A groundwater flow and solute transport prediction method based on a latent diffusion model

Abstract

The present invention belongs to the technical field of groundwater flow and solute transport prediction, and provides a method for predicting groundwater flow and solute transport based on a latent diffusion model, including: generating aquifer lithology structure samples by using a random algorithm; obtaining corresponding head and concentration distribution field samples; generating corresponding low-dimensional latent random variable samples; training a conditional constrained denoising diffusion probability model based on the low-dimensional latent random variable samples and the aquifer lithology structure samples; randomly generating latent random variables, given the aquifer lithology structure, and inputting them into the trained denoising diffusion probability model; inputting the predicted latent random variables into the trained variational autoencoder; The present invention can utilize the aquifer lithology structure parameters and the given initial and boundary conditions, and by inputting different aquifer lithology structures, output the corresponding head and concentration distribution fields, realizing the rapid prediction of groundwater flow and solute transport simulation.

Description

Technical Field

[0001] The present invention belongs to the technical field of groundwater flow and solute transport prediction, and particularly relates to a method for predicting groundwater flow and solute transport based on a potential diffusion model. Background Art

[0002] Groundwater pollution monitoring, resource management, and pollution control rely on a profound understanding and accurate prediction of the flow and solute transport behavior.

[0003] However, traditional numerical simulation methods face challenges of high computational load and low efficiency. Especially when real-time decision support is required or rapid simulation of multiple scenarios is needed, the time-consuming nature of traditional methods limits their application scope. Achieving rapid simulation of groundwater flow and solute transport while ensuring accuracy is a key issue urgently to be solved in groundwater numerical simulation.

[0004] In recent years, as a new generation of generative artificial intelligence model, the potential diffusion model has shown significant advantages in dealing with complex spatial distributions and simulating non-linear characteristics. Compared with traditional numerical models, this deep learning-based prediction technology not only reduces the demand for computing resources but also enables rapid response, providing flexible and efficient technical support for pollution emergency treatment and groundwater management, providing users with a groundwater flow and solute transport simulation technology that combines speed and accuracy, and providing a new solution for practical applications in hydrogeology and environmental science. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a method for predicting groundwater flow and solute transport based on a potential diffusion model to solve the problems in the prior art. The technical solution adopted by the present invention is as follows:

[0006] A method for predicting groundwater flow and solute transport based on a potential diffusion model includes the following steps:

[0007] Step 1: Obtain the prior distribution of the aquifer lithological structure parameters, and use the stochastic simulation method to generate aquifer lithological structure samples;

[0008] Step 2: Set the initial and boundary conditions of the groundwater flow and solute transport simulation model, set the parameters of each grid of the groundwater flow and solute transport simulation model based on the generated aquifer lithological structure samples, run the groundwater flow and solute transport simulation, obtain the head and concentration distribution fields corresponding to different aquifer lithological structures, establish training samples for the head and concentration distribution fields, and perform normalization processing on the obtained training samples;

[0009] Step 3: Use a variational autoencoder to learn and train the head and concentration distribution field training samples obtained in Step 2, and represent the high-dimensional head and concentration distribution field with low-dimensional latent random variables;

[0010] Step 4: Input the head and concentration distribution field training samples into the trained variational autoencoder in sequence to obtain the corresponding low-dimensional latent random variable samples;

[0011] Step 5: Use the low-dimensional latent random variable samples as training samples and the aquifer lithology structure samples as conditional constraints to train a conditional denoising diffusion probability model to achieve accurate prediction of the low-dimensional latent random variables;

[0012] Step 6: Select an aquifer lithology structure and randomly generate a latent random variable. Input the generated latent random variable and the selected aquifer lithology structure into the conditional denoising diffusion probability model trained in Step 5 to predict the denoised latent random variable;

[0013] Step 7: Input the denoised latent random variable predicted in Step 6 into the variational autoencoder trained in Step 3 to generate the head and concentration distribution field, and perform inverse normalization to obtain the head and concentration distribution field, which is the result of the groundwater flow and solute transport simulation of the aquifer lithology structure selected in Step 6 under the initial and boundary conditions set in Step 2.

