Soil thickness inversion method based on physical information neural network

Abstract

The invention discloses a soil thickness inversion method based on a physical information neural network, and belongs to the technical field of soil thickness calculation, and the method comprises the following steps: S1, data collection and preprocessing: obtaining landform data, geological data, hydrological data, related parameter data of a GIST model part and a soil thickness sample of a target area; s2, a physical information neural network model GIST-PINN is constructed; and S3, soil thickness simulation and mapping: simulating the soil thickness of the target area by using the trained GIST-PINN model, and generating a corresponding spatial distribution diagram. According to the soil thickness inversion method based on the physical information neural network, the soil thickness inversion model is constructed, the soil thickness of the target area is simulated, soil thickness inversion under physical condition constraints is achieved, and the soil thickness is simulated more accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of soil thickness measurement, and in particular to a soil thickness inversion method based on a physical information neural network. Background Art

[0002] Soil thickness (i.e., the depth from the surface to bedrock) is a key input parameter for many environmental models and has widespread applications in areas such as hillslope hydrology, landslide stability analysis, earthquake site effect assessment, and landscape evolution. However, obtaining high-precision soil thickness data in large-scale applications still faces many challenges. Traditional measurement methods (such as drilling), while highly accurate, are limited by cost and time, making them difficult to scale up on a large scale. Therefore, effectively predicting the spatial distribution of soil thickness has become a key research topic.

[0003] Traditional soil thickness prediction methods rely primarily 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 thickness and simple geological conditions, but their prediction accuracy is often difficult to guarantee 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 the capabilities of data-driven modeling. However, these methods rely primarily on large-scale data training and lack physical constraints. When dealing with areas with complex geological structures or data scarcity, they still suffer from insufficient adaptability and large prediction errors. In particular, they struggle to accurately capture the nonlinear variation characteristics of soil thickness. Summary of the Invention

[0004] The purpose of the present invention is to provide a soil thickness inversion method based on a physical information neural network. Based on relevant environmental factors such as topographic data, geological data, and hydrological data, the neural network PINN is physically constrained by the GIST model to construct a soil thickness inversion model, simulate the soil thickness of the target area, realize soil thickness inversion under physical conditions constraints, and simulate soil thickness more accurately.

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

[0006] S1. Data collection and preprocessing: Obtain topographic data, geological data, hydrological data, some 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, simulate the soil thickness of the target area and generate the corresponding spatial distribution map.

[0009] Preferably, the topographic data in S1 include digital elevation model DEM, land use data and soil type data, the geological data include geological maps, the hydrological data include topographic moisture index, some relevant parameter data of 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, and soil thickness measurement data include drilling data. The above data are spatially matched and unified to a resolution of 12.5 meters to ensure data consistency, extract environmental factors, and construct a data set for modeling.

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

[0011] Digital elevation model (DEM), slope, geological lithology, plan curvature, profile curvature, aspect, land use, soil type, Normalized Difference Vegetation Index (NDVI), Terrain Wetness Index (TWI), Terrain Roughness Index (TRI), and some relevant parameters of the GIST model: maximum soil thickness (K), index based on profile curvature (C), and actual relative position (P) of a point on the hillside;

[0012] The calculation formula of the index C based on the cross-sectional curvature is as follows:

[0013]

[0014] Where c is the profile curvature value, and a few values outside the range of profile curvature values from -2 to 2 are interpreted as outliers; the index C of the profile curvature within the range applies 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 by the DEM using Python code. P is calculated as follows:

[0016]

[0017] Preferably, the extracted environmental factor data is used as input in S2 to train the GIST-PINN network model, and the network output layer directly simulates the soil thickness and the soil loss index S of the GIST model parameters based on the slope threshold; 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 the network output layer S 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: 14 environmental factors are used as the network input layer to build a deep learning neural network model. The output layer of the network has two parameters, S and soil_thickness1.

[0020] S2.2, Physical empirical model GIST constraint: Input the parameter S output by the neural network and the three pre-prepared parameters K, C, and p into the GIST model equation 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] Where K is the maximum soil thickness, C is an index based on the profile curvature, P is the actual relative position of a point on the hillside, and S is a soil loss index based on the slope threshold.

