Groundwater storage constraint-based PINN-transformer groundwater level prediction method and system

Abstract

The PINN-Transformer groundwater level prediction method and system based on groundwater storage constraints relate to the field of groundwater management and hydrology and water resources. The method solves the limitations of large data requirements, weak physical law constraints and weak interpretation, and unclear hydrogeological information in existing groundwater level prediction. The method includes collecting precipitation data P, groundwater level data GWL and groundwater storage data GWS, and correcting the time scales of the three types of data. Based on the LRM model, a groundwater level change physical constraint equation is constructed to embed the physical information neural network loss function. Based on the Transformer framework, the physical constraint is introduced to construct a GWS-LRM-PINN-Transformer groundwater level prediction model. The precipitation, groundwater level data and groundwater storage data are used as inputs, and the one-step and multi-step recursive methods are used to complete the groundwater level time series prediction.

Description

Technical Field

[0001] This invention relates to the field of groundwater management and hydrological and water resources technology, specifically to a PINN-Transformer groundwater level prediction method and system based on groundwater storage constraints. Background Technology

[0002] Groundwater level is an important indicator of the dynamic changes in the groundwater system. It is closely related to ecological environment protection, groundwater resource regulation and regional water resource security. Accurately predicting the trend of groundwater level changes is of great significance for the prevention and control of groundwater overflow, ecological environment protection and water resource management.

[0003] Groundwater prediction often relies on governing equations such as groundwater flow equations and numerical models (e.g., MODFLOW and GMS) to simulate dynamic groundwater processes. However, these models often depend on complex hydrogeological information and have high data requirements. In recent years, machine learning models have been able to extract complex information from historical groundwater level data and influencing factors (P, precipitation), gradually evolving into an important technical approach for predicting groundwater levels (GWL). Compared to artificial neural networks, which have demonstrated high prediction accuracy, long short-term memory networks and gated recurrent loops are better suited to characterizing time-series features and are widely used in prediction tasks. Furthermore, the Transformer, with its unique mechanism to enhance the representation of long-range dependencies, has been gradually introduced into GWL prediction.

[0004] However, existing data-driven groundwater level prediction methods still have shortcomings. On the one hand, GWL predictions are highly dependent on external driving factors such as precipitation (P) and artificial extraction, and the model performance is often limited by the temporal discontinuity and spatial scarcity of data. On the other hand, although pure data has a strong ability to fit nonlinearity, it often lacks constraints on the groundwater movement mechanism, which can easily lead to inconsistencies between the predicted results and the actual groundwater physical processes, thus limiting the interpretability of the model.

[0005] Groundwater Storage (GWS), as a state variable representing macroscopic changes in the groundwater system, can characterize the dynamic evolution of groundwater resources at a regional scale. With remote sensing inversion, groundwater storage data can be readily obtained from publicly available data sources, providing new data support for prediction. In existing studies, GWS is primarily used for assessing regional groundwater storage changes, groundwater monitoring, or validating model results. However, research on GWS as a core variable in groundwater level prediction models, and its further coupling with physical constraint equations and deep learning models, remains relatively insufficient.

[0006] Furthermore, existing prediction models often use variables such as P and GWL as input factors, but do not fully consider the physical response relationships between different variables and their constraints on groundwater level changes. For P and GWL, LRM (Linear Reservoir Model) can describe the driving effect of the former on the latter in a relatively simplified form. If GWS can be introduced into LRM to construct a physical constraint equation for groundwater level changes that includes groundwater storage information, and this constraint can be embedded into a deep model, it is expected to simultaneously improve the accuracy and physical consistency of the prediction results.

[0007] Therefore, there is an urgent need to propose a groundwater level prediction method that can comprehensively utilize P, GWL, and GWS, and combine physical constraint models with deep learning prediction models, in order to solve the problems of insufficient usability of existing methods due to data scarcity, insufficient physical constraints of pure data-driven models, and insufficient utilization of groundwater storage data. Summary of the Invention