[0014] Further, the random simulation method in Step 1 is an indicator Kriging simulation algorithm based on the analytical solution of the transition probability.

[0015] Further, for the pollutant migration in the steady-state flow field in the solute transport simulation model in Step 2, its control equation is as follows:

[0016]

[0017] In formula (2), C is the solute concentration, t is the time, D is the hydrodynamic dispersion tensor, u is the pore water velocity, and S is the sink / source term

[0018] Further, the normalization process of the training samples in Step 2 is to scale the data range to [-1, 1]. The normalization calculation formulas for the head and concentration distribution fields are as follows:

[0019]

[0020] In formula (3): c i and respectively represent the head or concentration values before and after normalization at grid i, c min and c maxrespectively represent the minimum and maximum values of the water head or concentration in all training samples.

[0021] Further, the length and width of the latent random variable generated by the variational autoencoder in step 3 are both 1 / 4 of the input water head and concentration distribution fields.

[0022] Further, the loss function used in the training of the variational autoencoder in step 3 includes a reconstruction loss and an adversarial loss, and their expressions are as follows:

[0023]

[0024] In formula (4), K represents the batch size, and x i is the i-th input water head and concentration distribution field, is the water head and concentration distribution fields reconstructed by the variational autoencoder, is the predicted output of the discriminator for the reconstructed water head and concentration distribution fields, and λ is the weight that controls the adversarial loss in the training of the generator in the variational autoencoder.

[0025] Further, the mean square error is used as the loss function in the training of the denoising diffusion probabilistic model in step 5, and its expression is as follows:

[0026]

[0027] In formula (5), K represents the batch size, is the predicted value of the denoising diffusion probabilistic model for the latent random variable, and z is the actual latent random variable.

[0028] Further, the learning rate in the training processes of the variational autoencoder and the denoising diffusion probabilistic model in steps 3 and 5 uses a dynamic adjustment strategy to accelerate convergence and avoid falling into local minima. The expression of the learning rate decay strategy is:

[0029] l r-new = l r-current*α (6)

[0030] In formula (6), l r-current represents the current learning rate, l r-new represents the updated learning rate, and α represents the learning rate decay coefficient.

[0031] The present invention has the following beneficial effects: The present invention can utilize the aquifer lithology structure parameters and the given initial and boundary conditions, and by inputting different aquifer lithology structures, output the corresponding water head and concentration distribution fields at multiple moments, realizing the rapid prediction of groundwater flow and solute transport simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is the overall process schematic diagram of the present invention;

[0033] Figure 2 This is the schematic diagram of the potential diffusion model structure proposed by the present invention for predicting water flow and solute transport. Specific implementation manners

[0034] Next, in combination with Figure 1 - Figure 2 in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. If not specifically specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0035] Step 1: According to the prior site data, obtain the prior distribution of the aquifer lithology structure parameters, and use the stochastic simulation method to generate a large number of aquifer lithology structure samples;

[0036] Step 2: According to the site data, set the initial and boundary conditions of the groundwater flow and solute transport simulation model, set the parameters of each grid of the groundwater flow and solute transport simulation model based on the generated aquifer lithology structure samples, run the groundwater flow and solute transport simulation, obtain the head and concentration distribution fields corresponding to different aquifer lithology structures, establish the training samples of the head and concentration distribution fields, and perform normalization processing on the obtained training samples;

[0037] Step 3: Use the variational autoencoder to learn and train the training samples of the head and concentration distribution fields obtained in Step 2, and represent the high-dimensional head and concentration distribution fields with low-dimensional latent random variables;

[0038] Step 4: After the training is completed, input the training samples of the head and concentration distribution fields into the trained variational autoencoder in sequence to obtain the corresponding low-dimensional latent random variable samples;

[0039] Step 5: Use the low-dimensional latent random variable samples generated in Step 4 as training samples, and use the aquifer lithology structure samples as conditional constraints to train the conditional denoising diffusion probability model to achieve accurate prediction of the low-dimensional latent random variables;

