Aquifer Characterization Method and System Based on Hybrid Prior Strategy and Deep Learning

Abstract

The present invention discloses an aquifer characterization method and system based on a hybrid prior strategy and deep learning. The method includes: constructing a hybrid prior set; obtaining the model outputs corresponding to each parameter sample in the hybrid prior set; subtracting each pair of the parameter samples and the corresponding model outputs in the hybrid prior set to obtain a plurality of model output differences and the corresponding parameter differences; training a deep learning model; generating an innovation vector and substituting it into the deep learning model to obtain the update vectors of each sample parameter; adding the update vectors to the original parameter prior samples to obtain an updated parameter sample set; and analyzing the aquifer parameter characterization effect and its uncertainty distribution according to the updated parameter sample set. By combining the hybrid prior strategy with deep learning, the present invention effectively improves the aquifer characterization effect under the condition of insufficient prior information and improves the solution effect of the data assimilation method for the coexisting problems of biased prior and non-Gaussian distribution challenges.

Description

Technical Field

[0001] The present invention belongs to the field of hydrogeoscience, and particularly relates to an aquifer characterization method and system based on a hybrid prior strategy and deep learning. Background Art

[0002] The heterogeneity of aquifers, especially the preferential flow phenomenon brought about by preferential flow channels in highly heterogeneous channel fields and fracture fields, has an important impact on water flow and solute transport. Considering the importance of groundwater management, characterizing the hydraulic parameter field of heterogeneous aquifers is of great significance for groundwater resource management. However, directly observing the hydraulic parameters of aquifers is often very difficult due to factors such as their spatial heterogeneity, high cost, and scale effect. In this context, data assimilation technology can provide a solution to enhance the understanding of the groundwater system by integrating indirect observation data information and model information, and has been widely used in the problem of aquifer hydraulic parameter characterization.

[0003] To address the common non-linear and non-Gaussian challenges in data assimilation, the prior art proposes a data assimilation method based on deep learning, that is, using a deep learning model to replace the Kalman update operator. Specifically, this method uses the deep learning model to learn the complex relationship between the model output difference and the parameter difference between every two sets of samples in the prior ensemble, so as to carefully capture the effective information in the prior ensemble, making the deep learning model a powerful update operator. Therefore, this method is not restricted by the Gaussian assumption, and can achieve results comparable to the benchmark algorithm in Gaussian problems, and achieve results significantly better than the benchmark algorithm in non-Gaussian problems that the benchmark algorithm cannot handle. However, most of the prior art focuses on the performance of the data assimilation method and the influence of the information content contained in the observation data on the update process from the prior distribution to the posterior distribution, lacking a systematic analysis of the influence of the setting of the prior distribution on its update effect. It is found in the prior art that considering parameter correlation in the prior distribution can greatly improve the data assimilation effect, highlighting the importance of informative prior assumptions. In the case of limited information content in the observation data, the importance of prior information is even more significant. In fact, informative priors improve the data assimilation effect by introducing more restrictions on the prior distribution of parameters. However, in many practical problems, the selected prior deviates greatly from the actual situation, reducing the data assimilation effect. In this context, the rationality of the prior distribution assumption needs to be carefully considered because its setting is often somewhat subjective. Summary of the Invention

[0004] Purpose of the invention: To address the adverse effects of biased prior assumptions on aquifer characterization, a method and system for aquifer characterization based on a hybrid prior strategy and deep learning are provided. By combining the hybrid prior strategy with deep learning, the aquifer characterization effect under conditions of insufficient prior information is effectively improved, and the data assimilation method is improved in solving the coexistence of biased priors and non-Gaussian distribution challenges. This provides a new solution for aquifer characterization under conditions of insufficient prior information or even prior knowledge deviation.

