Nonlinear simulation method of land subsidence and rebound coupled with physical mechanism and machine learning
By combining recurrent neural networks (RNNs) and convolutional neural networks (CNNs) and introducing nonlinear factors, a coupled model constrained by physical mechanisms is constructed. This solves the problems of nonlinear description and decreased accuracy in machine learning in traditional models, and achieves accurate simulation and efficient prediction of the ground subsidence-rebound process.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CAPITAL NORMAL UNIVERSITY
- Filing Date
- 2025-11-17
- Publication Date
- 2026-07-21
AI Technical Summary
In existing methods for simulating ground subsidence and rebound, traditional numerical models cannot accurately describe nonlinear changes, while machine learning models suffer from decreased accuracy and poor interpretability in complex multivariate and multiscale problems. Existing coupled models have failed to fully and accurately support geological disaster prevention and control.
A fusion model of recurrent neural network (RNN) and convolutional neural network (CNN) is adopted. By combining physical mechanisms and incorporating nonlinear factors into the coupled model through a mechanism-integrated learning approach, the RNN unit structure is modified to construct a nonlinear coupled model based on physical mechanism constraints.
It enhances the nonlinear characterization of the ground subsidence-rebound process, improves the physical interpretability and prediction accuracy of the model, and strengthens the scientific basis for geological disaster prevention and control.
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Figure CN121503265B_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of ground subsidence rebound simulation technology, specifically, it relates to a nonlinear simulation method for ground subsidence rebound that couples physical mechanisms with machine learning. Background Technology
[0002] Currently, accurate simulation and prediction of land subsidence and rebound can provide a scientific basis for groundwater resource management and geological disaster prevention. Land subsidence simulation methods mainly include physical mechanism-based numerical models and data-driven machine learning models. Numerical simulation methods establish governing equations based on the water-soil interaction mechanism and solve them according to boundary and initial conditions. Machine learning models, on the other hand, are data-driven, starting from time-series data itself to uncover the implicit nonlinear relationship between land subsidence and influencing factors, thereby establishing a data-driven model that effectively achieves accurate simulation of land subsidence.
[0003] In traditional numerical models, soil compression and rebound are assumed to be "linear elastic," meaning that stress and strain are directly proportional. However, in the actual process of ground settlement and rebound, rising water levels lead to increased pore water pressure and reduced effective soil stress. At the same time, the soil is affected by factors such as lithology and layered compression characteristics, resulting in nonlinear changes in soil rebound. This makes it impossible for traditional physical models to accurately describe the complex settlement and rebound behavior.
[0004] Machine learning models possess powerful nonlinear learning capabilities, partially addressing the issues of low accuracy and high uncertainty inherent in traditional numerical models. However, for complex problems involving multiple variables and scales, relying solely on data-driven methods for long-term time-series predictions leads to decreased accuracy and poor interpretability in machine learning models. Furthermore, the generalization ability of data-driven models depends on the coverage of the training data; extreme water level variations can significantly reduce simulation accuracy.
[0005] Considering the reliable extrapolation capabilities of physics-based numerical models and the strong fitting capabilities of machine learning models, scholars both domestically and internationally have attempted to couple physics models and machine learning models in the geosciences field. This has led to three paradigm frameworks: learning-embedded mechanisms, cascaded mechanism learning, and mechanism-integrated learning. Learning-embedded mechanisms maintains the basic architecture of the numerical model and possesses stronger physical interpretability. However, when using machine learning to replace a process in a traditional numerical model, it often faces the problem of difficulty in obtaining a large number of intermediate variables. Cascaded mechanism learning is suitable for most scenarios and is simple to apply; however, it does not modify the internal processes of the model, and the simulation results are not subject to substantial physical constraints. Mechanism-integrated learning embeds physical mechanisms by modifying the structure of neural network units, making the model's results subject to physical constraints. However, existing coupled models do not consider the nonlinear changes in the ground subsidence-rebound process, making it difficult for simulation predictions to comprehensively and accurately support geological disaster prevention and control. Summary of the Invention
[0006] To address the aforementioned problems and technical deficiencies, this application adopts the following technical solution: a nonlinear simulation method for ground subsidence and rebound that couples physical mechanisms with machine learning, comprising the following steps: Step 1: Fuse the long-term trend features of the recurrent neural network (RNN) with the local detail features of the convolutional neural network (CNN); Step 2: Using a mechanism-integrated learning approach, the physical mechanism is embedded into the recurrent neural network (RNN) model unit structure after the fusion of local detail features, resulting in a coupled model based on physical mechanism constraints. Step 3: Introduce a nonlinear factor n into the coupled model to reflect the nonlinear process of soil compression-rebound, and modify the unit structure of the recurrent neural network (RNN). Step 4: Based on physical parameters and construct a nonlinear coupling model, use the nonlinear coupling model to output the predicted value of ground subsidence-rebound.