[0040] Step 6: Select an aquifer lithology structure and randomly generate a latent random variable, input the generated latent random variable and the selected aquifer lithology structure into the conditional denoising diffusion probability model trained in Step 5 to predict the denoised latent random variable;

[0041] Step 7: Input the potentially denoised random variables predicted in Step 6 into the variational autoencoder trained in Step 3 to generate the water head and concentration distribution fields, and perform inverse normalization. The obtained water head and concentration distribution fields are the results of the groundwater flow and solute transport simulation for the aquifer lithology structure selected in Step 6 under the initial and boundary conditions set in Step 2;

[0042] Preferably, the aquifer lithology structure parameters in Step 1 are mainly: the volume ratios of different lithologies and the average extension lengths in each direction;

[0043] Preferably, the training samples in Steps 1 and 2 are both stored and processed in the form of image pixel point values;

[0044] Preferably, in Step 1, by writing a Python program, according to the aquifer structure parameter samples, the input file of the stochastic simulation program is automatically generated, and the corresponding aquifer lithology structure samples are automatically generated;

[0045] Preferably, in Step 1, the exponential Kriging simulation based on the analytical solution of the transition probability is used to generate the aquifer lithology structure, and its analytical solution of the transition probability is:

[0046]

[0047] In formula (1), t ij (h φ ) is the probability that the lithofacies at the interval h φ from the lithofacies i in the φ direction is lithofacies j, p i is the volume ratio of lithofacies i, N is the number of lithofacies, δ ij is the Kronecker function, L i,φ is the average extension length of lithofacies i in the φ direction, i, j = {1, 2, 3,..., N}.

[0048] Preferably, in Step 2, by writing a Python program, based on the generated aquifer lithology structure, the corresponding water head and concentration distribution fields are automatically simulated, and the training samples of the generated aquifer lithology structure and the corresponding water head and concentration distribution fields are automatically generated;

[0049] Preferably, the solute transport simulation model in Step 2 mainly considers the pollutant migration scenario in the steady-state flow field, and its control equation is as follows, and the TOUGHREACT simulation software is used for solution:

[0050]

[0051] In formula (2), C is the solute concentration, t is the time, D is the hydrodynamic dispersion tensor, u is the pore water velocity, and S is the sink / source term.

[0052] Preferably, the head and concentration distribution data in step 2 need to be normalized to scale the data range to [-1, 1]. The normalization calculation formulas for the head and concentration distribution field parameters are as follows:

[0053]

[0054] In formula (3): c i and respectively represent the head or concentration values before and after normalization at grid i. c min and c max respectively represent the minimum and maximum values of the head or concentration values in all training samples;

[0055] Preferably, the length and width of the latent random variable in step 3 are both 1 / 4 of the input head and concentration distribution field;

[0056] Preferably, the loss function used in the variational autoencoder training in step 3 includes a reconstruction loss and an adversarial loss, and its expression is as follows:

[0057]

[0058] In formula (4), K represents the batch size, x i is the head and concentration distribution field of the i-th input, is the image reconstructed by the variational autoencoder, is the predicted output of the discriminator for the reconstructed image, and λ is the weight that controls the adversarial loss in the training of the generator in the variational autoencoder;

[0059] Preferably, in the variational autoencoder training process in step 3, the discriminator in PatchGAN is also used to judge the authenticity of different parts of the head and concentration distribution field generated by the decoder. Instead of classifying the whole image, each local area is classified to avoid over-focusing on the global information of the image and paying more attention to the local details of the image, so as to improve the accuracy of the head and concentration distribution field reconstructed by the variational autoencoder.

