CN119558171B - Methods and models for inversion of key parameters in numerical model of biodegradation of groundwater pollutants based on neural network algorithm - Google Patents

Abstract

The invention discloses a method for inverting key parameters in a groundwater pollutant biodegradation numerical model based on a neural network algorithm. The method comprises the steps of preprocessing data, carrying out fine dimension reduction, processing high-dimensional multi-scale data, constructing a multi-layer neural network framework under a physical information neural network framework, embedding a related reaction equation of a natural pollutant attenuation process, coupling a biochemical reaction mechanism and a data driving model, training the neural network model, calculating errors in the training process, improving the accuracy of inversion results by means of an Adam optimization algorithm, integrating observation data and model prediction results, determining final parameter settings of a numerical model, carrying out quantification of groundwater damage objects, carrying out comparison verification of the neural network parameter inversion model, and ensuring the feasibility and accuracy of the parameter inversion method. The method solves the problem that key parameters of the biodegradation numerical model are difficult to accurately invert in the real object quantification process of groundwater pollution under complex geological conditions.

Description

Method and model for inverting key parameters in groundwater pollutant biodegradation numerical model based on neural network algorithm

Technical Field

The invention relates to the field of groundwater pollution evaluation, in particular to a method and a model for inverting key parameters of a groundwater pollutant biodegradation model based on a neural network algorithm.

Background

Groundwater is one of the important fresh water resources on earth and is critical to support ecosystems, agricultural irrigation and human daily life. However, with the acceleration of industrialization and expansion of agricultural activities, groundwater resources are facing serious pollution threats. Therefore, the development of an effective groundwater pollutant numerical simulation optimization method has great significance for evaluating groundwater pollution risk and making a subsequent repair scheme. Conventional groundwater solute transport models are generally based on physical and chemical principles, and predict migration and transformation behavior of contaminants in groundwater through numerical simulation methods. These models present challenges in parameter determination and model verification, especially in cases of data scarcity or highly uncertain parameters. The biodegradation process of groundwater contaminants presents significant challenges to the parameter accuracy of the numerical model due to their dynamics and complex interactions with groundwater chemical components. Furthermore, the high dimensional parameter space and the non-homogeneity of the parameters involved in the biodegradation model lead to a significant increase in computational costs. These challenges highlight the urgent need to develop new methods to improve the simulation efficiency and accuracy of the biodegradation process.

Aiming at challenges of dynamic performance, complexity, high dimensionality and the like of biodegradation model parameters, the invention provides a method for inverting key parameters in a groundwater pollutant biodegradation numerical model based on a neural network algorithm. The method utilizes deep learning techniques, particularly neural networks, to simulate and predict the biodegradation process of contaminants in groundwater. By this method, key parameters affecting biodegradation of contaminants, such as microbial degradation rate, half saturation constant, etc., can be more accurately inverted and determined.

Disclosure of Invention

The invention overcomes the defects of the prior art and provides a method for inverting key parameters in a groundwater pollutant biodegradation numerical model based on a neural network algorithm.

In order to achieve the aim, the technical scheme adopted by the invention is that the method for inverting key parameters in the groundwater pollutant biodegradation numerical model based on the neural network algorithm comprises the following steps:

1) The high-dimensional multi-scale data is effectively processed by preprocessing and refining dimension reduction of input data from different sources;

2) Constructing a multi-layer neural network architecture under a physical information neural network framework, embedding a relevant reaction equation of a pollutant natural attenuation process, and coupling a biochemical reaction mechanism and a data driving model;

3) Training a neural network model for inverting key parameters of the pollutant biodegradation numerical model, calculating errors in the training process, and improving the accuracy of inversion results by using an Adam optimization algorithm;

4) And integrating the observation data and the model prediction result, determining the final parameter setting of the numerical model, and carrying out quantification of the groundwater damage real object.

Further, in the present invention, the step 1) performs preprocessing on input data from different sources, and performs fine dimension reduction on high-dimension data, so as to effectively process multidimensional and multi-scale data, and specifically includes:

collecting and sorting multi-source multi-scale multi-source input data;

performing data cleaning and standardization processing, executing characteristic engineering, and normalizing the data;

performing dimension reduction on the high-dimensional data by using a kernel principal component analysis method;

in the invention, step 2) builds a multi-layer neural network architecture under a physical information neural network framework, embeds a relevant reaction equation of a natural pollutant attenuation process, and couples a biochemical reaction mechanism and a data driving model, and specifically comprises the following steps:

Constructing a neural network parameter inversion model combining a groundwater pollutant degradation mechanism and a data driving model based on a convolutional neural network architecture in a physical information neural network framework;

Defining an input layer and an output layer, constructing a neural network structure of a plurality of hidden layers, and capturing global dynamic changes of model parameters on a long time scale;

Designing a comprehensive loss function, quantifying the difference between the output result of the neural network model and the groundwater numerical model, embedding a biodegradation related equation of pollutants into the loss function in a residual form, and realizing the unification of a reaction mechanism and data driving.

Further, in the present invention, the step 3) trains a neural network model for inverting key parameters of the biodegradation numerical model of the pollutant, calculates an error in the training process, and improves the accuracy of the inversion result by using an adam optimization algorithm, which specifically includes:

calculating the output of the network model from the input layer to generate a prediction result;

Calculating a loss value of the model by using the loss function, and adjusting the weight in the network output and the loss function by minimizing the loss function;

Calculating gradient of the loss function about output from the output layer, reversely transmitting the gradient back to each layer by using a chain rule, and selecting an Adam optimization algorithm to update network parameters;

And the loss function value and the performance index in the training process are monitored, so that the problem of over fitting is avoided.

Further, in the present invention, the step 4) integrates the observed data and the model prediction result, determines the final parameter setting of the numerical model, and performs the quantification of the groundwater damage real object, and specifically includes:

constructing an aggregate Kalman filter, integrating observation data and model prediction, and iteratively updating the aggregate members;

Fine tuning the model on the validation set, using the output of the ensemble kalman filter to guide the tuning of the model parameters;

Evaluating generalization capability of the model on the test set, and evaluating prediction accuracy and reliability of the model;

and (5) carrying out contrast verification of the neural network parameter inversion model, and ensuring feasibility and accuracy of the parameter inversion method.

