A method for predicting groundwater dynamic evolution

Abstract

The present invention provides a method for predicting the dynamic evolution of groundwater, which belongs to the field of groundwater prediction technology based on deep learning. The method collects hydrological parameters and geographical location data of monitoring points to construct a regional hydrogeological input tensor. Then, an initial finite element model is established to perform spatial extrapolation and flow field completion on the groundwater level distribution. Based on the initial finite element model structure, a global optimization algorithm based on target decomposition is designed to perform real-time structural optimization on the finite element model. Then, the finite element numerical solution is used to simulate the evolution of groundwater in non-monitoring areas, and multi-node, physically consistent hydrological time series data with improved resolution is generated. The generated hydrological time series data is input into the designed perceptual water level prediction model, and the groundwater level prediction results and corresponding groundwater level heat maps for multiple future time periods and multiple locations are output. The present invention realizes a more accurate, continuous and interpretable high-precision prediction of the groundwater system, providing reliable support for the scientific management of groundwater resources.

Description

Technical Field

[0001] The present invention belongs to the technical field of groundwater prediction based on deep learning, and in particular relates to a method for predicting the dynamic evolution of groundwater. Background Art

[0002] As an important underground freshwater resource, groundwater's dynamic changes are directly related to a variety of socioeconomic activities, including agricultural irrigation, water resource scheduling, ecological protection, and urban water supply. Influenced by multiple factors such as rainfall, evaporation, soil properties, geological structure, and human activities, groundwater systems typically exhibit significant spatiotemporal heterogeneity and highly nonlinear evolutionary characteristics. Currently, commonly used groundwater prediction methods rely on time series analysis of monitoring points, lacking modeling of groundwater physical mechanisms and sufficient exploration of spatial flow field information, making it difficult to achieve reliable inferences in non-monitored areas. Furthermore, due to limited sensor deployment density and incomplete data collection, existing methods still have significant limitations in data completion, boundary response, and evolution trend prediction, making it difficult to meet the needs of refined management and regional regulation.

[0003] At present, the prediction of groundwater dynamic evolution mainly includes the following methods:

[0004] Prediction methods based on statistical regression and time series: This type of method is based on traditional mathematical statistics and time series modeling, including multiple linear regression (MLR), autoregressive moving average (ARMA / ARIMA), grey prediction models, etc., and mainly achieves short-term prediction of groundwater levels by fitting time-varying trends with historical water level data. This type of method has certain practicality in early groundwater research, with simple modeling and high computational efficiency. However, it generally relies on the stationarity of data and single time dimension modeling, and cannot effectively characterize the nonlinear evolution characteristics of groundwater in complex hydrogeological environments. It also has limited response capabilities to sudden events and changes in boundary conditions, resulting in poor prediction accuracy and adaptability;

[0005] Numerical simulation method based on physical modeling: This method establishes the governing equations of groundwater movement (such as Darcy's law, groundwater continuity equation, Richards equation, etc.), and combines regional boundary conditions, initial water level field and geological parameters, and uses numerical methods such as finite difference (FDM), finite element (FEM) or finite volume (FVM) to solve, thereby achieving spatial distribution simulation of groundwater flow and evolution process. Its advantage is that it has the ability to clearly explain the physical mechanism and is suitable for studying groundwater systems under multi-boundary and multi-layer structures. However, this type of method is usually sensitive to the model structure setting, relies on a large number of measured parameters and geological information, and has a high acquisition cost, making it difficult to quickly deploy in actual projects. At the same time, the extrapolation ability in areas where data is missing is limited, and the simulation results are easily affected by initial and boundary errors;

[0006] Data-driven machine learning prediction methods: With the advancement of data acquisition and computing power, groundwater level prediction has gradually incorporated machine learning and deep learning techniques, such as support vector regression (SVR), random forests (RF), long short-term memory networks (LSTM), and gated recurrent units (GRU). These methods excel at modeling nonlinear sequences and can directly learn evolutionary patterns from historical data without requiring explicit physical equations. However, they generally suffer from the following issues: insufficient spatial information modeling capabilities, limited to predictions for single or a small number of points; a lack of physical constraints on the extrapolated region, resulting in poor interpretability of the results; and poor adaptability to boundary changes and extreme conditions. Model stability is easily affected by the quality of the training data, making it difficult to generalize to areas with highly heterogeneous formations.

[0007] In summary, existing groundwater dynamic evolution prediction methods have obvious deficiencies in physical mechanism characterization, spatial completion capability, and model stability, making it difficult to simultaneously take into account the spatiotemporal evolution characteristics under complex geological structures and engineering application requirements. Summary of the Invention

[0008] To address the above problems, the present invention aims to design a new groundwater prediction method that integrates physical constraint modeling and data-driven prediction, and has good spatial generalization and dynamic evolution expression capabilities, so as to achieve more accurate, continuous and interpretable high-precision predictions of groundwater systems, thereby providing reliable support for the scientific management and regulation of groundwater resources.

[0009] The present invention proposes a method for predicting the dynamic evolution of groundwater, comprising the following steps:

[0010] S1, collects hydrological parameter data, including groundwater level monitoring data, hydrogeological parameters and initial water level information, and collects geographical location data of monitoring points to construct a regional hydrogeological input tensor;

[0011] S2, based on the input data constructed in S1, establish an initial finite element model FEM to perform spatial extrapolation of groundwater level distribution and flow field completion;

[0012] S3, based on the initial finite element model FEM structure designed in S2, designs a global optimization algorithm based on target decomposition, and performs real-time structural optimization on the regional division method, mesh density distribution and boundary condition setting of the finite element model;

[0013] S4, simulates the groundwater evolution in non-monitoring areas through finite element numerical solution to generate multi-node, physically consistent hydrological time series data with improved resolution;

[0014] S5, inputs the hydrological time series data generated by S4 into the constructed and trained flow field-aware water level prediction model, and outputs the groundwater level prediction results at multiple time points and multiple locations in the future and their corresponding groundwater level heat maps; the flow field-aware water level prediction model includes a spatiotemporal feature fusion encoder, a physical constraint groundwater level prediction module and a heat map generation module.

