A method for generating heterogeneous structures by coupling latent diffusion model and stochastic model

Abstract

The present invention belongs to the technical field of generating heterogeneous structures of aquifers, and provides a method for generating heterogeneous structures by coupling a potential diffusion model and a random model. The present invention can utilize the prior distribution of aquifer structural parameters and the geostatistical parameters of permeability coefficients corresponding to different lithologies to generate heterogeneous structures of aquifers at different scales, and can constrain the spatial distribution of permeability coefficients according to the spatial distribution of large-scale lithological structures, thereby ensuring that the spatial distribution characteristics of permeability coefficients within different lithologies meet the given geostatistical distribution of permeability coefficients of different lithologies, thereby realizing the reasonable characterization of heterogeneous structures of aquifers at different scales.

Description

Technical Field

[0001] The invention belongs to the technical field of aquifer heterogeneous structure generation, and in particular relates to a heterogeneous structure generation method for coupling a potential diffusion model and a random model. Background Art

[0002] Aquifer structures are highly complex in space and have multi-scale characteristics, such as large-scale lithofacies distribution and permeability distribution within each lithofacies. The heterogeneity at different scales has different effects on groundwater flow and solute transport processes.

[0003] In geological bodies, heterogeneous features at different scales constitute the multi-scale structure of aquifers. Accurate modeling and simulation of this structure are crucial for applications such as groundwater protection, pollution control, and resource exploitation.

[0004] Traditional aquifer modeling methods mostly rely on stochastic modeling (such as random field models) or geostatistical methods, and can only generate heterogeneous structures of aquifers at a single scale. In recent years, the potential diffusion model has been used as a new generation of image generation models, providing new possibilities for generating complex geological structures. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a method for generating a heterogeneous structure by coupling a potential diffusion model and a random model to solve the problems in the prior art. The technical solution adopted by the present invention is:

[0006] A method for generating heterogeneous structures by coupling a potential diffusion model and a stochastic model comprises the following steps:

[0007] Step 1: Obtain the prior distribution of large-scale lithology structural parameters of the aquifer and the geostatistical parameters of the permeability coefficients of different lithologies contained in the aquifer;

[0008] Step 2: Randomly generate aquifer large-scale lithology structure parameter samples, input them into the indicator kriging simulation program, generate the corresponding aquifer large-scale lithology structure, and obtain large-scale lithology structure training samples;

[0009] Step 3: Using the Karhunen-Loeve expansion of the geostatistical parameters of the permeability coefficients of different lithologies contained in each aquifer, the permeability coefficient distribution is randomly generated for different lithologies in the generated large-scale lithology structure, and the small-scale permeability coefficient field training samples are generated. At the same time, both the large-scale lithology structure and the small-scale permeability coefficient field are normalized;

[0010] Step 4: Use the variational autoencoder to learn and train the training data composed of large-scale lithology and structure samples, and represent the large-scale lithology and structure samples with low-dimensional latent random variables;

[0011] Step 5: After the training is completed, the large-scale lithology structure training samples are sequentially input into the trained variational autoencoder to obtain low-dimensional potential random variable samples for generating large-scale lithology structure;

[0012] Step 6: The low-dimensional potential random variable samples used to generate large-scale lithological structures are used as training samples and input into the unconditionally constrained denoising diffusion probability model to train the unconditionally constrained denoising diffusion probability model to achieve accurate prediction of the low-dimensional potential random variables;

[0013] Step 7: Randomly generate a potential random variable and input it into the unconditionally constrained denoising diffusion probability model obtained by training in step 6 to predict the corresponding denoised potential random variable;

[0014] Step 8: Input the denoised latent random variables predicted in step 7 into the variational autoencoder obtained in step 4 to generate the corresponding large-scale lithological structure and perform denormalization;

[0015] Step 9: Using a variational autoencoder to learn and train the training data consisting of the small-scale permeability field training samples, the small-scale permeability field training samples are represented by low-dimensional latent random variables;

[0016] Step 10: After the training is completed, the small-scale permeability coefficient field is sequentially input into the trained variational autoencoder to obtain a low-dimensional latent random variable sample for generating the small-scale permeability coefficient field;

[0017] Step 11: The low-dimensional potential random variable samples used to generate the small-scale permeability field are used as training samples, and the large-scale lithology structure training samples are used as conditional constraints. They are input into the conditionally constrained denoising diffusion probability model, and the conditionally constrained denoising diffusion probability model is trained to achieve accurate prediction of the low-dimensional potential random variables.