[0005] Technical solution: To achieve the above objectives, the present invention provides an aquifer characterization method based on a hybrid prior strategy and deep learning, comprising the following steps:

[0006] S1: Construct a mixed prior set consisting of parameter prior samples of different geological structure hypotheses;

[0007] S2: Run the forward model of the groundwater system to obtain the model output corresponding to each parameter sample in the hybrid prior set;

[0008] S3: Subtract all parameter samples and corresponding model outputs in the mixed prior set from each other to obtain multiple model output differences and corresponding parameter differences;

[0009] S4: Using the output difference and parameter difference obtained in step S3 as input and output respectively to train the deep learning model;

[0010] S5: Subtract the observed data from the model output of each sample in the mixed prior set to generate an innovation vector, which is then substituted into the trained deep learning model to obtain the update vector of each sample parameter;

[0011] S6: Add the updated vector to the original parameter prior sample to obtain the updated parameter sample set;

[0012] S7: Complete the aquifer parameter characterization based on the updated parameter sample set, and analyze the aquifer parameter characterization effect and the aquifer parameter uncertainty distribution.

[0013] Furthermore, the implementation of step S1 specifically includes:

[0014] Generate corresponding prior samples based on m common geological structure assumptions, , ,……, , where the superscript pm represents the mth geological structure prior hypothesis, and the subscript Indicates the number of samples in the mth prior hypothesis set;

[0015] Mix the prior sample sets of the above m types of geological structure hypotheses to obtain a mixed prior set consisting of m common geological structure hypotheses .

[0016] Further, the specific steps of step S2 include:

[0017] Substitute all samples in the mixed prior set into the groundwater system forward model, and obtain the groundwater state variables at a specified time and specified location by solving the following equation :

[0018]

[0019] where is the aquifer storage coefficient, is the source / sink term, is the position parameter, represents time; among them, the flux is solved by the following equation:

[0020]

[0021] where is the hydraulic conductivity at position ; is position, the hydraulic gradient at time ; After solving the above equations, the corresponding head simulation value can be obtained from the mixed prior set .

[0022] Further, the specific steps of step S3 include:

[0023] For the mixed prior set parameters , and the model output , subtract them pairwise to obtain the parameter differences between groups of samples and the model output differences, where is the number of samples in the mixed prior set.

[0024] Further, the specific steps of step S4 include:

[0025] According to and 's data formats, build a suitable deep learning model in programming languages such as MATLAB and Python, and then use groups of as the input, as the output and substitute them into the deep learning model for training, and set appropriate training hyperparameters according to the training data volume and the deep learning model structure.

[0026] Further, the specific steps of step S5 include:

[0027] The observation data Subtract the model output in the mixed prior set to obtain the innovation vector ,in , then Substitute the trained deep learning model to obtain the update vector for each sample parameter .

[0028] Furthermore, the step S6 specifically includes:

[0029] Will update the vector The parameter samples corresponding to the mixed prior set Add together to get an updated understanding of the prior sample, that is, , where a represents the updated sample.

[0030] Furthermore, the step S7 specifically includes:

[0031] According to the updated parameter set , draw the updated parameter mean field and compare it with the reference field to verify the accuracy of aquifer characterization; in addition, draw the uncertainty distribution diagram of the updated parameters to verify the uncertainty change of aquifer understanding during the characterization process; finally, show the comparative analysis diagram of the influence of the proportion of prior samples of each model in the mixed prior on the aquifer characterization effect.

[0032] Based on the above content, the present invention also provides an aquifer characterization system based on a hybrid prior strategy and deep learning, comprising:

[0033] A mixed priori set construction module is used to construct a mixed priori set consisting of parameter prior samples of different geological structure hypotheses;

[0034] The model output acquisition module is used to obtain the model output corresponding to each parameter sample in the mixed prior set;

[0035] The output difference and parameter difference calculation module is used to perform pairwise subtraction on all parameter samples in the mixed prior set and the corresponding model outputs to obtain multiple model output differences and corresponding parameter differences;

[0036] A deep learning model training module is used to train the deep learning model using the output difference and parameter difference as input and output respectively;

[0037] A parameter updating module is used to obtain an updated parameter sample set;

[0038] The aquifer parameter characterization module is used to implement aquifer parameter characterization based on the updated parameter sample set.