[0007] Preferably, the local detail feature fusion includes: The time series dataset is input into the recurrent neural network (RNN) model, and the overall time series simulation is performed through the RNN model to obtain the dynamic change process of deformation and capture the time-dimensional dependencies. The simulation results of the recurrent neural network (RNN) are input into the convolutional neural network (CNN) model, which then captures the correlation patterns within a local time range. Simulation results from both Recurrent Neural Network (RNN) and Convolutional Neural Network (CNN) models are simultaneously input into a stitching layer for feature stitching. Combining the overall temporal changes and local deformation features, the simulated values for the monitoring results of Synthetic Aperture Interferometer Radar (SIA) are output.
[0008] Furthermore, the convolutional neural network (CNN) model captures association patterns including: Convolutional Neural Networks (CNNs) extract local features from input data through convolution operations. Enhance the expressive power of the model by using nonlinear activation functions; Extract local temporal dependency patterns from time series using one-dimensional convolution operations.
[0009] Preferably, the physical mechanism embedding couples the physical mechanism of ground subsidence with a recurrent neural network (RNN), so that the model is subject to physical constraints during operation, and the simulated deformation results based on physical mechanism constraints are obtained.
[0010] Furthermore, the physical mechanism constraints include using the ordinary differential equations of the physical process of ground subsidence and its parameters as functions of the recurrent neural network (RNN) model, as shown in the following formula:
[0011]
[0012] in, for The state variable at time t, This represents the input at the current time step. This indicates the output at the current time step. and These represent the parameter sets of the state function and the output function, respectively.
[0013] Furthermore, the physical mechanism constraint also includes incorporating the formulas for ground settlement and soil rebound into the hidden layers of the recurrent neural network (RNN) model, as follows:
[0014]
[0015] in, Represented as The state variable at time t, For input items, This represents the weights of the hidden layers in an RNN. Young's modulus during the settling and rebound stages and , For the bias term of the RNN model, and For activation function, for The state variable at time t, For the weights of the output layer, For the bias term of the output layer, for The predicted value of the deformation at time t.
[0016] Preferably, the modification of the recurrent neural network (RNN) unit structure includes modifying the hidden layer, and the formula is modified as follows:
[0017] Furthermore, the modification of the recurrent neural network (RNN) unit structure also includes modifying the stress-strain relationship formula into a nonlinear form:
[0018] When the nonlinear factor n=1, it means that the stress is proportional to the strain, which corresponds to the assumption of linear Hooke's law; When n≠1, it indicates that stress and strain exhibit nonlinearity.
[0019] Furthermore, the formulas for ground settlement and soil rebound are modified to the following two formulas:
[0020]
[0021] The two formulas represent the ground subsidence and rebound processes, respectively.
[0022] Preferably, the nonlinear coupling model includes an input layer, an RNN layer that integrates physical mechanisms, a CNN layer, a splicing layer, and an output layer; Input layer: Contains water level data of three confined aquifers and thickness of the compressible layer, serving as the basic input for the nonlinear coupling model; RNN layers incorporating physical mechanisms: Physical equations are embedded in the RNN model unit structure, so the model is subject to physical constraints during operation; CNN layer: Consists of three one-dimensional convolutional layers, focusing on the extraction of local features, used to capture short-term fluctuations and detailed features; Concatenation layer: fuses the global dynamic features output by RNN with the local detail features extracted by CNN in the feature dimension; Output layer: Performs a linear transformation on the stitched and fused features to map them into predicted values of ground subsidence and rebound.
