A Soil Thickness Inversion Method Based on Physical Information Neural Network

Abstract

This invention discloses a soil thickness inversion method based on a physical information neural network, belonging to the field of soil thickness measurement technology. The method includes the following steps: S1, Data collection and preprocessing: acquiring topographic data, geological data, hydrological data, relevant parameter data of the GIST model, and soil thickness samples of the target area; S2, Constructing a physical information neural network model GIST-PINN; S3, Soil thickness simulation and mapping: using the trained GIST-PINN model, simulating the soil thickness of the target area and generating a corresponding spatial distribution map. This invention employs the above-mentioned soil thickness inversion method based on a physical information neural network to construct a soil thickness inversion model, simulate the soil thickness of the target area, achieve soil thickness inversion under physical constraints, and provide a more accurate simulation of soil thickness.

Description

Technical Field

[0001] This invention relates to the field of soil thickness measurement technology, and in particular to a soil thickness inversion method based on a physical information neural network. Background Technology

[0002] Soil thickness (i.e., the depth from the surface to the bedrock) is a key input parameter for many environmental models, with wide applications in slope hydrology, landslide stability analysis, seismic site effect assessment, and landscape evolution. However, obtaining high-precision soil thickness data remains a significant challenge in large-scale applications. Traditional measurement methods (such as drilling), while highly accurate, are limited by cost and time constraints, making widespread adoption difficult. Therefore, effectively predicting the spatial distribution of soil thickness has become an important research topic.

[0003] Traditional methods for predicting soil thickness primarily rely on empirical relationships between topographic factors (such as slope, curvature, and elevation) and soil thickness, or on estimations using multivariate statistical models. These methods perform well in areas with shallow soil and simple geological conditions, but their accuracy often suffers in complex geological environments. In recent years, machine learning methods (such as random forests and support vector machines) have been introduced into soil thickness prediction research, enhancing data-driven modeling capabilities. However, these methods mainly rely on large-scale data training and lack physical constraints. When dealing with areas with complex geological structures or scarce data, they still suffer from insufficient adaptability and large prediction errors, particularly in accurately capturing the nonlinear variation characteristics of soil thickness. Summary of the Invention

[0004] The purpose of this invention is to provide a soil thickness inversion method based on physical information neural networks. Based on topographic data, geological data, hydrological data and other relevant environmental factors, the method uses the GIST model to apply physical constraints to the PINN neural network, constructs a soil thickness inversion model, simulates the soil thickness of the target area, realizes soil thickness inversion under physical constraints, and simulates soil thickness more accurately.

[0005] To achieve the above objectives, this invention provides a soil thickness inversion method based on a physical information neural network, comprising the following steps:

[0006] S1. Data Collection and Preprocessing: Acquire topographic and geomorphological data, geological data, hydrological data, relevant parameter data of the GIST model, and soil thickness samples of the target area;

[0007] S2. Construct the physical information neural network model GIST-PINN;

[0008] S3. Soil thickness simulation and mapping: Using the trained GIST-PINN model, the soil thickness of the target area is simulated and the corresponding spatial distribution map is generated.

[0009] Preferably, the topographic data in S1 includes a digital elevation model (DEM), land use data, and soil type data; the geological data includes geological maps; the hydrological data includes the topographic humidity index; the relevant parameter data of the GIST model includes the maximum soil thickness K, the index C based on the profile curvature, and the actual relative position P of a point on the hillside; and the soil thickness measurement data includes drilling data. The above data are spatially matched and unified to a resolution of 12.5 meters to ensure data consistency. Environmental factors are extracted to construct a dataset for modeling.

[0010] Preferably, the environmental factors in S1 are selected as follows:

[0011] The digital elevation model (DEM) includes parameters such as slope, geological lithology, plane curvature, profile curvature, aspect, land use, soil type, normalized difference vegetation index (NDVI), topographic moisture index (TWI), topographic roughness index (TRI), and some relevant parameters of the GIST model: maximum soil thickness (K), profile curvature-based index (C), and actual relative position (P) of a point on the hillside.

[0012] The formula for calculating the exponent C based on the profile curvature is as follows:

[0013]

[0014] Where c is the profile curvature value, and a few values ​​outside the range of -2 to 2 are interpreted as outliers; the exponent C of the profile curvature within the range is applied with a linear negative correlation function with the profile curvature value c within the range.