[0039] Beneficial effects: Compared with the prior art, the present invention proposes a concept of hybrid prior, that is, considering parameter prior samples of multiple different geological structure hypotheses in the prior set to enrich the prior information. The concept of hybrid prior can easily be combined with the data assimilation method based on deep learning. The diversity of prior samples enables the data assimilation method based on deep learning to capture more pattern data, enhancing the robustness of the method. The present invention can improve the aquifer characterization effect under the condition of insufficient prior information, improve the solution effect of the data assimilation method on the coexistence problem of biased prior and non-Gaussian distribution challenges, and provide scientific support for groundwater management and protection. Brief Description of the Drawings

[0040] Figure 1 is the flow chart of the method of the present invention;

[0041] Figure 2 is the schematic diagram of the model setting and the reference field and prior hypothesis of three cases; where (a) is the model setting diagram; (b) is the training data for generating a random channel field; (c) is the training data for generating a random three-phase field; (d) is the reference field of the Gaussian case; (e) is the reference field of the channel case; (f) is the reference field of the three-phase field case; (g) is the Gaussian prior set; (h) is the hybrid prior set composed of Gaussian samples and channel samples; (i) is the prior hypothesis of the channel;

[0042] Figure 3 is the schematic diagram of the deep learning model structure;

[0043] Figure 4 is the mean field diagram estimated by ES under different proportions of Gaussian samples in the prior set in the Gaussian case DL ;

[0044] Figure 5 is the standard deviation field diagram estimated by ES under different proportions of Gaussian samples in the prior set in the Gaussian case DL ;

[0045] Figure 6 is the mean field diagram estimated by ES under different proportions of Gaussian samples in the prior set in the Gaussian case K ;

[0046] Figure 7 is the standard deviation field diagram estimated by ES under different proportions of Gaussian samples in the prior set in the Gaussian case K ;

[0047] Figure 8 is the parameter error diagram estimated by ES / ES under different proportions of Gaussian samples in the prior set in the Gaussian case DL / ES K ;

[0048] Fig. 9 For different proportions of Gaussian samples in the prior set in the Gaussian case, the model output error graph estimated by ES DL / ES K ;

[0049] Fig.10 For different proportions of channel feature samples in the prior set in the channel field case, the mean field graph estimated by ES DL ;

[0050] Fig.11 For different proportions of channel feature samples in the prior set in the channel field case, the standard deviation field graph estimated by ES DL ;

[0051] Fig.12 For different proportions of channel feature samples in the prior set in the channel field case, the mean field graph estimated by ES K ;

[0052] Figure 13 For different proportions of channel feature samples in the prior set in the channel field case, the standard deviation field graph estimated by ES K ;

[0053] Fig.14 For different proportions of channel feature samples in the prior set in the channel field case, the histogram of parameter distribution estimated by ES DL / ES K ;

[0054] Fig.15 For different proportions of channel feature samples in the prior set in the channel field case, the parameter error graph estimated by ES DL / ES K ;

[0055] Figure 16 For different proportions of channel feature samples in the prior set in the channel field case, the model output error graph estimated by ES DL / ES K ;

[0056] Fig.17 For different proportions of channel feature samples in the prior set in the three-phase field case, the mean field graph estimated by ES DL ;

[0057] Fig.18 For different proportions of channel feature samples in the prior set in the three-phase field case, the standard deviation field graph estimated by ES DL ;

[0058] Fig.19For the three-phase field case, the proportion of different channel feature samples in the prior set is determined by ES K estimated mean field plot;

[0059] Fig. 20 For the three-phase field case, the proportion of different channel feature samples in the prior set is determined by ES K Estimated standard deviation field plot;

[0060] Fig.21 For the three-phase field case, the proportion of different channel feature samples in the prior set is determined by ES DL / ES K histogram of the estimated parameter distribution;

[0061] Figure 22 For the three-phase field case, the proportion of different channel feature samples in the prior set is determined by ES DL / ES K estimated parameter error plots;

[0062] Fig.23 For the three-phase field case, the proportion of different channel feature samples in the prior set is determined by ES DL / ES K Estimated model output error plot. DETAILED DESCRIPTION

[0063] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0064] Embodiment 1:

[0065] In order to verify that the present invention is a data assimilation framework that can achieve a relatively accurate aquifer characterization in the case of insufficient prior information or even prior knowledge bias, three common aquifer characterization scenarios are considered: aquifers with logarithmic Gaussian distribution (Gaussian case), aquifers with channel field characteristics (channel field case), and aquifers with three-phase field characteristics (three-phase field case). The verification is carried out in a confined transient aquifer, such as Figure 2 As shown in (a), the area size is The left and right sides of the region are bounded by fixed water heads of 202 (L) and 198 (L), respectively. The upper and lower boundaries of the region are impermeable boundaries. Except for the 202 (L) on the left boundary, the initial water head at the rest of the region is 198 (L). In addition, the region also contains a well with a water injection rate of With the pumping rate Injection wells (indicated by inverted triangle symbols) and production wells (indicated by upright triangle symbols), where L is a general term for length units and T is a general term for time units.