[0015] Preferably, the hydrological parameter data includes underground water level monitoring values ​​collected by pressure water level gauges. , using soil moisture sensors to collect soil moisture , pore water pressure sensor collects pore water pressure , conductivity sensor monitors conductivity , deploy rain gauges to collect surface precipitation , using evaporation dishes combined with temperature and humidity sensors to estimate surface evaporation , weather sensor obtains temperature and humidity ; The above parameters together constitute the hydrological parameter data ;

[0016] The geographical location data of the monitoring points are collected in the area where the groundwater dynamic evolution is to be carried out. Monitoring points, record The longitude and latitude coordinates of the monitoring points are obtained to obtain the geographical location sequence of the monitoring points. .

[0017] Preferably, the S2 specifically includes:

[0018] S21, regional modeling and initial boundary setting: Based on the acquired multi-monitoring point location coordinate data , establish a two-dimensional spatial network coordinate system containing all monitoring points in the area , and obtain the initial time point based on the hydrological parameter data of the complete sampling time point The initial hydrological data of all monitoring points at time t is recorded as the initial groundwater level field The initial groundwater level field is used as the starting state of the finite element simulation; in addition, the boundary conditions are set as mixed boundaries including constant boundary, no-flow boundary, and communication boundary;

[0019] S22, grid structure design and parameter preset:

[0020] Region division method initialization and optimization range: The region division method parameters are defined as , whose value range includes: Regular network partitioning, Delaunay triangulation, Quadtree partitioning, and Geological unit guided zoning, i.e. ;

[0021] Grid density parameter initialization and optimization range: Under the selected area division method, a total of sub-regions, set the grid density for different sub-regions , Indicates the The grid density of the region, and ; and set the maximum grid density to , the minimum grid density is ; Therefore, the grid density parameter to be optimized is ,and ;

[0022] S23, Multi-parameter driven joint finite element modeling: Construct a multi-physics field coupled finite element model based on the regional grid and the initial field As input, a multi-physics field coupling control equation system is constructed according to the existing physical constraint equations, including: groundwater flow control equation, Richards equation, head-pressure conversion formula, conductivity migration equation, surface evaporation estimation equation and heat conduction equation.

[0023] Preferably, said S3 establishes a multi-index optimization problem of a multi-physics field coupled finite element model structure based on the established decision variables and the established objective function;

[0024] The decision variables are defined as:

[0025] Based on the determined parameters to be optimized 、 、 Determine decision variables and boundary parameters ,in , 、 is the boundary flux adjustment parameter; the regional division method parameter ,and ; The grid density parameter to be optimized is ,and ; The complete set of decision variables is defined as: ;

[0026] Among them, the objective function is designed as a multi-index weighted objective function:

[0027]

[0028] in 、 、 is the hyperparameter weight;

[0029] Completion precision loss , used to measure the predicted hydrological parameters of monitored locations during the FEM completion process Compared with the measured monitoring value The error between

[0030] Physical consistency error , a residual measure used to measure the violation of the governing equations in the solution obtained by FEM inference;

[0031] Mesh complexity penalty , which is used to limit the computational burden caused by excessive mesh refinement.

[0032] Preferably, the specific process of S4 includes:

[0033] S41, initial value assignment and boundary condition loading: According to the initial groundwater level field , and set the initial boundary parameter combination to , initial area division method for Regular network partitioning, initial grid density All preset ;

[0034] S42, using implicit finite element time-stepping strategy, using coupled control equations For each time step Perform a step-by-step evolutionary solution to obtain the coordinate system of the entire region at the corresponding moment Estimated values ​​of all hydrological parameters;

[0035] S43, based on the complete estimation results of the hydrological parameters in the region, select the parameter supplement degree as , and in the regional coordinate system Sampling is performed under Group supplementary hydrological data , and the corresponding locations of the supplementary data ; Combine the supplemented data with the original collected data to form Complete hydrological data and ;and , , and constitute the physical consistency water level time series data .

[0036] Preferably, the spatiotemporal feature fusion encoder in the flow field perception water level prediction model is used to extract enhanced spatiotemporal features, including a graph convolutional network layer, a hole convolution layer, a gated unit layer and a spatiotemporal cross attention mechanism layer; for the obtained physical consistency water level time series data ,in is the time step, is the number of water level space location nodes, is the feature dimension, and the specific processing steps are as follows:

[0037] S51, will The input graph convolutional network layer gradually extracts spatial topological features. The graph convolutional network layer consists of two graph convolutional layers, each of which contains a 32-channel graph convolution kernel, a batch normalization layer, and a GeLU activation function;

[0038] S52, will The dilated convolution layer is input to capture long-term patterns through dilated convolution, learn the seasonal variation trend of water level, and obtain long-term time series features;

[0039] S53, will The input gated unit layer learns the short-term fluctuation pattern of the data, learns the extreme change pattern of the water level, and obtains the short-term time series features;

[0040] S54, the spliced ​​temporal features after channel splicing of spatial topological features, long-period temporal features and short-period temporal features are input into the spatiotemporal cross attention mechanism to obtain the spatiotemporal feature weights;

[0041] S55, multiplying the spatiotemporal feature weight by the concatenated temporal feature and then adding the result to the spatial topological feature to obtain the enhanced spatiotemporal feature.

[0042] Preferably, the physical constraint groundwater level prediction module in the flow field sensing water level prediction model is used to obtain groundwater level prediction results at multiple moments in the future; this module is implemented based on the gated unit and Darcy's law physical constraints, and the cell state update formula of the physical constraint groundwater level prediction module is as follows:

[0043]

[0044] in for The cell state at any moment, for The forget gate output at the moment, for The input gate output at time t, for Estimated cell state at moment in time; is the constraint strength coefficient of Darcy's law, which controls the constraint strength of Darcy's law on the predicted groundwater level of the gated unit; is the discretized residual of Darcy's law, reflecting the degree to which the groundwater level predicted by the gated unit violates the physical law. The specific calculation formula is as follows:

[0045]

[0046] in, represents the gradient symbol, is the groundwater permeability, obtained using a pumping test; is the hydraulic gradient calculated based on the spatial position, Calculation of groundwater level monitoring values ​​of adjacent spatial nodes in is the source-sink term, representing the net increase or decrease of water volume per unit area per unit time, which is The difference between surface precipitation and surface evaporation.