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

[0024] loss=λ1·loss1+λ2·loss2;

[0025] Among them, loss1 and loss2 are data-driven loss and 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 to the range allowed by physical laws.

[0026] S2.4. Soil thickness under the constraints of the physical model GIST: Using the optimal weight parameter combination automatically adjusted according to the total loss value during the GIST-PINN network training process, the weighted average of Soil_thickness1 directly predicted by the neural network and Soil_thickness2 calculated by the GIST model is taken 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, the present invention adopts the above-mentioned soil thickness inversion method based on physical information neural network. Based on relevant environmental factors such as topographic data, geological data, and hydrological data, the neural network PINN is physically constrained through the GIST model to construct a soil thickness inversion model, simulate the soil thickness of the target area, realize soil thickness inversion under physical conditions constraints, and simulate the soil thickness more accurately.

[0029] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of a soil thickness inversion method based on physical information neural network of the present invention;

[0031] Figure 2 is an environmental factor graph of a soil thickness inversion method based on a physical information neural network of the present invention, wherein: Figure 2 (a) is DEM, Figure 2 (b) is the slope, Figure 2 (c) in the equation is the slope direction, Figure 2 (d) in the equation is the maximum soil thickness parameter K, Figure 2 (e) in the equation is the index C based on the curvature of the cross section. Figure 2 (f) is the actual relative position P of a point on the hillside, Figure 2 (g) in the equation is land use, Figure 2 (h) is the soil type, Figure 2 (i) in the equation is the Normalized Difference Vegetation Index (NDVI), Figure 2 (j) in the equation is the geological rock group, Figure 2 (k) is the surface roughness TRI, Figure 2 (l) in the equation is the terrain wetness index TWI, Figure 2 (m) in is the plane curvature, Figure 2 (n) in is the cross-sectional curvature;

[0032] Figure 3 This is a diagram of the GIST-PINN model training process of a soil thickness inversion method based on a physical information neural network of the present invention, wherein: Figure 3 (a) in the figure is the learning rate change curve of the GIST-PINN model. Figure 3 (b) is the loss change curve of the GIST-PINN model;

[0033] Figure 4 This is an accuracy verification diagram of the soil thickness inversion method based on physical information neural network of the present invention, in which: Figure 4 (a) is the accuracy verification of the soil thickness simulated by the physical model GIST. Figure 4 (b) is the accuracy verification of the direct simulation of soil thickness by the neural network layer. Figure 4 (c) is the accuracy verification of soil thickness simulated by GIST-PINN model;

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

[0035] Figure 6 The invention discloses a soil thickness map simulated by a GIST-PINN model of a soil thickness inversion method based on a physical information neural network. DETAILED DESCRIPTION

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

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

[0038] Example 1

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

[0040] S1. Data collection and preprocessing: Obtain topographic data, geological data, hydrological data, some relevant parameter data of the GIST model and soil thickness samples of the target area;

[0041] Topographic and geomorphological data include digital elevation models (DEMs), land use data, and soil type data. Geological data include geological maps. Hydrological data include the terrain moisture index. Some relevant parameter data of the GIST model include the maximum soil thickness K, the index C based on profile curvature, and the actual relative position P of a certain point on the hillside. Soil thickness measurement data include 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.

[0042] The environmental factors are:

[0043] Digital elevation model (DEM), slope, geological lithology, plan curvature, profile curvature, aspect, land use, soil type, Normalized Difference Vegetation Index (NDVI), Terrain Wetness Index (TWI), Terrain Roughness Index (TRI), and some relevant parameters of the GIST model: maximum soil thickness K, index C based on profile curvature, and actual relative position P of a point on the hillside; K is the maximum thickness measured on soil samples from different geological rock formations;

[0044] The calculation formula of the index C based on the cross-sectional curvature is as follows:

[0045]

[0046] Where c is the profile curvature value, and a few values outside the range of profile curvature values from -2 to 2 are interpreted as outliers; the index C of the profile curvature within the range applies 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. P is calculated as follows:

[0048]