[0066] In three cases, Figure 2 As shown at the red circle in (a) of The observation wells are at The water head measurement values are used to infer Figure 2 The log-Gaussian reference field, channel reference field, and three-phase reference field shown in (d)-(f) of , Figure 2 (b) and (c) of DL respectively show the training images generated by the channel field and the three-phase field. In three cases, in this embodiment, a hybrid prior set composed of channel feature samples and Gaussian features is taken as an example to illustrate, and the influence of different sample mixing ratios in the hybrid prior on the data assimilation effect of the present invention (hereinafter referred to as ES Figure 2 is explored. Specifically, by controlling the proportion of Gaussian samples in the hybrid prior set (10%, 20%, …, 90%) to achieve (as shown in Figure 2 (h) of Figure 2 ), and comparing with the benchmark results of the Gaussian prior hypothesis (the prior samples all conform to the Gaussian distribution, as shown in K (g) of

[0067] Based on the above, this embodiment provides an aquifer characterization method based on a hybrid prior strategy and deep learning, as shown in Figure 1 and includes the following steps:

[0068] Step 1: Construct a hybrid prior set composed of prior samples of hydraulic conductivity fields assumed by different geological structures. In this embodiment, a hybrid prior set composed of channel feature samples and Gaussian feature samples is taken as an example to illustrate, where the data format of the hydraulic conductivity field is ;

[0069] Generate groups of channel feature prior samples based on the channel field training image ; Generate groups of Gaussian feature prior samples based on the geological software statistical library ; Mix the prior sample sets of the above two modes to obtain a hybrid prior set composed of channel feature and Gaussian feature samples , as shown in Figure 2As shown in (h), the hydraulic conductivity field data format is .

[0070] Step 2: Run the groundwater numerical simulation software MODFLOW to obtain the uniformly distributed hydraulic conductivity coefficient field sample in the study area corresponding to each sample in the mixed prior. The transient hydraulic head simulation values obtained from the observation well at 10 observation moments are in the format of .

[0071] Substitute all samples in the mixed prior set into the groundwater numerical simulation software MODFLOW and solve the following equation to obtain the uniform distribution in the study area. Groundwater state (such as water head) of an observation well at 10 observation moments :

[0072]

[0073] in, is the aquifer storage coefficient, is the source / sink term, is a positional parameter, represents time. Among them, flux Solve by the following equation:

[0074]

[0075] in, For location The hydraulic conductivity coefficient, for Location, The hydraulic gradient at the moment. After solving the above equation, the mixed prior set The corresponding head simulation value is obtained, that is, The data format of the transient head observation value is .

[0076] Step 3: Perform pairwise subtraction on all samples in the mixed prior set and the corresponding model outputs, including Gaussian feature sample and Gaussian feature sample pairs, Gaussian feature sample and channel feature sample pairs, and channel feature and channel feature sample pairs, so as to obtain multiple model output differences and corresponding parameter differences.

[0077] For the mixed prior set parameters , and the model output , and subtract the two matchings to get Parameter difference between group samples Difference with model output , including Gaussian feature samples and pairs of Gaussian feature samples, pairs of Gaussian feature samples and channel feature samples, and pairs of channel features and channel feature samples, where is the number of samples in the mixed prior set.

[0078] Step 4: Use the obtained output difference and parameter difference as input and output respectively to train the deep learning model.