[0018] Step 12: randomly generate a potential random variable, input the generated potential random variable and the large-scale lithology structure into the conditionally constrained denoising diffusion probability model obtained by training in step 11, and predict the corresponding denoised potential random variable;

[0019] Step 13: Input the denoised latent random variable predicted in step 12 into the variational autoencoder obtained in step 9 to generate the corresponding small-scale permeability field, and perform denormalization.

[0020] Furthermore, the indicator kriging simulation in step 2 is based on the analytical solution of transition probability, and its analytical solution is obtained by the lithofacies volume ratio and the average extension length. The analytical solution of transition probability is shown in formula (1):

[0021] ;

[0022] In formula (1), yes The distance from lithofacies i in the direction The probability of lithofacies j is, is the volume fraction of lithofacies i, N is the number of lithofacies, is the Kronecker function, Is the lithofacies The average extension length in the direction, .

[0023] Furthermore, the Karhunen-Loeve algorithm is used in step 2 to generate the permeability field. A random simulation is performed based on the mean, variance and correlation length of the logarithmic permeability corresponding to the two different lithologies in the aquifer lithology structure obtained in step 2. The formula used in the random simulation is:

[0024] ;

[0025] in, and represents any two points in space, represents the variance of the logarithmic permeability of the lithology, and They represent the correlation lengths of the lithology permeability in the X and Y directions, respectively.

[0026] Furthermore, the data normalization in step 3 is to scale the data range to [-1, 1], where the normalization calculation formulas for lithology and permeability coefficient distribution field parameters are:

[0027] ;

[0028] In formula (3): and Respectively represent the lithology and permeability values ​​before and after normalization at grid k, and They represent the minimum and maximum values ​​of lithology and permeability at grid k in the training samples, respectively.

[0029] Furthermore, the length and width of the potential random variables in step 4 and step 9 are both 1 / 4 of the input large-scale lithology structure or permeability distribution field.

[0030] Furthermore, the loss functions used in the variational autoencoder training in steps 4 and 9 include reconstruction loss and adversarial loss, and their expressions are as follows:

[0031] ;

[0032] In formula (4), 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 training of the generator in the variational autoencoder.

[0033] Furthermore, the denoising diffusion probability model training in steps 6 and 11 uses a loss function, which is expressed as follows:

[0034] ;

[0035] In formula (5) is the true value of the potential random variable of the ith sample, is the predicted value of the latent random variable for the ith sample, and n is the number of samples in the batch.

[0036] Furthermore, the learning rate of the training process of the variational autoencoder and the denoising diffusion probability model in step 4, step 6, step 9, and step 11 uses a dynamic adjustment strategy, and the expression of the learning rate decay strategy is:

[0037] ;

[0038] In formula (6) represents the current learning rate, represents the updated learning rate, Represents the decay rate, and epoch is the current training round.

[0039] Furthermore, the spatial distribution of the small-scale aquifer permeability distribution field obtained in step 13 is constrained by the lithology spatial distribution knot in the large-scale lithology structure input in step 12, that is, the geostatistical parameters of the permeability values ​​within different lithologies conform to the given geostatistical parameters of the permeability values ​​of different lithologies.

[0040] The present invention has the following beneficial effects: the present invention utilizes the prior distribution of aquifer structural parameters and the geostatistical parameters of permeability coefficients corresponding to different lithologies to generate large-scale lithological structures, and can constrain the spatial distribution of permeability coefficients based on the spatial distribution of large-scale lithological structures, thereby ensuring that the spatial distribution characteristics of permeability coefficients within different lithologies meet the given geostatistical distribution of permeability coefficients of different lithologies, thereby achieving a reasonable characterization of the heterogeneous structure of multi-scale aquifers. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0042] Figure 2 This is a schematic diagram of the network structure of the aquifer structure generation model proposed in the present invention;

[0043] Figure 3 Aquifer lithology structure and permeability distribution field generated randomly. 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 present invention utilizes the prior distribution of aquifer structural parameters and the geostatistical parameters of permeability coefficients corresponding to different lithologies to generate aquifer heterogeneous structures at different scales. At the same time, the method can constrain the spatial distribution of permeability coefficients based on the spatial distribution of large-scale lithological structures, ensuring that the spatial distribution characteristics of permeability coefficients within different lithologies conform to the preset geostatistical distribution of lithological permeability coefficients, thereby achieving a reasonable characterization of aquifer heterogeneous structures at different scales.