[0047] Preferably, the heat map generation module in the flow field sensing water level prediction model outputs a groundwater level heat map; the module includes a raster conversion layer and a hierarchical upsampling decoder, specifically as follows:

[0048] The groundwater level prediction results are input into the raster conversion layer and converted into a 64×64 low-resolution raster using the inverse distance weighted algorithm;

[0049] The low-resolution raster is input into the hierarchical upsampling decoder to obtain a spatial distribution heat map of the groundwater level prediction results. The hierarchical upsampling decoder consists of four sequentially connected upsampling networks, which extract the features of the groundwater level prediction results layer by layer and improve the resolution to obtain a 1024×1024 high-resolution spatial distribution heat map of the water level prediction results. Each upsampling network consists of a transposed convolution layer, a sub-pixel convolution layer, and a bilinear interpolation layer connected in sequence. The transposed convolution layer is used to capture the characteristics of non-uniform groundwater distribution. The sub-pixel convolution layer improves the resolution by channel reorganization of the features. The bilinear interpolation layer is used to ensure the smoothness of the groundwater level at different spatial locations and eliminate the step-like artifacts in the transition zone of geological units.

[0050] Preferably, the flow field sensing water level prediction model uses a YES optimization model training strategy, specifically including:

[0051] Constructing a joint training parameter set for the spatiotemporal feature fusion encoder and the physical constraint groundwater level prediction module ,in is the network structure parameter set of the spatiotemporal feature fusion encoder, is the network structure parameter set of the physical constraint groundwater level prediction module, is the learning rate, is the Darcy's law constraint strength coefficient;

[0052] Generate M joint training parameter samples using the Latin hypercube sampling method ;

[0053] Construct a parameter design space optimization problem based on KL divergence as follows:

[0054]

[0055] in Prior distribution of groundwater level, ,in for The mean groundwater level, for Standard deviation of groundwater level; represents Gaussian distribution; is the variational posterior distribution of groundwater level, ,in To utilize The average value of the groundwater level prediction results obtained by configuring the spatiotemporal feature fusion encoder and the physical constraint groundwater level prediction module for multiple future predictions is: is the standard deviation of the groundwater level prediction results; represents Gaussian distribution;

[0056] for For each sample in , solve the parameter design space optimization problem based on KL divergence and obtain the parameter set that satisfies Darcy's law ;

[0057] The root mean square error between the groundwater level prediction result output by the physical constraint groundwater level prediction module and the actual groundwater level result is used as the loss function to calculate the The root mean square error obtained by configuring the spatiotemporal feature fusion encoder and the physical constraint groundwater level prediction module respectively is recorded as the optimal parameter set of the model. .

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] (1) Flow field completion mechanism based on multi-physics coupling: Integrate the multi-physics control equations into the finite element simulation process to build a groundwater system completion mechanism with strong physical consistency and tight spatiotemporal coupling, significantly improving the integrity of groundwater level data and the credibility of modeling;

[0060] (2) Structural adaptive finite element modeling optimization strategy: A multi-objective joint optimization method integrating boundary adjustment, grid density control, and region division selection is proposed to achieve automatic adaptation and optimal configuration of the finite element modeling structure, significantly improving the generalization ability and evolution simulation accuracy of the model under heterogeneous strata and complex boundary conditions;

[0061] (3) Flow field-aware water level prediction model: It can fully capture the spatiotemporal evolution characteristics of hydrological data and generate a thermal map of the spatial distribution of groundwater levels at multiple moments in the future that meets physical constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a flow chart of the overall technical route of the present invention.

[0063] Figure 2 This is the overall framework diagram of the physical modeling optimization module.

[0064] Figure 3 Schematic diagram of the flow field sensing water level prediction model structure.

[0065] Figure 4 This is a thermal map of groundwater dynamic prediction at different time steps in the embodiment.

[0066] Figure 5 This is a comparison chart of groundwater level prediction accuracy of the three models under the RMSE index in the embodiment.

[0067] Figure 6 This is a comparison chart of groundwater level prediction accuracy of the three models under the MAE index in the embodiment. DETAILED DESCRIPTION

[0068] The present invention proposes a method for predicting the dynamic evolution of groundwater. The overall technical path includes the following core steps: first, a regional hydrogeological dataset containing multi-source sensor data such as groundwater level, soil moisture, pore water pressure, conductivity, rainfall, evaporation, temperature and humidity is constructed, and an input tensor with time and space constraints is formed based on geographic location and time series structure; then a finite element model containing multi-physics field control equations is established to perform spatial extrapolation and dynamic completion of the groundwater level distribution in non-monitoring areas, thereby enhancing the spatial integrity and physical consistency of the observed data; in addition, the present invention further designs an adjustable modeling structure, which realizes adaptive alignment of the finite element model structure with the actual hydrological evolution process by jointly optimizing the regional division method, grid density layout and boundary condition parameters; finally, a deep learning model with flow direction perception capability is constructed, and the completed high-quality time series data is used as input to jointly model the evolution trend of groundwater, thereby realizing accurate predictions of multiple moments and multiple spatial locations in the future, thereby realizing a closed-loop modeling process from physical drive to intelligent prediction.

[0069] The overall process of this embodiment is as follows Figure 1 As shown:

[0070] Hydrogeological dataset construction: Collect hydrological parameter data, including groundwater level monitoring data, hydrogeological parameters, and initial water level information, as well as geographic location data of monitoring points, to construct a regional hydrogeological input tensor. This provides multidimensional input data for finite element simulation and structural optimization. Furthermore, future groundwater level observations are used as labels to construct a prediction target set for supervised training.

[0071] Design a finite element driven flow field completion module: Based on the constructed input data, an initial finite element model (FEM) is established to perform spatial extrapolation of groundwater level distribution and flow field completion, providing more comprehensive data for prediction tasks.

[0072] Structurally adjustable physical modeling optimization module: Based on the designed initial finite element simulation structure, a global optimization algorithm based on target decomposition is designed to perform real-time structural optimization of the finite element model's regional division method, mesh density distribution, and boundary condition settings. This ensures that finite element simulation results are more consistent with measured water level data, improving model accuracy and spatial adaptability.

[0073] Generate multi-node, high-resolution physically consistent hydrological time series data: Use finite element numerical solution to simulate groundwater evolution in non-monitoring areas and generate multi-node, high-resolution physically consistent hydrological time series data;

[0074] Flow field-aware water level prediction model: The generated hydrological time series data is input into the constructed and trained flow field-aware water level prediction model, and the groundwater level prediction results at multiple times and locations in the future and their corresponding groundwater level heat maps are output.