[0023] Compared to existing technologies, the beneficial effects of this application are as follows: (1) In view of the problem that numerical models cannot well describe the nonlinear changes of ground settlement and rebound, this application introduces a nonlinear change factor, which effectively improves the ability to characterize the nonlinearity of the settlement and rebound process. (2) This application addresses the problem of insufficient physical interpretability and poor prediction timeliness caused by the lack of physical mechanism in the output of data-driven models. By coupling the physical mechanism with the machine learning model, the machine learning training process is constrained by the physical mechanism. (3) This application considers the nonlinear evolution characteristics of ground subsidence-rebound. Based on the effective stress principle, it introduces nonlinear factors through mechanism integration learning and constructs a nonlinear model that couples physical mechanism and machine learning to accurately characterize the subsidence-rebound evolution process. Attached Figure Description
[0024] In the attached diagram: Figure 1 This is a schematic diagram of the method steps in an embodiment of this application; Figure 2 This is an example of an RNN-CNN model used in this application. Figure 3 This is a diagram of the RNN network structure in an embodiment of this application; Figure 4 This is a diagram of the CNN network structure according to an embodiment of this application; Figure 5 This is a structural diagram of the RNN model for the coupled physical mechanism in an embodiment of this application; Figure 6 This is a schematic diagram of the coupling physical mechanism and machine learning structure in an embodiment of this application; Figure 7 This is a structural diagram of the nonlinear mechanism-learning model in an embodiment of this application; Figure 8 This is a table of optimal hyperparameters and input variables for the model in this application embodiment; Figure 9 This is a table comparing the accuracy of embodiments of this application. Detailed Implementation
[0025] 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 some embodiments of this application, but not all embodiments. Generally, the components of the embodiments of this application described and shown in the accompanying drawings can be arranged and designed in various different configurations.
[0026] Example 1 like Figure 1 As shown, the nonlinear simulation method for ground subsidence rebound that couples physical mechanisms with machine learning includes the following steps: By fusing the long-term trend features of the recurrent neural network (RNN) with the local detail features of the convolutional neural network (CNN), the simulated values of the monitoring results of synthetic aperture interferometry radar are output. Local detail feature fusion includes: The time series dataset is input into the recurrent neural network (RNN) model, and the overall time series simulation is performed through the RNN model to obtain the dynamic change process of deformation and capture the time-dimensional dependencies. The simulation results of the recurrent neural network (RNN) are input into the convolutional neural network (CNN) model, which then captures the correlation patterns within a local time range. Simulation results from both Recurrent Neural Network (RNN) and Convolutional Neural Network (CNN) models are simultaneously input into a stitching layer for feature stitching. Combining the overall temporal changes and local deformation features, the simulated values for the monitoring results of Synthetic Aperture Interferometer Radar (SIA) are output.
[0027] Convolutional Neural Network (CNN) models capture association patterns including: Convolutional Neural Networks (CNNs) extract local features from input data through convolution operations. Enhance the expressive power of the model by using nonlinear activation functions; Extract local temporal dependency patterns from time series using one-dimensional convolution operations.
[0028] By adopting a mechanism-integrated learning approach, physical mechanisms are embedded into the unit structure of recurrent neural network (RNN) models to obtain a coupled model based on physical mechanism constraints. The physical mechanism embedding couples the physical mechanism of ground subsidence with the recurrent neural network (RNN), subjecting the model to physical constraints during operation and obtaining simulated deformation results based on physical mechanism constraints.
[0029] The physical mechanism constraints include using the ordinary differential equations of the physical processes and parameters of land subsidence as functions of the recurrent neural network (RNN) model, as shown in the following formula:
[0030]
[0031] in, for The state variable at time t, This represents the input at the current time step. This indicates the output at the current time step. and These represent the parameter sets of the state function and the output function, respectively.