[0046] A method for generating heterogeneous structures by coupling a potential diffusion model and a stochastic model, the method comprising the following steps:

[0047] Step 1: Based on the site drilling data, obtain the prior distribution of the large-scale lithology structural parameters of the aquifer, and use the field lithology samples to measure the permeability coefficient multiple times on the same lithology samples using laboratory permeability tests to obtain the geostatistical parameters of the permeability coefficient corresponding to different lithology types;

[0048] Step 2: Based on the prior distribution of the large-scale lithology structure parameters of the aquifer, randomly generate large-scale lithology structure parameter samples of the aquifer, input them into the indicator kriging simulation program, generate the corresponding large-scale lithology structure of the aquifer, and obtain large-scale lithology structure training samples;

[0049] Step 3: Using the Karhunen-Loeve expansion of the small-scale permeability geostatistical parameters based on each lithology, the permeability distribution of different lithologies in the generated large-scale lithology structure is randomly generated to generate small-scale permeability field training samples, and both the large-scale lithology structure and the small-scale permeability field are normalized at the same time;

[0050] Step 4: Use the variational autoencoder to learn and train the training data composed of large-scale lithology and structure samples, and represent the large-scale lithology and structure samples with low-dimensional latent random variables;

[0051] Step 5: After the training is completed, the large-scale lithology structure training samples are sequentially input into the trained variational autoencoder to obtain low-dimensional potential random variable samples for generating large-scale lithology structure;

[0052] Step 6: The low-dimensional potential random variable samples used to generate large-scale lithological structures are used as training samples and input into the unconditionally constrained denoising diffusion probability model to train the unconditionally constrained denoising diffusion probability model to achieve accurate prediction of the low-dimensional potential random variables;

[0053] Step 7: Randomly generate a potential random variable and input it into the unconditionally constrained denoising diffusion probability model obtained by training in step 6 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 obtained in step 4 to generate the corresponding large-scale lithological structure and perform denormalization;

[0055] Step 9: Using a variational autoencoder to learn and train the training data consisting of the small-scale permeability field training samples, the small-scale permeability field training samples are represented by low-dimensional latent random variables;

[0056] Step 10: After the training is completed, the small-scale permeability coefficient field is sequentially input into the trained variational autoencoder to obtain a low-dimensional latent random variable sample for generating the small-scale permeability coefficient field;

[0057] Step 11: The low-dimensional potential random variable samples used to generate the small-scale permeability field are used as training samples, and the large-scale lithology structure training samples are used as conditional constraints. They are input into the conditionally constrained denoising diffusion probability model, and the conditionally constrained denoising diffusion probability model is trained to achieve accurate prediction of the low-dimensional potential random variables.

[0058] Step 12: randomly generate a potential random variable, input the generated potential random variable and the large-scale lithology structure into the conditionally constrained denoising diffusion probability model obtained by training in step 11, and predict the corresponding denoised potential random variable;

[0059] Step 13: Input the denoised latent random variable predicted in step 12 into the variational autoencoder obtained in step 9 to generate the corresponding small-scale permeability field and perform inverse normalization processing;

[0060] Preferably, the aquifer lithology structural parameters in step 1 are mainly: volume ratios of different lithologies and average extension lengths in all directions, and the permeability geostatistical parameters corresponding to each lithology type are mainly: mean, variance and correlation length of permeability coefficients of different lithologies;

[0061] Preferably, the training samples in step 2 are stored and processed in the form of image pixel values;

[0062] Preferably, in step 2, a Python program is written to automatically generate an input file for indicator kriging simulation based on transition probability according to the aquifer structure parameter sample, generate the corresponding large-scale aquifer lithology structure, and based on the generated large-scale lithology structure and permeability geostatistical parameters, randomly generate permeability distribution inside different lithologies, and automatically generate small-scale permeability field training samples.

[0063] Preferably, step 2 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:

[0064] ;

[0065] In formula (1), yes The distance from lithofacies i in the direction The probability of lithofacies j is, is the volume fraction of lithofacies i, N is the number of lithofacies, is the Kronecker function, Is the lithofacies The average extension length in the direction, .

