduler defines the noise coefficient , the noise figure increases linearly with time, from Start to Finally, at each time step, the noise coefficient is defined as:
[0034] ;
[0035] in, and denote the initial and final noise levels, respectively, and T is the total number of time steps;
[0036] Under the action of the linear noise scheduler, the forward process equation for adding noise during the training process in step 5 is:
[0037] ;
[0038] in, is the noise latent variable at time t, is the original latent variable, is standard Gaussian noise, Represents the cumulative product of noise factors from step 0 to step t.
[0039] Furthermore, in step 7, under the same head and concentration distribution field constraints, different denoised latent random variables are input to generate latent random variables, which are then input into the variational autoencoder according to step 8 to obtain different aquifer lithology structures, thereby realizing uncertainty analysis of the aquifer lithology structure.
[0040] The present invention has the following beneficial effects: the present invention can directly predict the corresponding aquifer lithology structure by using aquifer lithology structure parameters and head and concentration observation data, and realize direct inversion of aquifer lithology structure without repeatedly calling groundwater flow and solute transport simulation. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] Figure 1 It is a schematic diagram of the process of the present invention;
[0042] Figure 2 This is a schematic diagram of the potential diffusion model structure proposed by the present invention for direct inversion identification of aquifer lithology structure;
[0043] Figure 3 This is a comparison diagram between the lithologic structure of the aquifer identified by the method proposed in the present invention and the actual structure. DETAILED DESCRIPTION
[0044] The following will be combined with the embodiments of the present invention Figure 1-Figure 3 , the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.
[0045] The technical problem to be solved by the present invention is to provide a method for identifying the lithologic structure of a heterogeneous aquifer based on a potential diffusion model. The method can directly realize the inversion identification of the lithologic structure of the aquifer by utilizing the prior distribution of the aquifer structural parameters and the head and concentration observation data, and can predict multiple possible lithologic structures of the aquifer based on the same head and concentration observation data, thereby realizing the uncertainty analysis of the lithologic structure of the aquifer.
[0046] A method for identifying lithofacies structure of heterogeneous aquifers based on a potential diffusion model, the method comprising the following steps:
[0047] Step 1: Based on the prior information from the field, obtain a certain amount of drilling data and the prior distribution of the large-scale lithological characteristics of the aquifer. Use the geostatistical simulation software to randomly generate a number of aquifer lithology structure samples and standardize their data;
[0048] Step 2: Based on the prior data of the site, set the initial conditions and boundary conditions, use the groundwater flow and solute migration simulation tool, and simulate and predict the head and concentration distribution at multiple time nodes according to the different lithological structures obtained in step 1, so as to obtain the head and concentration distribution data samples and perform standardization processing;
[0049] Step 3: Based on the aquifer lithology sample obtained in step 1, the variational autoencoder is trained so that it can use low-dimensional latent random variables to represent the high-dimensional aquifer lithology;
[0050] Step 4: Input the aquifer lithology samples obtained in step 1 into the variational autoencoder trained in step 3 in sequence to obtain the corresponding low-dimensional latent random variable samples;
[0051] Step 5: Using the low-dimensional potential random variable samples obtained in step 4 as training data, and the head and concentration distribution field data corresponding to the lithology structure of each aquifer obtained in step 2 as image condition constraints, the denoised diffusion probability model under the image constraints is trained so that it can predict the corresponding denoised potential random variables based on the input low-dimensional potential random variables under the constraints of the head and concentration distribution fields;
[0052] Step 6: Based on the site water head and concentration observation data, use the interpolation method to obtain the water head and concentration distribution field and normalize them;
[0053] Step 7: Randomly generate a potential random variable that satisfies the Gaussian distribution, and use the site water head and concentration distribution field obtained in step 6 as conditional constraints, and input them into the denoised diffusion probability model trained in step 5 to predict the corresponding denoised potential random variable;
[0054] Step 8: Input the denoised latent random variables predicted in step 7 into the variational autoencoder trained in step 3, denormalize the output results, and predict the lithology of the aquifer at the site;
[0055] Preferably, the aquifer lithology structural parameters in step 1 are mainly: volume ratios of different lithologies and average extension lengths in all directions;
[0056] Preferably, the training samples in steps 1 and 2 are stored and processed in the form of image pixel values;
[0057] Preferably, in step 1, a Python program is written to automatically generate an input file of a random simulation program based on the aquifer structure parameter sample, and a corresponding aquifer lithology structure sample is automatically generated;
[0058] Preferably, step 1 uses exponential kriging simulation based on the analytical solution of transition probability to generate the lithology structure of the aquifer, and the analytical solution of the transition probability is:
[0059] ;
[0060] In formula (1), yes The distance between the lithology i and the The probability of the lithology being j, is the volume fraction of lithology i, N is the number of lithology, is the Kronecker function, Is the lithology i The average extension length in the direction, .