[0032] The physical mechanism constraints also include incorporating the formulas for ground settlement and soil rebound into the hidden layers of the recurrent neural network (RNN) model, as follows:
[0033]
[0034] in, Represented as The state variable at time t, For input items, This represents the weights of the hidden layers in an RNN. Young's modulus during the settling and rebound stages and , For the bias term of the RNN model, and For activation function, for The state variable at time t, For the weights of the output layer, For the bias term of the output layer, for The predicted value of the deformation at time t.
[0035] A nonlinear factor n is introduced into the coupled model to reflect the nonlinear process of soil compression-rebound, and the unit structure of the recurrent neural network (RNN) is modified accordingly. The modification to the unit structure of a recurrent neural network (RNN) includes changes to the hidden layers; the formula is modified as follows:
[0036] The modification to the recurrent neural network (RNN) unit structure also includes changing the stress-strain relationship formula to a nonlinear form:
[0037] When the nonlinear factor n=1, it means that the stress is proportional to the strain, which corresponds to the assumption of linear Hooke's law; When n≠1, it indicates that stress and strain exhibit nonlinearity.
[0038] The formulas for ground settlement and soil rebound are revised to the following two formulas:
[0039]
[0040] The two formulas represent the ground subsidence and rebound processes, respectively.
[0041] Based on physical parameters and a nonlinear coupled model, the predicted values of ground subsidence and rebound are output using the nonlinear coupled model.
[0042] The nonlinear coupling model includes an input layer, an RNN layer that integrates physical mechanisms, a CNN layer, a concatenation layer, and an output layer; Input layer: Contains water level data of three confined aquifers and thickness of the compressible layer, serving as the basic input for the nonlinear coupling model; RNN layers incorporating physical mechanisms: Physical equations are embedded in the RNN model unit structure, so the model is subject to physical constraints during operation; CNN layer: Consists of three one-dimensional convolutional layers, focusing on the extraction of local features, used to capture short-term fluctuations and detailed features; Concatenation layer: fuses the global dynamic features output by RNN with the local detail features extracted by CNN in the feature dimension; Output layer: Performs a linear transformation on the stitched and fused features to map them into predicted values of ground subsidence and rebound.
[0043] Example 2 By combining the Recurrent Neural Network (RNN) model and the Convolutional Neural Network (CNN) model, and adopting an architecture of "RNN temporal modeling → CNN local feature extraction → feature concatenation → output deformation result", the "long-term trend features" of the RNN and the "local detail features" of the CNN are integrated to resolve the contradiction of "the inability to take into account both the whole and the part".
[0044] The process of deformation simulation using the RNN-CNN model is shown in the appendix. Figure 2 .
[0045] First, the time series dataset is input into the RNN model, and the RNN model is used to perform overall time series simulation to obtain the dynamic change process of deformation and capture the dependencies in the time dimension.
[0046] like Figure 3 As shown, recurrent neural networks (RNNs) in the time domain pass information from the previous time step to the current time step and then to the next time step through a self-looping structure, making them suitable for time series data models.
[0047] Secondly, the RNN simulation results are input into the CNN model, which captures the correlation patterns (such as short-term deformation fluctuation patterns) within a local time range, thus compensating for the shortcomings of RNN in extracting local detailed features.
[0048] Using a convolutional neural network (CNN) to extract local features from the input data during convolution operations; like Figure 4 As shown, Convolutional Neural Networks (CNNs) extract local features from input data through convolution operations, enhance the model's expressive power using nonlinear activation functions, and extract local time-dependent patterns of time series, such as trends and periodic fluctuations, through one-dimensional convolution operations.
[0049] Then, the simulation results of the recurrent neural network (RNN) and the cumulative neural network (CNN) are simultaneously input into the stitching layer for feature concatenation, effectively combining the overall temporal changes and local deformation features. The final output is the simulated value of the monitoring results for interferometric interferometric radar (InSAR).
[0050] The physical process of ground settlement can be explained by the effective stress principle. For a soil particle in a soil layer, the total stress at that point is borne by both the soil skeleton and the water. The stress borne by the water is the pore water pressure. When the total stress remains constant, a decrease in pore water pressure will result in an equal increase in the effective stress borne by the soil skeleton. , .
