Underground water reactive solute transport inversion method, device and system and storage medium

Abstract

The invention discloses an underground water reactive solute transport inversion method, device and system and a storage medium, and the method comprises the steps: building a potential nonlinear mapping relation between a low-fidelity substitution model and a high-fidelity numerical model through a series neural network based on a multi-fidelity substitution model adaptive updating strategy through a deep neural network; in an iterative inversion process, a training sample data set is adaptively updated, and the prediction precision of the substitution model in a real parameter posterior distribution region is gradually improved, so that a final inversion identification result of model parameters is improved. By adopting the technical scheme of the invention, an accurate model parameter inversion recognition result can be given under the condition of limited forward model implementation times, and the calculation efficiency and the prediction precision are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of groundwater inversion, and particularly relates to a method and device, a system and a storage medium for inverting reactive solute transport in groundwater. Background Art

[0002] The reactive solute transport model in groundwater is an important tool for predicting the migration and evolution laws of material components in the aquifer environment, and is of great significance for groundwater resource management and ecological environment protection. However, the parameter conditions of the reactive solute transport model in actual research are usually difficult to accurately obtain, and it is necessary to use easily obtained observation data to identify unknown model parameter information through inverse simulation. The tandem neural network algorithm (TNNA) is a model parameter inversion framework based on deep learning, and the prediction accuracy of the surrogate model in the region of the true posterior distribution of parameters is the key to ensuring the reliability of the inversion results. Establishing a surrogate model for multi-component reactive solute transport simulation based on the prior distribution of model parameters requires a large number of training samples, and it is difficult to ensure the prediction accuracy of the surrogate model in the region of the true posterior distribution. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method and device, a system and a storage medium for inverting reactive solute transport in groundwater.

[0004] To achieve the above object, the present invention adopts the following technical solutions:

[0005] A method for inverting reactive solute transport in groundwater, comprising:

[0006] Step S1, establishing a numerical model of reactive solute transport in groundwater according to the research object, clarifying the model system response variable and the model parameter m to be inverted; obtaining the training sample data set D of the surrogate model L , and establishing an initial surrogate model according to this data set; taking the current initial surrogate model as the low-fidelity surrogate model F before iteration LF ;

[0007] Step S2, using the observation data and the current F LF model, establishing an inversion simulation constraint condition, and obtaining a random inversion result data set M of the model parameter through tandem stochastic inverse mapping modeling iter =[m iter(1) ,…,m iter(n) ; wherein, the model parameter is the reactive solute transport model parameter in groundwater;

[0008] Step S3, setting a local sampling interval according to the range of the model parameter values reflected by the current model parameter inversion result data set M iter , and then obtaining the preset number N locLocal parameter samples After obtaining the corresponding numerical model output add {M loc ; Y loc} to the training sample dataset to obtain the updated training sample dataset D L ;

[0009] Step S4: Based on the updated training sample dataset D L obtained in step S3 and the current low-fidelity surrogate model F LF , establish a multi-fidelity surrogate model F MF ;

[0010] Step S5: Use the multi-fidelity surrogate model F MF obtained in step S4 as the forward simulation solver, combine the observed data and the inversion constraint conditions in step S2 to update the weight parameters of the inverse neural network model again, and obtain the random inversion result dataset M iter = [m iter(1) , …, m iter(n) ;

[0011] Step S6: Determine whether the current model parameter inversion result meets the termination condition; if it meets the termination condition, terminate the iterative loop process and use the current M iter as the final random inversion result of the model parameters; if it does not meet the termination condition, return to step S3 to continue the iterative calculation.

[0012] Preferably, in step S2, the inversion constraint conditions for realizing the random inverse mapping modeling are as follows:

[0013]

[0014] In the above formula, N prior represents the initial estimation of N prior groups of model parameters sampled based on the prior information of the model parameters; ε represents the random perturbation term; and respectively represent the inverses of the variance matrices of the system response observed data and the model parameter prior; represents the i-th prior sample of the model parameter; F Forward (·) represents the surrogate model used in the current inversion (the initial surrogate model before the iterative loop and the multi-fidelity surrogate model during the iterative loop).

[0015] Preferably, in step S2, establish an inverse neural network based on the constraint conditions of the inversion simulation After that, the random inversion results of the model parameters are generated based on the Monte Carlo method with different random perturbation terms ε.

