Hydrogeological parameter inversion method for non-homogeneous weakly permeable layer and application thereof
By constructing a seepage-consolidation coupled numerical forward model and a surrogate model, and combining dimensionality reduction and adaptive weighted optimization algorithms, the computational efficiency and consistency issues in parameter inversion of heterogeneous weakly permeable layers were solved, achieving efficient and accurate parameter identification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING CENT CHINA GEOLOGICAL SURVEY
- Filing Date
- 2026-02-26
- Publication Date
- 2026-05-29
AI Technical Summary
Existing technologies suffer from low computational efficiency, difficulty in identifying multiple parameters, and poor physical consistency of models when acquiring hydrogeological parameters of heterogeneous and weakly permeable aquifers, making it difficult to meet the requirements of timeliness and accuracy in engineering projects.
A seepage-consolidation coupled numerical forward model was constructed, and parameter samples were generated using a sampling method. Parameter inversion was achieved by using principal component analysis (PCA) for dimensionality reduction and Gaussian process regression (GPR) as a surrogate model, combined with HS adaptive weighting and particle swarm optimization (PSO) algorithms.
It improves the evaluation speed of the inversion optimization process, can accurately resolve the formation stress history, overcome the differences in the magnitude of multi-physics field data, ensure the reliability of prediction and physical consistency, and meet the needs of long-term engineering calculations.
Smart Images
Figure CN122113739A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of hydrogeology and geological engineering technology, specifically relating to a method for inverting hydrogeological parameters of heterogeneous weakly permeable layers and its application. Background Technology
[0002] As a crucial component of multi-aquifer systems, weakly permeable layers play a key role in groundwater flow regulation, reservoir response, and formation consolidation and deformation. These strata typically exhibit low permeability and high compressibility, and their hydraulic-mechanical properties directly influence the dissipation rate of pore water pressure and the overflow process. Actual engineering and geological surveys show that weakly permeable layers, influenced by sedimentary environment, stress history, and subsequent structural disturbances, often exhibit significant vertical heterogeneity and time-varying characteristics. Key parameters such as permeability coefficient, elastic framework reservoir capacity, and inelastic framework reservoir capacity vary markedly across different depths and geological units.
[0003] Currently, methods for obtaining parameters of weakly permeable layers mainly include analytical methods, geostatistical inversion, and numerical simulation-based inversion. Traditional analytical methods rely on strong geometric assumptions (such as ideal layered structures), making them difficult to apply to complex boundary conditions. Geostatistical inversion is prone to non-uniqueness when data is sparse or multiple parameters are coupled. While high-fidelity numerical simulation-based inversion methods offer high accuracy, they require extensive forward modeling calculations, resulting in huge computational costs. Furthermore, in high-dimensional parameter spaces, traditional optimization methods are prone to getting trapped in local optima, making it difficult to simultaneously meet the requirements of timeliness and accuracy in engineering projects. In addition, existing methods often lack a unified constraint mechanism for pore water pressure (hydraulic response) and formation deformation (mechanical response), leading to insufficient parameter identification under multiphysics coupling. Summary of the Invention
[0004] Purpose of the invention: The purpose of this invention is to address the problems of low computational efficiency, difficulty in identifying multiple parameters, and poor physical consistency of models in existing technologies. This invention provides a method for inverting hydrogeological parameters of heterogeneous weakly permeable layers and its application.
[0005] Technical solution: The method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers described in this invention includes the following steps:
[0006] Step S1: Construct a flow-consolidation coupled numerical forward model for a heterogeneous, weakly permeable layer, determine the parameter space to be inverted, and generate multiple sets of parameter samples in the parameter space using a sampling method. Calculate the time-series response data corresponding to each set of parameter samples using the numerical forward model to generate a training dataset. The parameters to be inverted include permeability coefficient, elastic skeleton water storage rate, and inelastic skeleton water storage rate.