The invention has the following beneficial effects:

the input data from different sources are preprocessed by determining network input and output data, the quality and consistency of the data are ensured, and the high-dimensional parameters are subjected to dimension reduction by using a nuclear principal component analysis method, so that the model can capture the key attributes of the groundwater pollutants more accurately.

The convolution long-short-term memory network architecture is designed in the physical information neural network framework to adapt to the space-time characteristics of groundwater solute transport, the physical consistency of the model is enhanced, and the network is ensured to effectively process multidimensional input data.

The invention designs a loss function introducing regularization term and optimizes the loss function by utilizing Adam algorithm, embeds a microbial degradation dynamics equation and an interaction equation into the loss function in a residual form, allows the model to consider dynamics and interaction of groundwater pollutant biodegradation in the training process, and improves reliability and accuracy of groundwater pollutant biodegradation parameter inversion.

The invention integrates observation data and model prediction by utilizing a set Kalman filtering method, divides a data set, carries out cross verification, checks the generalization capability of the model, carries out the participation of key parameters, carries out prediction by utilizing a trained model, combines physical constraints of a physical information neural network, accurately inverts the key parameters, and improves the practical application value of the model.

By using field observation data, a traditional numerical simulation model and a neural network model for inverting biodegradation parameters, the accuracy of groundwater pollutant distribution prediction can be improved by verifying the neural network parameter inversion method and the model, and the accuracy and reliability of a physical quantization link of groundwater ecological damage can be ensured.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other embodiments of the drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a schematic overall flow diagram;

FIG. 2 is a flow chart of data preprocessing;

FIG. 3 is a block diagram of a neural network;

FIG. 4 is a schematic diagram of the loss function content;

The parameter inversion method of FIG. 5 has the effects that a is actual observation, b is parameter inversion, and c is non-parameter inversion.

Detailed Description

In order that the above-recited objects, features and advantages of the present application can be more clearly understood, a more particular description of the application will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings, it being understood that embodiments of the application and features of the embodiments may be combined with each other without departing from the scope of the appended claims.

In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those described herein, and therefore the scope of the present invention is not limited to the specific embodiments disclosed below.

As shown in fig. 1, the invention provides a method for inverting key parameters in a groundwater pollutant biodegradation numerical model based on a neural network algorithm, which comprises the following steps:

S101, effectively processing high-dimensional multi-scale data by preprocessing and refining dimension reduction of input data from different sources, S102, constructing a multi-layer neural network architecture under a physical information neural network frame, embedding a relevant reaction equation of a pollutant natural attenuation process, and coupling a biochemical reaction mechanism and a data driving model;

s103, training a neural network model for inverting key parameters of the pollutant biodegradation numerical model, calculating errors in the training process, and improving the accuracy of inversion results by using an Adam optimization algorithm;

S104, integrating the observation data and the model prediction result, determining the final parameter setting of the numerical model, and carrying out quantification of the groundwater damage real object.

The invention solves the problem that the key parameters of the biodegradation numerical simulation model of the pollutants in the underground water are difficult to accurately invert under the complex geological condition, realizes the accurate inversion of the key parameters of the numerical simulation model of the biodegradation process of the pollutants in the underground water with long period and wide range, effectively improves the simulation prediction accuracy of migration of the pollutants in the underground water, and provides a basis for the subsequent development of the underground water recovery of a polluted site.

S101, in one embodiment of the invention, the high-dimensional multi-scale data is effectively processed by preprocessing and refining the input data from different sources, as shown in FIG. 2, and the method specifically comprises the following steps:

collecting and sorting multi-source multi-scale multi-source input data;

It should be noted that the multi-source multi-scale input data includes physical parameters such as permeability, porosity, flow rate, etc. of groundwater, such as chemical parameters such as dissolved oxygen, pH value, heavy metal ion concentration, etc., biological parameters such as the number and activity of microorganism population, microorganism growth rate, etc., and space data such as change data of groundwater pollutant concentration at different time and space positions. The biodegradation process of groundwater contaminants is affected by a variety of factors including physical, chemical and biological characteristics. The data sources may include groundwater samples from monitoring stations, laboratory test results, and remote sensing or Geographic Information System (GIS) data, which may have different spatial, temporal resolutions, and acquisition modes, requiring uniform format and processing;

performing data cleaning filling, performing standardized processing, executing characteristic engineering, and performing data normalization;

Cleaning the data refers to identifying and processing abnormal values in the data. Before starting the processing, the obviously wrong data points and invalid data lines are removed, so that the measured value of each observation point has logical consistency, for example, the temperature cannot extremely jump, and the change of the pollutant concentration is consistent with normal. Outlier identification the outlier identification was performed on the data using the Z-score method. Z-score calculates the degree of anomaly for each data point based on standard deviation, with the formula: Where x is the sample value, μ is the feature mean, and σ is the standard deviation. If the Z value of a data point exceeds 3 (i.e., the data point lies outside three standard deviations of the mean), then the data point is considered an outlier. The method can effectively identify potential abnormal data points and ensure the overall quality of the data. For the missing value to be filled, a K nearest neighbor (K-NN) algorithm is used for filling, which is a distance-based filling method, firstly, euclidean distances among samples are calculated, K samples closest to the sample are selected, and the average value of the K samples is used for filling the missing value. The Euclidean distance is calculated as: Where x _i and y _i are the values of the i-th feature for the two samples, respectively. For missing value processing, a K value (typically 5) is selected and all samples with missing values are processed to ensure data integrity.

It should be noted that, the normalization of the data is to eliminate the dimensional differences between different features, so that the numerical values of all the features are distributed in a similar range, so that the neural network model is easier to converge. The normalized formula is still the Z-score formula. After normalization, the mean of all features will be 0 and the standard deviation 1. This approach helps the optimization algorithm to avoid the problem of gradient extinction due to excessive values of certain features during training.