[0079] According to and 's data format, build a U-net model with an input format of and an output format of in programming languages such as MATLAB and Python, as shown in Figure 3 . Then, use groups of as input and as output to substitute into the U-net model for training. In this embodiment, the deep learning models used in the three cases are all the U-net models shown in Figure 3 . Generally speaking, this model includes two parts: an encoder and a decoder. The encoder downsamples the input 's data size to through a batch normalization layer, a two-dimensional transposed convolutional layer, a Gaussian error linear unit layer, a two-dimensional convolutional layer, a rectified linear unit, a max pooling layer, a leaky rectified linear unit, and a dropout layer (30%); subsequently, the decoder upsamples the data size to as the Unet model output . The above U-net model abstracts the input information through multiple layers of networks. Through multiple linear transformations and non-linear activation functions, it can gradually extract complex patterns in the information at different levels, including local correlations, temporal structures, etc. This hierarchical information abstraction ability enables deep learning to gradually refine the original information, thereby more deeply exploring and 's relationship. There are differences in the training parameters in each case. Specifically, in the Gaussian case, the number of mini-batch samples is set to 256, the learning rate is 0.0001, and it is trained for 200 epochs; in the channel case, the number of mini-batch samples is 512, the learning rate is 0.0005, and it is trained for 150 epochs; in the three-phase field case, the number of mini-batch samples is 512, the learning rate is 0.0005, and it is trained for 100 epochs; in all three cases, the Adam optimizer is used for training the U-net model, and the training data is re-shuffled before each training epoch.

[0080] Step 5: Subtract the transient head observation data from the transient head model value of each sample in the hybrid prior to generate an innovation vector, and substitute it into the trained U-net model to obtain the update vector of each sample parameter.

[0081] Transient head observation data Subtract the transient head simulation value in the prior set respectively to obtain the new information vector ,in ; Then Substitute the trained U-net model to obtain the update vector for each sample parameter .

[0082] Step 6: Add the updated vector to the original mixed prior sample to obtain the updated parameter sample set.

[0083] Will update the vector The parameter samples corresponding to the mixed prior set Add together to get an updated understanding of the prior sample, that is, .

[0084] Step 7: Complete the aquifer parameter characterization based on the updated parameter sample set, and analyze the aquifer parameter characterization effect and the aquifer parameter uncertainty distribution.

[0085] According to the updated parameter set The updated parameter mean field is plotted and compared with the reference field to verify the characterization accuracy. Furthermore, the uncertainty distribution of the updated parameters is plotted to verify the uncertainty changes in the aquifer understanding during the characterization process. Finally, a comparative analysis of the impact of the proportion of prior samples for each model in the hybrid prior on the aquifer characterization effect is presented.

[0086] Embodiment 2:

[0087] Based on the content of Example 1, this embodiment provides an aquifer characterization system based on a hybrid prior strategy and deep learning, including:

[0088] A mixed priori set construction module is used to construct a mixed priori set consisting of parameter prior samples of different geological structure hypotheses;

[0089] The model output acquisition module is used to obtain the model output corresponding to each parameter sample in the mixed prior set;

[0090] The output difference and parameter difference calculation module is used to perform pairwise subtraction on all parameter samples in the mixed prior set and the corresponding model outputs to obtain multiple model output differences and corresponding parameter differences;

[0091] A deep learning model training module is used to train the deep learning model using the output difference and parameter difference as input and output respectively;

[0092] A parameter updating module is used to obtain an updated parameter sample set;

[0093] The aquifer parameter characterization module is used to implement aquifer parameter characterization based on the updated parameter sample set.

[0094] Embodiment 3:

[0095] In this embodiment, data acquisition and analysis are performed for the three cases in Example 1, as follows:

[0096] like Figures 4 to 7 As shown, it shows the Gaussian case with different proportions of Gaussian samples in the prior set, which is obtained by ES DL / ES K The estimated mean field and its corresponding standard deviation field, where Figure 4 For ES DL The estimated mean field; Figure 5 For ES DL The estimated standard deviation field; Figure 6 For ES K The estimated mean field; Figure 7 For ES K The estimated standard deviation field; Figures 4 to 7 (a) to (d) are the cases where the proportion of Gaussian samples in the mixed prior is 0%, 10%, 90%, and 100%, respectively. It can be seen that in the Gaussian case, the channel characteristic prior hypothesis (i.e., biased prior hypothesis) cannot accurately describe the reference field, even the ES method, which is very suitable for Gaussian data assimilation problems. K In addition, a small number of Gaussian feature samples (10%) in the prior can significantly improve the estimation effect of the log-Gaussian field, highlighting the effectiveness of the mixed prior strategy.