[0075] The specific implementation process of the present invention is described in detail below with reference to specific embodiments.

[0076] 1. Construction of hydrogeological dataset

[0077] This paper aims to predict the dynamic evolution of groundwater based on regional groundwater monitoring data. Therefore, a hydrogeological dataset is first constructed. The specific contents include:

[0078] Hydrological parameter selection: Based on the needs of regional groundwater system modeling, key physical parameters that affect groundwater flow and evolution are selected, including: using pressure water level gauges to collect groundwater level monitoring values , using soil moisture sensors to collect soil moisture , pore water pressure sensor collects pore water pressure , conductivity sensor monitors conductivity , deploy rain gauges to collect surface precipitation , using evaporation dishes combined with temperature and humidity sensors to estimate surface evaporation , weather sensor obtains temperature and humidity ; These parameters together constitute the hydrological parameter combination [gl, sc, wp, cd, sp, ei, tp,hm].

[0079] Multi-point monitoring data collection: Since the groundwater corresponding to different spatial locations is different and has a direct impact on each other, it is necessary to select the area where the groundwater dynamic evolution is to be studied. monitoring points and collect multi-point monitoring data; specifically:

[0080] (1) Records The longitude and latitude coordinates of the monitoring points are obtained to obtain the geographical location sequence of the monitoring points. ,Right now ,in Indicates the The latitude and longitude coordinates of the monitoring points, and ;

[0081] (2) At the time point collection Hydrological parameter data of monitoring points ,in, Indicates at the time point , No. Hydrological parameters collected at each monitoring point;

[0082] (3) Targeting Monitoring points, collecting Hydrological data at complete sampling time points ,and ;

[0083] Therefore, the overall input data includes the geographical location sequence of all monitoring points in the region , and hydrological parameters at the complete sampling time points .

[0084] Groundwater level label: To achieve supervised modeling of the dynamic evolution of groundwater, the present invention constructs a groundwater level label corresponding to the monitoring input as the target output of the prediction model training; specifically:

[0085] (1) Set the prediction time step to , and collect the time points Groundwater level series at each monitoring point ,in Indicates the Monitoring points at time groundwater level, and , ;

[0086] (2) Collection Monitoring points in the complete prediction time step Groundwater level below , and use it as the output data of the prediction model.

[0087] Hydrogeological dataset construction: The input data obtained and , and the output data obtained As a set of hydrogeological data sets, based on this method, a total of The collected and constructed complete datasets are finally combined into a hydrogeological dataset.

[0088] 2. Design of flow field completion model based on finite element drive

[0089] Due to the spatiotemporal heterogeneity of groundwater systems, it is difficult to fully reflect the regional groundwater dynamic process by relying solely on hydrological data collected from a limited number of monitoring points. In addition, densely deployed sensors are complex and costly. Therefore, in order to solve the problems of incomplete data collection information and high costs caused by too many monitoring points, this paper designs a flow field completion model based on finite element drive; this model uses multi-monitoring point data constructed in stages to complete the flow field. and As input, a regional groundwater finite element model (FEM) with physical constraints is established. Under the control of boundary conditions and geological parameters, the water level state of the unobserved area is spatially deduced and dynamically completed, so as to obtain more complete hydrological information.

[0090] 1. Regional modeling and initial boundary setting: Based on the multi-monitoring point location coordinate data obtained in , establish a two-dimensional spatial network coordinate system containing all monitoring points in the area , and according to The data is obtained at the initial time point The initial hydrological data of all monitoring points at time t is recorded as the initial groundwater level field The initial groundwater level field is used as the starting state of the finite element simulation;

[0091] In addition, to ensure the physical rationality of the simulation, the boundary conditions are set to a mixed boundary including constant boundary, no-flow boundary, and communication boundary:

[0092]

[0093] in, Indicates at the time point , the coordinate point is The hydrological data corresponding to the monitoring points; represents the transmission coefficient, is the normal vector outside the boundary, and are the constant reference value and far-field benchmark value of each hydrological parameter respectively; , 、 is the boundary flux adjustment parameter. These three parameters together constitute the boundary parameters to be optimized ,Right now .

[0094] 2. Grid structure design and parameter preset: After completing the regional boundary condition setting, in order to support the stability of subsequent finite element calculations, the spatial grid within the region is divided and the structural parameters are preliminarily set; specifically:

[0095] (1) Region division method initialization and optimization range: The region division method parameters are defined as , whose value range includes: (Regular network division), (Delaunay triangulation), (quadtree partitioning), and (geological unit guided zoning), i.e. ;

[0096] (2) Grid density parameter initialization and optimization range: Under the selected area division method, a total of sub-regions, set the grid density for different sub-regions , Indicates the The grid density of the region, and ; and set the maximum grid density to , the minimum grid density is ; Therefore, the grid density parameter to be optimized is ,and .

[0097] 3. Multi-parameter driven joint finite element modeling: Construct a multi-physics field coupled finite element model based on the regional grid and the initial field. As input, a multi-physics field coupling control equation system is constructed based on the existing physical constraint equations, including: groundwater flow control equation, Richards equation, head-pressure conversion formula, conductivity migration equation, surface evaporation estimation equation, and heat conduction equation; the final expression is:

[0098]

[0099] in, is the state vector, which contains All hydrological parameters in; represents the time partial derivative of all variables, represents the spatial gradient of all variables; is the two-dimensional space coordinate, is the time variable; is the total coupled control equation system including the above physical constraint equations.

[0100] 3. Construction of a structurally adjustable physical modeling optimization module

[0101] Since the simulation accuracy of the finite element completion process is highly dependent on its modeling structure (including regional division, grid density and boundary condition setting), and manual setting is difficult to take into account both multi-region adaptability and hydrological evolution characteristics fitting effect, the present invention designs a physical modeling optimization module with adjustable structure. This module automatically adjusts the finite element structural parameters by introducing a joint optimization strategy. 、 ,as well as , so that the completion results are closer to the measured data; physical modeling optimization modules such as Figure 2 As shown, the specific process is as follows:

[0102] 1. Decision variable definition: based on the determined parameters to be optimized 、 、 Identify the decision variables, specifically, the boundary parameters ,in , 、 is the boundary flux adjustment parameter; the regional division method parameter ,and ; The grid density parameter to be optimized is ,and ;

[0103] Therefore, the complete set of decision variables is defined as: .