[0066] Preferably, in step 2, the Karhunen-Loeve expansion algorithm is used to generate the permeability field, and a random simulation is performed based on the mean, variance and correlation length of the logarithmic permeability corresponding to the two different lithologies in the aquifer lithology structure obtained in step 2. The formula used in the random simulation is:

[0067] ;

[0068] In formula (2), and represents any two points in space, represents the variance of the logarithmic permeability of the lithology, and They represent the correlation lengths of the lithology permeability in the X and Y directions, respectively.

[0069] Preferably, the training sample data in step 3 needs to be normalized to scale the data range to [-1, 1], wherein the normalized calculation formulas for lithology and permeability field parameters are:

[0070] ;

[0071] In formula (3): and Respectively represent the lithology and permeability values ​​before and after normalization at grid k, and They represent the minimum and maximum values ​​of lithology and permeability at grid k in the training sample respectively;

[0072] Preferably, the length and width of the potential random variables in steps 4 and 9 are both 1 / 4 of the input large-scale lithology structure or permeability coefficient distribution field;

[0073] Preferably, the loss function used in the variational autoencoder training in steps 4 and 9 includes reconstruction loss and adversarial loss, and the expressions thereof are as follows:

[0074] ;

[0075] In formula (4), 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 training of the generator in the variational autoencoder.

[0076] Preferably, in the training process of the denoising diffusion probability model in step 11, the scale and number of channels of the large-scale lithology structure need to be transformed into the same as the potential random variable through the convolution layer. Preferably, the denoising diffusion probability model training in steps 6 and 11 uses the L2 loss function, which is expressed as follows:

[0077] ;

[0078] In formula (5) is the true value of the potential random variable of the ith sample, is the predicted value of the latent random variable for the ith sample, and n is the number of samples in the batch.

[0079] Preferably, the variational autoencoder in steps 4 and 9 and the denoising diffusion probability model in steps 6 and 11 are trained by combining an early stopping strategy with optimal model preservation. That is, during the training process, the loss value of the validation set is monitored, and the training is stopped in advance when the validation set loss has not been significantly improved for several consecutive epochs, thereby avoiding overfitting, and the model parameters corresponding to the epoch with the smallest validation set loss are verified to ensure that the model with the best performance on the validation set is finally used.

[0080] Preferably, when training the denoising diffusion probability model in step 5, a cosine noise scheduler is used in the noise diffusion stage. At the beginning, the noise changes slowly, and as time goes by, the noise increases. The cosine curve has a smooth transition, which makes the introduction of noise more stable and helps to achieve the stable generation of the aquifer lithology structure and permeability coefficient field. The cosine noise scheduler is used to adjust the noise coefficient at each time step. is defined as:

[0081] ;

[0082] In formula (6) is the total number of steps, is the noise intensity at step t, and Indicates the maximum and minimum noise levels that have been set.

[0083] Preferably, the learning rate of the training process of the variational autoencoder and the denoising diffusion probability model in steps 4, 6, 9, and 11 uses a dynamic adjustment strategy to accelerate convergence and avoid falling into a local minimum. The expression of the learning rate decay strategy is:

[0084] ;

[0085] In formula (7) represents the current learning rate, represents the updated learning rate, Represents the decay rate, and epoch is the current training round.

[0086] Preferably, the parameter samples in step 2 are all obtained by sampling using Latin hypercube.

[0087] The present invention provides a test case for the generation of a two-dimensional multi-scale aquifer structure. This case sets 5 hypothetical borehole data, which contain two lithology types, named high permeability lithology and low permeability lithology, respectively, and sets relevant geological statistical parameters of lithofacies distribution and permeability coefficient distribution. Based on these data, the generation of large-scale aquifer lithology structure and small-scale permeability coefficient field is achieved;

[0088] In this case:

[0089] The prior distribution of aquifer structural parameters and geostatistical parameters of permeability distribution in step 1 are shown in Table 1:

[0090] In step 2, 10,000 sets of aquifer lithology and structural parameters were extracted using the Latin hypercube sampling method;

[0091] Step 3, the indicator kriging model program and the Karhunen-Loeve expansion program are automatically called in sequence through the program, and the generated results are finally saved in the form of numpy arrays, and finally 10,000 large-scale lithology structure training samples and the corresponding 10,000 small-scale permeability field training samples are obtained, and normalized;

[0092] In step 4, the large-scale lithology training samples are used as training samples to train the variational autoencoder for large-scale lithology generation. 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;

[0093] Table 1. Geostatistical parameters of lithofacies distribution and permeability distribution

[0094] 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] Mean logarithmic permeability 4 0 Variance of logarithmic permeability 0.5 0.5 Permeability correlation length 15 10

[0095] In step 5, 10,000 large-scale lithology and structure training samples are sequentially input into the variational autoencoder trained in step 4 to obtain 10,000 potential random variables;

[0096] In step 6, the 10,000 potential random variables obtained in step 5 are used as training samples to train the unconditionally constrained denoising diffusion probability model. The initial learning rate and decay coefficient of the unconditionally constrained denoising diffusion probability model are set to 0.00005 and 0.5, respectively, and the number of iterations is 100.