It should be noted that, the feature engineering is performed on the data by evaluating the correlation between different features and the target variable through a statistical method (pearson correlation coefficient). The calculation formula of the pearson correlation coefficient is as follows:

Wherein X _i and Y _i are the characteristic value and the target value of the sample respectively, AndRespectively their average values. By calculating the correlation coefficient of each feature, the feature most relevant to the biodegradation process is selected. To increase the expressive power of the model, nonlinear relationships can also be captured by constructing polynomial features (e.g., quadratic, cubic). Assuming the original feature is x ₁,x₂, the constructed polynomial feature includes x ₁,x₂,x₁x₂. Such non-linear combination features can help the model better fit the complex groundwater contaminant degradation process.

It should be noted that normalization of the data helps to speed up the training process of the neural network and ensures that the contribution of different features to the model is approximately the same. The normalization of the data can be performed by using a min-max normalization method to scale the eigenvalues to the range of [0,1], and the formula is as follows: wherein min (x) and max (x) are the minimum and maximum values of the feature, respectively.

Performing dimension reduction on the high-dimension parameters by using a kernel principal component analysis method, selecting principal components based on the magnitude of the characteristic values, and projecting data onto the selected principal components to finish dimension reduction;

In order to reduce the dimension of high-dimensional data and extract the most important features, kernel Principal Component Analysis (KPCA) is applied. Unlike conventional Principal Component Analysis (PCA), KPCA is capable of processing nonlinear data, mapping the data to a high-dimensional space by gaussian kernel functions. The formula of the gaussian kernel function is:

Where σ is the bandwidth parameter, controlling the similarity between data points. The KPCA reflects the interrelation among the samples in the high-dimensional space by calculating a kernel matrix, then performs eigenvalue decomposition, and selects an eigenvector corresponding to the maximum eigenvalue for the reduced-dimension data representation. After the data preprocessing and dimension reduction are completed, the data set is divided into a training set, a verification set and a test set, the data preprocessing and dimension reduction are carried out according to the proportion of 70%, 15% and 15%, and the independence of the data is maintained in the model training and evaluation process.

S102, in one embodiment of the invention, a multi-layer neural network architecture under a physical information neural network framework is built, a relevant reaction equation of a contaminant natural attenuation process is embedded, and a coupling biochemical reaction mechanism and a data driving model specifically comprise:

Constructing a neural network parameter inversion model combining a groundwater pollutant degradation mechanism and a data driving model based on a convolution long-short term neural network architecture in a physical information neural network framework;

It should be noted that, the physical information neural network framework (PINNs) reduces the requirement of the neural network for the data quantity by introducing physical information, and simplifies the processing of nonlinear terms by introducing an automatic differentiation technology, thereby reducing the dimension difficulty to a certain extent. PINNs is a schematic diagram of the principle that priori knowledge in physics is embedded into a neural network, the output result of the neural network is constrained by a physical rule summarized by the former, and the physical process is predicted by combining sparse data and physical information (such as differential equations and physical parameters thereof). The physical equation PINNs may be a biochemical reaction kinetic equation or the like. The patent provides a novel method and a model for predicting underground water pollution plume distribution under a physical information neural network framework, and can realize effective fusion of a pollutant biochemical degradation reaction mechanism rule and monitoring data. Selecting convolutional long-short-term memory neural network

(ConvLSTM) architecture, combining the advantages of Convolutional Neural Network (CNN) and long-term memory network (LSTM). CNN is responsible for extracting spatial features of data, LSTM is used to capture dynamic information in time series. This architecture is particularly useful for treating time-varying spatial and temporal characteristics of groundwater contaminants. In the training process, a biochemical reaction dynamics equation is embedded into a model, a Logistics form Monod equation and other biochemical reaction interaction equations are used as mathematical equations of microbial degradation dynamics, a loss function is introduced in a residual form, and the unification of mechanism and data driving is realized.

Defining an input layer and an output layer, constructing a neural network structure of a plurality of hidden layers, and capturing global dynamic changes of model parameters on a long time scale;

It should be noted that the input layer is designed to receive groundwater monitoring data including multi-dimensional and multi-scale spatio-temporal data such as contaminant concentration, dissolved oxygen, pH, temperature, etc., and other known model parameters, so as to ensure that the model can effectively process data from different sources and at different time resolutions. Prior to this, a data tensor should be constructed, integrating the spatio-temporal data into a tensor format as follows: wherein T is a time step, H and W are space dimensions, and C is a feature dimension. The data shape of the input layer corresponds to the number of time steps and the number of features, ensuring that the network is able to handle the timing features.

When the hidden layer is constructed, a neural network structure including a plurality of layers is provided. And constructing a convolution layer to extract local spatial characteristics of pollutants, constructing an LSTM layer to extract dynamic characteristics of time series data, accessing a conversion layer based on a self-attention mechanism, and describing global dynamic changes of model parameters on a long time scale. The convolution layer captures local spatial features of the contaminant, while the LSTM layer is better able to handle time series characteristics, especially the dynamic changes of the contaminant over time. The convolution layer detects local features in the pollutant concentration distribution by utilizing the local perception field and the sharing weight, and then carries out convolution operation on input data by applying a filter (convolution kernel) to generate a feature map. Applying a convolution kernel formula to the input tensor:

Where X _i,j is the input matrix, W is the convolution kernel, b is the offset, and Z _i,j is the convolution output. The LSTM layer is constructed to capture dynamics of time series data, maintaining long-term dependencies. Defining an LSTM layer, setting the number of LSTM cells, and using the convolution output as an input to the LSTM layer. The gating mechanism of the LSTM layer controls the flow of information through three gates, the formula:

f_t＝σ(W_f·[h_t-1,x_t]+b_f)

i_t＝σ(W_i·[h_t-1,x_t]+b_i)

o_t＝σ(W_o·[h_t-1,x_t]+b_o)

C_t＝f_t·C_t-1+i_t·tanh(W_C·[h_t-1,x_t]+b_C)

h_t＝o_t·tanh(C_t)