[0015] P is the actual relative position of a point on the hillside. The index of position p is determined by the shortest uphill distance a and downhill distance β calculated from the DEM using Python code. The calculation method for P is as follows:

[0016]

[0017] Preferably, in S2, the extracted environmental factor data is used as input to train the GIST-PINN network model. The soil thickness directly simulated by the network output layer and the soil loss index S of the GIST model based on the slope threshold are used. According to the GIST model, the soil thickness under the physical model is estimated by using the mathematical relationship between the relevant parameters K, C, P and S of the network output layer and the soil thickness.

[0018] Preferably, the method for constructing the physical information neural network model in S2 specifically includes the following steps:

[0019] S2.1, GIST-PINN Neural Network Model Construction: Using 14 environmental factors as the network input layer, a deep learning neural network model is constructed. The output layer of the network has two parameters, S and Soil_thickness1.

[0020] S2.2, Physical Empirical Model GIST Constraints: The parameters S output by the neural network, along with the pre-prepared parameters K, C, and p, are input into the GIST model equations to calculate the soil thickness Soil_thickness2 under the physical model. The specific process is as follows:

[0021] Soil_thickness2=K·C·P·S;

[0022] In the formula, K is the maximum soil thickness, C is the index based on the profile curvature, P is the actual relative position of a point on the hillside, and S is the soil loss index based on the slope threshold.

[0023] S2.3 The GIST-PINN model utilizes physical laws to guide model training. Its core lies in incorporating physical knowledge into the loss function. During model training, the loss function is designed as a weighted sum of data-driven and physics-driven losses. The optimal weight combination is automatically adjusted based on the total loss value during the GIST-PINN network training optimization process.

[0024] loss=λ1·loss1+λ2·loss2;

[0025] Here, loss1 and loss2 are the data-driven loss and the physics-driven loss, respectively; weights λ1 and λ2 are hyperparameters that weigh the importance of the two error terms. By selecting appropriate hyperparameters, the GIST-PINN model can fit the data while constraining the predicted physical quantities within the range allowed by the physical laws.

[0026] S2.4 Soil thickness under GIST physical model constraints: Utilizing the optimal weight parameter combination automatically adjusted based on the total loss value during GIST-PINN network training, the soil thickness Soil_thickness1 directly predicted by the neural network and Soil_thickness2 calculated by the GIST model are weighted and averaged to obtain the final soil thickness Soil_thickness. The calculation formula is as follows:

[0027] Soil_thickness=λ1·Soil_thickness1+λ2·Soil_thickness2.

[0028] Therefore, this invention adopts the above-mentioned soil thickness inversion method based on physical information neural network. Based on topographic data, geological data, hydrological data and other relevant environmental factors, the GIST model is used to physically constrain the neural network PINN to construct a soil thickness inversion model, simulate the soil thickness of the target area, realize soil thickness inversion under physical constraints, and simulate soil thickness more accurately.

[0029] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0030] Figure 1 This is a flowchart of a soil thickness inversion method based on a physical information neural network according to the present invention;

[0031] Figure 2 This is an environmental factor map of a soil thickness inversion method based on a physical information neural network according to the present invention, wherein, Figure 2 (a) in the image is a DEM. Figure 2 (b) in the figure represents the slope. Figure 2 (c) in the text represents the slope aspect. Figure 2 In this context, (d) represents the maximum soil thickness parameter K. Figure 2 In this context, (e) represents the exponent C based on the profile curvature. Figure 2 In this context, (f) represents the actual relative position P of a point on the hillside. Figure 2 (g) in the text refers to land use. Figure 2 (h) in the text represents the soil type. Figure 2 In this context, (i) represents the Normalized Difference Vegetation Index (NDVI). Figure 2 (j) in the text represents the geological rock group. Figure 2 In this context, (k) represents the surface roughness TRI. Figure 2 (l) in the figure represents the topographic humidity index TWI. Figure 2 In this context, (m) represents the curvature of the plane. Figure 2 In this context, (n) represents the curvature of the cross-section;

[0032] Figure 3 This is a diagram illustrating the training process of the GIST-PINN model for a soil thickness inversion method based on a physical information neural network, as described in this invention. Figure 3 In the figure, (a) is the learning rate change curve of the GIST-PINN model. Figure 3 (b) in the figure shows the loss variation curve of the GIST-PINN model;

[0033] Figure 4 This is an accuracy verification image of the soil thickness inversion method based on physical information neural network of the present invention, wherein, Figure 4 (a) in the figure shows the accuracy verification of the soil thickness simulation by the physical model GIST. Figure 4 (b) in the diagram represents the accuracy verification of directly simulating soil thickness using neural network layers. Figure 4 (c) in the figure is a verification of the accuracy of the GIST-PINN model in simulating soil thickness;

[0034] Figure 5 S is the output parameter S of the GIST-PINN model for a soil thickness inversion method based on a physical information neural network according to the present invention.