[0008] This invention aims to overcome the limitations of existing groundwater level prediction methods, such as high data requirements, weak constraints and interpretability of physical laws, and unclear hydrogeological information. To address these limitations, this invention proposes a PINN-Transformer groundwater level prediction method and system based on groundwater storage constraints. To solve the aforementioned technical problems, this invention is implemented through the following technical solutions: Option 1: This invention proposes a PINN-Transformer groundwater level prediction method based on groundwater storage constraints. The method includes the following steps: Step 1: Collect precipitation data P, groundwater level data GWL, and groundwater storage data GWS. Use precipitation data P as the driving factor for dynamic changes in groundwater, and groundwater storage data GWS as the state variable for macroscopic changes in the groundwater system. Perform time-scale uniform correction on the three types of data. Step 2: Based on the response correlation between precipitation and groundwater level in the LRM model, by introducing the groundwater storage variable, the physical constraint equation for groundwater level change that integrates groundwater storage is obtained. Step 3: Construct the corresponding physical residual term based on the physical constraint equation of groundwater level change, and embed the physical residual term as a physical constraint condition into the loss function of the physical information neural network; Step 4: Using the Transformer model as the basic framework for groundwater level time series prediction, the PINN (Physics-Informed Neural Networks) physical constraints corresponding to the loss function are introduced during the Transformer model training process to construct the GWS-LRM-PINN-Transformer groundwater level prediction model. Step 5: Using precipitation data P, groundwater level data GWL, and groundwater storage data GWS as input variables, and the physical constraint equations constructed by the LRM model as constraint conditions, the groundwater level prediction is completed using both one-step and multi-step recursive methods. Step 6: Input the precipitation data P and groundwater level data GWL into the trained GWS-LRM-PINN-Transformer model, and perform parameter inversion according to the physical constraint equation of groundwater level change to achieve quantitative inversion of regional hydrogeological parameters.

[0009] Furthermore, a preferred embodiment is provided, wherein in step 2, based on the response correlation between precipitation and groundwater level in the LRM model, a groundwater storage variable is introduced to obtain the physical constraint equation for groundwater level change that incorporates groundwater storage: The LRM model is based on the mathematical response relationship between groundwater level and precipitation, and establishes the basic mechanism of groundwater dynamics to simulate the dynamic change process of groundwater level driven by precipitation. Based on the principle of groundwater balance, a balance equation for groundwater storage changes per unit area is established. In this balance equation, the physical variables—precipitation, groundwater level, and groundwater storage—are all time-series variables that change with time t. Differentiating both sides of the groundwater storage change balance equation with respect to time t yields the time-series rate of change relationships for each hydrological variable. By combining the precipitation-groundwater dynamics coupling constraint relationship of the LRM model, a groundwater storage change rate term is introduced into the groundwater dynamics equation, and the physical constraint equation of groundwater level change that simultaneously couples precipitation-driven, groundwater level dynamics and groundwater storage surplus and deficit changes is derived iteratively.

[0010] Furthermore, a preferred embodiment is provided, wherein the LRM model establishes a basic mechanism of groundwater dynamics based on the mathematical response relationship between groundwater level and precipitation, and is used to simulate the dynamic change process of groundwater level driven by precipitation. Specifically:

[0011] Changes in groundwater storage, where A is the area per unit area:

[0012]

[0013] All the above variables are related to time t. Taking the derivative of both sides with respect to time t:

[0014] in, The aquifer storage coefficient, Groundwater level, This is the groundwater discharge coefficient. Here, P is the precipitation infiltration recharge coefficient, and P is the precipitation amount.

[0015] Furthermore, a preferred embodiment is provided in which the loss function in step 3 includes a data loss term between the predicted and measured groundwater values, and a physical loss term calculated using the physical constraint equation for groundwater level changes.

[0016] Furthermore, a preferred embodiment is provided, wherein the Transformer model described in step 4 is used to extract the temporal characteristics of precipitation data P, groundwater level data GWL, and groundwater storage data GWS, and the PINN physical constraint term is used to constrain the model prediction results so that they satisfy the physical constraint equation for groundwater level change jointly determined by the LRM model and the groundwater storage data GWS.

[0017] Furthermore, a preferred embodiment is provided, wherein the one-step recursive method described in step 5 is used to predict the groundwater level of the next time step based on the data of the current time step and the previous time steps; and the multi-step recursive method is used to use the predicted groundwater level as the input information for the subsequent time steps to recursively obtain the prediction result of at least one time step.

[0018] Furthermore, a preferred embodiment is provided, wherein the input variables in step 5 include a combination of precipitation data P, groundwater level data GWL, and groundwater storage data GWS. The physical constraint equations corresponding to the two combination distributions are the LRM physical constraint equation and the GLRM (GWS - LRM) physical constraint equation. The LRM physical constraint equation is based on the basic water balance dynamic equation constructed from precipitation and groundwater level, while the GLRM physical constraint equation is based on the improved water balance dynamic equation that incorporates the temporal variation characteristics of groundwater storage.