Where f _t is the forgetting gate, i _t is the input gate, o _t is the output gate, C _t is the cell state, and h _t is the hidden state. The next layer is set to capture the long-term dependent transition layer. The conversion layer identifies the dependency between all positions in the modeling sequence under the self-attention mechanism, and is suitable for treating the long-time migration process of groundwater pollutants. While LSTM layers can handle time dependencies, they may perform poorly for longer time sequences, and the global self-attention of the conversion layer can effectively compensate for this. And adding a conversion layer on the basis of the part space-time characteristic diagram extracted by ConvLSTM. Through a global self-attention mechanism, the conversion layer is able to capture the global properties of the contaminant diffusion pattern and global dynamics, in particular microbial biodegradation, on a long time scale. The data feature map from ConvLSTM after processing is represented as a translation layer input matrix. The pixel values in each feature map are used as inputs to the conversion layer. Designing a conversion layer, generating Q, K, V a matrix, generating a query (Q), key (K) and value (V) matrix from the output of LSTM:

Q=W_Q·h

K=W_K·h

V=W_V·h

where W _Q、W_K、W_V is the weight matrix and h is the hidden state of the LSTM. The attention weights are calculated using dot products:

Where dk is the dimension of the key used to scale the dot product. The conversion layer captures long-term dependencies and global features in the contaminant migration process using self-attention mechanisms. The effect of factors including porosity, flow rate and the like on the diffusion of pollutants is captured by ConvLSTM layers in the dynamic change of the pollutants in short-term time and local space ranges. Based on the local features extracted by ConvLSTM, the conversion layer further captures contaminant migration patterns and global dynamic features over a long time horizon through a global self-attention mechanism. Therefore, the short-term and long-term pollutant migration rules can be comprehensively considered in the model, and the prediction precision of the biodegradation process is effectively improved, so that the accurate inversion of key parameters is realized.

It should be noted that the design goal of the output layer is to invert the key parameters of biodegradation of the contaminants in the groundwater. The output data mainly comprises two parts, namely key parameters of a biochemical degradation numerical model of pollutants in the underground water and pollution plume space-time distribution of the pollutants in the natural attenuation process of the pollutants in the underground water. The number of output nodes is designed according to the number of the predicted parameters, the pollutant concentration at the future moment is predicted by using the output layer, and powerful support is provided for the migration path prediction and concentration distribution of pollutants. Key parameters such as microbial maximum degradation rate (μ _max) and half-saturation constant (K _s) can be predicted by regression through linear activation functions: Where W is the weight matrix, h is the feature after convolution and LSTM processing, b is the bias, Is a predicted degradation parameter. The difference between the output result of the neural network model and the underground water numerical model is quantified by a loss function, and the key biochemical degradation parameters are accurately inverted by minimizing the loss function, so that the natural attenuation process of pollutants in the underground water is predicted more accurately.

Designing a comprehensive loss function, quantifying the difference between the output result of the neural network model and the groundwater numerical model, embedding a biodegradation-related dynamics equation of pollutants into the loss function in a residual form, and realizing unification of a reaction mechanism and data driving;

It should be noted that, as shown in fig. 4, a comprehensive loss function including a data error term, a physical error term, and a regularization term is designed. The main part of the loss function is a data error term, i.e. the Mean Square Error (MSE), used to measure the difference between the model predicted and real values. The formula is as follows: Wherein, Is the model predictor, y _i is the true value, and N is the number of samples. By comparing the actual degradation rate to the rate predicted by the Monod equation, a physical error term can be defined: wherein r _i is the theoretical degradation rate calculated by the Monod equation, The rate is predicted for the model. To prevent model overfitting, add the L2 regularization term: Where λ is the regularization coefficient and θ _i is the model parameter. The final total loss function combines the three parts as shown in l=αl _data+βL_physics+γL_reg, where α, β, and γ are important hyper-parameters to balance the losses, L _data is a data error term representing the difference between model predictions and observed data, L _physics is a physical error term representing whether the model satisfies the physical equation, and L _reg is a regularization term to prevent overfitting.

It should be noted that, when constructing the physical error term, to ensure that the model is consistent with the rule of biodegradation of the groundwater pollutants, a Logistics form of Monod equation and a biochemical reaction interaction equation are added into the physical constraint term. The Monod equation in form Logistics is a nonlinear kinetic equation describing the degradation rate of contaminants by microorganisms, incorporating the growth characteristics of the microorganisms during biodegradation. First, the Monod equation describes the degradation rate of contaminants by microorganisms: Where r is the degradation rate of the contaminant by the microorganism, mu _max is the maximum specific growth rate (the maximum growth rate of the microorganism under optimal conditions), S is the concentration of the contaminant, and K _s is the half saturation constant, indicating the concentration of the contaminant when the degradation rate reaches half the maximum rate. To incorporate the Logistics growth form into the Monod equation, the degradation rate can be made to exhibit an S-shaped curve by introducing environmental capacity or resource limitation factors, a common Logistics form is as follows: In this equation, S _max is the maximum allowable concentration of contaminants in the system. This form takes into account the upper limit of the contaminant concentration, so that at high contaminant concentrations the degradation rate is no longer infinitely increased but gradually tends to a stable value.

In addition to the kinetics of microbial degradation, the natural attenuation of contaminants involves a variety of biochemical reactions that degrade the contaminants, including contaminants, microorganisms, and environmental factors. These reactions can be described by corresponding equations and can likewise be embedded in the loss function of the neural network to ensure that the model can not only be trained from data, but also follow realistic physical and chemical laws. The relationship between Dissolved Oxygen (DO) and nitrate (NO ₃) and contaminant biodegradation and their use in loss functions are exemplified below. Dissolved Oxygen (DO) is one of the important electron acceptors when microorganisms degrade contaminants. When the oxygen concentration is insufficient, the degradation rate of microorganisms decreases. Thus, the change in dissolved oxygen can be described by the Michaelis-Menten equation: Where r _DO is the effect of oxygen on the degradation rate, K _DO is the coefficient of influence of oxygen on the microbial degradation rate, DO is the dissolved oxygen concentration, and K _DO is the half-saturation constant of dissolved oxygen. In the loss function, the physical error term can be defined by the difference between the model predicted dissolved oxygen impact rate and the actual measured degradation rate:

Under anoxic conditions, nitrates may become electron acceptors, affecting the degradation rate of the contaminant. The nitrate reduction reaction can be described by a similar Monod equation: Where r _NO3 is the effect of nitrate on degradation rate, K _NO3 is the coefficient of influence of nitrate reduction on degradation rate, NO ₃ is nitrate concentration, and K _NO3 is the half-saturation constant of nitrate. The nitrate influence term in the loss function can be written as:

it should be noted that in groundwater pollutant degradation, multiple reactions may occur simultaneously, such as competing uses of oxygen, nitrate, and other electron acceptors. At this time, the kinetic equations of different biochemical reactions can be combined to generate a comprehensive degradation rate equation. For the reaction of other electron acceptors, its reduction rate r _other can be defined similarly. The kinetic equations of the reactions can be combined to produce a comprehensive degradation rate equation, taking into account competing uses of the reactions. If there are multiple reactions, including microbial degradation and other biochemical reactions (e.g., oxygen, nitrate, etc.), their rates can be combined in a weighted manner. Let w _i be the weight of the ith reaction, the overall degradation rate r _total can be expressed as: Where w _i is the weight of the ith reaction, r _i is the rate of the ith reaction (e.g., microbial degradation rate, oxygen impact rate, nitrate reduction rate, etc.), and m is the total number of reactions considered. The weight w _i may be based on the competing relationship between the concentration of the reaction substrate, the relative importance of the reaction rate. For example, the weights may be calculated by normalizing the substrate concentration: The rate of each reaction can be calculated by their corresponding equations and collectively affect the overall degradation rate in a cumulative form. In the loss function of the neural network, the physical error term becomes the sum of residuals of all reaction rates. The predicted and actual values for the multiple reaction rates are set to be r _pred,i and r _true,i, where i represents the ith reaction. The physical error term L _physical is the sum of residuals between predicted and actual values of all reaction rates, and can be expressed as: Where r _pred,i is the predicted rate of the ith reaction, r _true,i is the actual rate of the ith reaction, and m is the total number of reactions considered (e.g., microbiological degradation, oxygen consumption, nitrate reduction, etc.). The final loss function will include a number of error terms reflecting the combined effects of data errors, physical errors, and regularization. Where w _i is the weight of the ith reaction. r _i is the rate of the ith reaction:

Where dl=data Loss (Data error term), pl=physical Loss (Physical error term), PL _Monod =Monod equation error, PL _DO =dissolved oxygen (DO) related error, PL _NO3 =nitrate (NO ₃ -) related error, and other biochemical reaction errors reg= Regularization Loss (regularization term).

It should be noted that the design of the loss function generally requires consideration of all processes related to migration and degradation of groundwater pollutants to ensure that the model accurately reflects the actual behavior of the pollutants. In addition to using biodegradation equations such as Monod equations, the following physical equations related to contaminant migration can be embedded in the loss function. Contaminants are diluted by the flow in groundwater. This effect can be modeled by adding a model of the dilution process, such as the convection-diffusion equation:

where v is the flow velocity vector, D is the diffusion coefficient, and C is the contaminant concentration. Contaminants may volatilize from the groundwater into the gas phase. Modeling of the volatilization process can be achieved by including related mass transfer equations, such as Henry's law: Where Q is the adsorption capacity, Q _max is the maximum adsorption capacity, K _a is the adsorption constant, and C is the contaminant concentration. The adsorption of contaminants on soil particles affects their migration in groundwater. This process can be described by an adsorption model, such as the Langmuir adsorption equation:

q=K_fCⁿ

Where Q is the adsorption capacity, Q _max is the maximum adsorption capacity, K _a is the adsorption constant, and C is the contaminant concentration.

S103, training a neural network model for inverting key parameters of a pollutant biodegradation numerical model, calculating errors in the training process, and improving the accuracy of inversion results by using an Adam optimization algorithm, wherein the method specifically comprises the following steps:

calculating the output of the network model from the input layer to generate a prediction result;

It should be noted that, the forward propagation process starts from the input layer, transfers the input data layer by layer, and outputs the prediction result through the convolution layer, the LSTM layer and the conversion layer. Starting from the input layers, the output of the network is calculated by the weights and activation functions of each layer. Activation value calculation for layer i:

a ^(l)＝f(W^(l)·a^(l-1)+b^(l)) wherein a ^(l) is the activation value of the first layer, W ^(l) is the weight matrix of the first layer, b ^(l) is the bias of the first layer, and f is the activation function, such as ReLU or Sigmoid. This step requires a layer-by-layer processing of the input data (e.g., the space-time characteristics of contaminant concentration, groundwater flow speed, etc.) to generate a predictive output of the model.

It should be noted that the input layer receives multidimensional input of the groundwater pollution system, including pollutant concentration, flow speed, temperature, porosity, dissolved oxygen concentration, etc., and initial parameters of physical constraint (such as maximum degradation rate μ _max of microorganism and half saturation constant K _s). Input data is processed by a convolution layer, and the function of the convolution kernel is to extract local characteristics of pollutants in space. The convolution operation operates on the input matrix through a sliding window to generate a new feature map. The LSTM layer processes the feature map from the convolution layer and captures the dynamics of the time series data. The core steps of convolution LSTM are the calculation of forgetting gate, input gate, hidden gate, the calculation of cell state and the calculation of hidden gate. The LSTM layer models the dynamic changes of contaminants over time. The LSTM layer handles long-term and short-term dependencies in time series data through gating mechanisms (forget gates, input gates, output gates), where forget gates decide which information to discard, input gates decide which new information to store into the cell state, and output gates decide which information to output.