[0051] The one-dimensional consolidation model based on Terzaghi's principle assumes that the soil undergoes linear elastic deformation, and the stress-strain relationship of the soil satisfies Hooke's law. Assuming that both principal stresses and deformations are vertical, the stress-strain relationship formula is as follows:
[0052] in, The stress is the vertical stress (Pa). This represents Young's modulus (Pa) during the settling process.
[0053] The formula for the change in ground settlement is as follows:
[0054] The formula for the change in effective stress caused by changes in a confined aquifer is as follows:
[0055] in, The effective vertical stress change (kPa); The thickness of the compressible layer is (m).
[0056] When soil settles and rebounds, the Young's modulus changes.
[0057] Assuming when Ground subsidence occurs, and the formula for expressing the amount of ground subsidence is:
[0058] when When rebound occurs, the formula for expressing the amount of soil rebound is:
[0059] We employ a mechanism-integrated learning approach to embed the physical mechanisms of ground subsidence into the RNN model unit structure.
[0060] The simplest form of the RNN model is as follows:
[0061] in, This represents the input at the current time step. Indicates the previous time step The output, This indicates the time step of the current sequence.
[0062] The recursive relationship between the model input and output is shown below:
[0063]
[0064] By using the ordinary differential equations of the physical processes and parameters of land subsidence as functions of the RNN model, the formula can be rewritten as:
[0065]
[0066] In the formula and The parameter sets for the state function and output function are shown in the appendix. Figure 5 As shown.
[0067] Then, the above formulas for ground settlement and soil rebound are introduced into the hidden layer of the RNN model, resulting in the following formula:
[0068]
[0069] in, Represented as The state variable at time t, For input items, This represents the weights of the hidden layers in an RNN. Young's modulus during the settling and rebound stages and , For the bias term of the RNN model, and For activation function, for The state variable at time t, For the weights of the output layer, For the bias term of the output layer, for The predicted value of the deformation at time t.
[0070] By coupling physical mechanisms with RNNs, the model is subjected to physical constraints during operation, resulting in simulated deformation results based on physical mechanism constraints, as shown in the appendix. Figure 6 As shown.
[0071] In traditional numerical models, soil compression and rebound are assumed to be "linear elastic," meaning that stress and strain are directly proportional. However, in the actual process of ground settlement and rebound, rising water levels lead to increased pore water pressure and reduced effective soil stress. At the same time, the soil is affected by factors such as lithology and layered compression characteristics, resulting in nonlinear changes in soil rebound. This makes it impossible for traditional physical models to accurately represent the complex settlement and rebound behavior.
[0072] To make the coupled model more realistically reflect the nonlinear physical process of ground settlement-rebound, a "nonlinear factor n" is introduced to reflect the nonlinear process of soil compression-rebound, and the stress-strain relationship formula is modified into a nonlinear form:
[0073] When the nonlinear factor n=1, it means that the stress and strain are directly proportional, corresponding to the assumption of linear Hooke's law; when n≠1, it means that the stress and strain are nonlinear.
[0074] For the settlement process, the nonlinear factor nc represents the nonlinear process in which the rate of increase of vertical strain gradually slows down as the effective vertical stress increases. For the rebound stage, due to the influence of residual inelastic deformation during soil porosity recovery and particle rearrangement, the formulas for ground settlement and soil rebound are modified to the following two formulas:
[0075]
[0076] The formulas represent the ground subsidence and rebound processes, respectively.
[0077] By introducing a nonlinear factor into the coupled model, the unit structure of the RNN is modified, and the hidden layer formula of the RNN model is modified as follows:
[0078] The nonlinear coupling model includes an input layer, an RNN layer that integrates physical mechanisms, a CNN layer, a concatenation layer, and an output layer, such as... Figure 7 As shown.
[0079] (1) Input layer: contains water level data of three confined aquifers and thickness of compressible layer, which serve as the basic input of nonlinear coupling model.
[0080] (2) RNN layer with physical mechanism: The physical equations are embedded in the RNN model unit structure, so the model is subject to physical constraints during operation.
[0081] (3) CNN layer: It consists of three one-dimensional convolutional layers, focusing on the extraction of local features and used to capture short-term fluctuations and detailed features.