[0035] Figure 6 This invention relates to a soil thickness inversion method based on a physical information neural network, using the GIST-PINN model to simulate soil thickness maps. Detailed Implementation

[0036] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0037] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0038] Example 1

[0039] like Figure 1 As shown, this invention provides a soil thickness inversion method based on a physical information neural network, comprising the following steps:

[0040] S1. Data Collection and Preprocessing: Acquire topographic and geomorphological data, geological data, hydrological data, relevant parameter data of the GIST model, and soil thickness samples of the target area;

[0041] Topographic data includes digital elevation models (DEM), land use data, and soil type data; geological data includes geological maps; hydrological data includes topographic humidity index; relevant parameter data for the GIST model include maximum soil thickness K, index C based on profile curvature, and actual relative position P of a point on the hillside; soil thickness measurement data includes drilling data. The above data are spatially matched and unified to a resolution of 12.5 meters to ensure data consistency. Environmental factors are extracted to construct a dataset for modeling.

[0042] The selection of environmental factors is as follows:

[0043] The parameters included in the Digital Elevation Model (DEM), slope, geological lithology, plan curvature, profile curvature, aspect, land use, soil type, Normalized Difference Vegetation Index (NDVI), Topographic Moisture Index (TWI), Topographic Roughness Index (TRI), and some relevant parameters from the GIST model: maximum soil thickness K, the index C based on profile curvature, and the actual relative position P of a point on the hillside; K represents the maximum thickness measured on soil samples from different geological rock groups.

[0044] The formula for calculating the exponent C based on the profile curvature is as follows:

[0045]

[0046] Where c is the profile curvature value, and a few values ​​outside the range of -2 to 2 are interpreted as outliers; the exponent C of the profile curvature within the range is applied with a linear negative correlation function with the profile curvature value c within the range.

[0047] P is the actual relative position of a point on the hillside. The index of position p can be determined by the shortest uphill distance a and downhill distance β calculated from the DEM using Python code. The calculation method for P is as follows:

[0048]

[0049] Among the selected factors, DEM (Digital Elevation Model) serves as the foundational elevation data, revealing topographic relief. Slope directly influences water flow velocity and erosion processes, thus determining soil accumulation thickness. Planar curvature and profile curvature respectively demonstrate the characteristics of water convergence or dispersion in the horizontal and vertical directions of the land surface, helping to identify differences in soil deposition and erosion within microenvironments. Aspect influences soil moisture balance and temperature conditions by regulating solar radiation and rainfall distribution. Geological lithology, as a reflection of parent material characteristics, directly determines the soil formation rate and maximum possible thickness, while land use and soil type reflect the impact of human activities on soil erosion, improvement, and protection, as well as the soil's formation history and developmental stages. Furthermore, TWI (Total Weighing Indicator) reflects the potential for soil moisture accumulation by comprehensively considering slope and catchment area, while TRI (Total Retention and Deposition) describes the impact of local microscale topography on water flow distribution and deposition processes, further revealing local variations in soil thickness. Finally, among the GIST-related factors, the K value directly reflects the upper limit of the maximum soil thickness, the C factor reinforces the role of profile curvature in water convergence and dispersion, and the P factor distinguishes soil accumulation at different locations on the slope, thus comprehensively revealing the differences in soil thickness at the top, middle, and bottom of the slope due to water flow, erosion, and deposition effects. In summary, these factors were selected to comprehensively capture the topographic, geological, hydrological, and human factors influencing soil thickness, providing information support from multiple perspectives, thereby improving the accuracy and reliability of the model's soil thickness inversion.

[0050] Based on the above factors, the study obtained relevant data for the Liuyang City area in Hunan Province, such as... Figure 2 As shown, where, Figure 2 (a) in the image is a DEM. Figure 2 (b) in the figure represents the slope. Figure 2 (c) in the text represents the slope aspect. Figure 2 In this context, (d) represents the maximum soil thickness parameter K. Figure 2 In this context, (e) represents the exponent C based on the profile curvature. Figure 2 In this context, (f) represents the actual relative position P of a point on the hillside. Figure 2 (g) in the text refers to land use. Figure 2 (h) in the text represents the soil type. Figure 2 In this context, (i) represents the Normalized Difference Vegetation Index (NDVI). Figure 2 (j) in the text represents the geological rock group. Figure 2 In this context, (k) represents the surface roughness TRI. Figure 2 (l) in the figure represents the topographic humidity index TWI. Figure 2 In this context, (m) represents the curvature of the plane. Figure 2 In this context, (n) represents the curvature of the cross section.

