Aquifer description method and system based on hybrid prior strategy and deep learning

Abstract

The invention discloses a mixed prior strategy and deep learning-based aquifer description method and system. The method comprises the following steps of: constructing a mixed prior set; obtaining model output corresponding to each parameter sample in the mixed prior set; performing pairwise subtraction on all the parameter samples in the mixed prior set and the corresponding model outputs to obtain a plurality of model output differences and corresponding parameter differences; training the deep learning model; generating an innovation vector, and substituting the innovation vector into the deep learning model to obtain an update vector of each sample parameter; adding the update vector and an original parameter prior sample to obtain an updated parameter sample set; and analyzing the aquifer parameter description effect and the uncertainty distribution thereof according to the updated parameter sample set. According to the method, the mixed prior strategy is combined with deep learning, the aquifer description effect under the condition of insufficient prior information is effectively improved, and the solution effect of the data assimilation method on the biased prior and non-Gaussian distribution challenge coexistence problem is improved.

Description

Technical Field

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

[0002] The heterogeneity of aquifers, especially the preferential flow phenomenon caused by the 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, direct observation of the hydraulic parameters of aquifers is often difficult due to factors such as spatial heterogeneity, high cost and scale effect. In this context, data assimilation technology can provide a solution that integrates indirect observation data information and model information to enhance the understanding of groundwater systems, and has been widely used in the problem of hydraulic parameter characterization of aquifers.

[0003] To cope with the common nonlinear 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 a deep learning model to learn the complex relationship between the model output difference and the parameter difference of each two groups of samples in the prior set, so as to capture the effective information in the prior set in detail, 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 impact of the amount of information contained in the observed data on the update process from the prior distribution to the posterior distribution, lacking a systematic analysis of the impact 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. When the amount of information in the observed data is limited, the importance of prior information is more significant. In fact, the informative prior is to improve the data assimilation effect by introducing more restrictions on the parameter prior distribution. However, in many practical problems, the selected prior deviates greatly from the actual situation, which reduces the data assimilation effect. In this context, the rationality of the prior distribution assumption needs to be carefully considered, because its setting is often 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 effect of data assimilation methods in solving the coexistence of biased priors and non-Gaussian distribution challenges is improved, providing a new solution for aquifer characterization under conditions of insufficient prior information or even prior knowledge bias.

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

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

[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, and substitute it into the trained deep learning model to obtain the update vector of each sample parameter;

[0011] S6: Add the update vector to the original parameter prior sample to obtain an 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 represents 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] Furthermore, the step S2 specifically includes:

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

[0018]

[0019] in, is the aquifer storage coefficient, is the source / sink term, is a positional parameter, represents time; where flux Solve by the following equation:

[0020]

[0021] in, For location The hydraulic conductivity at ; for Location, The hydraulic gradient at the moment; after solving the above equation, it can be obtained from the mixed prior set The corresponding head simulation value is obtained, that is, .

[0022] Furthermore, the step S3 specifically includes:

[0023] For the mixed prior set parameters , and the model output , and subtract the two matching to get Parameter difference between group samples Difference with model output ,in is the number of samples in the mixed prior set.

[0024] Furthermore, the step S4 specifically includes:

[0025] according to and data format, build a suitable deep learning model in programming languages ​​such as MATLAB and Python, and then Group As input, The output is substituted into the deep learning model for training, and appropriate training hyperparameters are set according to the amount of training data and the deep learning model structure.

