Underground water pollutant migration simulation method coupled with physical mechanism and data driving

Abstract

The invention discloses an underground water pollutant migration simulation method coupled with a physical mechanism and data driving, which comprises the following steps: establishing a statistical model through a machine learning method to correct the structural error of an underground water model, and expressing the output of the underground water model as the sum of a physical mechanism model, a structural error model and an observation error. According to the method, underground water pollutant migration simulation under complex conditions can be carried out, structural errors existing in the model are effectively corrected based on a data driving method, the defect that a traditional underground water model is poor in simulation precision under the complex conditions is overcome, and the application scene of underground water pollutant migration simulation is expanded; according to the method, underground water pollution migration simulation can be carried out aiming at novel and macromolecular organic pollutants such as polycyclic aromatic hydrocarbon, the defect that a traditional underground water model cannot accurately describe pollutant and colloid co-migration behaviors is overcome, the uncertainty of a model prediction result is remarkably reduced, the accuracy and reliability of the model prediction result are improved, and the method is suitable for popularization and application. And the model prediction performance is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of groundwater numerical simulation, and specifically to a method for simulating the transport of groundwater pollutants by coupling physical mechanisms and data-driven approaches. Background Art

[0002] In groundwater numerical simulation work, due to the complexity and concealment of the groundwater system, as well as the lack of hydrogeological information in actual investigations, the established groundwater models usually have unreasonable parameters and structures, resulting in the simulation results of the models containing random and systematic prediction errors, and the simulation accuracy being affected. Currently, hydrological and groundwater researchers generally believe that model structure errors are widespread and unavoidable.

[0003] In the prior art, the Bayesian Model Averaging (BMA) method provides an effective way to quantify model structure uncertainty. This method describes the structural uncertainty of groundwater models by considering multiple credible models under different hydrogeological conditions. However, there are also some problems in the actual application of BMA, such as the subjectivity of the established models, the difficulty in considering the correlation between models, and the subjectivity in assigning prior weights to models, which limits the practical use of the multi-model method.

[0004] The principle of simulating pollutant transport based on groundwater models is simple and easy to operate, but there are the following problems in the application process:

[0005] (1) The structural error of the groundwater model cannot be avoided, resulting in systematic biases in the model prediction results;

[0006] (2) Relying solely on observed data to identify model parameters will lead to parameter overfitting and affect the effect of parameter identification;

[0007] (3) For some organic pollutants, traditional groundwater models cannot accurately depict the co-transport behavior of pollutants and colloids, resulting in poor model prediction effects. Summary of the Invention

[0008] The purpose of the present invention is to provide a method for simulating the transport of groundwater pollutants by coupling physical mechanisms and data-driven approaches, establishing a statistical model based on machine learning methods to correct the structural error of the groundwater model, representing the output of the model as the sum of a physical mechanism model, a structural error model, and an observation error, and compensating for factors not considered by the physical model with the structural error model.

[0009] To solve the above technical problems, the present invention provides the following technical solutions:

[0010] A method for simulating the transport of groundwater pollutants by coupling physical mechanisms and data-driven approaches, the steps of which include:

[0011] Construct a groundwater model and use the groundwater model to predict the migration of groundwater pollutants;

[0012] The groundwater model:

[0013]

[0014] In the formula, f(θ) represents the groundwater numerical model, represents the structural error correction model, ε represents the measurement error; y is the input of the structural error correction model b, and the input value y includes but is not limited to time information and position information; represents the hyperparameter of the structural error correction model; among them, taking the groundwater pollutant migration model as an example, the input value y can specifically refer to: the pollutant concentration value at a certain position in the aquifer at a certain moment.

[0015] Quantitatively evaluate the prediction performance of the groundwater model through the Nash coefficient NSE, mean absolute error MAE, and root mean square error RMSE indicators.

