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CN-121981006-A - Underground water flow field physical information neural network modeling method considering spatial heterogeneity

CN121981006ACN 121981006 ACN121981006 ACN 121981006ACN-121981006-A

Abstract

The application discloses a modeling method of a physical information neural network of a groundwater flow field in consideration of space heterogeneity, which belongs to the technical field of the groundwater flow field and comprises the steps of 1, selecting a two-dimensional groundwater unsteady flow equation as a physical law, collecting hydrogeologic parameters, rainfall, groundwater exploitation and geographic coordinate data, carrying out normalization pretreatment, 2, constructing PINNs models based on the pretreatment data, dividing the data sets according to 7:3, dynamically adjusting loss function weights by means of NTK technology, updating parameters by an optimization algorithm, 3, extracting PINNs models, simulating residual errors, obtaining residual error space distribution by Kriging interpolation after fitting the models, and superposing PINNs simulation results to obtain a final groundwater flow field simulation result, wherein the application can dynamically adjust the loss function weights of PINNs by means of fusion neural tangent kernel technology, thereby being capable of adapting the space heterogeneity characteristics of the hydrogeologic parameters, avoiding the weight imbalance characteristics of physical constraints and data information, meeting the physical law, and ensuring the actual data distribution.

Inventors

  • ZHU LIN
  • YU HUILIN
  • LV XIAOWEN
  • Qian Chenzhihao
  • GONG HUILI
  • YE SHUJUN

Assignees

  • 首都师范大学

Dates

Publication Date
20260505
Application Date
20260127

Claims (8)

  1. 1. The modeling method of the physical information neural network of the underground water flow field taking the spatial heterogeneity into consideration is characterized by comprising the following steps of: Step 1, data acquisition and preprocessing, namely selecting a two-dimensional groundwater unsteady flow equation as a physical law, collecting hydrogeologic parameters, source and sink items and geographic coordinate data corresponding to the equation, wherein the source and sink items comprise rainfall and groundwater exploitation quantity, and carrying out normalization preprocessing on the rainfall, groundwater exploitation quantity and geographic coordinates; Step 2, PINNs loss function weight optimization of fused neural tangent kernel technology, namely constructing PINNs model based on Darcy's law and water balance principle and based on preprocessed data, wherein input data of PINNs model comprises geographic coordinates, permeability coefficient, rainfall infiltration coefficient, water supply degree, water release coefficient, underground water exploitation amount and precipitation amount in time nodes, randomly dividing a data set according to the proportion of 70% training set and 30% validation set, analyzing characteristic value distribution of each loss term under kernel function space by NTK technology, dynamically adjusting weights of physical loss, data loss and boundary loss in PINNs model loss function, constructing the loss function by embedding physical law, calculating derivative by means of automatic differential architecture, and updating neural network parameters by an optimization algorithm To minimize the loss function; The method comprises the steps of constructing a coupling model of GTWR-PINNs, namely extracting a residual error of a PINNs model simulating underground water flow field at a monitoring well and measuring water level at a time sequence, taking the residual error as a dependent variable, taking a geographic coordinate, rainfall, underground water yield, permeability coefficient, water supply degree, water release coefficient and rainfall infiltration coefficient as independent variables to input the independent variables into a GTWR model, determining an optimal GTWR bandwidth parameter through cross verification, capturing a nonlinear relation between the dependent variable and the independent variable, obtaining spatial distribution of the residual error of the underground water flow field through Kriging spatial interpolation, and superposing the residual error obtained by the GTWR model and a simulation result of the PINNs model to obtain a final underground water flow field simulation result.
  2. 2. The modeling method of a physical information neural network of a groundwater flow field in consideration of spatial heterogeneity according to claim 1, wherein the process of dynamically adjusting weights by NTK technique in step 2 comprises: Determining initial weights, namely determining initial weights of loss functions by analyzing NTK matrixes corresponding to loss items under initial network parameters; And (3) in the training process, self-adaptively adjusting the weight, namely periodically calculating the gradient norms of each loss item relative to the network parameters and the corresponding NTK matrix, and self-adaptively updating the weight according to the gradient of each loss item.
  3. 3. The modeling method of the physical information neural network of the groundwater flow field considering the spatial heterogeneity according to claim 1, wherein the construction of the PINNs model in the step 2 includes three parts of construction of a loss function, adjustment of self-adaptive weight and a feedback mechanism, the feedback mechanism updates the neural network parameter θ through an optimization algorithm, and minimizes the loss function to obtain an approximate solution of a two-dimensional groundwater unsteady flow equation.
  4. 4. The modeling method of a physical information neural network of a groundwater flow field considering spatial heterogeneity according to claim 1, wherein the two-dimensional groundwater unsteady flow equation in step 1 comprises the following control equation: Wherein, the Is an underground water seepage area; the water level elevation of the aquifer is obtained; Is a aquifer source sink item; the water storage rate of the water-containing medium is achieved; Time is; the permeability coefficient is the normal direction of the boundary surface; is the water supply degree; the method is a source sink for evaporation, precipitation and the like of the diving layer; is the upper boundary of the percolation region; Is a mixed boundary of an aquifer; Is the lower boundary of the percolation region; is the initial water level distribution of the aquifer; , Respectively, the two components are shown as follows, 、 Permeability coefficient in the direction.
  5. 5. The modeling method of a physical information neural network of a groundwater flow field considering spatial heterogeneity according to claim 1, wherein the expression of the GTWR model in step 3 is: Wherein the method comprises the steps of As a residual error, the residual error is determined, Is a constant term which is used to determine the degree of freedom, Is the first Regression coefficients of the individual independent variables are used, 、 In the form of a geographic coordinate of the device, In order to be able to take time, Is the first Sample number The number of independent variables that can be used to determine the desired degree of freedom, Is an error term.
  6. 6. The modeling method of a physical information neural network of a groundwater flow field considering spatial heterogeneity according to claim 1, wherein the expression of the loss function in step 2 is: Wherein the method comprises the steps of The weight of the loss of data is calculated, The data is lost and, in response to the loss of data, In order to physically lose the weight of the weight, In the event of a physical loss, For the loss of weight for the boundary, Is a boundary loss.
  7. 7. The modeling method of a physical information neural network of a groundwater flow field considering spatial heterogeneity according to claim 1, wherein the expression of updating the neural network parameters by an optimization algorithm in step 2 is as follows: Wherein, the In order to update the parameters of the data, As a function of the current parameters, In order for the rate of learning to be high, Is the gradient of the loss function at the current parameter.
  8. 8. The modeling method of a physical information neural network of a groundwater flow field considering spatial heterogeneity according to claim 1, wherein the hydrogeologic parameters include permeability coefficient, rainfall infiltration coefficient, water supply and water release coefficient.