[0104] 2. Objective function design: To measure the consistency between the finite element completion results and the measured data under the current structural settings, a multi-index weighted objective function is constructed. ,in 、 、 is the hyperparameter weight, and the objective function specifically includes:

[0105] (1) Completion accuracy loss , used to measure the predicted hydrological parameters of monitored locations during the FEM completion process Compared with the measured monitoring value The error between them is:

[0106]

[0107] in, and Respectively indicate the time points , No. Predicted and measured hydrological data for each monitoring point;

[0108] (2) Physical consistency error , which is used to measure the residual measure of the violation of the governing equations in the solution obtained by FEM inference, namely:

[0109]

[0110] in, is the total coupled governing equation system, is the regional spatial domain, For all A moment, A set of predicted hydrological data for each monitoring point;

[0111] (3) Mesh complexity penalty , which is used to limit the computational burden caused by excessive mesh refinement, is defined as:

[0112]

[0113] Therefore, the optimization goal of the structure-adjustable physical modeling optimization module is ;

[0114] Based on the established decision variables and the established objective function, a multi-index optimization problem of the multi-physics field coupled finite element model structure is established.

[0115] 3. Design a global optimization algorithm based on target decomposition to solve the multi-index optimization problem of the physical field coupled finite element model structure and obtain the optimal decision variable set , the specific steps are as follows:

[0116] 1) First, the Latin hypercube sampling method is used to 、 、 、 and Sampling within its value range Obtained The method is to use each group of decision variables as the parameters of the physical field coupled finite element model, and then simulate the physical field coupled finite element model to calculate the transformation volume and fracture permeability corresponding to each group of decision variables. The method is to use each group of decision variables and their corresponding completion accuracy loss, physical consistency error and mesh complexity penalty to calculate the objective function value. Finally, the decision variables and the target value are combined to obtain the population. , among which Solution ,in For the The target value of a solution;

[0117] 2) Yes The completion accuracy loss, physical consistency error and mesh complexity penalty of all solutions in the rank order are sorted in ascending order, and the completion accuracy loss is ranked first. The solution gives skill factor Composition of populations , the physical consistency error ranks first The solution gives skill factor Composition of populations , the mesh complexity penalty is ranked first The solution gives skill factor Composition of populations , the solutions that are not given skill factors are organized into a diverse population ;

[0118] 3) Initialize the number of evaluations, set the maximum number of evaluations, and set the cross-task evolution value ;

[0119] 4) Generate a random number between 0 and 1 ;

[0120] 5) When When, respectively 、 and Perform crossover and mutation operations to obtain the offspring population 、 and This method of evolution within the population enables the solutions of the three skill factors to explore the decision space with three types of indicators as optimization targets: completion accuracy loss, physical consistency error, and mesh complexity penalty, and obtain solutions that can achieve smaller values ​​in completion accuracy loss, physical consistency error, and mesh complexity penalty respectively; when When two skill factor solutions are randomly selected, crossover and mutation operations are performed to obtain the offspring population 、 and This method of migration evolution between populations can promote knowledge transfer between populations with different skill factors and guide the population to the global optimal target value in the target space. convergence;

[0121] 6) Update the number of evaluations and compare the number of evaluations with Addition;

[0122] 7) Respectively and The combined population 、 and The combined population as well as and The combined population Perform natural selection based on indicators. The smaller the indicator value, the higher the ranking of the solution. The completion accuracy loss indicator is used as The selection index is selected as the first The population individuals form the next generation population and update ; Physical consistency error index as The selection index is selected as the first The population individuals form the next generation population and update ; The grid complexity penalty index is used as The selection index is selected as the first The population individuals form the next generation population and update ;

[0123] 8) Yes Perform crossover and mutation operations to obtain the offspring population ;

[0124] 9) Update the number of evaluations and compare the number of evaluations with scale Addition;

[0125] 10) Yes and The combined population performs natural selection based on the objective function value. The smaller the objective function value, the higher the ranking of the solution. The solution is used as the next generation population and updated ;

[0126] 11) Yes 、 、 and The combined population performs natural selection based on the objective function value, and selects the top The solution is used as the next generation population and updated ;

[0127] 12) Determine whether the number of evaluations is greater than the maximum number of evaluations. If so, output Otherwise, repeat steps 2)-11);

[0128] Step 12) Output That is the optimal solution set for the multi-index optimization problem of the physical field coupled finite element model structure. Select the solution with the minimum objective function value The decision variables As the optimal physical field coupling finite element model structural parameters; the optimal physical field coupling finite element model structural parameters are input into the finite element model to obtain the optimal physical field coupling finite element model.

[0129] 4. Use the optimal physical field coupled finite element model to simulate the groundwater evolution in the non-monitoring area and generate multi-node, high-resolution physically consistent hydrological time series data. Joint time series simulation and completion process:

[0130] (1) Initial value assignment and boundary condition loading: Based on the initial groundwater level field , and set the initial boundary parameter combination to , initial area division method for (Regular network partitioning), initial grid density All preset ;

[0131] (2) Using implicit finite element time-stepping strategy, using coupled control equations For each time step Perform a step-by-step evolutionary solution to obtain the coordinate system of the entire region at the corresponding moment Estimated values ​​of all hydrological parameters;

[0132] (3) Complete data output: Based on the complete estimation results of the hydrological parameters in the area, the parameter supplement degree is selected as , and in the regional coordinate system Sampling is performed under Group supplementary hydrological data , and the corresponding locations of the supplementary data ; Combine the supplemented data with the original collected data to form Complete hydrological data and ;and , ;

[0133] Therefore, the final output of the finite element driven flow field completion module is and , and constitute the physical consistency water level time series data .

[0134] 4. Design of flow field sensing water level prediction model

[0135] The flow field sensing water level prediction model designed in this invention can intelligently generate high-precision groundwater level prediction results and thermal maps at multiple future moments based on the FEM completion data after structural optimization; the model mainly consists of three parts: a spatiotemporal feature fusion encoder, a physical constraint groundwater level prediction module, and a thermal map generation module. Figure 3 shown.