[0007] Step S2: Perform feature extraction and dimensionality reduction on the time-series response data in the training dataset to obtain a low-dimensional feature vector that can characterize the time-series response features;
[0008] Step S3: Construct a proxy model based on the dimensionality-reduced data, establish the mapping relationship between the parameters to be inverted and the low-dimensional feature vectors, and audit the prediction accuracy of the proxy model;
[0009] Step S4: Construct an inversion objective function that includes hydraulic response error terms and mechanical response error terms; use a global optimization algorithm to search for the optimal parameter solution that minimizes the inversion objective function in the parameter space;
[0010] Step S5: Substitute the optimal parameter solution into the numerical forward model for verification simulation, and compare the simulation results with the measured observation data to determine the final hydrogeological parameters.
[0011] This invention also provides applications of the above-mentioned method in groundwater flow field simulation, ground subsidence prediction, aquifer-permeable layer coupling analysis, or geological safety assessment during underground space development.
[0012] Beneficial effects: Compared with the prior art, the advantages of the present invention are: The present invention replaces the time-consuming COMSOL numerical forward modeling process by constructing a Gaussian process regression (GPR) surrogate model, which greatly improves the evaluation speed of the objective function in the inversion optimization process and can meet the engineering calculation needs of long time series and multi-layered geological structures.
[0013] This invention introduces an HS adaptive weighting mechanism, which effectively overcomes the problem of "different parameters with the same effect" caused by the differences in the magnitude and sensitivity of multi-physics data by adjusting the weights of hydraulic response (pore water pressure) and mechanical response (settlement) in the objective function in real time. At the same time, it clearly distinguishes between elastic and inelastic skeleton water storage rates, and can accurately analyze the stress history of the formation (overconsolidation and normal consolidation state).
[0014] By combining principal component analysis (PCA) dimensionality reduction techniques, noise interference in the observation data is effectively filtered out; and the particle swarm optimization (PSO) algorithm is used for global optimization, avoiding the defect of traditional gradient-based algorithms that are prone to getting trapped in local optima.
[0015] By using parallel leave-one-out cross-validation (pLOO) and active learning mechanisms, the uncertainty regions of the surrogate model can be identified and samples can be automatically supplemented, forming a closed loop of "training-evaluation-update" to ensure the reliability of predictions in complex parameter spaces. Attached Figure Description
[0016] Figure 1This is a schematic diagram of the overall process of the method of the present invention, which shows the integrated process from parameter sampling, forward simulation, surrogate model construction to inversion verification.
[0017] Figure 2 This is a schematic diagram of the seepage-consolidation model of a multi-layered heterogeneous weakly permeable layer, showing the stratigraphic stratification and the layout of monitoring points.
[0018] Figure 3 This diagram illustrates the training and validation process of the surrogate model, showcasing the logic of PCA dimensionality reduction and GPR construction.
[0019] Figure 4 The flowchart for parameter inversion and optimization based on the surrogate model illustrates the closed loop of PSO optimization and active learning. Detailed Implementation
[0020] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the embodiments described.
[0021] Example 1: As Figure 1 As shown, the method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers provided by this invention includes the following steps:
[0022] Step S1: Construct a numerical forward model and generate a training dataset
[0023] 1. Establish a seepage-consolidation coupled numerical model
[0024] In numerical simulation platforms (such as COMSOL Multiphysics), the weakly permeable layer is divided into several stratigraphic units in the vertical direction, such as... Figure 2 As shown, along the direction of groundwater flow, the stratigraphic units sequentially include: clay, silty clay, silty clay, silt, and silty clay. Each stratigraphic unit is assigned independent hydrogeological parameters to accurately describe its vertical heterogeneity.