[0049] Among the selected factors, DEM, as the basic elevation data, reveals the terrain undulations, while the slope directly affects the water flow velocity and erosion process, thereby determining the cumulative thickness of the soil. Plane curvature and profile curvature respectively show the characteristics of water flow convergence or dispersion in the horizontal and vertical directions of the surface, which helps to identify the differences in soil deposition and erosion in microenvironments; slope aspect affects the soil water balance and temperature conditions by regulating solar radiation and rainfall distribution. Geological lithology, as a manifestation 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 formation history and development stage of the soil. In addition, TWI reflects the potential for soil moisture accumulation by comprehensively considering slope and catchment area, while TRI describes the impact of local micro-scale topography on water flow distribution and deposition processes, further revealing the local variation 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 emphasizes the role of profile curvature in the convergence and dispersion of water flow, and the P factor is used to distinguish soil accumulation at different locations on the slope, thereby comprehensively revealing the differences in soil thickness at the top, middle, and toe of the slope caused by water flow, erosion, and sedimentation. In summary, these factors were selected to comprehensively capture the topographic, geological, hydrological, and human factors that influence soil thickness, providing information support from multiple perspectives, thereby improving the accuracy and reliability of the model's inversion of soil thickness.

[0050] Based on the above factors, the study obtained relevant data of Liuyang City, Hunan Province, such as Figure 2 As shown, Figure 2 (a) is DEM, Figure 2 (b) is the slope, Figure 2 (c) in the equation is the slope direction, Figure 2 (d) in the equation is the maximum soil thickness parameter K, Figure 2 (e) in the equation is the index C based on the curvature of the cross section. Figure 2 (f) is the actual relative position P of a point on the hillside, Figure 2 (g) in the equation is land use, Figure 2 (h) is the soil type, Figure 2 (i) in the equation is the Normalized Difference Vegetation Index (NDVI), Figure 2 (j) in the equation is the geological rock group, Figure 2 (k) is the surface roughness TRI, Figure 2 (l) in the equation is the terrain wetness index TWI, Figure 2 (m) in is the plane curvature, Figure 2 (n) in is the cross-sectional curvature.

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

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

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

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

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

[0056] S2.1. Construction of the GIST-PINN neural network model: A deep learning neural network model was constructed using 14 environmental factors as the network input layer. The network output layer consists of two parameters, S and Soil_thickness1. The former reflects the relevant physical parameters in the GIST model and comprehensively considers the influence of slope on 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 constraint: Input the parameter S output by the neural network and the three pre-prepared parameters K, C, and p into the GIST model equation 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] Where K is the maximum soil thickness, C is an index based on the profile curvature, P is the actual relative position of a point on the hillside, and S is a soil loss index based on the slope threshold.

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

[0061] loss=λ1·loss1+λ2·loss2;

[0062] Among them, loss1 and loss2 are data-driven loss and 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 to the range allowed by physical laws.

[0063] S2.4. Soil thickness under the constraints of the physical model GIST: Using the optimal weight parameter combination automatically adjusted according to the total loss value during the GIST-PINN network training process, the weighted average of Soil_thickness1 directly predicted by the neural network and Soil_thickness2 calculated by the GIST model is taken 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, the accuracy is verified by drilling soil thickness data and ten-fold cross validation, such as Figure 4As shown in Figure 2, the R2 of the GIST-PINN model is 0.83, which is improved compared to the direct use of physical models (R2≈0.75) and neural networks (R2≈0.82), and the results take into account the constraints of physical conditions, where Figure 4 (a) is the accuracy verification of the soil thickness simulated by the physical model GIST. Figure 4 (b) is the accuracy verification of the direct simulation of soil thickness by the neural network layer. Figure 4 (c) in the figure is the accuracy verification of the soil thickness simulated by the GIST-PINN model.

[0066] Through the above method, we can further integrate the actual environmental characteristics of the region on the basis of combining objective physical laws, so as to achieve a more accurate simulation of soil thickness.

[0067] S3. Soil thickness simulation and mapping: Using the trained GIST-PINN model, the soil thickness of the target area is simulated based on the obtained environmental factor dataset, and the output parameter S is as follows: Figure 5 As shown in the figure, the output parameter S and the corresponding soil thickness prediction results of Liuyang City, Hunan Province are obtained to obtain the soil thickness prediction data set under physical conditions. In order to better display the prediction results of soil thickness, the corresponding soil thickness spatial distribution map is generated, as shown in the figure. Figure 6 shown.