[0097] like Figure 8 As shown, it shows the Gaussian case with different proportions of Gaussian samples in the prior set, which is obtained by ES DL / ES K The root mean square error between the estimated parameters and the parameter field; Fig. 9 The results show that the ES DL / ES K The root mean square error between the estimated model output and the observed data. It can be seen that ES DL When the proportion of Gaussian samples in the mixed prior is higher than 40%, the results comparable to those of the Gaussian prior hypothesis can be obtained, which reflects the ES DLCombined with the hybrid prior strategy, it can reduce the need for unbiased prior in the data assimilation process.

[0098] As Figures 10 to 14 shown, the mean field, standard deviation field estimated by ES DL / ES K and their distribution histograms are presented under the condition of different proportions of channel feature samples in the prior ensemble in the channel field case, where Fig.10 is the mean field estimated by ES DL ; Fig.11 is the standard deviation field estimated by ES DL ; Fig.12 is the mean field estimated by ES K ; Figure 13 is the standard deviation field estimated by ES K ; Fig.14 is the parameter distribution histogram estimated by ES DL / ES K ; In (a)-(d) of Figures 10 to 14 , the proportions of Gaussian samples in the hybrid prior are 0%, 10%, 70%, and 100% respectively. It can be seen that ES DL can depict some channel features of the reference field under the hybrid prior condition, but its histogram fails to characterize the multi-peak feature of the channel field (as shown in (a)-(c) of Fig.14 ). Fig.14 In (d) of DL , ES K can depict the bimodality of the channel field under the channel prior hypothesis, while ES DL

[0099] As Fig.15 shown, the root mean square error of the parameters and parameter fields estimated by ES / ES K is presented under the condition of different proportions of channel feature samples in the prior ensemble in the channel field case; Figure 16 shows the root mean square error of the model output and observed data estimated by ES DL / ES K under the condition of different proportions of channel feature samples in the prior ensemble in the channel field case. It can be seen that with the increase of the proportion of channel field feature samples in the hybrid prior, the performance of ES DL becomes better, both in terms of parameter characterization and observation value matching.

[0100] As Figures 17 to 21 shown, the mean field, standard deviation field estimated by ES DL / ES K and their distribution histograms are presented under the condition of different proportions of channel feature samples in the prior ensemble in the three-phase field case, where Fig.17 is ES DL the estimated mean field; Fig.18 is ES DL the estimated standard deviation field; Fig.19 is ES K the estimated mean field; Fig. 20 is ES K the estimated standard deviation field; Fig.21 is ES DL / ES K the estimated parameter distribution histogram; Figures 17 to 21 In (a) - (d), the cases are where the Gaussian sample proportion in the mixed prior is 0%, 10%, 100%, and TPF (three - phase prior hypothesis), respectively. It can be seen that although ESK can achieve better aquifer characterization effect than ES in the TPF case, under a biased prior understanding, ES DL combined with the mixed prior strategy can also achieve an effect close to that in the case of an unbiased prior (three - phase field prior hypothesis). DL

[0101] Such as Figure 22 shown, it shows the root - mean - square error of the parameters and the parameter field estimated by ES DL / ES K under different proportions of channel - feature samples in the prior ensemble in the three - phase field case; Fig.23 It shows the root - mean - square error of the model output and the observed data estimated by ES DL / ES K under different proportions of channel - feature samples in the prior ensemble in the three - phase field case. It can be seen that in the case of a mixed prior composed of two biased prior samples, the aquifer characterization effect of ES DL is significantly better than that of ES K , and the characterization effect is less affected by the mixing ratio of the two biased prior samples, highlighting the stability of ES DL in dealing with the problem of inaccurate prior data assimilation.