[0016] Preferably, the multi-fidelity surrogate model F in step S4 MF has an input layer dimension equal to the sum of the observation data dimension and the model parameter dimension (N m +N obs ), and an output layer dimension consistent with the observation data dimension (N obs ). Its general functional form is expressed as (y LF represents the output of the current low-fidelity surrogate model). According to the updated dataset D obtained in step S3 L a loss function based on the L-1 norm constraint condition is established:

[0017]

[0018] In the formula: N represents the number of samples in the dataset D L , y i represents the output of the numerical model established in step S1.

[0019] After training according to the constraint conditions in the above loss function, the multi-fidelity surrogate model is established

[0020] Preferably, during the iterative loop process of executing step S4 - step S6, a multi-fidelity neural network structure with a multi-level nested structure will be constructed, and its functional expression is as follows:

[0021] F MF(i) =F MF-DNN (m,…F MF-DNN (m,F0(m),θ MF(1) ),θ MF(2) ),…θ MF(i) )

[0022] In the formula, F MF-DNN (·) represents the neural network operator adopted by the multi-fidelity surrogate model; F0(·) represents the neural network operator of the initial surrogate model established in step S1; θ MF(i) represents the neural network weight parameter of the multi-fidelity surrogate model in the i-th iteration.

[0023] Preferably, the termination condition in step S6 will be set from the following two aspects:

[0024] Ⅰ. According to the model parameters with the best fitting effect in the current M iter compare their corresponding forward neural network prediction results The error between the model output value of the high-fidelity numerical model and whether it is less than a preset error value;

[0025] II. Whether the number of iteration loops reaches the preset maximum number of iterations.

[0026] The fitting effect in the above I is based on the root mean square error between the actual observed data to judge.

[0027] The present invention also provides a device for groundwater reactive solute transport inversion, including:

[0028] The first processing module is used to establish a numerical model of groundwater reactive solute transport according to the research object, clarify the model system response variables and the model parameters m to be inverted; obtain the training sample data set D of the surrogate model L , and establish an initial surrogate model according to this data set; use the current initial surrogate model as the low-fidelity surrogate model F before iteration LF ;

[0029] The second processing module is used to use the observed data and the current F LF model to establish inversion simulation constraint conditions, and obtain a stochastic inversion result data set M of the model parameters through serial stochastic inverse mapping modeling iter =[m iter(1) ,…,m iter(n) ; where the model parameters are the groundwater reactive solute transport model parameters;

[0030] The third processing module is used to set a local sampling interval according to the range of the model parameter values reflected by the current model parameter inversion result data set M iter , and then obtain a preset number N loc of local parameter samples After obtaining the corresponding numerical model output , supplement {M loc ; Y loc} to the training sample data set to obtain an updated training sample data set D L ;

[0031] The fourth processing module is used to establish a multi-fidelity surrogate model F L according to the updated training sample data set D obtained by the third processing module and the current low-fidelity surrogate model F LF ; MF ;

[0032] The fifth processing module is used to use the multi-fidelity surrogate model F MF obtained in step S4 as a forward simulation solver, combined with the observed data and the inversion constraint condition in step S2, update the weight parameters of the reverse neural network model again, and obtain the random inversion result dataset M of the model parameters again iter =[m iter(1) ,…,m iter(n) ;

[0033] The sixth processing module is used to determine whether the current inversion result of the model parameters meets the termination condition; if the termination condition is met, terminate the iterative loop process, and use the current M iter as the final random inversion result of the model parameters; if the termination condition is not met, return to the third processing module to continue the iterative calculation

[0034] The present invention also provides a groundwater reactive solute transport inversion system, including: a memory and a processor, where a computer program run by the processor is stored on the memory, and the computer program executes the groundwater reactive solute transport inversion method when run by the processor

[0035] The present invention also provides a storage medium, on which a computer program is stored, and the computer program executes the groundwater reactive solute transport inversion method when running

[0036] Based on the tandem neural network with multi-fidelity surrogate model adaptive update strategy (TNNA-AUS-MF), the present invention uses a deep neural network to establish a potential non-linear mapping relationship between a low-fidelity surrogate model and a high-fidelity numerical model, adaptively updates the training sample dataset during the iterative inversion process, and gradually improves the prediction accuracy of the surrogate model in the posterior distribution region of the true parameters, thereby improving the final inversion recognition result of the model parameters. At the same time, the present invention introduces random perturbations when establishing the reverse mapping neural network, so as to realize the random inversion solution of the model parameters, and can analyze the uncertainty of the inversion result while giving the optimal parameter estimation BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts

[0038] Figure 1 is a flowchart of a groundwater reactive solute transport inversion method according to an embodiment of the present invention

[0039] Figure 2 is an inversion flowchart of a tandem neural network based on an initial surrogate model

[0040] Figure 3 Flow chart of the cascaded neural network inversion based on the multi-fidelity surrogate model:

[0041] Figure 4 Flow chart of another groundwater reactive solute transport inversion method according to an embodiment of the present invention;

[0042] Figure 5 Structural schematic diagram of the reverse neural network model;

[0043] Figure 6 Schematic diagram of the conceptual model of the hypothetical cation exchange experiment;

[0044] Figure 7 For the distribution diagram of the observed data of various components in the case under the ε-N(1,0.05 2 ) noise scenario. Detailed implementation manners

[0045] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0046] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0047] Embodiment 1:

[0048] As Figures 1 to 3 shown, an embodiment of the present invention provides a groundwater reactive solute transport inversion method, including:

[0049] Step 1. Establish a numerical model and obtain a training sample data set: For the groundwater reactive solute transport problem, establish a corresponding numerical model based on TOUGHREACT, and clarify the parameters to be inverted in the model and the simulated output of the observed data corresponding to the concentrations of each component (N m and N obs respectively represent the dimensions of the unknown parameters of the model and the observed data vector); at the same time, according to the prior information (the value range of each dimension) of the parameters m to be inverted in the model, use Latin hypercube sampling to obtain N groups of parameter sampling data sets M = [m1,..., m N ; and use the numerical model in this step to obtain the corresponding model response output Y = [y1,..., y N, thus establishing the training sample dataset D of the initial surrogate model L ={M; Y};

[0050] Step 2. Establish the initial surrogate model: Construct a neural network model with an input layer dimension of N m , and an output layer dimension of N obs as the initial surrogate model y = F LF (m, θ LF ); Combine with the dataset D obtained in Step 1 L to establish a loss function based on the L-1 norm constraint condition, update and train the weight parameter θ LF . When the constraint condition of the loss function is satisfied, the initial surrogate model of the numerical model in Step 1 is established Take this surrogate model as the forward neural network model y = F before iteration Forward (m);

[0051] Step 3. Serial neural network inversion based on the initial surrogate model: Construct a reverse neural network model with an input layer dimension of N obs , and an output layer dimension of N m for inverse solution of model parameters ( represents the model response observed data); Substitute the m output by F Reverse into the forward neural network model F in Step 2 Forward (m), and establish a constraint based on the L2 norm between the surrogate model output y obtained therefrom and the actual observed data . At the same time, establish a regularization term based on the prior sample parameter set, and consider the sum of constraints with multiple different random perturbation coefficients ε in the constraint as the loss function of the reverse neural network; After optimizing and training the weight parameters of the reverse neural network with the goal of minimizing this loss function, use ( represents the weight parameters of the reverse neural network that satisfy the constraint conditions after training) to perform different ε perturbations; Obtain the model parameter random inversion result dataset M iter =[m iter(1) ,…,m iter(n) ;

[0052] Step 4. Establish a multi-fidelity dataset based on locally adaptive updated sampling: Set a local sampling interval according to the model parameter value range reflected by the current model parameter inversion result dataset M iter , and then obtain a preset number N loc of local parameter samples and use the numerical model established in Step 1 to calculate the corresponding numerical simulation output Combine Mloc and Y loc Supplement it to the training sample dataset in Step 1 to obtain the updated dataset D L .

[0053] Step Five: Establish a multi-fidelity surrogate model: Establish a neural network model with an input dimension of N m +N obs , and an output dimension of N obs as the basic structure of the multi-fidelity surrogate model y = F MF (m, y LF , θ MF ),(where y LF represents the output of the current low-fidelity surrogate model). According to the updated dataset D L obtained in Step Four, establish a loss function based on the L-1 norm constraint condition, update and train the weight parameter θ MF . When the constraint condition of the loss function is satisfied, the multi-fidelity surrogate model is established

[0054] Step Six: Series neural network inversion based on the multi-fidelity surrogate model: Use the multi-fidelity surrogate model obtained in the current Step Five as the forward neural network in the series neural network, combine it with the actual observed data and the inversion constraint condition in Step Three to update the weight parameters of the reverse neural network model again, and obtain the random inversion result dataset M iter = [m iter(1) , …, m iter(n) ;