[0025] A flow-consolidation coupling model based on Terzaghi's consolidation theory is established to accurately describe the changes in pore water pressure (H) and formation compression and settlement (S) response of heterogeneous, poorly permeable layers under the influence of external hydraulic head variations. This model should be able to systematically characterize the vertical heterogeneous structure of the poorly permeable layer. It is assumed that the poorly permeable layer satisfies one-dimensional vertical flow under conditions of sufficient horizontal extension, approximately horizontal bedding, and complete saturation; the flow motion obeys Darcy's law, the stress-flow coupling follows the effective stress principle, and the total vertical stress remains constant. The transient vertical flow equations for each formation element are as follows:
[0026]
[0027] in The head (m) is the water head. The vertical coordinate is... The water storage capacity (1 / m) can be decomposed into two parts: the skeleton and the pore water. , The water storage capacity of the skeleton (1 / m) Contributes (1 / m) to the compressibility of pore water. water density (kg / m³) 3 ), Acceleration due to gravity (m / s²) 2 ), Porosity ρ is the compressibility coefficient of water (1 / Pa).
[0028] According to the Jacob–Terzaghi theory, head changes The expected compression caused can be expressed as:
[0029]
[0030] in, This represents the initial thickness of the formation.
[0031] To reflect different stages of soil deformation, characterize the elastic and inelastic deformation of sediments, and demonstrate the different skeleton water storage rates under whether the effective stress exceeds the pre-consolidation stress, skeleton water storage rates are divided into elastic water storage rates. With inelastic storage rate :
[0032]
[0033] in, For effective stress, This refers to the pre-consolidation stress.
[0034] 2. Determine the parameter space to be inverted : Identify the key parameters affecting the hydraulic-mechanical response of a weakly permeable layer, including the permeability coefficient. , elastic skeleton water storage rate Inelastic skeleton water storage rate ,in, This corresponds to the elastic deformation characteristics of the formation when it is in an overconsolidated state (effective stress is less than preconsolidation stress). Corresponding to the plastic deformation characteristics of the formation in a normal consolidation state (effective stress greater than pre-consolidation stress), this distinction enables the model to reflect the stress history and complex consolidation behavior of the formation.
[0035] 3. Generate training samples: Define the value range of each parameter to be inverted. The Latin hypercube sampling (LHS) method is used to generate N sets of random parameter samples within the above parameter space. .
[0036] 4. Batch Forward Simulation: Batch call the COMSOL forward model and perform parameter analysis for each set. Perform simulation calculations to extract data from a specific time series. The following time-series observation data is used as the model output, i.e. This constitutes the original training dataset. .
[0037] Figure 3 It demonstrates the process of training data input, PCA feature dimensionality reduction, GPR surrogate model construction, cross-validation evaluation, and model output; it is used to illustrate steps S2 and S3.
[0038] Step S2: Principal Component Analysis (PCA) Dimensionality Reduction and Feature Extraction
[0039] 1. Centralization processing: The time-series output dataset Y generated in step S1 is centralized.
[0040] 2. Implement PCA dimensionality reduction: Use the principal component analysis (PCA) algorithm to perform orthogonal transformation on the high-dimensional time series output Y, and obtain the eigenvalues and eigenvectors (principal components) of the covariance matrix.
[0041] 3. Determine the dimensionality-reduced feature vector: Select the top P principal components based on the cumulative contribution rate threshold (e.g., 95%) to transform the high-dimensional time series data into low-dimensional feature vectors. .in, The dimensionality-reduced dataset is .
[0042] Principal component analysis (PCA) was used to analyze the centered output matrix. Perform an orthogonal transformation. Specifically, calculate... The covariance structure is obtained, and its eigenvalues are decomposed to obtain eigenvalues and corresponding eigenvectors sorted by information contribution. The eigenvectors form a set of pairwise orthogonal principal component directions. By projecting the original high-dimensional output vector onto the principal component directions, the corresponding principal component score vector 𝑍𝑖 can be obtained as the low-dimensional feature representation of the sample.
[0043] Covariance matrix: ,
[0044] Projection score: ,
[0045] in, It is the centered output matrix The covariance matrix, It is the centered high-dimensional output row vector of the i-th sample. It is the projection matrix, obtained It is a low-dimensional score.