[0102] From the above analysis, it can be seen that even under the condition of insufficient prior information, the present invention can still achieve effective characterization of the aquifer. At the same time, the characterization effect of the method of the present invention shows good robustness in the face of the mixing ratio of the mixed prior and the type of the mixed prior samples, and can provide scientific support for groundwater management and protection.​

Claims

1. An aquifer characterization method based on a hybrid prior strategy and deep learning, characterized in that, It includes the following steps: S1: Construct a mixed prior set composed of prior samples of parameters assumed by different geological structures; S2: Run the forward model of the groundwater system to obtain the model outputs corresponding to each parameter sample in the mixed prior set; S3: Subtract each pair of all parameter samples in the mixed prior set and their corresponding model outputs to obtain multiple model output differences and corresponding parameter differences; S4: Use the output differences and parameter differences obtained in step S3 as inputs and outputs respectively to train a deep learning model; S5: Subtract the observed data from the model outputs of each sample in the mixed prior set to generate an innovation vector, and substitute it into the trained deep learning model to obtain the updated vectors of each sample parameter; S6: Add the updated vectors to the original prior samples of the parameters to obtain an updated set of parameter samples; S7: Complete the characterization of the aquifer parameters based on the updated set of parameter samples, and analyze the effect of the aquifer parameter characterization and the uncertainty distribution of the aquifer parameters; The implementation of step S1 specifically includes: Generate its corresponding prior samples based on m geological structure assumptions, where the superscript pm represents the m-th prior assumption of the geological structure, and the subscript N m represents the number of samples in the m-th prior assumption set; Mix the prior sample sets of m geological structure hypotheses to obtain a mixed prior set X composed of m geological structure hypotheses, where X = {X p1 , X p2 ,..., X pm}; Step S2 specifically includes: Substitute all samples in the mixed prior set into the forward model of the groundwater system, and obtain the groundwater state quantity y(P,t) at a specified time and specified location by solving the following equation: Among them, S s is the aquifer storage coefficient, g(P, t) is the source / sink term, P = {p x , p y} is the position parameter, and t represents time; among them, the flux q(P, t) is solved by the following equation: where x(P) is the hydraulic conductivity at position P, is the hydraulic gradient at position P and time t; After solving the above equation, from the mixed prior set X = {X p1 , X p2 ,..., X pm}, the corresponding head simulation values are obtained, that is, Y = {Y p1 , Y p2 ,..., Y pm}; Step S3 specifically includes: For the parameters of the mixed prior set and the model output subtract pairwise and obtain the parameter difference Δx between groups of samples i,j = x i - x j and the model output difference Δy i,j = y i - y j , where is the number of samples in the mixed prior set; Step S4 specifically includes: According to Δy i,j and Δx i,j data format, build a deep learning model, and then a group of Δy i,j as input, and Δx i,j as output are substituted into the deep learning model for training, and training hyperparameters are set according to the amount of training data and the deep learning model structure; Step S5 specifically includes: Subtract the observed data from the model outputs in the mixed prior set respectively to obtain the innovation vector where i = 1,..., N e . Then substitute v i into the trained deep learning model to obtain the updated vector u of each sample parameter i .

2. The aquifer characterization method based on the hybrid prior strategy and deep learning according to claim 1, characterized in that The said step S6 specifically includes: Update the vector u i with the corresponding parameter sample x in the set of mixture priors i to obtain an updated understanding of the prior sample, i.e., where a represents the updated sample.

3. A method for aquifer characterization based on a hybrid prior strategy and deep learning according to claim 2, characterized in that, The said step S7 specifically includes: According to the updated parameter set Draw the updated parameter mean field and compare it with the reference field to verify the accuracy of aquifer characterization; draw the uncertainty distribution map of the updated parameters to verify the change in the uncertainty of the understanding of the aquifer during the characterization process; finally, show the comparative analysis diagram of the influence of the proportion of prior samples of each mode in the hybrid prior on the aquifer characterization effect.

4. An aquifer characterization system for the aquifer characterization method according to any one of claims 1 to 3, characterized in that, It includes: A mixed prior set construction module for constructing a mixed prior set composed of prior samples of parameters assumed by different geological structures; A model output acquisition module for obtaining the model outputs corresponding to each parameter sample in the mixed prior set; An output difference and parameter difference calculation module for subtracting each pair of all parameter samples in the mixed prior set and their corresponding model outputs to obtain multiple model output differences and corresponding parameter differences; A deep learning model training module for using the output differences and parameter differences as inputs and outputs respectively to train a deep learning model; A parameter update module for obtaining an updated set of parameter samples; An aquifer parameter characterization module for implementing aquifer parameter characterization based on the updated set of parameter samples.

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