[0055] Step Seven: Termination condition judgment: Judge whether the current model parameter inversion result satisfies the termination condition; if it satisfies the termination condition, terminate the iterative loop process and use the current M iter as the final random inversion result of the model parameters; if it does not satisfy the termination condition, return to Step S3 to continue the iterative calculation. The termination condition will be set from the following two aspects:

[0056] Ⅰ. According to the model parameter iter with the best fitting effect in the current M , compare whether the error between its corresponding forward neural network prediction result and the model output value of the high-fidelity numerical model is less than the preset error value;

[0057] Ⅱ. Whether the number of iterative loops reaches the preset maximum number of iterations

[0058] The fitting effect in the above Ⅰ is based on Judged by the root mean square error between the actual observed data.

[0059] Example 2:

[0060] As Figure 4 shown, an embodiment of the present invention provides a method for inverse analysis of reactive solute transport in groundwater, including:

[0061] Step S1: Establish a numerical model of reactive solute transport in groundwater according to the research object, clarify the response variables of the model system and the model parameters m to be inversed; obtain the training sample data set D L of the surrogate model, and establish an initial surrogate model according to this data set; take the current initial surrogate model as the low-fidelity surrogate model F LF before iteration;

[0062] Step S2: Use the observed data and the current F LF model to establish an inverse simulation constraint condition, and obtain a stochastic inverse result data set M iter = [m iter(1) , …, m iter(n) through cascaded stochastic inverse mapping modeling; where the model parameters are the reactive solute transport model parameters in groundwater;

[0063] Step S3: Set a local sampling interval according to the range of model parameter values reflected by the current model parameter inverse result data set M iter , and then obtain a preset number N loc of local parameter samples After obtaining the corresponding numerical model output , supplement {M loc ; Y loc} to the training sample data set to obtain an updated training sample data set D L ;

[0064] Step S4: According to the updated training sample data set D L obtained in step S3 and the current low-fidelity surrogate model F LF , establish a multi-fidelity surrogate model F MF ;

[0065] Step S5: Use the multi-fidelity surrogate model F MF obtained in step S4 as the forward simulation solver, combine the observed data and the inverse constraint condition in step S2 to update the weight parameters of the inverse neural network model again, and re-obtain the stochastic inverse result data set M iter = [m iter(1) , …, miter(n) ;

[0066] Step S6: Determine whether the current model parameter inversion result meets the termination condition; if it meets the termination condition, terminate the iterative loop process, and use the current M iter as the final random model parameter inversion result; if it does not meet the termination condition, return to Step S3 to continue the iterative calculation.

[0067] As an implementation manner of the embodiment of the present invention, in Step S1, the initial surrogate model is established based on the initial sampling of the prior distribution of the groundwater reactive solute transport model parameters (abbreviation: model parameters) to establish the non-linear mapping relationship between the input parameters and the model response:

[0068]

[0069] where F HF (·) and F Forward (·) respectively represent the operators of the numerical model and the surrogate model; θ Forward represents the trainable parameters of the forward neural network model; represents the numerical simulation result of the RTM model for the model parameter m. The main part of the neural network structure adopted in the embodiment of the present invention is a deep residual convolutional neural network. The input layer is in vector form. By connecting a fully connected layer, the parameter vector of any dimension is mapped into a fixed vector of 1600 dimensions. Then, the fixed vector is transformed into a rectangular data of 80×80 and input into the residual neural network model of the main part. The model output layer is a vector with the same dimension as the observed data, and the activation function used is Sigmoid. The model parameters and the model response vary depending on the model of the specific scenario. Taking the example in this article as an example, there are 7 parameters to be inverted, which are: the cation exchange selectivity coefficient K Na / K and K Na / Ca ; the initial concentrations of Na + and K + ; and the boundary concentrations of Ca 2+ and Cl - ; and and the cation exchange capacity CEC. The model response is the Ca 2+ , Na + , K + , Cl - of the four simulated components.

[0070] The training sample data of the initial surrogate model is several groups of model parameters (m i ) and the model output (y iThe set of []. They will perform Latin hypercube sampling according to the prior distribution of the model parameters and then obtain the results through numerical simulation. The weight parameters of the deep neural network are obtained by iterative optimization of the loss function designed according to the research objectives through the error backpropagation algorithm. The loss function of the initial surrogate model in the embodiments of the present invention will be established based on the L1 norm according to the sample data set:

[0071]

[0072] Wherein, represents, m i and respectively represent the model input and model output of the i-th group of samples in the training sample set, and N Train represents the number of training samples in the data set.