[0016] Among them,

[0017]

[0018] In the formula: O i is the i-th true observation value, S i is the i-th groundwater model simulation value, O avg represents the average value of all observation values, and n represents the number of observation values. The closer NSE is to 1 and the smaller MAE and RMSE are, the more reliable the simulation results are. Among them, the Nash coefficient NSE is mainly used to measure the fitting degree of measured data and simulated data, the mean absolute error MAE is used to reflect the size of the actual prediction error, and the root mean square error RMSE is used to reflect the dispersion degree of the simulation results and is greatly affected by simulation or observation outliers.

[0019] According to the above technical solution, the prediction steps of the groundwater model include:

[0020] Based on the predicted input value y * , obtain the predicted value of the groundwater numerical model at y * ;

[0021] Based on the predicted input value y * , obtain the predicted value of the structural error correction model b at y * ;

[0022] Use multivariate normal sampling to obtain the observation error;

[0023] Calculate the predicted value of the groundwater numerical model at y * , the predicted value of the structural error correction model b at y* The sum of the predicted values and the observation errors at

[0024] According to the above technical solution, the steps executed by the structural error correction model include:

[0025] Construct a structural error correction model corresponding to the groundwater model based on Gaussian process regression (GPR) according to the observation data;

[0026] Obtain the prior distributions of the groundwater model parameters θ and the hyperparameters φ of the structural error correction model;

[0027] For the predicted input value y * , based on the prior distributions of the groundwater model parameters θ and the hyperparameters φ of the structural error correction model, use Bayesian theory and Markov chain Monte Carlo (MCMC) method to simulate and jointly identify the posterior distribution of the structural error correction model

[0028] Based on the posterior distribution of the structural error correction model b at y * ; Use multivariate normal sampling to obtain the predicted value of the structural error correction model b at y * .

[0029] Among them, according to the squared exponential covariance function, represents the observation error. After obtaining the posterior of , the observation error can be directly sampled and generated through the Gaussian distribution .

[0030] According to the above technical solution, the hyperparameters λ, σ and σ δ in the squared exponential covariance function of the observation data and the prior mean function μ of the structural error correction model together constitute the hyperparameters of the structural error correction model

[0031] The squared exponential covariance function C i,j :

[0032]

[0033] In the formula, C i,j and q(y i , y j ) both represent the squared exponential covariance of the two-point values of y i and y j ; λ represents the characteristic length; represents the observation error; σ 2Denote the marginal likelihood, T denote the transpose; where X denotes the indicator function, which equals 1 when i = j and 0 otherwise. Taking the groundwater pollutant transport model as an example, the input value y i can specifically refer to: the pollutant concentration value at a certain location in the aquifer at time i; the input value y j , can specifically refer to: the pollutant concentration value at a certain location in the aquifer at time j.

[0034] According to the above technical solution, the prior mean function μ:

[0035] μ(y) = E(b(y));

[0036] In the formula, E(.) represents the expected value function, and b(y) is the structural error correction model.

[0037] According to the above technical solution, the posterior mean of the structural error correction model b

[0038]

[0039] In the formula, C* is the prior covariance between the training data and the prediction data, μ * represents the prior mean of the predicted value, T represents the transpose, C represents the prior covariance between the training data, f represents the predicted value of the groundwater numerical model, D represents the observed data, and u represents the prior mean of the observed data.

[0040] The observed data D is generally divided into two parts: training data and prediction data. The training data is generally used to train the model, and the observed data is used to verify whether the model prediction result is reliable. And it can be used to calculate the prior covariance C* between the training data and the prediction data.

[0041] The observed data D generally includes the input value x and the output value y of the observed data (taking the groundwater model as an example, x can be the coordinate information at a certain time, and y is the water level information at the observed x, etc.).

[0042] According to the above technical solution, the posterior covariance Cb(b*) of the error correction model:

[0043] C b (b * ) = C ** -C *T C -1 C * ;

[0044] In the formula, C b (b * ) is the posterior covariance of the error correction model, C is the prior covariance between the training data, C *is the prior covariance between the training data and the prediction data, C ** is the prior covariance between the prediction data.

[0045] According to the above technical solution, the observed data D represents the sum of the output value of the groundwater numerical model, the output value of the structural error correction model, and the observation error.