Description

Underground water flow field physical information neural network modeling method considering spatial heterogeneity Technical Field The application belongs to the technical field of underground water flow fields, and particularly relates to a modeling method of an underground water flow field physical information neural network considering spatial heterogeneity. Background The underground water is an important water resource, the flow field simulation is a core foundation for hydrogeology research and water resource management, the traditional underground water flow field modeling method in the prior art is mainly divided into two types, namely a mechanism numerical model method, a model method based on underground water dynamics equations (such as Darcy's law and unsteady flow equations), the method has high requirements on the spatial distribution precision of hydrogeology parameters, the hydrogeology parameters of an actual area have significant spatial heterogeneity, so that the simulation error of a physical model is larger, and a machine learning model method (such as ANN and XGBoost) is dependent on a large amount of actual data training, can fit nonlinear relations, lacks physical law constraint, is easy to generate a physical infeasible prediction result, has strong dependence on data distribution, and has poor precision in a data sparse area. In recent years, a Physical Information Neural Network (PINNs) embeds a physical law into the neural network, and combines physical constraint and data fitting capability, but the existing PINNs model still has certain defects that the existing model does not fully consider the spatial heterogeneity of hydrogeologic parameters, so that the weight of physical loss and data loss is difficult to adaptively match, the model convergence is poor, and the residual error at a monitoring point is not spatially corrected only depending on a single simulation result of PINNs, so that the spatial precision of flow field simulation may be difficult to further improve. Disclosure of Invention In order to solve the problems and the technical defects, the application adopts the following technical scheme that the modeling method of the physical information neural network of the underground water flow field takes the spatial heterogeneity into consideration, and comprises the following steps: Step 1, data acquisition and preprocessing, namely selecting a two-dimensional groundwater unsteady flow equation as a physical law, collecting hydrogeologic parameters, source and sink items and geographic coordinate data corresponding to the equation, wherein the source and sink items comprise rainfall and groundwater exploitation quantity, and carrying out normalization preprocessing on the rainfall, groundwater exploitation quantity and geographic coordinates; Step 2, PINNs loss function weight optimization of fused neural tangent kernel technology, namely constructing PINNs model based on Darcy's law and water balance principle and based on preprocessed data, wherein input data of PINNs model comprises geographic coordinates, permeability coefficient, rainfall infiltration coefficient, water supply degree, water release coefficient, underground water exploitation amount and precipitation amount in time nodes, randomly dividing a data set according to the proportion of 70% training set and 30% validation set, analyzing characteristic value distribution of each loss term under kernel function space by NTK technology, dynamically adjusting weights of physical loss, data loss and boundary loss in PINNs model loss function, constructing the loss function by embedding physical law, calculating derivative by means of automatic differential architecture, and updating neural network parameters by an optimization algorithm To minimize the loss function; The method comprises the steps of constructing a coupling model of GTWR-PINNs, namely extracting a residual error of a PINNs model simulating underground water flow field at a monitoring well and measuring water level at a time sequence, taking the residual error as a dependent variable, taking a geographic coordinate, rainfall, underground water yield, permeability coefficient, water supply degree, water release coefficient and rainfall infiltration coefficient as independent variables to input the independent variables into a GTWR model, determining an optimal GTWR bandwidth parameter through cross verification, capturing a nonlinear relation between the dependent variable and the independent variable, obtaining spatial distribution of the residual error of the underground water flow field through Kriging spatial interpolation, and superposing the residual error obtained by the GTWR model and a simulation result of the PINNs model to obtain a final underground water flow field simulation result. Preferably, the dynamically adjusting weights by the NTK technique in step 2 includes: Determining initial weights, namely determining initial weight