[0073] As an implementation manner of the embodiments of the present invention, in step S2, the basic idea of the inverse mapping of the neural network is to hope to establish a deep neural network model mapping with as the input variable and m as the output variable through deep learning The embodiments of the present invention name it the reverse neural network, that is:

[0074]

[0075] Wherein, F Reverse represents the mathematical operator of the reverse neural network; θ Reverse represents the trainable parameters of the reverse neural network.

[0076] The structure of the reverse neural network model is as Figure 5 shown, which is a fully connected neural network including two hidden layers. The number of neurons in each hidden layer is 512. The activation function for the connection between the hidden layers is Swish, and the activation function for the output layer is Sigmoid. The loss function of the reverse neural network is as follows:

[0077]

[0078] Wherein, represents the weight parameters of the reverse neural network when the inversion constraint conditions are satisfied; σ i represents the standard deviation of the i-th observed data; represents the i-th element value in the output vector of the forward neural network F Forward ; represents the i-th element in the observed data vector. After completing the training of the reverse neural network, the inversion result of the model parameters can be obtained according to the following formula:

[0079]

[0080] As an implementation manner of an embodiment of the present invention, in step S4, the multi-fidelity surrogate model aims to use a neural network model to establish a surrogate model with a relatively low current accuracy (low-fidelity model F LF ) and a high-fidelity numerical model F HF (·). The input vector of F MF (·) will be composed of the model parameter m and the output F LF (m) of its corresponding low-fidelity model. The general form of the multi-fidelity surrogate model is expressed as:

[0081] F HF (m) ≈ F MF (m, F LF (m), θ MF )

[0082] F MF (·) adopts the same loss function as the initial surrogate model during the training process. The structure of the neural network will adopt a fully connected neural network model, and the model structure is the same as that adopted by the inverse neural network.

[0083] The idea of the multi-fidelity surrogate model is based on the fact that there is a certain correlation between the low-fidelity model and the high-fidelity model, and the non-linear degree of this correlation is generally lower than the correlation of the high-fidelity model itself. Therefore, the systematic approximation error between them usually shows a certain regularity. These regular systematic errors can be characterized by adding a small number of additional samples and combining a new neural network model. The position distribution of the additional points to some extent determines in which regions the prediction accuracy of the multi-fidelity surrogate model can be improved. Under the condition that the true solution region of the model parameters is unknown in the embodiment of the present invention, the sample distribution in the region near the true solution of the model parameters will be gradually improved by adaptively updating the sampling strategy, so as to finally improve the prediction accuracy of the surrogate model in this region.

[0084] As an implementation manner of an embodiment of the present invention, in step S6, the termination condition will be set from the following two aspects:

[0085] Ⅰ. According to the model parameter iter with the best fitting effect in the current M , compare whether the error between its corresponding forward neural network prediction result and the model output value of the high-fidelity numerical model is less than the preset error value;

[0086] Ⅱ. Whether the number of iteration cycles reaches the preset maximum number of iterations.

[0087] The embodiment of the present invention proposes an adaptive update series neural network inversion algorithm based on multi-fidelity surrogate models (TNNA-AUS-MF). TNNA-AUS-MF will establish a non-linear mapping relationship between the low-fidelity surrogate model and the high-fidelity numerical model after each adaptive sampling. This is used to reduce the approximation error of the surrogate model near the true parameter value, thereby gradually improving the inversion result of the model parameters.

[0088] The embodiment of the present invention will be verified through a hypothetical cation exchange experiment model case. As Figure 6 shown, this case is a 0.08 m long porous medium cylinder. The average porosity and density of the filled medium are 0.3 and 2650 kg / m 3 respectively. All pores in the porous medium are in a saturated water state. The initial solute components in the solution are 1 mmol / L sodium nitrate (NaNO3) and 0.2 mmol / L potassium nitrate (KNO3). A CaCl2 solution with a concentration of 0.6 mmol / L is injected at a rate of 0.1 m / h at one end of the experimental device. During the injection of the CaCl2 solution, the following two main cation exchange reactions occur in the experimental column solution:

[0089] Na + +K-X = K + +Na-X

[0090] Na + +0.5Ca-X2 = 0.5Ca 2+ +Na-X

[0091] where X represents the cation exchange site. The known cation exchange capacity (CEC) in the model is 0.01779 meq / 100 g. The cation exchange selectivity coefficients of K + and Ca 2+ relative to Na + are K Na / K = 0.1995 and K Na / Ca = 0.3981 respectively.