[0046] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: The present invention can carry out the simulation of groundwater pollutant transport under complex conditions. Gaussian process regression (GPR) clearly corrects the structural error of the model by establishing a statistical model, and represents the output (prediction) of the groundwater model as the sum of the physical mechanism model, the structural error model, and the observation error. This method does not require an explicit assumption of the error distribution, can learn the complex relationship between the dependent variable and the independent variable from historical data, can consider the spatio-temporal correlation of the structural error, avoid parameter compensation, and improve the model prediction ability.

[0047] Based on the data-driven method, the structural error existing in the model itself is effectively corrected, the defect of poor simulation accuracy of the traditional groundwater model under complex conditions is overcome, and the application scenario of groundwater pollutant transport simulation is expanded; it can carry out the simulation of groundwater pollution transport for new and high-molecular organic pollutants such as polycyclic aromatic hydrocarbons, overcome the deficiency of the traditional groundwater model in accurately depicting the co-transport behavior of pollutants and colloids, significantly reduce the uncertainty of the model prediction results, improve the accuracy and reliability of the model prediction results, and enhance the model prediction performance. The method provided by the present invention has a certain generality and is applicable to various new groundwater pollutants, which is conducive to carrying out scientific and efficient groundwater pollution remediation and risk assessment. Description of the Drawings

[0048] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention, but do not constitute a limitation to the present invention. In the drawings:

[0049] Figure 1 is a schematic diagram of the method for simulating groundwater pollutant transport by coupling physical mechanism and data-driven of the present invention;

[0050] Figure 2 is an experimental device for simulating the transport of fluoranthene and phenanthrene in the embodiment;

[0051] Figure 3 In [it], a is a simulation diagram of fluoranthene transport in the present embodiment without using the GPR to correct the structural error of the model;

[0052] Figure 3 In [it], b is a simulation diagram of fluoranthene transport in the present embodiment using the GPR to correct the structural error of the model;

[0053] Figure 4 In this, a is the simulation diagram of the non - GPR - corrected model structure error in this embodiment;

[0054] Figure 4 In this, b is the simulation diagram of the GPR - corrected model structure error in this embodiment. Specific implementation manner

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0056] Embodiment 1

[0057] The steps of the simulation method for groundwater pollutant transport coupling physical mechanisms and data - driven include:

[0058] S1. Construct a groundwater model, the groundwater model (such as Figure 1 ):

[0059]

[0060] In the formula, f(θ) represents the groundwater numerical model, represents the structure error correction model, ε represents the measurement error; y is the input of the structure error correction model b, and the input value y includes but is not limited to time information and position information; represents the hyperparameter of the structure error correction model;

[0061] S2. Use the groundwater model to predict the transport of groundwater pollutants. The specific steps include:

[0062] S201. Based on the predicted input value y * , obtain the predicted value of the groundwater numerical model at y * .

[0063] S202. Based on the predicted input value y * , obtain the predicted value of the structure error correction model b at y * . The specific steps include: construct the structure error correction model corresponding to the groundwater model based on Gaussian process regression (GPR) according to the observed data.

[0064] Obtain the prior distributions of the groundwater model parameters θ and the hyperparameters φ of the structure error correction model; among them, the hyperparameters λ, σ and σ in the squared - exponential covariance function of the observed data δTogether with the prior mean function μ of the structural error correction model, they constitute the hyperparameters of the structural error correction model

[0065] Squared exponential covariance function C i,j :

[0066]

[0067] In the formula, C i,j and q(y i , y j ) both represent the squared exponential covariance of the two-point values of y i and y j ; λ represents the characteristic length; represents the observation error; σ 2 represents the marginal likelihood, T represents the transpose; where X represents the indicator function, when i = j, X is equal to 1, otherwise equal to 0.

[0068] For the predicted input value y * , based on the prior distributions of the groundwater model parameters θ and the hyperparameters φ of the structural error correction model, the posterior distribution of the structural error correction model is simulated and jointly identified using Bayesian theory and Markov chain Monte Carlo (MCMC) methods

[0069] The observed data D is generally divided into two parts: training data and prediction data. The training data is generally used to train the model, and the observed data is used to verify whether the model prediction results are reliable.