[0097] Steps 7-8 are the large-scale lithology structure generation process. First, two potential random variables are randomly input, and the denoised potential random variables are predicted using the trained unconditionally constrained denoising diffusion probability model. The denoised potential random variables are input into the variational autoencoder trained in step 4 to obtain two different large-scale lithology structures, and then denormalized.

[0098] In step 9, the variational autoencoder is trained using the 10,000 small-scale permeability field training samples obtained in step 2;

[0099] In step 10, 10,000 small-scale permeability field training samples are sequentially input into the variational autoencoder trained in step 9 to obtain 10,000 potential random variables;

[0100] In step 11, the 10,000 potential random variables obtained in step 10 are used as training samples, and the 10,000 large-scale lithology structure training samples obtained in step 2 are used as conditional constraints to train the denoised diffusion probability model with conditional constraints. The initial learning rate and decay coefficient of the denoised diffusion probability model with conditional constraints are set to 0.0001 and 0.5, respectively, and the number of iterations is 100;

[0101] Steps 12-13 are the generation process of the small-scale permeability field. The two large-scale lithology structures generated in steps 7-8 are used as conditional constraints, and two potential random variables are randomly input. The two potential random variables are input into the trained conditionally constrained denoising diffusion probability model to predict the denoised potential random variables. The denoised potential random variables are input into the variational autoencoder trained in step 9, and two different small-scale permeability fields are obtained, and then inverse normalized.

[0102] It can be seen that the method for generating heterogeneous structures by coupling potential diffusion models and random models provided by the present invention utilizes the prior distribution of aquifer structural parameters and the geostatistical parameters of permeability corresponding to different lithologies to generate large-scale lithological structures, and can constrain the spatial distribution of permeability according to the spatial distribution of large-scale lithological structures, to ensure that the spatial distribution characteristics of permeability within different lithologies meet the given geostatistical distribution of permeability of different lithologies, thereby realizing the reasonable characterization of multi-scale aquifer heterogeneous structures.

[0103] 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 generating heterogeneous structures by coupling a potential diffusion model and a random model, characterized in that: The following steps are involved: Step 1: Obtain the prior distribution of large-scale lithology structural parameters of the aquifer and the geostatistical parameters of the permeability coefficients of different lithologies contained in the aquifer; Step 2: Randomly generate aquifer large-scale lithology structure parameter samples, input them into the indicator kriging simulation program, generate the corresponding aquifer large-scale lithology structure, and obtain large-scale lithology structure training samples; Step 3: Using the Karhunen-Loeve expansion of the geostatistical parameters of the permeability coefficients of different lithologies contained in each aquifer, the permeability coefficient distribution is randomly generated for different lithologies in the generated large-scale lithology structure, and the small-scale permeability coefficient field training samples are generated. At the same time, both the large-scale lithology structure and the small-scale permeability coefficient field are normalized; Step 4: Use the variational autoencoder to learn and train the training data composed of large-scale lithology and structure samples, and represent the large-scale lithology and structure samples with low-dimensional latent random variables; Step 5: After the training is completed, the large-scale lithology structure training samples are sequentially input into the trained variational autoencoder to obtain low-dimensional potential random variable samples for generating large-scale lithology structure; Step 6: The low-dimensional potential random variable samples used to generate large-scale lithological structures are used as training samples and input into the unconditionally constrained denoising diffusion probability model to train the unconditionally constrained denoising diffusion probability model to achieve accurate prediction of the low-dimensional potential random variables; Step 7: Randomly generate a potential random variable and input it into the unconditionally constrained denoising diffusion probability model obtained by training in step 6 to predict the corresponding denoised potential random variable; Step 8: Input the denoised latent random variables predicted in step 7 into the variational autoencoder obtained in step 4 to generate the corresponding large-scale lithological structure and perform denormalization; Step 9: Using a variational autoencoder to learn and train the training data consisting of the small-scale permeability field training samples, the small-scale permeability field training samples are represented by low-dimensional latent random variables; Step 10: After the training is completed, the small-scale permeability coefficient field is sequentially input into the trained variational autoencoder to obtain a low-dimensional latent random variable sample for generating the small-scale permeability coefficient field; Step 11: The low-dimensional potential random variable samples used to generate the small-scale permeability field are used as training samples, and the large-scale lithology structure training samples are used as conditional constraints. They are input into the conditionally constrained denoising diffusion probability model, and the conditionally constrained denoising diffusion probability model is trained to achieve accurate prediction of the low-dimensional potential random variables. Step 12: randomly generate a potential random variable, input the generated potential random variable and the large-scale lithology structure into the conditionally constrained denoising diffusion probability model obtained by training in step 11, and predict the corresponding denoised potential random variable; Step 13: Input the denoised latent random variable predicted in step 12 into the variational autoencoder obtained in step 9 to generate the corresponding small-scale permeability field, and perform denormalization.