[0092] Based on the above information, a numerical model is established using TOUGHREACT to simulate the concentration changes of four ionic components, namely Ca 2+ , Na + , K + , and Cl - , in the solution over time. During the modeling process, the porous medium cylinder is equally divided into 20 grid cells, and the length of each cell is Δx = 0.04 m. According to the upstream weighting rule in TOUGHREACT, the equivalent dispersion coefficient is α = Δx / 2 = 0.002 m. The main components set in the model, their initial concentrations, and boundary concentrations are shown in Table 1.

[0093] Table 1

[0094]

[0095] Using the above model, the variation of the concentrations of four ionic components with time at the midpoint of the solute was simulated. Based on the simulation results, Gaussian white noise with a standard deviation of 0.05 was added as the observed data (as Figure 7 shown). A total of 7 parameters to be inverted were set in this model, namely: the cation exchange selectivity coefficients K Na / K and K Na / Ca ; the initial concentrations of Na + and K + ; and the boundary concentrations of Ca 2+ and Cl - ; and and the cation exchange capacity CEC. The prior intervals of these parameters are shown in Table 2. Based on the observed data of the four simulated components in Figure 3 , the 7 unknown parameters in Table 2 will be inversely identified.

[0096] Table 2

[0097]

[0098] Example 3:

[0099] The embodiment of the present invention also provides a device for inverse analysis of reactive solute transport in groundwater, including:

[0100] A first processing module, configured to establish a numerical model of reactive solute transport in groundwater according to the research object, clarify the response variables of the model system and the model parameters m to be inverted; obtain the training sample data set D L of the surrogate model, and establish an initial surrogate model according to this data set; use the current initial surrogate model as the low-fidelity surrogate model F LF before iteration;

[0101] A second processing module, configured to use the observed data and the current F LF model to establish an inverse simulation constraint condition, and obtain a stochastic inverse result data set M iter =[m iter(1) ,…,m iter(n) of the model parameters through cascaded stochastic inverse mapping modeling; wherein, the model parameters are the reactive solute transport model parameters in groundwater;

[0102] A third processing module, configured to use the current model parameter inverse result data set M iterSet a local sampling interval for the range of values of the model parameters to be reflected, and then obtain a preset number N loc of local parameter samples After obtaining the corresponding numerical model output then supplement {M loc ; Y loc} to the training sample dataset to obtain an updated training sample dataset D L ;

[0103] The fourth processing module is used to establish a multi-fidelity surrogate model F L based on the updated training sample dataset D LF obtained by the third processing module and the current low-fidelity surrogate model F MF ;

[0104] The fifth processing module is used to use the multi-fidelity surrogate model F MF obtained in step S4 as a forward simulation solver, and jointly use the observed data and the inversion constraint conditions in step S2 to update the weight parameters of the inverse neural network model again, and re-obtain the random inversion result dataset M iter = [m iter(1) , …, m iter(n) ;

[0105] The sixth processing module is used to determine whether the current model parameter inversion result meets the termination condition; if it meets the termination condition, terminate the iterative loop process and use the current M iter as the final random inversion result of the model parameters; if it does not meet the termination condition, return to the third processing module to continue the iterative calculation.

[0106] As an implementation manner of this embodiment of the present invention, in the second module, the inversion constraint conditions for implementing random inverse mapping modeling are as follows:

[0107]

[0108] In the above formula, N prior represents the initial estimate of N prior groups of model parameters sampled based on the prior information of the model parameters; ε represents a random perturbation term; and respectively represent the inverses of the covariance matrices of the system response observation data and the model parameter prior; represents the i-th model parameter prior sample; F Forward (·) represents the surrogate model used in the current inversion (the initial surrogate model before the iterative loop and the multi-fidelity surrogate model during the iterative loop).

[0109] As an implementation manner of an embodiment of the present invention, in the second module, a reverse neural network is established based on the constraint conditions of the inversion simulation. After that, the random inversion results of the model parameters are generated based on the Monte Carlo method through different random perturbation terms ε.