[0026] Furthermore, the step S5 specifically includes:

[0027] The observation data Subtract the model outputs in the mixed prior set to obtain the new information 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 samples, 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 changes in the understanding of aquifers 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 priori strategy and deep learning, comprising:

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

[0034] A 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 of 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, used to train the deep learning model by taking the output difference and the parameter difference as input and output respectively;

[0037] A parameter updating module, 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 mixed priors, that is, considering parameter prior samples of multiple different geological structure assumptions in the prior set to enrich the prior information. The concept of mixed priors can be easily 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 patterns of data, thereby enhancing the robustness of the method. The present invention can improve the aquifer characterization effect under conditions of insufficient prior information, and improve the effect of data assimilation methods in solving the coexistence of biased priors and non-Gaussian distribution challenges, providing scientific support for groundwater management and protection. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0041] Figure 2 Schematic diagram of the model setting and the reference fields and prior assumptions of the three cases; (a) is the model setting diagram; (b) is the training data for generating random channel fields; (c) is the training data for generating random three-phase fields; (d) is the Gaussian case reference field; (e) is the channel case reference field; (f) is the three-phase field case reference field; (g) is the Gaussian prior set; (h) is the mixed prior set consisting of Gaussian samples and channel samples; (i) is the channel prior assumption;

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

[0043] Figure 4 For the Gaussian case, under different Gaussian sample proportions in the prior set, ES DL estimated mean field plot;

[0044] Figure 5 For the Gaussian case, under different Gaussian sample proportions in the prior set, ES DL Estimated standard deviation field plot;

[0045] Figure 6 For the Gaussian case, under different Gaussian sample proportions in the prior set, ES K estimated mean field plot;

[0046] Figure 7 For the Gaussian case, under different Gaussian sample proportions in the prior set, ES K Estimated standard deviation field plot;

[0047] Figure 8 For the Gaussian case, under different Gaussian sample proportions in the prior set, ES DL / ES K Estimated parameter error plots;

[0048] Fig. 9 For the Gaussian case, under different Gaussian sample proportions in the prior set, ES DL / ES K Estimated model output error plot;

[0049] Fig.10 For the proportion of samples with different channel characteristics in the prior set in the channel field case, ES DL estimated mean field plot;

[0050] Fig.11 For the proportion of samples with different channel characteristics in the prior set in the channel field case, ES DL Estimated standard deviation field plot;

[0051] Fig.12 For the proportion of samples with different channel characteristics in the prior set in the channel field case, ES K estimated mean field plot;

[0052] Fig.13 For the proportion of samples with different channel characteristics in the prior set in the channel field case, ES K Estimated standard deviation field plot;

[0053] Fig.14 For the proportion of samples with different channel characteristics in the prior set in the channel field case, ES DL / ES K Histogram of estimated parameter distribution;

[0054] Fig.15 For the proportion of samples with different channel characteristics in the prior set in the channel field case, ES DL / ES K Estimated parameter error plots;

[0055] Fig.16 For the proportion of samples with different channel characteristics in the prior set in the channel field case, ES DL / ES K Estimated model output error plot;

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

[0057] Fig.18 For the three-phase field case, the proportion of different channel feature samples in the prior set is determined by ES DL Estimated standard deviation field plot;

[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 estimated parameter distribution;

[0061] Fig. 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 explained below in conjunction with 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, various equivalent forms of modifications to the present invention 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 characterization of aquifers in the case of insufficient prior information or even prior knowledge bias, three common characterization scenarios of aquifer types are considered: aquifers that conform to logarithmic Gaussian distribution (Gaussian case), aquifers that conform to channel field characteristics (channel field case) and aquifers that conform to three-phase field characteristics (three-phase field case). The verification is carried out in a pressurized transient aquifer, such as Figure 2 As shown in (a), the area size is The left and right sides of the region are fixed head boundaries of 202 (L) and 198 (L) respectively. The upper and lower boundaries of the region are impermeable boundaries. Except for the left boundary of 202 (L), the initial head of the rest of the region is 198 (L). In addition, the region also contains a well with a water injection rate of With pumping rate Injection wells (indicated by inverted triangle symbols) and pumping wells (indicated by upright triangle symbols), where L refers to the general term for length units and T refers to the general term for time units.