[0070] Among them, the posterior mean of the structural error correction model b

[0071]

[0072] In the formula, C* is the prior covariance between the training data and the prediction data, μ * represents the prior mean of the predicted value, T represents the transpose, C represents the prior covariance between the training data, f represents the predicted value of the groundwater numerical model, D represents the observed data, and u represents the prior mean of the observed data. The observed data D represents the sum of the output value of the groundwater numerical model, the output value of the structural error correction model, and the observation error.

[0073] The posterior covariance C b (b * ): C b (b * ) = C ** - C *T C -1 C * ;

[0074] In the formula, C b (b * ) is the posterior covariance of the error correction model, C is the prior covariance between the training data, C * is the prior covariance between the training data and the prediction data, C ** is the prior covariance between the prediction data.

[0075] Based on the posterior distribution of the structural error correction model b at y * The predicted value of the structural error correction model b at y is obtained by using multivariate normal sampling. Using multivariate normal sampling to obtain the predicted value of the structural error correction model b at y * place.

[0076] S203. Obtain the observation error by using multivariate normal sampling.

[0077] S204. Calculate the sum of the predicted value of the groundwater numerical model at y * the predicted value of the structural error correction model b at y * and the observation error at the place to obtain the final predicted result of the groundwater model.

[0078] S3. Quantitatively evaluate the prediction performance of the groundwater model through the Nash coefficient NSE, the mean absolute error MAE, and the root mean square error RMSE indicators.

[0079] Example 2

[0080] Select fluoranthene and phenanthrene as the research objects, where phenanthrene is a typical low-molecular-weight PAH, and fluoranthene is a typical high-molecular-weight PAH. During the migration of PAHs, a certain amount of the bacterium Herbaspirillum chlorophenolicum FA1 is injected into the sand column and simplified as a colloid.

[0081] The experimental setup is as Figure 2 shown. Among them, the sand column is made of polytetrafluoroethylene, with a column height of 12 cm and an inner diameter of 2.5 cm. 50-μm stainless steel filters are placed at both the top and bottom ends of the sand column. The average density of the filled sand column is 1.69 g / cm 3 , and the average porosity is 0.36. A peristaltic pump connected to the bottom end of the sand column is used to introduce the solution into the sand column, controlling its flow direction upward, and the flow rate of the peristaltic pump is kept at 1.0 mL / min. A high-performance liquid chromatograph is used to measure the concentrations of polycyclic aromatic hydrocarbons (fluoranthene, phenanthrene) in the effluent at the top of the sand column.

[0082] Before the experiment started, it was rinsed with a 1.0 mmol / L NaCl background solution to ensure that the hydrochemical conditions in the porous medium reached equilibrium. Then the experiment began, and a bacterial FA1 suspension containing 0.2 mg / L phenanthrene / fluoranthene was injected into the sand column at a constant rate of 1.0 mL / min for 2 pore volumes (PV). Subsequently, 18 PV of the suspension without phenanthrene / fluoranthene was injected. At 20 - 22 PV, an NaCl solution without bacterial FA1 was injected, and at 22 - 26 PV, pure water was injected. During the experiment, an automatic fraction collector was used to collect the effluent samples every 4 minutes at the top of the sand column. 2 mL of the solution was taken from each sample and the concentration of fluoranthene / phenanthrene was measured.

[0083] Based on Hydrus 1D, the one-dimensional Richards equation was used to describe the water movement process, and its basic form is as follows:

[0084]

[0085] where θ(h) is the volumetric water content function [cm 3 ·cm -3 , t is the time [h], z is the migration distance [cm], K(h) is the unsaturated hydraulic conductivity function [cm·h -1 , and h is the pressure head [cm]. And θ(h) and K(h) are described by the Van Genuchten - Mualem model:

[0086]

[0087]

[0088] where, θ s is the saturated water content, θ r is the residual water content, K s is the saturated hydraulic conductivity, S e is the effective saturation, and α, n, and m are model parameters.