[0110] As an implementation manner of an embodiment of the present invention, in the fourth module, the input layer dimension of the multi-fidelity surrogate model F MF is the sum of the observation data dimension and the model parameter dimension (N m +N obs ), and the output layer dimension is the same as the observation data dimension (N obs ). Its general functional expression is (y LF represents the output of the current low-fidelity surrogate model). According to the updated data set D L obtained in step S3, a loss function based on the L-1 norm constraint condition is established:

[0111]

[0112] In the formula: N represents the number of samples in the data set D L , y i represents the output of the numerical model established in step S1.

[0113] After training according to the constraint conditions in the above loss function, the multi-fidelity surrogate model is established

[0114] As an implementation manner of an embodiment of the present invention, during the iterative loop process of executing the fourth to sixth modules, a multi-fidelity neural network structure with a multi-level nested structure will be constructed, and its functional expression is as follows:

[0115] F MF(i) =F MF-DNN (m,…F MF-DNN (m,F0(m),θ MF(1) ),θ MF(2) ),…θ MF(i) )

[0116] In the formula, F MF-DNN (·) represents the neural network operator adopted by the multi-fidelity surrogate model; F0(·) represents the neural network operator of the initial surrogate model established in step S1; θ MF(i) represents the neural network weight parameter of the multi-fidelity surrogate model in the i-th iteration.

[0117] As an implementation manner of an embodiment of the present invention, in the sixth module, the termination condition will be set from the following two aspects:

[0118] Ⅰ. According to the current M iter The model parameters with the best fitting effect in Compare the corresponding forward neural network prediction results With the model output values of the high-fidelity numerical model Whether the error between them is less than the preset error value;

[0119] Ⅱ. Whether the number of iteration cycles reaches the preset maximum number of iterations.

[0120] The fitting effect in the above Ⅰ is judged according to The root mean square error between the actual observed data.

[0121] Example 4:

[0122] An embodiment of the present invention further provides a groundwater reactive solute transport inversion system, including: a memory and a processor, a computer program is stored on the memory and run by the processor, and the computer program executes the groundwater reactive solute transport inversion method when run by the processor.

[0123] Example 5:

[0124] An embodiment of the present invention further provides a storage medium, a computer program is stored on the storage medium, and the computer program executes the groundwater reactive solute transport inversion method when running.

[0125] The above embodiments are only descriptions of the preferred embodiments 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 and improvements made by those of ordinary skill in the art to the technical solution of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for inverse modeling of reactive solute transport in groundwater, characterized in that, Including: Step S1: Establish a numerical model for reactive solute transport in groundwater based on the research object, and clarify the response variables of the model system and the model parameters m to be inverted; Obtain the training sample dataset D of the surrogate model L , and establish an initial surrogate model based on this dataset; use the current initial surrogate model as the low-fidelity surrogate model F before iteration LF ; Step S2: Use the observed data and the current F LF model to establish the inversion simulation constraint conditions, and obtain the stochastic inversion result dataset M iter = [m iter(1) , …, m iter(n) ; where the model parameters are the groundwater reactive solute transport model parameters; Step S3: Invert the result data set M with the current model parameters iter Set a local sampling interval based on the range of model parameter values reflected by loc and then obtain local parameter samples of a preset number N After obtaining the corresponding numerical model output add {M loc ; Y loc} to the training sample data set to obtain an updated training sample data set D L ; Step S4. Based on the updated training sample dataset D obtained in step S3 L and the current low-fidelity surrogate model F LF , establish a multi-fidelity surrogate model F MF ; Step S5: Using the multi-fidelity surrogate model F obtained in Step S4 MF as the forward simulation solver, combining the observed data and the inversion constraint conditions in Step S2, update the weight parameters of the inverse neural network model again, and re-obtain the random inversion result dataset M iter = [m iter(1) , …, m iter(n) ; Step S6: Determine whether the current inversion result of the model parameters meets the termination condition; if it meets the termination condition, terminate the iterative loop process, and use the current M iter as the final random inversion result of the model parameters; if it does not meet the termination condition, return to step S3 to continue the iterative calculation.

2. The groundwater reactive solute transport inversion method according to claim 1, wherein In step S2, the inversion constraint conditions for implementing the stochastic inverse mapping modeling are as follows: In the above formula, N prior represents the initial estimate of N prior sets of model parameters sampled based on the prior information of the model parameters; ε represents the random disturbance term; and respectively represent the inverses of the covariance matrices of the system response observation data and the prior of the model parameters; represents the i-th prior sample of the model parameter; F Forward (·) represents the surrogate model adopted during the current inversion (the initial surrogate model before the iterative loop and the multi-fidelity surrogate model during the iterative loop).