[0019] Option 2: A PINN-Transformer groundwater level prediction system based on groundwater storage constraints, the system comprising: The data processing module is used to collect precipitation data P, groundwater level data GWL, and groundwater storage data GWS. It uses precipitation data P as the driving factor for dynamic changes in groundwater and groundwater storage data GWS as the state variable for macroscopic changes in the groundwater system. It performs time-scale uniform correction on the three types of data. The physical constraint equation derivation module is used to derive the physical constraint equation for groundwater level change by introducing the groundwater storage variable based on the response correlation between precipitation and groundwater level in the LRM model and integrating the groundwater storage. The physical residual loss construction module is used to construct the corresponding physical residual term based on the physical constraint equation of groundwater level change, and to embed the physical residual term as a physical constraint condition into the loss function of the physical information neural network. The coupled model construction module is used to use the Transformer model as the basic framework for groundwater level time series prediction. During the training process of the Transformer model, the PINN physical constraint corresponding to the loss function is introduced to construct the GWS-LRM-PINN-Transformer groundwater level prediction model. The adaptive prediction module is used to predict groundwater level by taking precipitation data P, groundwater level data GWL and groundwater storage GWS as input variables and physical constraint equations constructed by the GLRM model as constraints, and using one-step recursion and multi-step recursion methods respectively. The parameter inversion module is used to input precipitation data P and groundwater level data GWL into the trained GWS-LRM-PINN-Transformer model, and perform parameter inversion based on the physical constraint equation of groundwater level change to achieve quantitative inversion of regional hydrogeological parameters.

[0020] Option 3: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described in Option 1.

[0021] Option 4: A computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method described in Option 1.

[0022] The advantages of this invention are: The PINN-Transformer groundwater level prediction method based on groundwater storage constraints described in this invention is derived from the LRM formula and introduces GWS as a state variable into the model. This method can fully utilize the ability of GWS to represent macroscopic changes in the groundwater system and provide stable data support for prediction.

[0023] The PINN-Transformer groundwater level prediction method based on groundwater storage constraints described in this invention enables the groundwater prediction process to be constrained by both actual values ​​and physical laws, thereby improving the physical consistency and interpretability of the prediction results. Furthermore, it utilizes the Transformer model's ability to characterize long-term series dependencies, thus enhancing the ability to predict groundwater level time series.

[0024] The PINN-Transformer groundwater level prediction method based on groundwater storage constraints described in this invention can select different combinations of input variables, supports one-step prediction and multi-step recursive prediction, and is applicable to various prediction needs and data conditions. The prediction results are not limited to generating predicted values; furthermore, the prediction process can incorporate physical constraint equations to invert hydrogeological parameters, providing a basis for regional groundwater assessment and management. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the PINN-Transformer groundwater level prediction method based on groundwater storage constraints as described in Implementation Method 1.

[0026] Figure 2 This is a schematic diagram of the PINN-Transformer groundwater level prediction results based on groundwater storage constraints as described in Implementation Method 1. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0028] Implementation Method 1, see [link] Figures 1 to 2 This embodiment proposes a PINN-Transformer groundwater level prediction method based on groundwater storage constraints. The method incorporates GWS, LRM, PINN, and Transformer time series prediction models to construct a physically constrained groundwater level prediction model. This combines data-driven prediction with constraints imposed by the physical laws of groundwater, providing stability and physical consistency in the prediction results and offering technical support for water resource management and hydrogeological parameter information acquisition. The method specifically includes the following steps: Step 1: Data Acquisition and Time-Scale Unification. Acquire data P, GWL, and GWS; where P is the driving factor of groundwater change, and GWS is the state variable of macroscopic state change of the groundwater system. Perform time-scale unification processing on the above data to ensure that all types of data correspond at the same time step.

[0029] Step 2: Derivation of the physical constraint equations for GWS. LRM summarizes the basic groundwater dynamics through the mathematical relationship between groundwater levels H and P, and is widely used to simulate precipitation-driven runoff and GWL changes. The formula is as follows:

[0030] Changes in groundwater storage, where A is the area per unit area:

[0031]

[0032] All the above variables are related to time t. Take the derivative of both sides with respect to time t:

[0033] in, The aquifer storage coefficient, Groundwater level, This is the groundwater discharge coefficient. Here, P is the precipitation infiltration recharge coefficient, and P is the precipitation amount.