[0136] 1. Spatiotemporal feature fusion encoder

[0137] The spatiotemporal feature fusion encoder extracts enhanced spatiotemporal features. The spatiotemporal feature fusion encoder includes a graph convolutional network layer, a hole convolution layer, a gated unit layer, and a spatiotemporal cross attention mechanism layer. The physical consistency water level time series data obtained by S4 is used to extract the enhanced spatiotemporal features. ,in is the time step, is the number of water level space location nodes, is the feature dimension. The specific steps are as follows:

[0138] 1) The input graph convolutional network layer gradually extracts spatial topological features and explicitly models the spatial heterogeneity of aquifers. The graph convolutional network layer consists of two graph convolutional layers, each of which contains a 32-channel graph convolution kernel, a batch normalization layer, and a GeLU activation function.

[0139] 2) The dilated convolution layer is input to capture long-term patterns through dilated convolution, learn the seasonal variation trend of water level, and obtain long-term time series features;

[0140] 3) The input gated unit layer learns the short-term fluctuation pattern of the data, learns the extreme change pattern of the water level, and obtains the short-term time series features;

[0141] 4) The spliced ​​temporal features after channel splicing of spatial topological features, long-period temporal features, and short-period temporal features are input into the spatiotemporal cross attention mechanism to obtain the spatiotemporal feature weights. The specific calculation formula is as follows:

[0142]

[0143] in The spatial topological feature Dimension and splicing time series features dimensional attention weight, The first spatial topological feature dimension, The first dimension;

[0144] 5) Multiply the spatiotemporal feature weights by the concatenated temporal features and then add them to the spatial topological features to obtain enhanced spatiotemporal features.

[0145] 2. Physically constrained groundwater level prediction module

[0146] The physical constraint groundwater level prediction module is used to obtain groundwater level prediction results at multiple future moments. This module is implemented based on gated cells and Darcy's law physical constraints. Unlike traditional gated cells, the cell state update formula of the physical constraint groundwater level prediction module is as follows:

[0147]

[0148] in for The cell state at any moment, for The forget gate output at the moment, for The input gate output at time t, for Estimated cell state at moment in time; is the Darcy law constraint strength coefficient, which controls the constraint strength of Darcy's law on the predicted groundwater level of the gated unit; is the discretized residual of Darcy's law, reflecting the degree to which the groundwater level predicted by the gated unit violates the physical law. The specific calculation formula is as follows:

[0149]

[0150] in, represents the gradient symbol, is the groundwater permeability, obtained using a pumping test; is the hydraulic gradient calculated based on the spatial position, Calculation of groundwater level monitoring values ​​of adjacent spatial nodes in is the source-sink term, representing the net increase or decrease of water volume per unit area per unit time, which is The difference between surface precipitation and surface evaporation.

[0151] 3. Heat map generation module

[0152] The heat map generation module outputs a groundwater level heat map; this module includes a raster conversion layer and a hierarchical upsampling decoder, as follows:

[0153] 1) Input the groundwater level prediction results into the raster conversion layer and use the inverse distance weighted algorithm to convert the groundwater level prediction results into a 64×64 low-resolution raster;

[0154] 2) The low-resolution raster is input into the hierarchical upsampling decoder to obtain a spatial distribution heat map of the groundwater level prediction results. The hierarchical upsampling decoder consists of four sequentially connected upsampling networks, which extract the features of the groundwater level prediction results layer by layer and improve the resolution to obtain a 1024×1024 high-resolution spatial distribution heat map of the water level prediction results. Each upsampling network consists of a transposed convolution layer (kernel size: 5×5, stride: 2, void ratio: 2), a sub-pixel convolution layer, and a bilinear interpolation layer connected in sequence. The transposed convolution layer is used to capture the characteristics of non-uniform groundwater distribution and enhance the characteristic differences of groundwater level distribution in spatial locations. The sub-pixel convolution layer improves the resolution by channel reorganization of features. The bilinear interpolation layer is used to ensure the smoothness of groundwater levels at different spatial locations and eliminate the step-like artifacts in the transition zone of geological units.

[0155] 4. Model training strategy based on Yesian optimization

[0156] 1) Construct a joint training parameter set for the spatiotemporal feature fusion encoder and the physical constraint groundwater level prediction module ,in is the network structure parameter set of the spatiotemporal feature fusion encoder, is the network structure parameter set of the physical constraint groundwater level prediction module, is the learning rate, is the Darcy's law constraint strength coefficient;

[0157] 2) Generate M joint training parameter samples using Latin hypercube sampling method ;

[0158] 3) Construct a parameter design space optimization problem based on KL divergence, as follows:

[0159]

[0160] in Prior distribution of groundwater level, ,in for The mean groundwater level, for Standard deviation of groundwater level; represents Gaussian distribution; is the variational posterior distribution of groundwater level, ,in To utilize The average value of the groundwater level prediction results obtained by configuring the spatiotemporal feature fusion encoder and the physical constraint groundwater level prediction module for multiple future predictions is: is the standard deviation of the groundwater level prediction results; represents Gaussian distribution;

[0161] 4) For For each sample in , solve the parameter design space optimization problem based on KL divergence and obtain the parameter set that satisfies Darcy's law ;

[0162] 5) The root mean square error between the groundwater level prediction result output by the physical constraint groundwater level prediction module and the actual groundwater level result is used as the loss function to calculate the The root mean square error obtained by configuring the spatiotemporal feature fusion encoder and the physical constraint groundwater level prediction module respectively is recorded as the optimal parameter set of the model. .

[0163] 5. Experimental Results

[0164] To verify the effectiveness and advancement of the proposed multi-physics field driven groundwater dynamic evolution prediction method (hereinafter referred to as the “method”), two types of comparative experiments were designed to evaluate the performance of the method from two aspects: spatial visualization of dynamic evolution results and prediction accuracy. The comparative models include: (1) LSTM model: using traditional long short-term memory network to predict groundwater level time series; (2) GRU model: using the gating mechanism-based temporal modeling method as another comparative model.

[0165] 1. Analysis of thermal maps for groundwater dynamic distribution prediction

[0166] This example selects 25 representative monitoring points within the region and, based on a high-dimensional hydrogeological dataset, constructs a multi-physics field coupled finite element prediction model. This model then performs spatiotemporal completion and evolution simulation of the groundwater flow field. This model then integrates a water level prediction module that incorporates flow direction sensing to output groundwater level distributions at multiple future moments. To ensure data security and model consistency, both the monitoring point locations and water level values ​​are standardized. Figure 4 The heat map results of groundwater level prediction of this method at the 10th, 20th and 30th time steps are shown.