It should be noted that, integrating the conversion layer into the forward propagation, features are first mapped to the input embedding space of the conversion layer. For time series data, the input is typically a feature map extracted through ConvLSTM or a hidden state H _LSTM of LSTM where E is the embedded feature matrix. Since the translation layer structure does not have built-in time information, position coding must be introduced to help the model understand the positional relationship in the time series. The position coding can be expressed as e= Embedding (H _LSTM) where t is the time step, d is the embedding dimension, and Pt is the position coding vector. The formula of adding position codes to embedded features is changed to: P _t＝[sin(t/10000^2i/d),cos(t/10000^2i/d) ] for i=0, 1..d/2 calculates a self-attention matrix, and the self-attention mechanism in the conversion layer is used to capture the dependency between different time steps: The conversion layer typically uses a multi-head attention mechanism to compute multiple self-attention heads in parallel and then concatenates the results MultiHeadAttention (E _pos)＝Concat(head₁,head₂,...,head_h)·W₀ where the computation of each head is: After the attention mechanism, the data is further processed through the feed-forward neural network layer FeedForward (X) = max (0, x·w ₁+b₁)·W₂+b₂ where W ₁ and W ₂ are weights of the feed-forward network and b ₁ and b ₂ are bias terms.) after each attention and feed-forward network layer, the training is optimized using layer normalization and residual connection: layerNorm (x+Sublayer (X)), where Sublayer (X) represents the layer through the attention or feed-forward network. Combine the output Y-transform of the transform layer with the output of the other network layers. In the final stage of forward propagation, the transformed output is ultimately predicted as an input to the full connection layer: Y _final＝W_fc·Y_Transformer+b_fc applies the appropriate activation function (e.g., linear activation function) at the output layer to generate the final predicted value for the specific prediction task (e.g., biodegradation parameter inversion): In the forward propagation of a convolutional LSTM network incorporating a translation layer, data first passes through the convolutional layer to extract spatial features and then the time series dynamic features are processed by ConvLSTM. Then, the conversion layer captures long-term dependence and global features through a self-attention mechanism, and finally generates a prediction result. In this way, the model can simultaneously utilize local spatial information and global time dependence, thereby capturing the space-time variation and biodegradation dynamics of groundwater pollutants more accurately. The final output layer is responsible for predicting the target parameters of the model, such as the maximum degradation rate mu _max of the microorganism and the half-saturation constant K _s, which are the key to parameter inversion. The output result is AndThey are compared with the actual values and used to calculate the losses.

Calculating a loss value of the model by using the loss function, and adjusting the weight in the network output and the loss function by minimizing the loss function so as to balance the importance of the data error item and the physical error item;

It should be noted that the loss function is used to calculate the difference between the model output and the actual tag, resulting in a loss value. The choice of the loss function depends on the specific task. The difference between the predicted and true values is measured using Mean Square Error (MSE), and the accuracy of the prediction class is assessed using cross entropy loss. The network output is adjusted by minimizing the loss function so that the network output accords with the physical laws of biodegradation dynamics and chemical component interaction. The weights in the loss function are adjusted to balance the effects of the data error term and the physical error term to optimize the predictive performance of the model. The predicted values of the model are obtained from the output layer of the neural network. Assume that the predicted value of the output layer is Where is the network's prediction for each sample, the shape is (B, N), where B is the lot size and N is the number of predictors (typically the number of single predictors). The actual tag value is obtained from the dataset. The actual label Y is the target value of the network, andThe shape of (a) is the same, i.e., (B, N). Calculating the square of the difference between each sample predicted value and the actual value: Wherein SquaredError _i is the square error of the i-th sample. Averaging the square errors of all samples to obtain the mean square error of the batch:

Where B is the batch size and N is the number of predictors. During training, MSE was calculated once per batch. The MSEs for all batches may be averaged for the entire training set to obtain the final loss value.

Calculating the gradient of the loss function about output from the output layer, reversely transmitting the gradient back to each layer, finishing gradient accumulation by applying a chain rule, and updating network parameters by using an Adam optimization algorithm;

it should be noted that the weights are updated layer by back-propagating through calculating the gradient of the loss function to the network parameters. First the gradient of the loss function to the output layer activation value is calculated. For the mean square error loss function:

wherein, delta ^(L) is the error of the output layer, Is a predicted value and y is a true value. Then calculate the gradient of the loss function to the output layer weight: where a ^(L-1) is an activation value of a layer preceding the output layer. For the hidden layer, the error is propagated forward layer by layer. The gradient of each layer is calculated as δ ^(l)＝(W^(l+1))^T·δ^(l+1)·f′(z^(l)) where δ ^(l) is the weight matrix of the error W ^(l+1) of the first layer from the first layer to the first +1st layer, f' (z ^(l)) is the derivative of the activation function of the first layer, and z ^(l) is the weighted input of the first layer. Then calculate the gradient of the layer-i weight: And updating the network weight through an Adam optimization algorithm by using the calculated gradient. Adam's algorithm uses first order momentum (mean) and second order momentum (variance) to adjust the learning rate: And Where m _t is the first order momentum of the gradient, v _t is the second order momentum of the gradient, and β ₁ and β ₂ are the decay rates of the momentums. The calculation deviation of the first-order momentum and the second-order momentum is corrected, and the formula is as follows: And The weights are updated according to the corrected momentum, and the formula is as follows: Where η is the learning rate and ε is a constant to prevent divide-by-zero errors.

And the loss function value and the performance index in the training process are monitored, so that the problem of over fitting is avoided.

It should be noted that, the change of the loss value is monitored in real time during the training process, so as to ensure that the loss function is gradually reduced. The possible overfitting phenomenon of the model can be judged by the increase of the loss value of the verification set. In addition to the loss function, performance metrics of the model, such as gradient, recall, etc., need to be monitored. The gradient values are monitored, and changes in the gradient are periodically checked and monitored. The method mainly focuses on the mean value and standard deviation of the gradient, draws a histogram or a box diagram of the gradient, checks whether the gradient is uniformly distributed, has abnormal values, and tracks the change trend of the gradient. And adjusting a training strategy according to the gradient monitoring result. If a gradient explosion (too large) or a gradient disappearance (too small) is observed, these problems can be alleviated by adjusting the learning rate (e.g., using a learning rate scheduler or learning rate decay strategy). In the case of gradient explosion, gradient clipping may be applied to limit the maximum value of the gradient, preventing excessive parameter updates. If gradient problems occur frequently, it may be necessary to check and adjust the weight initialization strategy of the model. Gradient monitoring data is recorded and analyzed to identify potential problems or improvement points. A visual chart of the training process, such as a gradient change curve, is generated to facilitate in-depth analysis of the model training process. And carrying out necessary adjustment on the model training process and super-parameter settings (such as learning rate, optimizer and the like) according to the analysis result so as to ensure the stability of the training process and the effectiveness of the model.