[0046] Step S3: Construction and Auditing of the Gaussian Process Regression (GPR) Surrogate Model
[0047] 1. Constructing a proxy model: utilizing the dimensionality-reduced dataset A Gaussian process regression (GPR) model is used to construct a surrogate model that maps parameters to dimensionality-reduced feature vectors. This replaces the time-consuming COMSOL forward model.
[0048] 1) Since the output is a multi-dimensional feature vector, to avoid the complexity of directly modeling multiple outputs, a "dimensional modeling" strategy is adopted: for each feature component... ( Train a GPR sub-model separately. This forms a set of multi-output proxy models. .
[0049] 2) For each GPR sub-model, select a kernel function to characterize the relevant structure of the input parameter space. The kernel function is preferably a radial basis function (RBF) kernel or a Matérn kernel. Set the mean function (preferably zero mean or constant mean).
[0050] 3) The kernel function hyperparameters (such as correlation length scale, signal variance and noise variance) are automatically determined by maximizing the marginal likelihood of the training data (or equivalent hyperparameter optimization) to obtain the trained GPR model.
[0051] Therefore, for any parameter vector to be evaluated The surrogate model can output predicted low-dimensional feature vectors. This allows for the replacement of the dimensionality reduction feature results from the COMSOL forward modeling output with a low computational cost.
[0052] 2. Physical Consistency Audit: A parallel leave-one-out cross-validation (pLOO) mechanism is employed to rigorously evaluate and audit the prediction accuracy and uncertainty of the constructed GPR surrogate model. This is achieved by comparing the feature vectors predicted by the surrogate model. The error between the surrogate model and the actual COMSOL output Z ensures physical consistency and reliability of the surrogate model throughout the parameter space.
[0053] Parallel Leave-One-Out Cross-Validation (pLOO) is used to audit the prediction accuracy and uncertainty of a GPR surrogate model across the entire parameter space without reducing the coverage of training samples. The steps include:
[0054] (1) Sample partitioning and parallel strategy: for the training sample set Perform the "leave one" operation one by one according to the sample index. That is, for each sample... One of these is used as the validation sample, and the remaining N-1 samples are used as the training set. Each "leave-one" subtask is independent of the others, and therefore can be executed in parallel in a multi-core CPU or cluster environment to reduce the overall audit time.
[0055] (2) Proxy model retraining and prediction: For each leave-one subtask Train a GPR surrogate model based on the corresponding N−1 samples (preferably train a GPR sub-model for each principal component score dimension), and at the parameter points The low-dimensional feature vector predicted at the output. At the same time, record the prediction uncertainty information (such as prediction variance or confidence interval) provided by GPR.
[0056] (3) Error calculation and statistical summary: The prediction results are... Compared with actual output Compare and calculate the error vector and error indices. Preferred error indices include: mean absolute error (MAE), root mean square error (RMSE), normalized error (e.g., NRMSE normalized to the standard deviation of each dimension), and maximum error / 95th percentile error. Summarize and statistically analyze all results for i=1,…,N to obtain the overall error level and error distribution of the surrogate model in the global parameter domain.
[0057] (4) Uncertainty Consistency Audit: The actual output of each sample Whether the prediction falls within the confidence interval of the surrogate is used as a consistency test indicator, and the coverage is statistically analyzed. When the coverage meets a preset threshold, the surrogate uncertainty estimate is considered to match the error level; otherwise, the surrogate is judged to have the risk of underfitting / overfitting, and the kernel function type, noise term setting, or training samples need to be adjusted.
[0058] (5) Criteria and corrective measures: When the pLOO statistical error is lower than the preset threshold and the error does not show a systematic shift within the parameter domain (e.g., there is no banded bias of continuous overestimation / underestimation in certain parameter ranges), the GPR proxy model is judged to have passed the audit and can be used for subsequent global optimization; otherwise, it is preferable to take measures such as increasing the number of samples, optimizing sampling coverage, adjusting the principal component number P, or changing / combining kernel functions and then re-perform the pLOO audit until the requirements are met.