3. The groundwater reactive solute transport inversion method according to claim 1, wherein In step S2, a reverse neural network is established based on the constraint conditions of the inversion simulation. After that, the random inversion results of the model parameters are generated based on the Monte Carlo method with different random perturbation terms ε.

4. The groundwater reactive solute transport inversion method according to claim 1, wherein The multi-fidelity surrogate model F in step S4 MF The dimension of the input layer is the sum of the dimension of the observed data and the dimension of the model parameters (N m + N obs ), and the dimension of the output layer is the same as the dimension of the observed data (N obs ). Its general functional form is expressed as (y LF represents the output of the current low-fidelity surrogate model). According to the updated dataset D obtained in step S3 L Establish a loss function based on the L-1 norm constraint condition: Where: N represents the number of samples in the data set D L , and y i represents the output of the numerical model established in step S1. After training according to the constraint conditions in the above loss function, a multi-fidelity surrogate model is established.

5. The groundwater reactive solute transport inversion method according to claim 1, characterized in that During the iterative loop process of executing steps S4 - S6, a multi-fidelity neural network structure with a multi-level nested structure will be constructed, and its functional expression is as follows: F MF(i) = F MF-DNN (m, … F MF-DNN (m, F0(m), θ MF(1) ), θ MF(2) ), … θ MF(i) ) Where, F MF-DNN (·) represents the neural network operator adopted by the multi-fidelity surrogate model; F0(·) represents the neural network operator of the initial surrogate model established in step S1; θ MF(i) represents the neural network weight parameter of the multi-fidelity surrogate model at the i-th iteration.

6. The groundwater reactive solute transport inversion method according to claim 1, wherein In step S6, the termination conditions will be set from the following two aspects: Ⅰ. According to the current M iter The model parameters with the best fitting effect in Compare the corresponding forward neural network prediction results with the model output values of the high-fidelity numerical model to see if the error between them is less than the preset error value; II. Whether the number of iterative loops reaches the preset maximum number of iterations. The fitting effect in the above I is judged according to the root mean square error between and the actual observed data.

7. A groundwater reactive solute transport inversion device for implementing the groundwater reactive solute transport inversion method according to any one of claims 1 to 6, characterized in that Including: The first processing module is used to establish a numerical model for reactive solute transport in groundwater based on the research object, and clarify the response variables of the model system and the model parameters m to be inverted; Obtain the training sample dataset D of the surrogate model L , and establish an initial surrogate model based on this dataset; take the current initial surrogate model as the low-fidelity surrogate model F before iteration LF ; The second processing module is used to utilize the observation data and the current F LF model to establish inversion simulation constraint conditions, and obtain a stochastic inversion result dataset M iter =[m iter(1) ,…,m iter(n) through cascaded stochastic inverse mapping modeling; wherein, the model parameters are groundwater reactive solute transport model parameters; The third processing module is used to invert the result data set M with the current model parameters iter Set a local sampling interval according to the range of model parameter values reflected by loc and then obtain local parameter samples of a preset number N After obtaining the corresponding numerical model output Supplement {M loc ; Y loc} to the training sample data set to obtain an updated training sample data set D L ; The fourth processing module is used to establish a multi-fidelity surrogate model F based on the updated training sample dataset D obtained by the third processing module L and the current low-fidelity surrogate model F LF , and establish a multi-fidelity surrogate model F MF ; The fifth processing module is used to use the multi-fidelity surrogate model F obtained in step S4 MF as a forward simulation solver, combine the observation data and the inversion constraint conditions in step S2 to update the weight parameters of the inverse neural network model again, and obtain a random inversion result data set M of the model parameters again iter =[m iter(1) ,…,m iter(n) ; The sixth processing module is used to determine whether the current inversion result of the model parameters meets the termination condition; if the termination condition is met, the iterative loop process is terminated, and the current M iter is used as the final random inversion result of the model parameters; if the termination condition is not met, the process returns to step S3 to continue the iterative calculation.

8. A reactive solute transport inversion system for groundwater, characterized in that Including: A memory and a processor, where a computer program run by the processor is stored on the memory, and the computer program, when run by the processor, executes the method for inverting reactive solute transport in groundwater according to any one of claims 1 - 6.

9. A storage medium, characterized in that, A computer program is stored on the storage medium, and the computer program, when running, executes the method for inverting reactive solute transport in groundwater according to any one of claims 1 - 6.

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