Underground water flow and solute transport prediction method based on potential diffusion model

Abstract

The invention belongs to the technical field of groundwater flow and solute transport prediction, and provides a potential diffusion model-based groundwater flow and solute transport prediction method, which comprises the following steps of: generating a lithologic structure sample of an aquifer by using a random algorithm; obtaining a corresponding water head and concentration distribution field sample; generating a corresponding low-dimensional potential random variable sample; training a denoising diffusion probability model with conditional constraints based on the low-dimensional potential random variable sample and the water-bearing stratum lithologic structure sample; randomly generating potential random variables, giving a lithologic structure of an aquifer, and inputting the lithologic structure into the trained de-noising diffusion probability model; the predicted potential random variables are input into the trained variational auto-encoder; according to the method, the lithologic structure parameters of the aquifer and the given initial and boundary conditions can be utilized, the corresponding water head and the concentration distribution field are output by inputting different lithologic structures of the aquifer, and rapid prediction of underground water flow and solute migration simulation is achieved.

Description

Technical Field

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

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

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

[0004] In recent years, potential diffusion models, as a new generation of generative artificial intelligence models, have shown significant advantages in processing complex spatial distributions and simulating nonlinear characteristics. Compared with traditional numerical models, this prediction technology based on deep learning 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 new solutions for the practical application of hydrogeology and environmental science. Summary of the invention

[0005] In order 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: A method for predicting groundwater flow and solute transport based on a potential diffusion model comprises the following steps: Step 1: Obtain the prior distribution of aquifer lithology parameters and generate aquifer lithology samples using random simulation methods; Step 2: Based on 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 head and concentration distribution field corresponding to different aquifer lithology structures, establish the 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.

[0006] Furthermore, the random simulation method in step 1 is to adopt an indicator kriging simulation algorithm based on the analytical solution of the transition probability.

[0007] Furthermore, the control equation of the solute transport simulation model in step 2 for pollutant migration in a steady-state flow field is as follows: ; In formula (2), is the solute concentration, For time, is the hydrodynamic diffusion tensor, is the pore water velocity, is the sink / source term.

[0008] Furthermore, 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 (3): 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.

[0009] Furthermore, 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.

[0010] 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: ; 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.

[0011] 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: ; 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.

[0012] Furthermore, the learning rate of the training process of the variational autoencoder and the 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.

[0013] The present invention has the following beneficial effects: the present invention can utilize the aquifer lithology 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, thereby realizing rapid prediction of groundwater flow and solute transport simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of the potential diffusion model structure for water flow and solute transport prediction proposed in the present invention. DETAILED DESCRIPTION

[0015] The following will be combined with the embodiments of the present invention Figure 1-Figure 2, 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.

[0016] Step 1: Based on the site prior data, obtain the prior distribution of the aquifer lithology parameters and use the random simulation method to generate a large number of aquifer lithology samples; 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 sample, run the groundwater flow and solute transport simulation, obtain the head and concentration distribution field corresponding to different aquifer lithology, establish the 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: After the training is completed, the water head and concentration distribution field training samples are sequentially input into the trained variational autoencoder to obtain the corresponding low-dimensional potential random variable samples; Step 5: Use the low-dimensional potential random variable samples generated in step 4 as training samples, use the aquifer lithology and structure samples as conditional constraints, train the conditionally constrained denoising diffusion probability model, and 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 potential random variables predicted in step 6 into the variational autoencoder trained in step 3 to generate the water head and concentration distribution field, and perform anti-normalization. The water head and concentration distribution field obtained are the results of the simulation of groundwater flow and solute transport under the initial and boundary conditions set in step 2 for the aquifer lithology structure selected in step 6; Preferably, the aquifer lithology structural parameters in step 1 are mainly: volume ratios of different lithologies and average extension lengths in all directions; Preferably, the training samples in steps 1 and 2 are stored and processed in the form of image pixel values; 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; 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: ; 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, .