[0059] Step S4: Particle Swarm Optimization (PSO) inversion under H–S adaptive weighting, such as... Figure 4 This demonstrates the steps of surrogate model prediction, inversion objective function calculation, global optimization algorithm search, and inversion parameter output:
[0060] 1. Establish the objective function: Define the inversion objective function. Feature vectors predicted by the surrogate model Output after inverse transformation Compared with measured observation data The sum of squared errors between them. Objective function The general form is as follows: ,
[0061] in, and These are measured pore water pressure and ground settlement data, respectively. and Predict reconstructed values for the surrogate model; and These are the weighting coefficients.
[0062] 2. Implement H-S adaptive weighting: Use an adaptive weighting strategy to determine the weight coefficients. and Based on the measurement accuracy or error statistics (e.g., standard deviation or variance) of pore water pressure observation data and settlement observation data, the two types of observations are standardized and weighted according to the principle of being inversely proportional to the observation uncertainty. The weights are adjusted in real time during the iteration process to enhance the joint constraint and synchronous identification capability of hydraulic parameters and mechanical parameters.
[0063] Specifically, this includes: acquiring observation accuracy parameters for pore water pressure and settlement observation data, preferably standard deviation or variance; calculating the weights of the hydraulic and mechanical response terms according to the principle of inverse proportionality to the observation variance, and normalizing the weights to maintain a stable weight scale; and dynamically adjusting the accuracy parameters during the inversion iteration process based on the updated observation accuracy parameters or the equivalent accuracy parameters obtained from residual statistics. and This is to balance the contributions of the two types of response data to the objective function and suppress the phenomenon of different parameters having the same effect in multi-parameter coupled inversion.
[0064] The H–S adaptive weighting method employs a standardized weighting strategy based on observation accuracy, ensuring that pore water pressure (H) and sedimentation (S) observations have comparable scales in the objective function and avoiding the dominance of one type of observation in the inversion due to differences in dimensions or noise levels. Its implementation includes:
[0065] (1) Output standard deviation estimation (accuracy characterization): Estimate the standard deviation of each observation channel (or output feature) for pore water pressure response and sedimentation response respectively. The standard deviation can be given by the accuracy of field observations or obtained by statistics of training samples / historical residuals; preferably, the standard deviation is estimated by the statistical dispersion of the corresponding output in the training data of the surrogate model.
[0066] (2) Baseline weight setting (standardization): For each type of observation, a baseline weight inversely proportional to the standard deviation is adopted, so that the weight of channels with higher noise levels or larger scales is reduced, and the weight of channels with lower noise levels or smaller scales is increased. This yields the baseline weight contribution of pore water pressure / level blocks and sedimentation blocks.
[0067] (3) H-S block weight balancing (adaptive adjustment): Based on the baseline weight, the total weight contribution of the pore water pressure block (H-block) and the sedimentation block (S-block) is balanced so that the overall influence of the two types of observations in the objective function is on the same order of magnitude, avoiding the excessive dominance of single-type observations in parameter search.
[0068] (4) Settlement Fitting Emphasis: To prioritize the quality of the settlement response fitting, an emphasis factor can be introduced into the settlement block. This increases the weight of the settlement term in the objective function.
[0069] Renormalization (optional): To maintain the stability of the objective function weight scale, the adjusted weights are normalized. and Perform normalization (e.g., make) + (where is a constant) to improve the convergence stability of the optimization.
[0070] 3. Global Optimization Inversion: The Particle Swarm Optimization (PSO) algorithm is used to optimize the objective function. In parameter space The PSO algorithm performs a global minimization search within the solution space. By iteratively updating particles in the solution space, it effectively overcomes the shortcomings of traditional optimization algorithms, such as being prone to getting trapped in local optima and being sensitive to initial conditions, and quickly converges to the optimal inversion parameter solution. .