[0082] (4) Concatenation layer: The global dynamic features output by RNN are fused with the local detail features extracted by CNN in the feature dimension.
[0083] (5) Output layer: Perform a linear transformation on the spliced fused features to map them into predicted values of ground subsidence-rebound.
[0084] Example 3 Ground subsidence-rebound simulation was performed using a nonlinear coupling model. Taking the Beijing plain as an example, the water levels of three confined aquifers and the thickness of the compressible layer were used as input data for the nonlinear coupling model. The input data first entered the RNN layer that integrates physical mechanisms for training. Part of the output results entered the CNN layer to further extract local change feature information, and the other part entered the stitching layer. After the information was extracted by the CNN layer, it was also input into the stitching layer to stitch the two features together. Finally, the output layer output the final predicted value.
[0085] The specific process is as follows: Part 1, Data Preparation: (1) Groundwater level data: Monthly groundwater level data of the first, second and third confined aquifers from 2010 to 2023.
[0086] (2) Compressible layer thickness: Contour data of compressible layer thickness.
[0087] (3) Simulated data: All InSAR-monitored deformation points in the Beijing Plain area from 2010 to 2023 were randomly divided into training and test sets. The sample set in the simulation area was randomly divided into 70% and 30% using the thinning tool in ArcGIS software. The training set contained 7,330 InSAR deformation points, and the test set contained 3,141 InSAR deformation points.
[0088] (4) Trainable parameters: The trainable parameters defined in this experiment are Young's modulus Ec and nonlinear factor nc during the settlement process, Young's modulus Er and nonlinear factor nr during the rebound process. There are 3 confined aquifers in the Beijing Plain area, with a total of 12 trainable parameters (Ec1, Ec2, Ec3, Er1, Er2, Er3, nc1, nc2, nc3, nr1, nr2, nr3). The Young's modulus ranges from 107 to 108 Pa.
[0089] Part Two, Model Building: The input consists of three confined aquifer water levels and the thickness of the compressible layer. Each input consists of batch_size samples. After one epoch (i.e., all samples have completed one training iteration), gradient descent is used to calculate the loss between the predicted deformation value and the deformation value monitored by InSAR at each time step. The model is iteratively trained (completing epochs of training) to obtain the minimum loss. Hyperparameters and input variables are listed below. Figure 8 .
[0090] Part Three, Accuracy Comparison: We selected the groundwater flow-soil deformation coupled model (MODFLOW-SUB) and the long short-term memory (LSTM) neural network model. While keeping the same input variables as the nonlinear coupled model, we compared the performance of the nonlinear coupled model with the numerical model and the LSTM model.
[0091] The simulation performance of the nonlinear coupled model, the numerical model (MODFLOW-SUB), and the LSTM model during the training period was compared. The results show that the nonlinear coupled model performs better in detail capture, exhibiting significant advantages in accuracy and fit in both the settlement and rebound zones. Figure 9 ).
[0092] Specifically, the root mean square error (RMSE) of the nonlinear coupling model was reduced by up to 88.1% compared to the MODFLOW-SUB model and by up to 61% compared to the LSTM model; the R² was increased by up to 0.56 and 0.16 compared to the MODFLOW-SUB and LSTM models, respectively.
[0093] Figure 9 The text in bold indicates monitoring wells located in the rebound zone, while the rest are monitoring wells located in the settlement zone.
[0094] The embodiments described above are merely preferred embodiments of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications, improvements, and substitutions without departing from the concept of this application, and these all fall within the protection scope of this application.