2. The method for generating a heterogeneous structure by coupling a potential diffusion model and a random model according to claim 1, characterized in that: The indicator kriging simulation in step 2 is based on the analytical solution of transition probability, and its analytical solution is obtained by the lithofacies volume ratio and the average extension length. The analytical solution of transition probability is shown in formula (1): ； In formula (1), yes The distance from lithofacies i in the direction The probability of lithofacies j is, is the volume fraction of lithofacies i, N is the number of lithofacies, is the Kronecker function, Is the lithofacies The average extension length in the direction, .

3. The method for generating a heterogeneous structure by coupling a potential diffusion model and a random model according to claim 1, characterized in that: In step 2, the Karhunen-Loeve algorithm is used to generate the permeability field. Based on the mean, variance and correlation length of the logarithmic permeability corresponding to the two different lithologies in the aquifer lithology structure obtained in step 2, random simulation is performed. The formula used for random simulation is: ； in, and represents any two points in space, represents the variance of the logarithmic permeability of the lithology, and They represent the correlation lengths of the lithology permeability in the X and Y directions, respectively.

4. The method for generating a heterogeneous structure by coupling a potential diffusion model and a random model according to claim 1, characterized in that: The data normalization in step 3 is to scale the data range to [-1, 1], where the normalization calculation formulas for lithology and permeability coefficient distribution field parameters are: ； In formula (3): and Respectively represent the lithology and permeability values ​​before and after normalization at grid k, and They represent the minimum and maximum values ​​of lithology and permeability at grid k in the training samples, respectively.

5. The method for generating a heterogeneous structure by coupling a potential diffusion model and a random model according to claim 1, characterized in that: The length and width of the potential random variables in steps 4 and 9 are both 1 / 4 of the input large-scale lithology structure or permeability distribution field.

6. The method for generating a heterogeneous structure by coupling a potential diffusion model and a random model according to claim 1, characterized in that: The loss functions used in the variational autoencoder training in steps 4 and 9 include reconstruction loss and adversarial loss, and their expressions are as follows: ； In formula (4), 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 training of the generator in the variational autoencoder.

7. The method for generating a heterogeneous structure by coupling a potential diffusion model and a random model according to claim 1, characterized in that: The loss function used in the denoising diffusion probability model training in steps 6 and 11 is expressed as follows: ； In formula (5) is the true value of the potential random variable of the ith sample, is the predicted value of the latent random variable for the ith sample, and n is the number of samples in the batch.

8. The method for generating a heterogeneous structure by coupling a potential diffusion model and a random model according to claim 1, characterized in that: The learning rate of the training process of the variational autoencoder and denoising diffusion probability model in step 4, step 6, step 9, and step 11 uses a dynamic adjustment strategy, and the expression of the learning rate decay strategy is: ； In formula (6) represents the current learning rate, represents the updated learning rate, Represents the decay rate, and epoch is the current training round.

9. The method for generating a heterogeneous structure by coupling a potential diffusion model and a random model according to claim 1, characterized in that: The spatial distribution of the small-scale aquifer permeability distribution field obtained in step 13 is constrained by the lithology spatial distribution knot in the large-scale lithology structure input in step 12, that is, the geostatistical parameters of the permeability values ​​within different lithologies conform to the given geostatistical parameters of the permeability of different lithologies.

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