[0071] Step S5: Verification and Analysis of Inversion Results
[0072] 1. Verification simulation: The optimal inversion parameters are... Substitute the data into the COMSOL high-fidelity simulation model for final verification simulation.
[0073] 2. Result Comparison: The final simulation results will be compared. and Results and measured observation data and Comparative analysis is performed. If the error exceeds the preset threshold, or if the prediction standard deviation of the GPR model near the optimal solution (obtained from the posterior variance of GPR) is large, then the region is determined to be a "high error region" or an "uncertain region".
[0074] Optional active learning mechanism: If the verification results do not reach the expected accuracy, an active learning mechanism can be used to expand the training set: identify high error regions based on the residual distribution; resample parameter points in the region; run numerical forward modeling to obtain supplementary samples; update the surrogate model and re-execute the inversion step.
[0075] The final simulation and Compared with measured observation data and Comparisons were made, and error indices were calculated. The preferred error indices were root mean square error (RMSE) or mean absolute error (MAE), with normalized error (e.g., NRMSE normalized to the standard deviation of each observation sequence) being even more preferred to eliminate the influence of dimensions. The pore water pressure error was then obtained. With settlement error And define a comprehensive error index:
[0076] ,
[0077] When satisfied When the corresponding parameter domain is determined to be a high-error region, Among them, the threshold A preset error threshold is set; further preferred is to use the 90th or 95th percentile of the error distribution of the validation samples as the threshold. To achieve adaptive decision-making.
[0078] System Operating Environment: The method of this invention can be implemented on a general-purpose computer platform, and can be linked with numerical simulation software such as COMSOL and software with interface capabilities such as MATLAB. Relying on script automation capabilities, the entire process of parameter sampling, batch forward modeling, data processing, surrogate model training, and parameter inversion can be completed. The method of this invention does not depend on a specific hardware platform or operating system.
[0079] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims
1. A method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers, characterized in that, The method includes the following steps: Step S1: Construct a flow-consolidation coupled numerical forward model for a heterogeneous, weakly permeable layer, determine the parameter space to be inverted, and generate multiple sets of parameter samples in the parameter space using a sampling method. Calculate the time-series response data corresponding to each set of parameter samples using the numerical forward model to generate a training dataset. The parameters to be inverted include permeability coefficient, elastic skeleton water storage rate, and inelastic skeleton water storage rate. Step S2: Perform feature extraction and dimensionality reduction on the time-series response data in the training dataset to obtain a low-dimensional feature vector that can characterize the time-series response features; Step S3: Construct a proxy model based on the dimensionality-reduced data, establish the mapping relationship between the parameters to be inverted and the low-dimensional feature vectors, and audit the prediction accuracy of the proxy model; Step S4: Construct an inversion objective function that includes hydraulic response error terms and mechanical response error terms; use a global optimization algorithm to search for the optimal parameter solution that minimizes the inversion objective function in the parameter space; Step S5: Substitute the optimal parameter solution into the numerical forward model for verification simulation, and compare the simulation results with the measured observation data to determine the final hydrogeological parameters.
2. The method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers according to claim 1, characterized in that, In step S1, the seepage-consolidation coupled numerical forward model is established using Terzaghi's one-dimensional consolidation theory, assuming that the weakly permeable layer satisfies one-dimensional vertical seepage, Darcy's law, and the effective stress principle. The numerical forward model characterizes the vertical heterogeneous structure of the weakly permeable layer by dividing it into several stratigraphic units in the vertical direction and assigning independent hydrogeological parameters to each unit; the transient vertical seepage equations for each stratigraphic unit are as follows: ， in, For the water head, The vertical coordinate is... Permeability coefficient, The water storage rate is calculated using the following formula: , For the water storage rate of the skeleton, Contributes to the compressibility of pore water. For the density of water, It is the acceleration due to gravity. Porosity is the compressibility coefficient of water; The time-series response data includes pore water pressure data for a specified time series and data based on a formula. The calculated formation compression and settlement data, among which, This represents the initial thickness of the formation.