[0061] Preferably, in step 2, a Python program is written to automatically simulate the corresponding hydraulic head and concentration distribution field based on the generated aquifer lithology structure, and automatically generate aquifer lithology structure and corresponding hydraulic head and concentration distribution field training samples;
[0062] Preferably, the solute transport simulation model in step 2 adopts TOUGHREACT simulation software;
[0063] Preferably, the head and concentration distribution data in step 2 need to be normalized to scale the data range to [-1, 1], where the normalized calculation formulas for lithology, head and concentration distribution field parameters are:
[0064] ;
[0065] In formula (2): and Respectively represent the lithology, hydraulic head and concentration values before and after normalization at grid k, and represent the minimum and maximum values of lithology, hydraulic head and concentration in all training samples respectively;
[0066] Preferably, the length and width of the potential random variable in step 3 are both 1 / 4 of the input water head and concentration distribution field;
[0067] Preferably, the loss function used in the variational autoencoder training in step 3 includes reconstruction loss and adversarial loss, and its expression is as follows:
[0068] ;
[0069] In formula (3), K represents the batch size. is the lithology or permeability distribution field of the ith input, is the image reconstructed by the variational autoencoder, is the predicted output of the discriminator for the reconstructed image, is the weight that controls the adversarial loss in the generator training in the variational autoencoder;
[0070] Preferably, the conditionally constrained denoising diffusion probability model training in step 5 uses mean square error as the loss function, and its expression is as follows:
[0071] ;
[0072] In formula (4), K represents the batch size. is the predicted value of the underlying random variable by the denoised diffusion probability model, is the actual underlying random variable.
[0073] Preferably, the denoising diffusion probability model in step 5 includes two stages, namely a noise diffusion stage and a reverse denoising stage, when predicting potential random variables.
[0074] Preferably, when the denoising diffusion probability model is trained in step 5, a linear noise scheduler is used to gradually add noise to the potential random variables obtained in step 4 during the noise diffusion stage. The noise scheduler defines a series of noise coefficients: , these noise figures increase linearly with time, from an initial noise level Start to End. At each time step, the noise coefficient is defined as:
[0075] ;
[0076] In formula (5), and denote the initial and final noise levels, respectively, and T is the total number of time steps.
[0077] Preferably, under the action of the linear noise scheduler, the forward process equation for adding noise during the training process in step 5 is:
[0078] ;
[0079] In formula (6), is the noise latent variable at time t, is the original latent variable, is standard Gaussian noise, Represents the cumulative product of noise factors from step 0 to step t.
[0080] Preferably, the head and concentration distribution field data in step 5 and step 7 need to pass through a layer of convolutional neural network, map its structure size to the same size as the potential random variable, and the number of channels needs to be changed to 1, and connected with the potential random variable after adding noise obtained in the noise diffusion stage as the input of the reverse denoising stage.
[0081] Preferably, when the denoising diffusion probability model is trained in step 5, a U-Net network is used for the reverse denoising stage to remove the noise added in the forward diffusion process step by step to restore the latent variables similar to the original data. It predicts the noise at each step and gradually reconstructs the latent variables. The denoising process of each step is updated as follows:
[0082] ;
[0083] In formula (7), is the randomly sampled noise, Represents the noise scaling factor.
[0084] Preferably, the activation functions in the variational autoencoder in step 3 and the denoising diffusion probability model in step 5 both adopt the SELU activation function.
[0085] Preferably, when training the variational autoencoder in step 3 and the denoising diffusion probability model in step 5, in order to ensure that the saved model parameters are optimal, the minimum loss preservation method is adopted, that is, the loss value of the model is monitored during the training process, and the model parameters corresponding to the epoch with the lowest loss are saved.
[0086] Preferably, the learning rate of the training process of the variational autoencoder in step 3 and the denoising diffusion probability model in step 5 uses a dynamic adjustment strategy to accelerate convergence and avoid falling into a local minimum. The expression of the learning rate decay strategy is:
[0087] ;
[0088] In formula (8) represents the current learning rate, represents the updated learning rate, represents the learning rate attenuation coefficient, and q represents the number of learning rate attenuation tolerances.
[0089] Preferably, the parameter samples in step 1 are all obtained by Monte Carlo sampling.