[0034] Step 3: Constructing the PINN model with embedded physical constraint equations. Based on the physical constraint equations for groundwater level changes obtained in Step 2, physical residual terms are constructed and added as physical constraint terms to the PINN loss function. The loss function includes a data loss term between predicted and measured groundwater values, and a physical loss term calculated from the physical constraint equations for groundwater level changes. Through the combined constraints of the data loss and physical loss terms, the model satisfies the physical response relationship of the groundwater system while fitting the measured data.

[0035] Step 4: Construction of the PINN and Transformer Coupled Model. Using the Transformer as the basic prediction framework, and applying the PINN physical constraints from Step 3 during the training process, a coupled model is constructed. The Transformer model is used to extract the temporal features of the three variables, while the PINN physical constraint term is used to constrain the model's prediction results, ensuring they satisfy the physical constraint equations for groundwater level changes jointly determined by LRM and GWS.

[0036] Step 5: Select input variable type and prediction method. Based on the variables required by the physical constraints, the input variable combinations include the P and GWL combination and the three-variable input combination. The physical constraint equations corresponding to these two combinations are LRM and GLRM.

[0037] The prediction methods include one-step prediction and multi-step recursive prediction. The one-step prediction method is used to predict the groundwater level for the next time step based on the data of the current time step and the previous time steps. The multi-step recursive prediction method is used to use the predicted groundwater level as the input information for subsequent time steps and recursively obtain the prediction results for multiple time steps.

[0038] Step 6: Hydrogeological parameter inversion. With P and GWL as inputs, the model training process uses LRM as the physical constraint equation, and the inversion results can provide parameter references for regional hydrogeological parameters.

[0039] Step 7: Evaluation of Prediction Results. The prediction accuracy of the prediction model is analyzed using RMSE, MaxAE, and NSE under both prediction methods.

[0040] In summary, this implementation method can select different combinations of input variables, supports one-step and multi-step recursive prediction, and is suitable for application scenarios with different prediction needs and data conditions. The prediction results are not limited to generated prediction values; furthermore, the prediction process can incorporate physical constraint equations to invert hydrogeological parameters, providing a basis for regional groundwater assessment and management.

[0041] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or technical solutions of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0042] Although preferred embodiments of the present invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended technical solutions are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the present invention. Clearly, those skilled in the art can make various modifications and variations to the present invention without departing from its spirit and scope. Thus, if these modifications and variations of the present invention fall within the scope of the present invention and its equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A PINN-Transformer groundwater level prediction method based on groundwater storage constraints, characterized in that, The method includes the following steps: Step 1: Collect precipitation data P, groundwater level data GWL, and groundwater storage data GWS. Use precipitation data P as the driving factor for dynamic changes in groundwater, and groundwater storage data GWS as the state variable for macroscopic changes in the groundwater system. Perform time-scale uniform correction on the three types of data. Step 2: Based on the response correlation between precipitation and groundwater level in the LRM model, by introducing the groundwater storage variable, the physical constraint equation for groundwater level change that integrates groundwater storage is obtained. Step 3: Construct the corresponding physical residual term based on the physical constraint equation of groundwater level change, and embed the physical residual term as a physical constraint condition into the loss function of the physical information neural network; Step 4: Using the Transformer model as the basic framework for groundwater level time series prediction, the PINN physical constraint corresponding to the loss function is introduced during the Transformer model training process to construct the GWS-LRM-PINN-Transformer groundwater level prediction model. Step 5: Using precipitation data P, groundwater level data GWL, and groundwater storage data GWS as input variables, and the physical constraint equations constructed by the LRM model as constraint conditions, the groundwater level prediction is completed using both one-step and multi-step recursive methods. Step 6: Input the precipitation data P and groundwater level data GWL into the trained GWS-LRM-PINN-Transformer model, and perform parameter inversion according to the physical constraint equation of groundwater level change to achieve quantitative inversion of regional hydrogeological parameters.