3. The method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers according to claim 1, characterized in that, Based on the relationship between effective stress and pre-consolidation stress, determine whether the skeleton water storage rate of the current formation unit is the elastic skeleton water storage rate or the inelastic skeleton water storage rate. The elastic skeleton water storage ratio characterizes the recoverable water storage characteristics of the weakly permeable layer when the effective stress is less than the pre-consolidation stress, corresponding to the overconsolidation state of the formation; the inelastic skeleton water storage ratio characterizes the unrecoverable water storage characteristics of the weakly permeable layer when the effective stress exceeds the pre-consolidation stress, corresponding to the normal consolidation state of the formation; the inversion method analyzes the stress history and consolidation state of the weakly permeable layer by simultaneously identifying the elastic and inelastic skeleton water storage ratios.
4. The method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers according to claim 1, characterized in that, In step S2, the principal component analysis algorithm is used to perform orthogonal transformation on the high-dimensional time-series response data, including: centering the time-series response data, calculating the covariance matrix and performing eigenvalue decomposition to obtain eigenvectors sorted by information contribution as principal component directions; projecting the centered high-dimensional data onto the first P principal component directions to obtain the corresponding low-dimensional principal component score vectors as the low-dimensional feature vectors, where P is selected according to the cumulative contribution rate threshold.
5. The method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers according to claim 1, characterized in that, In step S3, the surrogate model adopts a Gaussian process regression model; The proxy model is constructed using a dimension-by-dimensional modeling strategy, which is achieved by training a Gaussian process regression sub-model for each component of the low-dimensional feature vector. The audit of the prediction accuracy of the surrogate model includes: using a parallel leave-one-out cross-validation mechanism, comparing the error between the feature vector predicted by the surrogate model and the feature vector output by the numerical forward model, and statistically calculating the coverage rate of the verification samples falling into the prediction confidence interval of the surrogate model. When the error index is lower than a preset threshold and the coverage rate meets the preset requirements, the surrogate model is determined to have passed the audit.
6. The method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers according to claim 1, characterized in that, In step S4, the inversion objective function The construction format is as follows: ； in, and These are measured pore water pressure data and ground settlement data, respectively. and The values of pore water pressure and land settlement are predicted and reconstructed by the proxy model and inverse transformation. and These are the hydraulic response weighting coefficient and the mechanical response weighting coefficient, respectively.
7. The method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers according to claim 6, characterized in that, The weighting coefficient and An adaptive weighting strategy is adopted to determine the accuracy, including: obtaining the standard deviation of pore water pressure and settlement observation data as a characterization of accuracy; setting a baseline weight that is inversely proportional to the standard deviation to standardize and weight the observation data with different noise levels; and balancing the total weight contribution of the hydraulic response term and the mechanical response term so that the overall influence of the two types of observation data on the objective function is on the same order of magnitude.
8. The method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers according to claim 1, characterized in that, In step S4, the global optimization algorithm is a particle swarm optimization algorithm, which searches for the optimal inversion parameter solution by iteratively updating the particles in the solution space.
9. The method for inverting hydrogeological parameters of heterogeneous, weakly permeable aquifers according to claim 1 or 5, characterized in that, The method also includes a closed-loop update mechanism based on active learning: if the verification simulation results in step S5 do not meet the preset accuracy requirements, the normalized root mean square error is calculated, and the region where the error exceeds the preset quantile threshold is identified as a high error region. In the high error region, resample and run the numerical forward model to obtain supplementary samples, update the surrogate model with the supplementary samples, and re-execute step S4.
10. The application of the hydrogeological parameter inversion method for heterogeneous weakly permeable layers as described in claim 1 in groundwater flow field simulation, ground subsidence prediction, aquifer-weakly permeable layer coupling analysis, or geological safety assessment during underground space development.