[0167] Results demonstrate that the proposed method demonstrates good continuity and physical rationality in spatial completion and time-series prediction, clearly restoring the primary groundwater flow direction and accurately depicting trends in areas of significant groundwater fluctuation (e.g., the northwest region). Compared to traditional methods, the proposed method maintains high distribution stability even in heterogeneous strata and complex boundary conditions, validating the effectiveness of its finite element structure construction and multi-physics field-driven modeling.

[0168] 2. Comparative experiment on groundwater level prediction accuracy

[0169] To further quantify the prediction performance of the present invention, this example selects 10 monitoring points as target prediction points. The present method, LSTM, and GRU are used to predict groundwater levels at several future moments and compared with the measured values. The evaluation indicators used are: (1) Root Mean Square Error (RMSE), which reflects the error magnitude; and (2) Mean Absolute Error (MAE), which reflects the overall deviation. Figure 5 and Figure 6 The comparison results of RMSE and MAE indicators of the three models at 10 monitoring points are shown respectively. The horizontal axis is the monitoring point number and the vertical axis is the corresponding prediction error value.

[0170] The results show that the proposed method achieves the lowest prediction error across all monitoring points, with a stable RMSE of approximately 0.15 and a MAE between 0.12 and 0.13, significantly outperforming both the LSTM model (RMSE approximately 0.18, MAE approximately 0.15) and the GRU model (RMSE approximately 0.22, MAE approximately 0.19). Furthermore, the proposed method exhibits minimal error fluctuation across different monitoring points, demonstrating greater robustness and consistency across time and space.

[0171] Comprehensive analysis demonstrates that the proposed multi-physics coupled prediction framework maintains model accuracy while maintaining structural physical consistency and cross-regional generalization capabilities, making it particularly suitable for modeling groundwater evolution in heterogeneous strata and complex boundaries. Compared to traditional neural network methods, it offers significant advantages in error control, stability, and practical deployment feasibility, providing effective technical support for high-precision groundwater prediction and regional water resources management.

[0172] The above description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

[0173] Although the above describes the specific implementation methods of the present invention, it does not limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for predicting the dynamic evolution of groundwater, characterized in that: The following steps are involved: S1, collects hydrological parameter data, including groundwater level monitoring data, hydrogeological parameters and initial water level information, and collects geographical location data of monitoring points to construct a regional hydrogeological input tensor; S2, based on the input data constructed in S1, establish an initial finite element model FEM to perform spatial extrapolation of groundwater level distribution and flow field completion; Step S2 specifically includes: S21, regional modeling and initial boundary setting: Based on the acquired multi-monitoring point location coordinate data , establish a two-dimensional spatial network coordinate system containing all monitoring points in the area , and obtain the initial time point based on the hydrological parameter data of the complete sampling time point The initial hydrological data of all monitoring points at time t is recorded as the initial groundwater level field The initial groundwater level field is used as the starting state of the finite element simulation; in addition, the boundary conditions are set as mixed boundaries including constant boundary, no-flow boundary, and communication boundary; S22, grid structure design and parameter preset: Region division method initialization and optimization range: The region division method parameters are defined as , whose value range includes: Regular network partitioning, Delaunay triangulation, Quadtree partitioning, and Geological unit guided zoning, i.e. ; Grid density parameter initialization and optimization range: Under the selected area division method, a total of sub-regions, set the grid density for different sub-regions , Indicates the The grid density of the region is ; and set the maximum grid density to , the minimum grid density is ; Therefore, the grid density parameter to be optimized is ,and ; S23, Multi-parameter driven joint finite element modeling: Construct a multi-physics field coupled finite element model based on the regional grid and the initial field As input, a multi-physics field coupling control equation system is constructed based on the existing physical constraint equations, including: groundwater flow control equation, Richards equation, head-pressure conversion formula, conductivity migration equation, surface evaporation estimation equation and heat conduction equation; S3, based on the initial finite element model FEM structure designed in S2, designs a global optimization algorithm based on target decomposition, performs real-time structural optimization on the regional division method, mesh density distribution and boundary condition setting of the finite element model, and obtains the optimal physical field coupled finite element model; The step S3 establishes a multi-index optimization problem of a multi-physics field coupled finite element model structure based on the established decision variables and the established objective function; The decision variables are defined as: Based on the determined parameters to be optimized 、 、 Determine decision variables and boundary parameters ,in , 、 is the boundary flux adjustment parameter; the regional division method parameter ,and ; The grid density parameter to be optimized is ,and ; The complete set of decision variables is defined as: ; Among them, the objective function is designed as a multi-index weighted objective function: ； in 、 、 is the hyperparameter weight; Completion precision loss , used to measure the predicted hydrological parameters of monitored locations during the FEM completion process Compared with the measured monitoring value The error between Physical consistency error , a residual measure used to measure the violation of the governing equations in the solution obtained by FEM inference; Mesh complexity penalty , used to limit the computational burden caused by excessive grid refinement; S4, simulating the evolution of groundwater in the non-monitoring area by a finite element numerical solution method, generating multi-node, physically consistent hydrological time series data with improved resolution that meets boundary conditions; the model used in the finite element numerical solution method is the optimal physical field coupled finite element model obtained in S3; S5: Input the hydrological time series data generated in S4 into the constructed and trained flow field-aware water level prediction model, and output groundwater level prediction results at multiple future time points and multiple locations and their corresponding groundwater level heat maps; the flow field-aware water level prediction model includes a spatiotemporal feature fusion encoder, a physical constraint groundwater level prediction module, and a heat map generation module; The physically consistent hydrological time series data that meets the boundary conditions obtained by S4 are input into the spatiotemporal feature fusion encoder to obtain enhanced spatiotemporal features; the enhanced spatiotemporal features are input into the physical constraint groundwater level prediction module, and the state of the gated unit is updated through the discretization of the residual constraint of Darcy's law physical constraints to obtain the groundwater level prediction results at multiple moments in the future; the groundwater level prediction results are input into the heat map generation module to obtain the groundwater level heat map.