[0017] 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; 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 is solved using TOUGHREACT simulation software: ; In formula (2), is the solute concentration, For time, is the hydrodynamic diffusion tensor, is the pore water velocity, is the sink / source term.

[0018] Preferably, the water 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 the water head and concentration distribution field parameters are: ; In formula (3): and Respectively represent the water head or concentration value before and after normalization at grid i, and Respectively represent the minimum and maximum values ​​of water head or concentration in all training samples; 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; 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: ; In formula (4), K represents the batch size. is the head and concentration 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; 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 water head and concentration distribution field generated by the decoder, instead of classifying the entire image, but classifying each local area, so as to avoid excessive attention to the global information of the image, and pay more attention to the local details of the image, so as to improve the accuracy of the water head and concentration distribution field reconstructed by the variational autoencoder.

[0019] Preferably, the conditionally constrained denoising diffusion probability model training in step 5 uses The loss function is expressed 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 potential 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, rather than 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 predicted results of the surrogate model and the actual results. The calculation formula is shown in formula (5); Preferably, the variational autoencoder and denoising diffusion probability model in steps 3 and 5 both adopt residual network and self-attention mechanism; Preferably, when training the denoising diffusion probability model in step 5, in order to achieve rapid prediction of the water head and concentration distribution field, an exponential noise scheduler is used in 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 is defined as: ; In formula (6) is a hyperparameter that controls exponential decay, is the noise intensity at step t, and Indicates the maximum and minimum noise levels that have been set.

[0020] 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: ; In formula (7) 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.

[0021] Preferably, the parameter samples in step 1 are all obtained by sampling using Latin hypercube.

[0022] In order 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 two lithology types, high permeability and low permeability. Five drilling data are virtually set at the same time. Based on these data, the lithology structure of the aquifer is generated. Then, based on the lithology structure of the aquifer, a tracer test scenario is simulated using TOUGHREACT solute transport simulation software to generate a head distribution field corresponding to one moment and a concentration distribution field at five moments. Based on these data, the method proposed by the present invention is tested. In this case: The prior distribution of the aquifer structural parameters in step 1 is shown in Table 1. The Latin hypercube sampling method is used to extract 10,000 sets of aquifer lithology and structure parameters. The indicator kriging model program is automatically called in sequence through the program to obtain 10,000 lithology and structure training samples, which are saved as npy files: 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 six moments; In step 3, the 10,000 water 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, and the adversarial loss weight coefficient is Set to 0.1, the number of iterations is 40; Table 1. Lithological and structural geostatistical parameters 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] In step 4, 10,000 sets of water head and concentration distribution field data are sequentially input into the variational autoencoder trained in step 3 to obtain 10,000 potential random variables; In step 5, the 10,000 potential random variables obtained in step 4 are used as training samples to train the denoising diffusion probability model under the image constraint. The initial learning rate and decay coefficient of the denoising diffusion probability model under the image constraint are set to 0.0001 and 0.5 respectively, and the number of iterations is 100; In step 6, a potential random variable is first randomly input, an aquifer lithology structure is selected as a conditional constraint, and the potential random variable and the aquifer lithology structure are simultaneously input into the denoised diffusion probability model under the trained image constraint condition to predict the denoised potential random variable; In step 7, the denoised latent random variables predicted in step 6 are input into the variational autoencoder trained in step 3, so as to obtain the head distribution field at one moment and the concentration distribution field at five moments corresponding to the lithology structure of the aquifer, preferably denormalized; It can be seen that the method for predicting groundwater flow and solute transport based on the potential diffusion model provided by the present invention can utilize the aquifer lithology parameters and the given initial and boundary conditions, and by inputting different aquifer lithology structures, output the corresponding head and concentration distribution fields at multiple moments, thereby realizing rapid prediction of groundwater flow and solute transport simulation.

[0023] 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 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; 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 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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