[0066] In three cases, Figure 2 The red circle in (a) Observation well in The hydraulic head measurements were used to estimate Figure 2 The logarithmic Gaussian reference field, channel reference field and three-phase reference field shown in (d)-(f) of FIG. 1 are shown in FIG. 2 , where the observation error of the observation value conforms to , Figure 2 (b) and (c) show the training images generated by the channel field and the three-phase field respectively. In the three cases, this embodiment takes the mixed prior set composed of channel feature samples and Gaussian features as an example to explore the invention (hereinafter referred to as ES DL ) The effect of different sample mixing ratios in the mixed prior on the data assimilation effect. Specifically, it is achieved by controlling the ratio of Gaussian samples in the mixed prior set (10%, 20%, ..., 90%) (e.g. Figure 2 (h)), and the Gaussian prior assumption (the prior samples all conform to the Gaussian distribution, such as Figure 2 (g)) and the prior assumptions about channel field characteristics (the prior samples all conform to the channel field characteristics, such as Figure 2 The results of the ensemble smoother method (ES) are also compared with the baseline results of (i) of the Gaussian case. K ) combined with the hybrid prior strategy are also provided as a baseline.

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

[0068] Step 1: Construct a mixed priori set consisting of hydraulic conductivity field prior samples of different geological structure assumptions. This embodiment takes a mixed priori set consisting of channel feature samples and Gaussian feature samples as an example for explanation, where the hydraulic conductivity field data format is ;

[0069] Image generation based on channel field training Prior samples of group channel characteristics ; Generated based on the geological software statistical library Group Gaussian feature prior samples ; Mix the prior sample sets of the above two modes to obtain a mixed prior sample set consisting of channel feature and Gaussian feature samples ,like Figure 2As shown in (h) in the figure, the hydraulic conductivity field data format is .

[0070] Step 2: Run the groundwater numerical simulation software MODFLOW to obtain the uniformly distributed hydraulic conductivity 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 times 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 status (such as water head) of the observation well at 10 observation times :

[0072]

[0073] in, is the aquifer storage coefficient, is the source / sink term, is a positional parameter, represents time. Among them, the 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: Subtract all samples in the mixed prior set and the corresponding model outputs pairwise, 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 matching to get Parameter difference between group samples Difference with model output , including Gaussian feature samples and Gaussian feature sample pairs, Gaussian feature samples and channel feature sample pairs, and channel feature and channel feature sample pairs, 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 The data format is constructed in MATLAB, Python and other programming languages. , the output format is The U-net model, such as Figure 3 As shown, then Group As input, The output is substituted into the U-net model for training. The deep learning models used in the three cases in this embodiment are Figure 3 The U-net model shown in the figure is composed of two parts: encoder and decoder. The encoder converts the input into a linear unit through a batch normalization layer, a 2D transposed convolution layer, a Gaussian error linear unit layer, a 2D convolution layer, a rectified linear unit, a maximum pooling layer, a leaky rectified linear unit, and a dropout layer (30%). of The data size is downsampled to ; The decoder then passes through a depth concatenation, a 2D transposed convolution layer, a 2D convolution layer, a leaky rectified linear unit, a Gaussian error linear unit layer, and a batch normalization layer to convert The data size is upsampled to As Unet model output The above U-net model uses a multi-layer network to abstract input information. Through multiple linear transformations and nonlinear activation functions, it can gradually extract complex patterns in information at different levels, including local correlations, temporal structures, etc. This hierarchical information abstraction capability enables deep learning to gradually refine the original information, thereby digging deeper and The training parameters in each case are different, as follows: in the Gaussian case, the number of small batch samples is set to 256, the learning rate is 0.0001, and the training is repeated for 200 rounds; in the channel case, the number of small batch samples is set to 512, the learning rate is 0.0005, and the training is repeated for 150 rounds; in the three-phase field case, the number of small batch samples is set to 512, the learning rate is 0.0005, and the training is repeated for 100 rounds; in the three cases, the U-net model training uses the Adam optimizer, and the training data is reordered before each training round.