[0051] In addition, the soil thickness data obtained from drilling was used as the actual soil thickness data for the study. This data was provided by the Hunan Provincial Geological Survey.

[0052] The above data were spatially matched and standardized to a resolution of 12.5 meters to ensure data consistency. Based on the actual soil thickness data, relevant factor data for the corresponding spatiotemporal locations were obtained to construct a dataset for modeling, and the obtained relevant factor data was used as the prediction dataset.

[0053] S2. Construct the physical information neural network model GIST-PINN;

[0054] A soil thickness inversion model was constructed using the PINN neural network, while the GIST physical empirical model was introduced to physically constrain the neural network and improve simulation accuracy. Extracted environmental factor data was used as input to train the GIST-PINN network model. The network output layer directly simulated the soil thickness, and the GIST model parameters were based on the soil loss index S with a slope threshold. Based on the GIST model, the soil thickness under the physical model was estimated using the mathematical relationships between relevant parameters K, C, P, and the network output layer's S with the soil thickness.

[0055] The method for constructing a physical information neural network model specifically includes the following steps:

[0056] S2.1 GIST-PINN Neural Network Model Construction: Using 14 environmental factors as the input layer of the network, a deep learning neural network model is constructed. The output layer of the network has two parameters, S and Soil_thickness1. The former reflects the relevant physical parameters in the GIST model and comprehensively considers the influence of slope and the soil loss index of the slope threshold. The latter is the soil thickness value directly simulated by the neural network.

[0057] S2.2, Physical Empirical Model GIST Constraints: The parameters S output by the neural network, along with the pre-prepared parameters K, C, and p, are input into the GIST model equations to calculate the soil thickness Soil_thickness2 under the physical model. The specific process is as follows:

[0058] Soil_thickness2=K·C·P·S;

[0059] In the formula, K is the maximum soil thickness, C is the index based on the profile curvature, P is the actual relative position of a point on the hillside, and S is the soil loss index based on the slope threshold.

[0060] S2.3 The GIST-PINN model utilizes physical laws to guide model training. Its core lies in incorporating physical knowledge into the loss function. During model training, the loss function is designed as a weighted sum of data-driven and physics-driven losses. The optimal weight combination is automatically adjusted based on the total loss value during the GIST-PINN network training and optimization process. Figure 3 As shown, where, Figure 3 In the figure, (a) is the learning rate change curve of the GIST-PINN model. Figure 3 (b) in the figure shows the loss variation curve of the GIST-PINN model:

[0061] loss=λ1·loss1+λ2·loss2;

[0062] Here, loss1 and loss2 are the data-driven loss and the physics-driven loss, respectively; weights λ1 and λ2 are hyperparameters that weigh the importance of the two error terms. By selecting appropriate hyperparameters, the GIST-PINN model can fit the data while constraining the predicted physical quantities within the range allowed by the physical laws.

[0063] S2.4 Soil thickness under GIST physical model constraints: Utilizing the optimal weight parameter combination automatically adjusted based on the total loss value during GIST-PINN network training, the soil thickness Soil_thickness1 directly predicted by the neural network and Soil_thickness2 calculated by the GIST model are weighted and averaged to obtain the final soil thickness Soil_thickness. The calculation formula is as follows:

[0064] Soil_thickness=λ1·Soil_thickness1+λ2·Soil_thickness2.

[0065] For the constructed model, accuracy is verified using drilled soil thickness data and 10-fold cross-validation, such as... Figure 4As shown, the GIST-PINN model has an R² of 0.83, which is an improvement compared to directly using the physical model (R²≈0.75) and the neural network (R²≈0.82). Furthermore, the results take into account the constraints of physical conditions. Figure 4 (a) in the figure shows the accuracy verification of the soil thickness simulation by the physical model GIST. Figure 4 (b) in the diagram represents the accuracy verification of directly simulating soil thickness using neural network layers. Figure 4 (c) in the figure is a verification of the accuracy of the GIST-PINN model in simulating soil thickness.

[0066] By combining the above methods with objective physical laws, we can further integrate the actual environmental characteristics of the region, thereby achieving a more accurate simulation of soil thickness.