[0089] The transport process of polycyclic aromatic hydrocarbons in the saturated sand column was simulated using a two-site adsorption model coupled with the Freundlich equation. The two-site adsorption model divides the adsorption sites into two parts. Equilibrium (instantaneous) adsorption occurs at the Type-1 sites, and first-order kinetic adsorption occurs at the Type-2 sites. The governing equation (one-dimensional transport model) can be expressed as:

[0090]

[0091] S 1 = fS s ;

[0093]

[0094] Among them, C is the concentration of the pollutant in the liquid phase [mg·cm -3 ; θ is the volumetric water content [cm 3 ·cm -3 ; ρ is the soil bulk density [mg·cm -3 ; s s is the adsorption concentration of the pollutant at equilibrium in the liquid phase [mg·kg -1 ; s 1 and s 2 are the adsorption concentrations of the pollutant at Type-1 and Type-2 sites respectively [mg·kg -1 ; f is the proportionality coefficient of equilibrium adsorption; D a is the solute molecular diffusion coefficient [cm 2 ·h -1 ; k d is the isothermal adsorption coefficient [cm 3 ·g -1 ; η and β are the shape parameters of the isothermal linear adsorption model [-, cm 3 ·mmol -1 ; α k is the first-order rate constant of non-equilibrium adsorption [h -1 .

[0095] In the fluoranthene and phenanthrene migration models, the parameters θ r , θ s , K s , α and n have the same parameter values, while the values of the remaining parameters D a and α k are different. The parameter settings of the fluoranthene / phenanthrene migration model are shown in Table 1.

[0096] Table 1 Parameters of the fluoranthene / phenanthrene migration model

[0097]

[0098]

[0099] Under actual groundwater pollution conditions, due to the difficulty in accurately describing the colloid distribution and types in the underground environment, the influence of colloids on pollutant migration is usually ignored. Therefore, the established groundwater polycyclic aromatic hydrocarbon migration model does not consider the PAHs-colloid co-migration mechanism. Based on the established one-dimensional migration model of fluoranthene / phenanthrene in a saturated sand column and using GPR to establish an error correction model to correct the model structure error caused by not considering the PAHs-colloid co-migration mechanism.

[0100] Three physical model parameters (the proportionality coefficient of equilibrium adsorption f d , the isothermal adsorption coefficient kd and the shape parameter β of the isothermal linear adsorption model, as well as the hyperparameters of the GPR model, are regarded as the random variables to be identified. For the setting of the prior distribution, the prior distributions of the physical parameters are all defined as uniform distributions, and the hyperparameters σ, λ, and follow exponential, gamma, and uniform distributions respectively. Among them, the physical model parameters f, k d and β, as well as the hyperparameter σ, have the same prior ranges in the fluoranthene and phenanthrene transport models, while the hyperparameters λ and have different prior ranges in the two models, as shown in Table 2.

[0101] Table 2 Prior settings of the parameters of the fluoranthene / phenanthrene transport model for the coupled data-driven method

[0102]

[0103] For the polycyclic aromatic hydrocarbon (PAH) transport models of the coupled and uncoupled data-driven methods, the same MCMC parameter settings are used. The DREAMzs algorithm is used for parameter sampling, and three parallel Markov chains are used, with the iteration length of each Markov chain being 1000 and the warm-up period being set to 1000. In addition, for the fluoranthene transport model, a total of 129 concentration observation data are obtained. The 1st to 34th observation data are used as the identification data, and the 35th to 129th observation data are used as the verification data. For the phenanthrene transport model, a total of 63 concentration observation data are obtained. The 1st to 21st observation data are used as the identification data, and the 22nd to 63rd observation data are used as the verification data.

[0104] The PAH transport models without considering the co-transport mechanism (without using the GPR to correct the structural error) and considering the co-transport mechanism (using the GPR to correct the structural error) are respectively used for model prediction. The evaluation indicators Nash-Sutcliffe efficiency coefficient (NSE), root mean square error (RMSE), and mean absolute error (MAE) are used to quantitatively evaluate the prediction performance of the models.