S104, in one embodiment of the invention, integrating the observed data and the model prediction result, determining the final parameter setting of the numerical model, and carrying out quantification of the groundwater damage real object, wherein the method specifically comprises the following steps:

And constructing an ensemble Kalman filter, integrating the observed data and the model prediction, and iteratively updating the ensemble members.

It should be noted that, the ensemble kalman filter is an advanced data assimilation method combining observed data with model prediction results. In the inversion and verification process, an ensemble Kalman filter method (EnKF) is used for continuously updating the model state, and the estimation of key parameters is optimized by combining observation data and a numerical simulation result. Firstly, state prediction is carried out, and concentration distribution and change trend of pollutants in a groundwater system are predicted by using a numerical simulation model. And then, carrying out state updating, combining field observation data, updating a prediction result of the model through a set Kalman filter, and optimizing the estimation of the key parameters. The initialization set is first performed to construct the set kalman filter. A set of samples (set members) of the initial state is generated, which can be generated by perturbing the initial conditions. Let the model state be x, the initialization set be { x ₁ ⁰,x₂ ⁰,…,x_N ⁰ }, each member x _i ⁰ is the state sampled from the initial distribution. Predicting each set member through a model to obtain a prediction state: Where f (·) is the state transfer function. Calculating a mean value of the prediction set: Calculating covariance matrix P ^pred of the prediction set: and respectively calculating the mean and covariance matrix of the observed values: And And calculating a filter gain matrix K=P ^predH^T(HP^predH^T+R)^-1, wherein H is an observation operation matrix, and R is an observation noise covariance matrix. Updating the collection members: Where y is the observed data.

Fine tuning the model on the validation set, using the output of the ensemble kalman filter to guide the tuning of the model parameters;

it should be noted that, the current model is used to predict the data of the verification set, so as to obtain the error between the prediction result calculated by the prediction result and the observed data of the actual verification set: where y _valid is the actual observation of the validation set. The model parameters are adjusted based on statistical characteristics of the error, such as mean square error. Optimization algorithms (e.g., gradient descent) can be used to minimize the loss function and thereby update the model parameters. The updated state of the EnKF is taken as the initial state of the model so as to be better suitable for verification set data.

Evaluating generalization capability of the model on the test set, and evaluating prediction accuracy and reliability of the model;

The test set data is predicted by using the trained model to obtain a predicted result of the model, and an error between the predicted result and the actual test set observation data is calculated. Common evaluation metrics include Mean Square Error (MSE), root Mean Square Error (RMSE), and Mean Absolute Error (MAE). And analyzing the value of the evaluation index, and judging the performance of the model on unseen data.

Performing contrast verification of a neural network parameter inversion model, and ensuring feasibility and accuracy of the parameter inversion method;

It should be noted that by cross-verifying the different data sets, the performance of the model on the unknown data set is ensured. Cross-validation involves dividing the data set into a training set and a validation set, training the model on the training set, and evaluating the generalization ability of the model on the validation set. The dataset is divided into a plurality of folds. For example, 5-fold cross-validation divides the data into 5 subsets. For each fold, one of the subsets is taken as the validation set and the remaining subset is taken as the training set. The model is trained and performance is evaluated on the validation set. The evaluation index (e.g., MSE, RMSE, MAE) for each verification is recorded. The mean and standard deviation of the evaluation index of all folds are calculated to evaluate the mean performance and stability of the model. Based on the results of the cross-validation, the parameter settings that perform best in all tradeoffs are selected. These parameter settings should be such that the model performs well on both the training set and the validation set. And (3) carrying out final model evaluation, and evaluating finally selected model parameters on a complete test set to ensure the generalization capability of the model in practical application.

The underground water numerical model after the calibration parameters are operated simulates the natural attenuation process of pollutants in underground water, the pollutant concentration distribution obtained through simulation is compared with actual observation data, and the feasibility and the accuracy of the parameter inversion method are verified. And (3) combining an actual site recovery case, performing arrangement analysis on the pollutant concentration of each monitoring well at each site 150 days after the monitoring day, and drawing a concentration distribution diagram of the groundwater pollutant of the site, namely, a pollution plume (shown in fig. 5 a) obtained by actual observation data, which is used as a verification reference object. According to the traditional solute transport simulation method of groundwater pollutants, the biodegradation coefficient obtained by an experimental method or an empirical method is input into a numerical model, and numerical simulation programs such as MODIflow, RT3D and the like are operated. The prediction of the distribution of pollutants in the groundwater is realized by solving a mathematical model of the groundwater system, and the space-time distribution of pollution feathers is simulated by inputting known parameters such as model parameters, boundary conditions and the like into the model. The pollution plume space-time distribution (shown in figure 5 b) obtained by forward modeling is taken as a basic data set and is input into a parameter inversion model based on a neural network, a reverse mapping network model from output to input is established by using a reverse propagation algorithm, the value of a biodegradation parameter is continuously adjusted and updated, the updated value of the variable to be calculated is substituted into a numerical simulation model for calculation, and the corresponding pollution plume distribution (shown in figure 5 c) is obtained until the error between the value and the actual pollutant concentration distribution meets the minimum convergence rule. By analyzing the results of on-site observation, simulation and simulation-optimization of the actual pollution site, compared with the result of numerical simulation of the non-parametric inversion model, the accuracy of underground water pollution plume distribution is improved by about 20% under the condition that the neural network parametric inversion model performs biodegradation parameter calibration, and the accuracy is more similar to the on-site data of actual observation. By using field observation data, a traditional numerical simulation model and a neural network model for inverting biodegradation parameters, the accuracy of groundwater pollutant distribution prediction can be improved by verifying the neural network parameter inversion method and the model, and the accuracy and reliability of a physical quantization link of groundwater ecological damage can be ensured.