[0060] Preferably, the training of the conditional denoising diffusion probability model in step 5 uses a loss function, and its expression is as follows:

[0061]

[0062] In formula (5), K represents the batch size, is the predicted value of the denoising diffusion probability model for the latent random variable, and z is the actual latent random variable. Preferably, when training the denoising diffusion probability model in step 5, an early stopping strategy is adopted, that is, the optimal parameters of the network model are retained during the training process instead of the final parameters. The application of the early stopping strategy can effectively prevent the surrogate model from overfitting during the training process. The quality of the model parameters is evaluated by the mean square error between the prediction result and the true result of the surrogate model, and its calculation formula is shown in formula (5);

[0063] Preferably, both the variational autoencoder and the denoising diffusion probability model in steps 3 and 5 adopt residual networks and self-attention mechanisms;

[0064] Preferably, when training the denoising diffusion probability model in step 5, in order to achieve rapid prediction of the water head and concentration distribution fields, an exponential noise scheduler is adopted during the noise diffusion stage, so that the distribution of data can be significantly changed in fewer time steps. At each time step, the noise coefficient β t is defined as:

[0065] β t = β min +(β max - β min )(1 * exp(-αt)) (6)

[0066] In formula (6), α is a hyperparameter controlling the exponential decay, β t is the noise intensity at the t-th step, and β max and β min represent the set maximum and minimum noise intensities.

[0067] Preferably, the learning rate in the training processes 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 local minima. The expression of the learning rate decay strategy is:

[0068] l r-new = l r-current * α (if the loss value does not decrease for q consecutive iterations) (7)

[0069] In formula (7), l r-current represents the current learning rate, l r-new represents the updated learning rate, α represents the learning rate decay coefficient, and q represents the learning rate decay tolerance times.

[0070] Preferably, the parameter samples in step 1 are all obtained by Latin hypercube sampling.

[0071] To test the performance of the present invention, the present invention provides a test case for generating a two-dimensional multi-scale aquifer structure, which includes a total of two lithology types, high permeability and low permeability. At the same time, 5 borehole data are virtually set. Based on these data, the generation of the aquifer lithology structure is realized. Then, based on this aquifer lithology structure, the TOUGHREACT solute transport simulation software is used to simulate a tracer test scenario, generating a head distribution field at a corresponding moment and concentration distribution fields at 5 moments. Based on these data, the method proposed by the present invention is tested;

[0072] In this case:

[0073] The prior distribution of the aquifer structure parameters in step 1 is shown in Table 1. 10,000 groups of aquifer lithology structure parameters are extracted by the Latin hypercube sampling method. The indicator Kriging model program is automatically called successively through the program to obtain 10,000 lithology structure training samples, which are saved as npy files:

[0074] In step 2, the 10,000 lithology structure training samples obtained in step 1 are automatically input into the TOUGHREACT simulation program through the program, and the groundwater and solute transport simulations are run to obtain the corresponding 10,000 groups of head and concentration distribution field data. Among them, the head distribution field in each group of data is the data at one moment, and the concentration distribution field is the data at 6 moments;

[0075] In step 3, the 10,000 head and concentration distribution field data obtained in step 2 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, the adversarial loss weight coefficient λ is set to 0.1, and the number of iterations is 40 times;

[0076] Table 1. Geological statistical parameters of lithology structure

[0077]

[0078]

[0079] In step 4, the 10,000 groups of head and concentration distribution field data are successively input into the variational autoencoder trained in step 3 to obtain 10,000 latent random variables;

[0080] In step 5, the 10,000 latent random variables obtained in step 4 are used as training samples to train the denoising diffusion probabilistic model under the picture constraint. The initial learning rate and decay coefficient of the denoising diffusion probabilistic model under the picture constraint are set to 0.0001 and 0.5 respectively, and the number of iterations is 100 times;

[0081] In step 6, first, by randomly inputting a latent random variable and selecting an aquifer lithology structure as a conditional constraint, the latent random variable and the aquifer lithology structure are simultaneously input into the denoising diffusion probability model under the trained image constraint conditions to predict the denoised latent random variable;

[0082] In step 7, the denoised latent random variable predicted in step 6 is input into the variational autoencoder trained in step 3, and then the head distribution field at one moment and the concentration distribution fields at five moments corresponding to the aquifer lithology structure can be obtained. It is best to perform inverse normalization;

[0083] It can be seen that a groundwater flow and solute transport prediction method based on a latent diffusion model provided by the present invention can utilize the aquifer lithology structure parameters and the given initial and boundary conditions. By inputting different aquifer lithology structures, the head and concentration distribution fields at multiple corresponding moments are output, realizing the rapid prediction of groundwater flow and solute transport simulation.