[0090] Preferably, the interpolation method used in step 6 adopts the Kriging interpolation algorithm to infer the value of the unknown point based on the water head and concentration value of the known point, so as to obtain the complete water head and concentration distribution field for the unknown point. , Kriging estimate It can be expressed as:
[0091] ;
[0092] In formula (9) is the weight coefficient of each known point, which is determined by the autocovariance of the known points and the unknown points. is the head or concentration value at a known point.
[0093] The present invention provides a test case for inversion identification of lithologic structure of a two-dimensional aquifer. The aquifer in this case contains two lithologic types, high permeability and low permeability. Five borehole data are virtually set. Based on these data, the lithologic structure of the aquifer is generated. A tracer test scenario is simulated using TOUGHREACT solute transport simulation software to generate a head distribution field corresponding to one moment and concentration distribution fields at five moments. Based on these data, an inversion identification test of the lithologic structure of the aquifer is performed.
[0094] In this case:
[0095] The prior distribution of aquifer structural parameters and the geostatistical parameters of permeability distribution in step 1 are shown in Table 1. The Latin Monte Carlo method extracts 10,000 sets of aquifer lithology structural parameters, and the program automatically calls the exponential Kriging model program in succession to obtain 10,000 lithology structural training samples, which are saved as npy files;
[0096] In step 2, the 10,000 lithology training samples obtained in step 1 are automatically input into the TOUGHREACT simulation program through the program, and the groundwater and solute transport simulation is run to obtain the corresponding 10,000 sets of head and concentration distribution field data, where the head distribution field in each set of data is the data at one moment, and the concentration distribution field is the data at five moments;
[0097] In step 4, the 10,000 lithology and structure training samples obtained in step 1 are used as training samples to train the variational autoencoder. The initial learning rate and decay coefficient of the variational autoencoder training are set to 0.0001 and 0.5, respectively, and the adversarial loss weight coefficient is set to Set to 0.1, the number of iterations is 40;
[0098] Table 1. Geostatistical parameters of lithofacies distribution and permeability distribution
[0099] High permeability lithology Low permeability lithology Volume ratio [0.5,0.7] [0.3,0.5] Extension length in X direction [50,80] [10,50] Extension length in Z direction [6.0,10.0] [2.5,6.0]
[0100] In step 4, 10,000 lithology and structure training samples are sequentially input into the variational autoencoder trained in step 3 to obtain 10,000 potential random variables;
[0101] In step 5, the 10,000 potential random variables obtained in step 4 are used as training samples, and the 10,000 sets of head and concentration distribution field data obtained in step 2 are used as constraints to train the denoised diffusion probability model under the image constraint. The initial learning rate and decay coefficient of the denoised diffusion probability model under the image constraint are set to 0.0005 and 0.5, respectively, and the number of iterations is 200.
[0102] In step 6, the water head and concentration distribution field data obtained by simulation in the case setting are used as conditional constraints, and a potential random variable is randomly generated. The potential random variable and the water head and concentration distribution field are simultaneously input into the denoising diffusion probability model under the trained image constraint conditions to predict the denoised potential random variable;
[0103] In step 7, the denoised latent random variables predicted in step 6 are input into the variational autoencoder trained in step 3, and the output structure is denormalized to obtain the lithological structure of the aquifer corresponding to the head and concentration distribution field;
[0104] It can be seen that the method for identifying the lithologic structure of a heterogeneous aquifer based on a potential diffusion model provided by the present invention can directly predict the corresponding lithologic structure of the aquifer by utilizing the lithologic structure parameters of the aquifer and the head and concentration observation data, thereby realizing direct inversion of the lithologic structure of the aquifer without repeatedly calling groundwater flow and solute transport simulation.
[0105] The embodiments described above are only descriptions of the preferred modes of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations, modifications, and substitutions made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.
Claims
1. A method for identifying lithofacies structure of heterogeneous aquifers based on a potential diffusion model, characterized in that: The following steps are involved: Step 1: Obtain the prior distribution of borehole data and large-scale lithology and structural parameters of the aquifer, randomly generate lithology and structural samples of the aquifer, and normalize the data; Step 2: Set initial and boundary conditions, use groundwater flow and solute transport simulation software to predict the concentration distribution field and hydraulic head distribution field at multiple times based on the different aquifer lithology structures obtained in step 1, obtain hydraulic head and concentration distribution field sample data, and normalize the data at the same time; Step 3: Based on the aquifer lithology sample obtained in step 1, the variational autoencoder is trained to use low-dimensional latent random variables to represent the high-dimensional aquifer lithology; Step 4: Input the aquifer lithology samples obtained in step 1 into the variational autoencoder trained in step 3 in sequence to obtain the corresponding low-dimensional latent random variable samples; Step 5: Using the low-dimensional potential random variable samples obtained in step 4 as training data, and the head and concentration distribution field data corresponding to the lithological structure of each aquifer obtained in step 2 as image condition constraints, the denoised diffusion probability model under the image constraints is trained so that it can predict the corresponding denoised potential random variables based on the input low-dimensional potential random variables under the constraints of the head and concentration distribution fields; Step 6: Based on the site water head and concentration observation data, use the interpolation method to obtain the water head and concentration distribution field and normalize them; Step 7: Randomly generate a potential random variable, use the site water head and concentration distribution field obtained in step 6 as conditional constraints, and input them into the denoised diffusion probability model trained in step 5 to predict the corresponding denoised potential random variable; Step 8: Input the denoised latent random variable predicted in step 7 into the variational autoencoder trained in step 3, denormalize the output result, and predict the lithology of the aquifer at the site.