2. The PINN-Transformer groundwater level prediction method based on groundwater storage constraints according to claim 1, characterized in that, Step 2, based on the response correlation between precipitation and groundwater level in the LRM model, introduces the groundwater storage variable to obtain the physical constraint equation for groundwater level change that integrates groundwater storage: The LRM model is based on the mathematical response relationship between groundwater level and precipitation, and establishes the basic mechanism of groundwater dynamics to simulate the dynamic change process of groundwater level driven by precipitation. Based on the principle of groundwater balance, a balance equation for groundwater storage changes per unit area is established. In this balance equation, the physical variables—precipitation, groundwater level, and groundwater storage—are all time-series variables that change with time t. Differentiating both sides of the groundwater storage change balance equation with respect to time t yields the time-series rate of change relationships for each hydrological variable. By combining the precipitation-groundwater dynamics coupling constraint relationship of the LRM model, a groundwater storage change rate term is introduced into the groundwater dynamics equation, and the physical constraint equation of groundwater level change that simultaneously couples precipitation-driven, groundwater level dynamics and groundwater storage surplus and deficit changes is derived iteratively.

3. The PINN-Transformer groundwater level prediction method based on groundwater storage constraints according to claim 2, characterized in that, The LRM model, based on the mathematical response relationship between groundwater level and precipitation, establishes a fundamental mechanism of groundwater dynamics to simulate the dynamic change process of groundwater level driven by precipitation. Changes in groundwater storage, where A is the area per unit: All the above variables are related to time t. Taking the derivative of both sides with respect to time t: in, The aquifer storage coefficient, Groundwater level This is the groundwater discharge coefficient. Here, P is the precipitation infiltration recharge coefficient, and P is the precipitation amount.

4. The PINN-Transformer groundwater level prediction method based on groundwater storage constraints according to claim 1, characterized in that, The loss function described in step 3 includes a data loss term between the predicted and measured groundwater values, as well as a physical loss term calculated from the physical constraint equation for groundwater level changes.

5. The PINN-Transformer groundwater level prediction method based on groundwater storage constraints according to claim 1, characterized in that, The Transformer model described in step 4 is used to extract the temporal characteristics of precipitation data P, groundwater level data GWL, and groundwater storage data GWS. The PINN physical constraint term is used to constrain the model prediction results so that they satisfy the physical constraint equation for groundwater level change jointly determined by the LRM model and the groundwater storage data GWS.

6. The PINN-Transformer groundwater level prediction method based on groundwater storage constraints according to claim 1, characterized in that, The one-step recursive method described in step 5 is used to predict the groundwater level for the next time step based on the data of the current time step and the previous time steps; the multi-step recursive method is used to use the predicted groundwater level as the input information for subsequent time steps to recursively obtain the prediction result for at least one time step.

7. The PINN-Transformer groundwater level prediction method based on groundwater storage constraints according to claim 1, characterized in that, The input variables mentioned in step 5 include a combination of precipitation data P, groundwater level data GWL, and groundwater storage data GWS. The physical constraint equations corresponding to the two combination distributions are the LRM physical constraint equation and the GLRM physical constraint equation. The LRM physical constraint equation is based on the basic water balance dynamic equation constructed from precipitation and groundwater level, while the GLRM physical constraint equation is based on the improved water balance dynamic equation that incorporates the temporal variation characteristics of groundwater storage.

8. A PINN-Transformer groundwater level prediction system based on groundwater storage constraints, characterized in that, The system includes: The data processing module is used to collect precipitation data P, groundwater level data GWL, and groundwater storage data GWS. It uses precipitation data P as the driving factor for dynamic changes in groundwater and groundwater storage data GWS as the state variable for macroscopic changes in the groundwater system. It performs time-scale uniform correction on the three types of data. The physical constraint equation derivation module is used to derive the physical constraint equation for groundwater level change by introducing the groundwater storage variable based on the response correlation between precipitation and groundwater level in the LRM model and integrating the groundwater storage. The physical residual loss construction module is used to construct the corresponding physical residual term based on the physical constraint equation of groundwater level change, and to embed the physical residual term as a physical constraint condition into the loss function of the physical information neural network. The coupled model construction module is used to use the Transformer model as the basic framework for groundwater level time series prediction. During the training process of the Transformer model, the PINN physical constraint corresponding to the loss function is introduced to construct the GWS-LRM-PINN-Transformer groundwater level prediction model. The adaptive prediction module is used to take precipitation data P, groundwater level data GWL and groundwater storage GWS as input variables and the physical constraint equations constructed by the GLRM model as constraints. It completes the groundwater level prediction using one-step recursion and multi-step recursion methods respectively. The parameter inversion module is used to input precipitation data P and groundwater level data GWL into the trained GWS-LRM-PINN-Transformer model, and perform parameter inversion based on the physical constraint equation of groundwater level change to achieve quantitative inversion of regional hydrogeological parameters.

9. A computer storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1-7.

10. A computer device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the method of any one of claims 1-7.

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