It should be noted that, predicting the concentration distribution of groundwater pollutants in future sites is a key step for carrying out quantification of groundwater damage objects. And substituting the obtained key parameters (such as microbial degradation rate and the like) into a traditional groundwater numerical simulation model such as MODIflow, MT3D or TOUGH2 and the like to perform model calibration. By adjusting the parameters, the pollutant migration path and degradation rate simulated by the model are consistent with field observation data. And comparing the inverted parameters with actual observation data, and verifying the accuracy of model prediction. The test data may be from long-term observations of a groundwater monitoring well or field experimental data. The prediction capability of the model is ensured by comparing the simulation result with the concentration distribution of the actual observation data. Key parameters (such as degradation rate, reaction kinetic parameters and the like) obtained based on neural network inversion are integrated into a traditional groundwater numerical simulation model. For example, the transmission rate and reaction rate parameters are adjusted in MODFLOW, the contaminant migration and diffusion coefficients are adjusted in RT3D, and so on. And forming a complete groundwater pollutant simulation system through coupling the neural network model and the numerical simulation model. The neural network provides a preliminary estimate of the key parameters, and numerical modeling is used to predict the spatial and temporal distribution of the contaminants. According to the obtained result of the numerical simulation of the groundwater pollutants, relevant data can be obtained so as to carry out physical quantification of ecological environment damage, and partial formulas are as follows:

Wherein, the H-period damage amount, the period from the occurrence of the T-ecological environment damage to the recovery to the baseline period (between T ₀-t_n), T ₀ represents the initial year, which is the period from the occurrence of the ecological environment damage, T _n represents the end year, which is the period from the recovery to the baseline period, the T-reference year, which is the period from which the ecological environment damage identification evaluation is generally selected as the reference year, and the number of ecological environment service functions in the damaged region from R _t to T-th year. For a resource, the parameter may be the number of individuals, biomass, life time value, number of resources, energy, productivity or other measure of significant impact on the living being or ecosystem, the parameter may be the area of habitat affected (hectare) for servicing, the river length or other habitat area, etc. d _t -proportion of damaged area ecological environmental service function relative to baseline loss. The ratio varies with time and takes on a value of 0-1. r-the coefficient of the impression, the recommended value is 2% -5%. The groundwater pollutant simulation system realizes effective operation of a physical quantification link of groundwater ecological damage through a perfect and accurate simulation optimization mechanism, and provides basis and method for evaluating restoration feasibility and formulating restoration strategies for groundwater pollution sites taking natural attenuation monitoring as a restoration scheme.

The foregoing is merely illustrative embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think about variations or substitutions within the technical scope of the present invention, and the invention should be covered. Therefore, the protection scope of the invention is subject to the protection scope of the claims.

Claims (3)

1. The method for inverting the key parameters in the groundwater pollutant biodegradation numerical model based on the neural network algorithm is characterized by comprising the following steps of:

1) The high-dimensional multi-scale data is effectively processed by preprocessing and refining dimension reduction of input data from different sources;

2) Constructing a multi-layer neural network architecture under a physical information neural network framework, embedding a relevant reaction equation of a pollutant natural attenuation process, and coupling a biochemical reaction mechanism and a data driving model;

3) Training a neural network model for inverting key parameters of the pollutant biodegradation numerical model, calculating errors in the training process, and improving the accuracy of inversion results by using an Adam optimization algorithm;

4) Integrating the observation data and the model prediction result, determining the final parameter setting of the numerical model, and carrying out quantification of groundwater damage objects;

Step 2) constructing a multi-layer neural network architecture under a physical information neural network framework, embedding a relevant reaction equation of a pollutant natural attenuation process, and coupling a biochemical reaction mechanism and a data driving model, wherein the method comprises the following steps of:

Constructing a neural network parameter inversion model combining a groundwater pollutant degradation mechanism and a data driving model based on a convolutional neural network architecture in a physical information neural network framework;

Defining an input layer and an output layer, constructing a neural network structure of a plurality of hidden layers, and capturing global dynamic changes of model parameters on a long time scale;

designing a comprehensive loss function, quantifying the difference between the output result of the neural network model and the groundwater numerical model, embedding a biodegradation related equation of pollutants into the loss function in a residual form, and realizing unification of a reaction mechanism and data driving;

Step 3) training a neural network model for inverting key parameters of the pollutant biodegradation numerical model, calculating errors in the training process, and improving the accuracy of inversion results by using an Adam optimization algorithm, wherein the method comprises the following steps of:

calculating the output of the network model from the input layer to generate a prediction result;

Calculating a loss value of the model by using the loss function, and adjusting the weight in the network output and the loss function by minimizing the loss function;

Calculating gradient of the loss function about output from the output layer, reversely transmitting the gradient back to each layer by using a chain rule, and selecting an Adam optimization algorithm to update network parameters;

And the loss function value and the performance index in the training process are monitored, so that the problem of over fitting is avoided.

2. The method for inverting key parameters in a groundwater pollutant biodegradation numerical model based on a neural network algorithm according to claim 1, wherein the step 1) is to effectively process high-dimensional multi-scale data by preprocessing and refining dimension reduction of input data from different sources, specifically as follows:

Collecting and sorting multi-source multi-scale input data;

performing data cleaning and standardization processing, executing characteristic engineering, and normalizing the data;

And (5) performing dimension reduction on the high-dimensional data by using a kernel principal component analysis method.

3. The method for inverting key parameters in a groundwater pollutant biodegradation numerical model based on a neural network algorithm according to claim 1, wherein the step 4) integrates observation data and model prediction results, determines final parameter settings of the numerical model, and develops quantification of groundwater damage entities, and specifically comprises:

constructing an aggregate Kalman filter, integrating observation data and model prediction, and iteratively updating the aggregate members;

Fine tuning the model on the validation set, using the output of the ensemble kalman filter to guide the tuning of the model parameters;

Evaluating generalization capability of the model on the test set, and evaluating prediction accuracy and reliability of the model;

and (5) carrying out comparison verification of the neural network parameter inversion model, and ensuring feasibility and accuracy of the parameter inversion method.