[0068] Therefore, the present invention adopts the above-mentioned soil thickness inversion method based on physical information neural network. Based on relevant environmental factors such as topographic data, geological data, and hydrological data, the neural network PINN is physically constrained through the GIST model to construct a soil thickness inversion model, simulate the soil thickness of the target area, realize soil thickness inversion under physical conditions constraints, and simulate the 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 rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A soil thickness inversion method based on physical information neural network, characterized by: The following steps are involved: S1. Data collection and preprocessing: Obtain topographic data, geological data, hydrological data, some 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; S3. Soil Thickness Simulation and Mapping: Using the trained GIST-PINN model, simulate the soil thickness of the target area and generate the corresponding spatial distribution map.

2. The soil thickness inversion method based on physical information neural network according to claim 1 is characterized in that: The topographic data in S1 include digital elevation models (DEMs), land use data, and soil type data. The geological data include geological maps. The hydrological data include the terrain moisture index. Some relevant parameter data of the GIST model include the maximum soil thickness K, the index C based on profile curvature, and the actual relative position P of a certain point on the hillside. The soil thickness measurement data include 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 the dataset for modeling is constructed.

3. The soil thickness inversion method based on physical information neural network according to claim 2 is characterized in that: In S1, the environmental factors are: Digital elevation model (DEM), slope, geological lithology, plan curvature, profile curvature, aspect, land use, soil type, Normalized Difference Vegetation Index (NDVI), Terrain Wetness Index (TWI), Terrain Roughness Index (TRI), and some relevant parameters of the GIST model: maximum soil thickness (K), index based on profile curvature (C), and actual relative position (P) of a point on the hillside; The calculation formula of the index C based on the cross-sectional curvature is as follows: Where c is the profile curvature value, and a few values outside the range of profile curvature values from -2 to 2 are interpreted as outliers; the index C of the profile curvature within the range applies a linear negative correlation function with the profile curvature value c within the range; 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 by the DEM using Python code. P is calculated as follows:

4. The soil thickness inversion method based on physical information neural network according to claim 3 is characterized in that: In S2, the extracted environmental factor data are used as input to train the GIST-PINN network model. The network output layer directly simulates the soil thickness and the soil loss index S based on the slope threshold of the GIST model parameters. 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 the network output layer S and soil thickness.

5. The soil thickness inversion method based on physical information neural network according to claim 4 is characterized in that: The physical information neural network model construction method in S2 specifically includes the following steps: S2.

1. GIST-PINN neural network model construction: 14 environmental factors are used as the network input layer to build a deep learning neural network model. The output layer of the network has two parameters, S and soil_thickness1. S2.2, Physical empirical model GIST constraint: Input the parameter S output by the neural network and the three pre-prepared parameters K, C, and P into the GIST model equation to calculate the soil thickness Soil_thickness2 under the physical model. The specific process is as follows: Soil_thickness2=K·C·P·S; Where K is the maximum soil thickness, C is an index based on the profile curvature, P is the actual relative position of a point on the hillside, and S is a soil loss index based on the slope threshold. S2.

3. The GIST-PINN model uses physical laws to guide model training. Its core lies in introducing physical knowledge into the loss function. During the model training process, the loss function is designed as a weighted sum of data-driven loss and physics-driven loss. The optimal weight combination is automatically adjusted according to the total loss value during the GIST-PINN network training optimization process: loss=λ1·loss1+λ2·loss2; Among them, loss1 and loss2 are data-driven loss and 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 to the range allowed by physical laws. S2.

4. Soil thickness under the constraints of the physical model GIST: Using the optimal weight parameter combination automatically adjusted according to the total loss value during the GIST-PINN network training process, the weighted average of Soil_thickness1 directly predicted by the neural network and Soil_thickness2 calculated by the GIST model is taken to obtain the final soil thickness Soil_thickness. The calculation formula is as follows: Soil_thickness=λ1·Soil_thickness1+λ2·Soil_thickness2.

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