[0105] (1) Fluoranthene transport simulation:

[0106] Figure 3 are the fluoranthene transport simulation results and the 95% prediction confidence intervals obtained without using and using the GPR to correct the model structural error. Among them Figure 3 a is the fluoranthene transport simulation result and the 95% prediction confidence interval obtained without using the GPR to correct the model structural error, Figure 3In [b], it represents the simulation results of fluoranthene migration obtained by correcting the model structure error using GPR and the 95% prediction confidence interval. It can be seen from the figure that without using GPR to correct the model structure error, although the model can capture the changing trend of fluoranthene concentration, there is an obvious overestimation of the peak value of fluoranthene concentration, and the fitting effect is poor during the verification period, and the predicted fluoranthene concentration is on the low side. After using GPR to correct the model structure error, the fitting effect of the model on the peak value of fluoranthene concentration is significantly improved, and the error between the predicted results and the observed data during the verification period is reduced.

[0107] At the same time, after using GPR to correct the model structure error, the coverage rate of the 95% confidence interval for the observed data is higher. The coverage rate during the identification period increases from 79.41% to 100%, and the coverage rate during the verification period increases from 31.58% to 88.42%. The reliability of the model prediction results is significantly improved.

[0108] Table 3 Simulation results of fluoranthene migration without and with using GPR to correct the model structure error

[0109]

[0110] Table 3 shows the quantitative evaluation results of the prediction performance of the fluoranthene migration model during the identification period and the verification period without and with using GPR to correct the model structure error. During the identification period, after using GPR to modify the model structure error, NSE increases from 0.937 to 0.989; both RMSE and MAE decrease significantly, from 0.0277 and 0.0208 to 0.0126 and 0.0107 respectively. During the verification period, after using GPR to modify the model structure error, NSE increases significantly, from 0.681 to 0.954; both RMSE and MAE decrease significantly, from 0.0145 and 0.0125 to 0.0097 and 0.0085 respectively. Therefore, using the GPR method to correct the model structure error can significantly improve the prediction performance of fluoranthene migration simulation and enhance the reliability of the simulation results.

[0111] (2) Phenanthrene migration simulation:

[0112] Figure 4 They are the simulation results of phenanthrene migration obtained without and with using GPR to correct the model structure error and the 95% confidence interval. Similar to the simulation results of fluoranthene migration. Among them, Figure 4 In [a], it represents the simulation results of phenanthrene migration obtained without using GPR to correct the model structure error and the 95% confidence interval, Figure 4In this, b represents the simulated results of phenanthrene migration and the 95% confidence interval obtained by using the GPR to correct the model structure error. It can be seen from the figure that when the GPR is not used to correct the model structure error, the fitting effect between the model simulation results and the observed data is poor, and there is an obvious overestimation of the phenanthrene concentration during the identification period, especially at the peak of the phenanthrene concentration. After using the GPR to correct the model structure error, although the simulation effect of the model during the identification period is average and there is a certain degree of underestimation, the prediction performance during the verification period is significantly improved, and the fitting effect between the simulation results and the observed data is very good.

[0113] At the same time, after using the GPR to correct the model structure error, the 95% confidence interval of the simulation results becomes wider, and the uncertainty of the model prediction results becomes larger, but the coverage rate of the 95% confidence interval for the observed data is significantly improved. The coverage rate during the identification period increases from 66.67% to 85.71%, and the coverage rate during the verification period increases from 78.57% to 100%, and the reliability of the simulation results is significantly improved.

[0114] Table 4 Simulated results of phenanthrene migration without and with using the GPR to correct the model structure error

[0115]

[0116] Table 4 shows the quantitative evaluation results of the prediction performance of the phenanthrene migration model during the identification period and the verification period without and with using the GPR to correct the model structure error. After using the GPR to correct the structure error, although the NSE, RMSE, and MAE during the identification period perform average, all indicators have been significantly improved during the verification period. Among them, NSE is significantly improved, from 0.787 to 0.958. Both RMSE and MAE are significantly reduced, from 0.0195 and 0.0123 to 0.0087 and 0.0066 respectively. Therefore, using the GPR method to correct the model structure error may introduce additional uncertainties, which does not significantly improve the model performance during the identification period, but can significantly improve the prediction performance of the phenanthrene migration model during the verification period.