[0084] The embodiments described above are only used to describe the preferred mode of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations, variations, modifications, and substitutions made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for predicting groundwater flow and solute transport based on a potential diffusion model, characterized in that: The following steps are involved: Step 1: Obtain the prior distribution of aquifer lithology parameters and generate aquifer lithology samples using random simulation methods. The aquifer lithology samples include two types of lithology: high permeability and low permeability. Step 2: Set the initial and boundary conditions of the groundwater flow and solute transport simulation model, set the parameters of each grid of the groundwater flow and solute transport simulation model based on the generated aquifer lithology sample, run the groundwater flow and solute transport simulation, obtain the hydraulic head and concentration distribution field corresponding to different aquifer lithology, establish hydraulic head and concentration distribution field training samples, and normalize the obtained training samples; Step 3: Use the variational autoencoder to learn and train the water head and concentration distribution field training samples obtained in step 2, and represent the high-dimensional water head and concentration distribution field with low-dimensional potential random variables; Step 4: Input the water head and concentration distribution field training samples into the trained variational autoencoder in sequence to obtain the corresponding low-dimensional potential random variable samples; Step 5: Use the low-dimensional potential random variable samples as training samples and the aquifer lithology and structure samples as conditional constraints to train the conditionally constrained denoising diffusion probability model to achieve accurate prediction of the low-dimensional potential random variables; Step 6: Select an aquifer lithology structure and randomly generate a potential random variable. Input the generated potential random variable and the selected aquifer lithology structure into the conditionally constrained denoised diffusion probability model trained in step 5 to predict the denoised potential random variable. Step 7: Input the denoised latent random variables predicted in step 6 into the variational autoencoder trained in step 3 to generate the head and concentration distribution field, and perform inverse normalization to obtain the head and concentration distribution field, which is the result of the simulation of groundwater flow and solute transport of the aquifer lithology selected in step 6 under the initial and boundary conditions set in step 2.

2. A method for predicting groundwater flow and solute transport based on a potential diffusion model according to claim 1, characterized in that: The random simulation method in step 1 is to use the indicator kriging simulation algorithm based on the analytical solution of the transition probability.

3. A method for predicting groundwater flow and solute transport based on a potential diffusion model according to claim 1, characterized in that: The solute transport simulation model in step 2 has the following control equations for pollutant migration in a steady-state flow field: ； In formula (2), is the solute concentration, For time, is the hydrodynamic diffusion tensor, is the pore water velocity, is the sink / source term.

4. A method for predicting groundwater flow and solute transport based on a potential diffusion model according to claim 1, characterized in that: The training sample normalization process in step 2 is to scale the data range to [-1, 1], where the normalization calculation formulas for the water head and concentration distribution field are: ； In formula (2): and Respectively represent the water head or concentration value before and after normalization at grid i, and Represent the minimum and maximum values ​​of head or concentration in all training samples, respectively.

5. The method for predicting groundwater flow and solute transport based on a potential diffusion model according to claim 1, characterized in that: The length and width of the potential random variables generated by the variational autoencoder in step 3 are both 1 / 4 of the input water head and concentration distribution field.

6. A method for predicting groundwater flow and solute transport 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 (4), K represents the batch size. is the head and concentration distribution field of the ith input, is the water head and concentration distribution field reconstructed by the variational autoencoder, is the predicted output of the discriminator for reconstructing the water head and concentration distribution field, is the weight that controls the adversarial loss in the training of the generator in the variational autoencoder.

7. A method for predicting groundwater flow and solute transport based on a 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 (5), 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. A method for predicting groundwater flow and solute transport based on a potential diffusion 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 steps 3 and 5 uses a dynamic adjustment strategy to accelerate convergence and avoid falling into the local minimum. The expression of the learning rate decay strategy is: ； In formula (6) represents the current learning rate, represents the updated learning rate, Represents the learning rate decay coefficient.

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