[0080] Step 5: Subtract the transient water head observation data from the transient water head model value of each sample in the mixed 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 update 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 samples, 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 , draw the updated parameter mean field and compare it with the reference field to verify the characterization accuracy. In addition, draw the uncertainty distribution diagram of the updated parameters to verify the uncertainty change of the aquifer understanding during the characterization process. Finally, show the comparative analysis diagram of the influence of the proportion of each model prior sample in the mixed prior on the aquifer characterization effect.

[0086] Embodiment 2:

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

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

[0089] A 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 of 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, used to train the deep learning model by taking the output difference and the parameter difference as input and output respectively;

[0092] A parameter updating module, 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 three cases in Embodiment 1, as follows:

[0096] like Figure 4~Figure 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; Figure 4~Figure 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 characterize the reference field, even the ES method, which is very suitable for the Gaussian data assimilation problem. K In addition, a small number of Gaussian feature samples (10%) in the prior can significantly improve the estimation effect of the logarithmic 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 following table shows the Gaussian case with different proportions of Gaussian samples in the prior set, as determined by 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 DLCombining it with a hybrid prior strategy can reduce the need for unbiased priors in the data assimilation process.

[0098] like Figure 10~Figure 14 As shown, it shows the proportion of samples with different channel characteristics in the prior set in the channel field case, which is determined by ES DL / ES K The estimated mean field, standard deviation field and its distribution histogram, where Fig.10 For ES DL The estimated mean field; Fig.11 For ES DL The estimated standard deviation field; Fig.12 For ES K The estimated mean field; Fig.13 For ES K The estimated standard deviation field; Fig.14 For ES DL / ES K The estimated parameter distribution histogram; Figure 10~Figure 14 (a) to (d) are the cases where the proportion of Gaussian samples in the mixed prior is 0%, 10%, 70%, and 100%, respectively. It can be seen that ES DL In the case of mixed priors, some channel characteristics of the reference field can be characterized, but its histogram fails to characterize the multi-peak characteristics of the channel field (e.g. Fig.14 (a) to (c) in the figure). Fig.14 ES shown in (d) DL Under the channel prior hypothesis, the bimodal nature of the channel field can be characterized, while ES K This feature has never been portrayed.

[0099] like Fig.15 As shown, it shows the proportion of samples with different channel characteristics in the prior set in the channel field case, which is determined by ES DL / ES K The root mean square error between the estimated parameters and the parameter field; Fig.16 The figure shows the proportion of samples with different channel characteristics in the prior set in the channel field case, which is determined by ES. DL / ES K The root mean square error between the estimated model output and the observed data. It can be seen that as the proportion of channel field feature samples in the mixed prior increases, ES DL The effect is gradually improved, both in terms of parameter characterization and observation value matching.

[0100] like Figure 17~Figure 21 As shown, it shows the proportion of different channel feature samples in the prior set in the three-phase field case, which is determined by ES DL / ES K The estimated mean field, standard deviation field and its distribution histogram, where Fig.17 For ES DL The estimated mean field; Fig.18 For ES DL The estimated standard deviation field; Fig.19 For ES K The estimated mean field; Fig. 20 For ES K The estimated standard deviation field; Fig.21 For ES DL / ES K The estimated parameter distribution histogram; Figure 17~Figure 21 (a) to (d) are the cases where the proportion of Gaussian samples in the mixed prior is 0%, 10%, 100%, and TPF (three-phase prior hypothesis). It can be seen that although ESK can achieve better results than ES in the TPF case, DL However, under biased prior knowledge, ES DL Combined with the mixed prior strategy, it can also achieve results close to the unbiased prior (three-phase field prior assumption) case.

[0101] like Fig. 22 As shown, it shows the proportion of different channel feature samples in the prior set in the three-phase field case, which is determined by ES DL / ES K The root mean square error between the estimated parameters and the parameter field; Fig.23 The figure shows the proportion of samples of different channel characteristics in the prior set in the three-phase field case, which is obtained by ES DL / ES K The root mean square error between the estimated model output and the observed data. It can be seen that in the case of a mixed prior consisting of two biased prior samples, ES DL The effect of aquifer characterization is better than ES K The advantages are obvious, and the characterization effect is less affected by the mixing ratio of the two biased prior samples, highlighting the ES DL Robustness in the face of inaccurate prior data assimilation problems.