[0067] S3. Soil Thickness Simulation and Mapping: Using the trained GIST-PINN model and the acquired environmental factor dataset, the soil thickness of the target area is simulated, and the output parameter S is as follows: Figure 5 As shown, the output parameter S and the corresponding soil thickness prediction results for Liuyang City, Hunan Province, are used to obtain the soil thickness prediction dataset under physical constraints. To better illustrate the soil thickness prediction results, a corresponding spatial distribution map of soil thickness is generated, as shown below. Figure 6 As shown.

[0068] Therefore, this invention adopts the above-mentioned soil thickness inversion method based on physical information neural network. Based on topographic data, geological data, hydrological data and other relevant environmental factors, the GIST model is used to physically constrain the neural network PINN to construct a soil thickness inversion model, simulate the soil thickness of the target area, realize soil thickness inversion under physical constraints, and simulate soil thickness more accurately.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for soil thickness inversion based on a physical information neural network, characterized in that: Includes the following steps: S1. Data Collection and Preprocessing: Acquire topographic and geomorphological data, geological data, hydrological data, relevant parameter data of the GIST model, and soil thickness samples of the target area; S2. Construct the physical information neural network model GIST-PINN; The method for constructing a physical information neural network model specifically includes the following steps: S2.1, GIST-PINN Neural Network Model Construction: Using 14 environmental factors as the network input layer, a deep learning neural network model is constructed. The network's output layer has two parameters. and ; S2.2, Physical Empirical Model GIST Constraints: The parameters output by the neural network... With the preparation , and Three parameters are input into the GIST model equations to calculate the soil thickness under the physical model. The specific process is as follows: ； In the formula, It is the maximum soil thickness. An index based on profile curvature, It is the actual relative position of a point on the hillside. It is a soil loss index based on a slope threshold; S2.3 The GIST-PINN model utilizes physical laws to guide model training. Its core lies in incorporating physical knowledge into the loss function. During model training, the loss function is designed as a weighted sum of data-driven and physics-driven losses. The optimal weight combination is determined during the GIST-PINN network training optimization process based on the total loss value. Automatic adjustment yields: ； in, and These are data-driven loss and physics-driven loss, respectively; weights and It is a hyperparameter that weighs the importance of the two error terms. By selecting appropriate hyperparameters, the GIST-PINN model can fit the data while constraining the predicted physical quantities within the range allowed by the physical laws. S2.4, Soil thickness under GIST physical model constraints: This is achieved by using the GIST-PINN network training process based on the total loss value... The automatically adjusted optimal combination of weight parameters will enable the neural network to directly predict... Computed with GIST model The final soil thickness is obtained by performing a weighted average. The calculation formula is as follows: ； S3. Soil thickness simulation and mapping: Using the trained GIST-PINN model, the soil thickness of the target area is simulated and the corresponding spatial distribution map is generated.

2. The soil thickness inversion method based on a physical information neural network according to claim 1, characterized in that: S1 contains topographic data including a digital elevation model (DEM), land use data, and soil type data; geological data including geological maps; hydrological data including topographic humidity index; and relevant parameter data from the GIST model, including maximum soil thickness. Exponent based on profile curvature The actual relative position of a point on the hillside Soil thickness measurement data includes drilling data. The above data are spatially matched and unified to a resolution of 12.5 meters to ensure data consistency. Environmental factors are extracted, and a dataset for modeling is constructed.

3. The soil thickness inversion method based on a physical information neural network according to claim 2, characterized in that: In S1, the environmental factors are selected as follows: Digital Elevation Model (DEM), slope, geological lithology, plane curvature, profile curvature, aspect, land use, soil type, Normalized Difference Vegetation Index (NDVI), Topographic Moisture Index (TWI), Topographic Roughness Index (TRI), and some relevant parameters from the GIST model: maximum soil thickness. Exponent based on profile curvature The actual relative position of a point on the hillside ; Among them, the index based on profile curvature The calculation formula is as follows: ； in, The profile curvature value is defined as a few values ​​outside the range of -2 to 2, which are interpreted as outliers; the exponent of the profile curvature within the range is also considered. The profile curvature values ​​within the range were applied. The linear negative correlation function; It is the actual relative position of a point on the hillside. The index is the shortest uphill distance calculated from the DEM using Python code. and downhill distance To determine, The calculation method is as follows: ； 。 4. The soil thickness inversion method based on a physical information neural network according to claim 3, characterized in that: In S2, the extracted environmental factor data is used as input to train the GIST-PINN network model. The network output layer directly simulates the soil thickness, and the GIST model parameters are based on the soil loss index with a slope threshold. ; Based on the GIST model, using relevant parameters , , and network output layer The mathematical relationship between soil thickness and soil thickness is used to estimate the soil thickness under the physical model.

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