[0117] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device.

[0118] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for simulating groundwater contaminant transport by coupling physical mechanisms with data-driven methods, characterized by: Construct a groundwater model and use it to predict the migration of groundwater pollutants; The groundwater model: Where f(θ) represents the groundwater numerical model, represents the structural error correction model, ε represents the measurement error; y is the input of the structural error correction model b, and the input value y includes but is not limited to time information and position information; represents the hyperparameters of the structural error correction model; The prediction performance of the groundwater model is quantitatively evaluated by using the Nash coefficient NSE, mean absolute error MAE and root mean square error RMSE indicators.

2. The method for simulating groundwater pollutant migration by coupling physical mechanism and data-driven according to claim 1, characterized in that: The groundwater model prediction step includes: Based on the predicted input value y * , obtain the groundwater numerical model in y * The predicted value at Based on the predicted input value y * , obtain the structural error correction model b in y * The predicted value at Observation errors were obtained using multivariate normal sampling; Calculation of groundwater numerical model in y * The predicted value at y, the structural error correction model b * The final groundwater model prediction result is obtained by summing the predicted value at and the observation error.

3. The method for simulating groundwater pollutant migration by coupling physical mechanism and data-driven according to claim 1, characterized in that: The structural error correction model execution steps include: According to the observed data, a structural error correction model corresponding to the groundwater model is constructed based on Gaussian process regression (GPR); Obtain the prior distribution of the groundwater model parameters θ and the hyperparameters φ of the structural error correction model; The input value y for prediction * Based on the prior distribution of the groundwater model parameters θ and the hyperparameter φ of the structural error correction model, the posterior distribution of the joint identification structural error correction model is simulated using the Bayesian theory and the Markov Chain Monte Carlo (MCMC) method. Based on the structural error correction model b in y * The posterior distribution at Using multivariate normal sampling, we can obtain the structural error correction model b in y * The predicted value at .

4. The method for simulating groundwater pollutant migration by coupling physical mechanism and data-driven according to claim 3, characterized in that: The hyperparameters λ, σ and σ in the squared exponential covariance function corresponding to the observed data δ and the prior mean function μ of the structural error correction model together constitute the hyperparameters of the structural error correction model The squared exponential covariance function C i,h : In the formula, C i,j and q(y i ,y j ) all represent y i and j The squared exponential covariance of the two point values; λ represents the characteristic length; represents the observation error; σ 2 represents marginal likelihood, T represents transpose; X represents the indicator function, when i=j, X is equal to 1, otherwise it is equal to 0.

5. The method for simulating groundwater pollutant migration by coupling physical mechanism and data-driven according to claim 4, characterized in that: The prior mean function μ of the error correction model is: μ(y)=E(b(y)); Where E(.) represents the expected value function, and b(y) is the structural error correction model.

6. The method for simulating groundwater contaminant migration by coupling physical mechanism and data-driven according to claim 3, characterized in that: The posterior mean of the structural error correction model b Where C* is the prior covariance between the training data and the prediction data, μ * represents the prior mean of the predicted value, T represents the transpose, C represents the prior covariance between the training data, f represents the predicted value of the groundwater numerical model, D represents the observed data, and u represents the prior mean of the observed data.

7. The method for simulating groundwater contaminant migration by coupling physical mechanism and data-driven according to claim 3, characterized in that: The posterior covariance C of the error correction model is b (b * ): C b (b * )=C ** -C *T C -1 C * ; In the formula, C b (b * ) is the posterior covariance of the error correction model, C is the prior covariance between the training data, and C * is the prior covariance between training data and prediction data, C ** is the prior covariance between the predicted data.

8. The method for simulating groundwater contaminant migration by coupling physical mechanism and data-driven according to claim 6, characterized in that: The observation data D represents the sum of the output value of the groundwater numerical model, the output value of the structural error correction model and the observation error.

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