[0102] From the above analysis, it can be seen that the present invention can still effectively characterize the aquifer even when there is insufficient prior information. 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 sample, which can provide scientific support for groundwater management and protection.

Claims

1. A method for characterizing an aquifer based on a hybrid prior strategy and deep learning, characterized in that: The steps include: S1: Construct a mixed prior set consisting of parameter prior samples of different geological structure assumptions; S2: Run the forward model of the groundwater system to obtain the model output corresponding to each parameter sample in the hybrid prior set; 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; S4: Using the output difference and parameter difference obtained in step S3 as input and output respectively to train the deep learning model; S5: Subtract the observed data from the model output 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 update vector of each sample parameter; S6: Add the update vector to the original parameter prior sample to obtain an updated parameter sample set; 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.

2. According to claim 1, the aquifer characterization method based on hybrid prior strategy and deep learning is characterized in that: The implementation of step S1 specifically includes: Generate corresponding prior samples based on m geological structure hypotheses. , ,……, , where the superscript pm represents the mth geological structure prior hypothesis, and the subscript Represents the number of samples in the mth prior hypothesis set; Mix the prior sample set of m geological structure hypotheses to obtain a mixed prior set consisting of m geological structure hypotheses .

3. According to claim 2, the aquifer characterization method based on hybrid prior strategy and deep learning is characterized in that: The 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 at the specified time and location by solving the following equation : ； in, is the aquifer storage coefficient, is the source / sink term, is a positional parameter, represents time; where flux Solve by the following equation: ； in, For location The hydraulic conductivity coefficient at 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, .

4. The aquifer characterization method based on hybrid prior strategy and deep learning according to claim 3 is characterized in that: The step S3 specifically includes: For the mixed prior set parameters , and the model output , and subtract the two matching to get Parameter difference between group samples Difference with model output ,in is the number of samples in the mixed prior set.

5. The aquifer characterization method based on hybrid prior strategy and deep learning according to claim 4 is characterized in that: The step S4 specifically includes: according to and , build a deep learning model, and then Group As input, The output is substituted into the deep learning model for training, and the training hyperparameters are set according to the amount of training data and the deep learning model structure.

6. The aquifer characterization method based on hybrid prior strategy and deep learning according to claim 5 is characterized in that: The step S5 specifically includes: The observation data Subtract the model outputs in the mixed prior set to obtain the new information vector ,in , then Substitute the trained deep learning model to obtain the update vector for each sample parameter .

7. The aquifer characterization method based on hybrid prior strategy and deep learning according to claim 6 is characterized in that: The step S6 specifically includes: Will update the vector The parameter samples corresponding to the mixed prior set Add together to get an updated understanding of the prior samples, that is, , where a represents the updated sample.

8. The aquifer characterization method based on hybrid prior strategy and deep learning according to claim 7 is characterized in that: The 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 diagram of the updated parameters to verify the uncertainty changes in the understanding of aquifers 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.

9. An aquifer characterization system based on hybrid prior strategy and deep learning, characterized in that: include: A mixed priori set construction module is used to construct a mixed priori set consisting of parameter priori samples of different geological structure assumptions; A model output acquisition module is used to obtain the model output corresponding to each parameter sample in the mixed prior set; The output difference and parameter difference calculation module is used to perform pairwise subtraction of all parameter samples in the mixed prior set and the corresponding model outputs to obtain multiple model output differences and corresponding parameter differences; A deep learning model training module, used to train the deep learning model by taking the output difference and the parameter difference as input and output respectively; A parameter updating module, used to obtain an updated parameter sample set; The aquifer parameter characterization module is used to implement aquifer parameter characterization based on the updated parameter sample set.

Images