Claims
1. A nonlinear simulation method for ground subsidence and rebound that couples physical mechanisms with machine learning, characterized in that, Includes the following steps: Step 1: Fuse the long-term trend features of the recurrent neural network (RNN) with the local detail features of the convolutional neural network (CNN); Step 2: Employing a mechanism-integrated learning approach, the physical mechanism is embedded into the recurrent neural network (RNN) model unit structure after fusing local detail features, resulting in a coupled model based on physical mechanism constraints. These constraints also include introducing the formulas for ground settlement and soil rebound into the hidden layers of the RNN model, as follows: in, For vertical stress, This represents the change in effective vertical stress. For compressible layer thickness, Represented as The state variable at time t, For input items, This represents the weights of the hidden layers in an RNN. Young's modulus during the settling and rebound stages and , For the bias term of the RNN model, and For activation function, for The state variable at time t, For the weights of the output layer, For the bias term of the output layer, for The predicted value of the deformation at time t; The modification to the unit structure of a recurrent neural network (RNN) includes changes to the hidden layers; the formula is modified as follows: The modification to the recurrent neural network (RNN) unit structure also includes changing the stress-strain relationship formula to a nonlinear form: When the nonlinear factor n=1, it means that the stress is proportional to the strain, which corresponds to the assumption of linear Hooke's law; When n≠1, it indicates that the stress and strain exhibit nonlinearity; Step 3: Introduce a nonlinear factor n into the coupled model to reflect the nonlinear process of soil compression-rebound. Modify the unit structure of the recurrent neural network (RNN), and modify the formulas for ground settlement and soil rebound to the following two formulas: in, This is a nonlinear factor in the settling process. This refers to the nonlinear factor in the rebound process; The two formulas represent the ground settlement and rebound processes, respectively; Step 4: Based on physical parameters and construct a nonlinear coupling model, use the nonlinear coupling model to output the predicted value of ground subsidence-rebound.
2. The nonlinear simulation method for ground subsidence and rebound based on coupled physical mechanisms and machine learning as described in claim 1, characterized in that, The local detail feature fusion includes: The time series dataset is input into the recurrent neural network (RNN) model, and the overall time series simulation is performed through the RNN model to obtain the dynamic change process of deformation and capture the time-dimensional dependencies. The simulation results of the recurrent neural network (RNN) are input into the convolutional neural network (CNN) model, which then captures the correlation patterns within a local time range. Simulation results from both Recurrent Neural Network (RNN) and Convolutional Neural Network (CNN) models are simultaneously input into a stitching layer for feature stitching. Combining the overall temporal changes and local deformation features, the simulated values for the monitoring results of Synthetic Aperture Interferometer Radar (SIA) are output.
3. The nonlinear simulation method for ground subsidence and rebound based on coupled physical mechanisms and machine learning as described in claim 2, characterized in that, The convolutional neural network (CNN) model captures association patterns including: Convolutional Neural Networks (CNNs) extract local features from input data through convolution operations. Enhance the expressive power of the model by using nonlinear activation functions; Extract local temporal dependency patterns from time series using one-dimensional convolution operations.
4. The nonlinear simulation method for ground subsidence and rebound based on coupled physical mechanisms and machine learning as described in claim 1, characterized in that, The physical mechanism embedding couples the physical mechanism of ground subsidence with the recurrent neural network (RNN), subjecting the model to physical constraints during operation and yielding simulated deformation results based on physical mechanism constraints.
5. The nonlinear simulation method for ground subsidence and rebound based on coupled physical mechanisms and machine learning as described in claim 4, characterized in that, The physical mechanism constraints include using the ordinary differential equations of the physical process and parameters of ground subsidence as functions of a recurrent neural network (RNN) model, as shown in the following formula: in, for The state variable at time t, This represents the input at the current time step. This indicates the output at the current time step. and These represent the parameter sets of the state function and the output function, respectively.
6. The nonlinear simulation method for ground subsidence and rebound based on coupled physical mechanisms and machine learning as described in claim 1, characterized in that, The nonlinear coupling model includes an input layer, an RNN layer that integrates physical mechanisms, a CNN layer, a splicing layer, and an output layer. Input layer: Contains water level data of three confined aquifers and thickness of the compressible layer, serving as the basic input for the nonlinear coupling model; RNN layers incorporating physical mechanisms: Physical equations are embedded in the RNN model unit structure, so the model is subject to physical constraints during operation; CNN layer: Consists of three one-dimensional convolutional layers, focusing on the extraction of local features, used to capture short-term fluctuations and detailed features; Concatenation layer: fuses the global dynamic features output by RNN with the local detail features extracted by CNN in the feature dimension; Output layer: Performs a linear transformation on the stitched and fused features to map them into predicted values of ground subsidence and rebound.