2. A method for predicting the dynamic evolution of groundwater according to claim 1, characterized in that: The hydrological parameter data includes underground water level monitoring values ​​collected by using a pressure water level gauge , using soil moisture sensors to collect soil moisture , pore water pressure sensor collects pore water pressure , conductivity sensor monitors conductivity , deploy rain gauges to collect surface precipitation , using evaporation dishes combined with temperature and humidity sensors to estimate surface evaporation , weather sensor obtains temperature and humidity ; The above parameters together constitute the hydrological parameter data ; The geographical location data of the monitoring points are collected in the area where the groundwater dynamic evolution is to be carried out. Monitoring points, record The longitude and latitude coordinates of the monitoring points are obtained to obtain the geographical location sequence of the monitoring points. .

3. A method for predicting the dynamic evolution of groundwater according to claim 1, characterized in that: The specific process of S4 includes: S41, initial value assignment and boundary condition loading: According to the initial groundwater level field , and set the initial boundary parameter combination to , initial area division method for Regular network partitioning, initial grid density All preset ; S42, using implicit finite element time-stepping strategy, using coupled control equations For each time step Perform a step-by-step evolutionary solution to obtain the coordinate system of the entire region at the corresponding moment Estimated values ​​of all hydrological parameters; S43, based on the complete estimation results of the hydrological parameters in the region, select the parameter supplement degree as , and in the regional coordinate system The sampling is carried out under Supplementary hydrological data , and the corresponding locations of the supplementary data ; Combine the supplemented data with the original collected data to form Complete hydrological data and ;and , , and constitute the physical consistency water level time series data .

4. A method for predicting the dynamic evolution of groundwater according to claim 1, characterized in that: The spatiotemporal feature fusion encoder in the flow field perception water level prediction model is used to extract enhanced spatiotemporal features, including graph convolutional network layer, hole convolution layer, gated unit layer and spatiotemporal cross attention mechanism layer; for the obtained physical consistency water level time series data ,in is the time step, is the number of water level space location nodes, is the feature dimension, and the specific processing steps are as follows: S51, will The input graph convolutional network layer gradually extracts spatial topological features. The graph convolutional network layer consists of two graph convolutional layers, each of which contains a 32-channel graph convolution kernel, a batch normalization layer, and a GeLU activation function; S52, will The dilated convolution layer is input to capture long-term patterns through dilated convolution, learn the seasonal variation trend of water level, and obtain long-term time series features; S53, will The input gated unit layer learns the short-term fluctuation pattern of the data, learns the extreme change pattern of the water level, and obtains the short-term time series features; S54, the spliced ​​temporal features after channel splicing of spatial topological features, long-period temporal features and short-period temporal features are input into the spatiotemporal cross attention mechanism to obtain the spatiotemporal feature weights; S55, multiplying the spatiotemporal feature weight by the concatenated temporal feature and then adding the result to the spatial topological feature to obtain the enhanced spatiotemporal feature.

5. A method for predicting the dynamic evolution of groundwater according to claim 1, characterized in that: The physical constraint groundwater level prediction module in the flow field sensing water level prediction model is used to obtain groundwater level prediction results at multiple future moments. This module is implemented based on the gated unit and Darcy's law physical constraints. The cell state update formula of the physical constraint groundwater level prediction module is as follows: ； in for The cell state at any moment, for The forget gate output at the moment, for The input gate output at time t, for The estimated cell state at the moment; is the constraint strength coefficient of Darcy's law, which controls the constraint strength of Darcy's law on the predicted groundwater level of the gated unit; is the discretized residual of Darcy's law, reflecting the degree to which the groundwater level predicted by the gated unit violates the physical law. The specific calculation formula is as follows: ； in, represents the gradient symbol, is the groundwater permeability, obtained using a pumping test; is the hydraulic gradient calculated based on the spatial position, Calculation of groundwater level monitoring values ​​of adjacent spatial nodes in is the source-sink term, representing the net increase or decrease of water volume per unit area per unit time, which is The difference between surface precipitation and surface evaporation.

6. A method for predicting the dynamic evolution of groundwater according to claim 1, characterized in that: The heat map generation module in the flow field-sensing water level prediction model outputs a groundwater level heat map; this module includes a raster conversion layer and a hierarchical upsampling decoder, as follows: The groundwater level prediction results are input into the raster conversion layer and converted into a 64×64 low-resolution raster using the inverse distance weighted algorithm; The low-resolution raster is input into the hierarchical upsampling decoder to obtain a spatial distribution heat map of the groundwater level prediction results. The hierarchical upsampling decoder consists of four sequentially connected upsampling networks, which extract the features of the groundwater level prediction results layer by layer and improve the resolution to obtain a 1024×1024 high-resolution spatial distribution heat map of the water level prediction results. Each upsampling network consists of a transposed convolution layer, a sub-pixel convolution layer, and a bilinear interpolation layer connected in sequence. The transposed convolution layer is used to capture the characteristics of non-uniform groundwater distribution. The sub-pixel convolution layer improves the resolution by channel reorganization of the features. The bilinear interpolation layer is used to ensure the smoothness of the groundwater level at different spatial locations and eliminate the step-like artifacts in the transition zone of geological units.

7. A method for predicting the dynamic evolution of groundwater according to claim 1, characterized in that: The flow field sensing water level prediction model uses a Bayesian optimization model training strategy, specifically including: Constructing a joint training parameter set for the spatiotemporal feature fusion encoder and the physical constraint groundwater level prediction module ,in is the network structure parameter set of the spatiotemporal feature fusion encoder, is the network structure parameter set of the physical constraint groundwater level prediction module, is the learning rate, is the Darcy's law constraint strength coefficient; Generate M joint training parameter samples using the Latin hypercube sampling method ; Construct a parameter design space optimization problem based on KL divergence as follows: ； in Prior distribution of groundwater level, ,in for The mean groundwater level, for Standard deviation of groundwater level; represents Gaussian distribution; is the variational posterior distribution of groundwater level, ,in To utilize The average value of the groundwater level prediction results obtained by configuring the spatiotemporal feature fusion encoder and the physical constraint groundwater level prediction module for multiple future predictions is: is the standard deviation of the groundwater level prediction results; represents Gaussian distribution; for For each sample in , solve the parameter design space optimization problem based on KL divergence and obtain the parameter set that satisfies Darcy's law ; The root mean square error between the groundwater level prediction result output by the physical constraint groundwater level prediction module and the actual groundwater level result is used as the loss function to calculate the The root mean square error obtained by configuring the spatiotemporal feature fusion encoder and the physical constraint groundwater level prediction module respectively is recorded as the optimal parameter set of the model. .

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