2. The method for identifying the lithofacies structure of a heterogeneous aquifer based on a potential diffusion model according to claim 1, characterized in that: Step 1 uses exponential kriging simulation based on the analytical solution of transition probability to generate the aquifer lithology structure. The analytical solution of transition probability is: ; In formula (1), yes The distance between the lithology i and the The probability of the lithology being j, is the volume fraction of lithology i, N is the number of lithology, is the Kronecker function, Is the lithology i The average extension length in the direction, .
3. The method for identifying lithofacies structure of heterogeneous aquifers based on a potential diffusion model according to claim 1, characterized in that: The data normalization in step 1 and step 2 is to scale the data range to [-1, 1], where the normalization calculation formulas for lithology, hydraulic head and concentration distribution field parameters are: ; In formula (2): and Respectively represent the lithology, hydraulic head and concentration values before and after normalization at grid k, and Represent the minimum and maximum values of lithology, hydraulic head and concentration in all training samples, respectively.
4. The method for identifying lithofacies structure of heterogeneous aquifers based on a potential diffusion model according to claim 3, characterized in that: The data normalization in step 6 is to scale the data range to [-1, 1], and the normalization formula used is formula (2).
5. The method for identifying lithofacies structure of heterogeneous aquifers based on potential diffusion model according to claim 1, characterized in that: The length and width of the potential random variable in step 4 are both 1 / 4 of the input lithology structure.
6. The method for identifying lithofacies structure of heterogeneous aquifers based on a potential diffusion model according to claim 1, characterized in that: The loss function used in the variational autoencoder training in step 3 includes reconstruction loss and adversarial loss, and its expression is as follows: ; In formula (3), K represents the batch size. is the lithological structure of the ith input, is the lithological structure reconstructed by the variational autoencoder, is the predicted output of the discriminator for the reconstructed lithology structure, is the weight that controls the adversarial loss in the training of the generator in the variational autoencoder.
7. The method for identifying lithofacies structure of heterogeneous aquifers based on potential diffusion model according to claim 1, characterized in that: The denoising diffusion probability model training in step 5 uses the mean square error as the loss function, and its expression is as follows: ; In formula (4), K represents the batch size. is the predicted value of the underlying random variable by the denoised diffusion probability model, is the actual underlying random variable.
8. The method for identifying lithofacies structure of heterogeneous aquifers based on potential diffusion model according to claim 1, characterized in that: The learning rate of the training process of the variational autoencoder and the denoising diffusion probability model in step 5 uses a dynamic adjustment strategy, and the expression of the learning rate decay strategy is: ; In formula (5) represents the current learning rate, represents the updated learning rate, Represents the learning rate decay coefficient.
9. The method for identifying the lithofacies structure of a heterogeneous aquifer based on a potential diffusion model according to claim 1, characterized in that: The denoising diffusion probability model in step 5 includes two stages, namely, a noise diffusion stage and a reverse denoising stage, when predicting potential random variables; In the noise diffusion stage, a linear noise scheduler is used to gradually add noise to the potential random variables obtained in step 4. The noise scheduler defines the noise coefficient , the noise figure increases linearly with time, from Start to Finally, at each time step, the noise coefficient is defined as: ; in, and denote the initial and final noise levels, respectively, and T is the total number of time steps; Under the action of the linear noise scheduler, the forward process equation for adding noise during the training process in step 5 is: ; in, is the noise latent variable at time t, is the original latent variable, is standard Gaussian noise, Represents the cumulative product of noise factors from step 0 to step t.
10. The method for identifying lithofacies structure of heterogeneous aquifers based on potential diffusion model according to claim 1, characterized in that: In step 7, under the same head and concentration distribution field constraints, different denoised latent random variables are input to generate latent random variables, which are then input into the variational autoencoder according to step 8 to obtain different aquifer lithology structures, thereby realizing uncertainty analysis of the aquifer lithology structure.
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