Soil-hydraulic coupling simulation method and system based on physical information neural network

Abstract

The present invention discloses a soil hydraulic coupling simulation method and system based on a physical information neural network. In the present invention, two improved fully connected neural networks are first constructed to respectively predict the pore water pressure and deformation response in the soil; then, according to the soil hydraulic coupling partial differential equation group, the dimensionless control equation loss terms of the liquid phase and the solid phase are respectively established based on the fixed stress splitting method, and the total loss function of the liquid phase and the solid phase is established in combination with the initial boundary conditions; finally, the loss functions of the liquid phase and the solid phase are alternately trained based on the sequential training strategy and the gradient normalized adaptive loss balance strategy. The present invention adopts a sequential training strategy, an improved fully connected neural network and an adaptive loss balance scheme to improve the traditional physical information neural network, thereby improving the prediction accuracy and training stability. The physical information neural network trained by the present invention can be used as a proxy model to predict pore water pressure and deformation, and has great application potential.

Description

Technical Field

[0001] The present invention relates to the technical field of physical neural networks, and in particular to a soil hydraulic coupling simulation method and system based on physical information neural networks. Background Art

[0002] The hydraulic coupling of soil is a critical physical process in geotechnical engineering, impacting the safety of natural and artificial structures such as slopes, foundation pits, and dams. Numerical methods for simulating the hydraulic-mechanical coupling of soil have been extensively studied. These traditional numerical methods are based on physical laws described by partial differential equations. However, they often struggle to capture the true soil response due to inconsistencies between input parameters and actual site conditions. Recent advances in machine learning have introduced data-driven surrogate models that can establish direct nonlinear mappings, providing realistic predictions without any prior knowledge. However, without sufficient big data, the predictive performance and generalization of purely data-driven models cannot be guaranteed. Furthermore, data-driven models, acting as black boxes, often fail to reveal the underlying physical mechanisms, resulting in weak physical interpretability. Given the sparse nature of field monitoring data, developing hybrid approaches that combine physical information and data-driven approaches is an optimal approach.

[0003] Physically informed neural networks offer a promising paradigm for developing hybrid approaches driven by physical information and data. This approach utilizes neural networks to approximate unknown solutions that satisfy both physical laws and monitoring information. Physically informed neural networks can be used as pure partial differential equation solvers for forward modeling, as well as tools for inverse analysis to estimate unknown parameters. However, training physically informed neural networks is difficult, especially for multi-physics and multi-scale physics problems. The hydraulic coupling of soil is a typical multi-physics problem, and existing physical neural network methods for predicting the hydraulic coupling behavior of soil often suffer from low prediction accuracy and unstable training. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that the existing physical neural network method is difficult to accurately simulate the soil hydraulic coupling behavior process, and to provide a soil hydraulic coupling simulation method and system based on physical information neural network.

[0005] The technical solutions specifically adopted in the present invention are as follows:

[0006] In a first aspect, the present invention provides a soil-hydraulic coupling simulation method based on a physical information neural network, which comprises:

[0007] S1: For the target site where soil-hydraulic coupling simulation is required, obtain the simulation space domain, time domain, initial and boundary conditions, and soil parameters;

[0008] S2. Constructing a liquid-phase physical information neural network for predicting pore water pressure in soil, and setting the weighted sum of the liquid-phase dimensionless control equation loss term, the liquid-phase boundary condition loss term, and the liquid-phase initial condition loss term as the corresponding total loss function; constructing a solid-phase physical information neural network for predicting deformation in soil, and setting the weighted sum of the solid-phase dimensionless control equation loss term, the solid-phase boundary condition loss term, and the solid-phase initial condition loss term as the corresponding total loss function; wherein the liquid-phase dimensionless control equation loss term and the solid-phase dimensionless control equation loss term are constructed in a dimensionless manner after converting the soil hydraulic coupled partial differential equation group by the fixed stress splitting method;

[0009] S3. Based on the sequential training strategy, the liquid phase physical information neural network and the solid phase physical information neural network are trained alternately in an iterative manner until the iteration termination condition is reached, and the two trained networks are used to predict the pore water pressure and deformation of the soil; in each round of iteration, the liquid phase physical information neural network and the solid phase physical information neural network are frozen alternately, and the sampled configuration points in the spatial domain and the time domain are input into the two physical information neural networks to obtain the predicted values of pore water pressure and deformation. Finally, the total loss function value corresponding to the unfrozen physical information neural network is calculated, and the network parameters of the unfrozen physical information neural network are updated by backpropagation according to the total loss function value.

[0010] As a preferred embodiment of the above-mentioned first aspect, the liquid-phase physical information neural network and the solid-phase physical information neural network both adopt the same fully connected network with an attention mechanism, and the network inputs are configuration points composed of spatial points collected from the spatial domain and time points collected from the time domain. The configuration points are mapped to the first attention feature and the second attention feature respectively through two additional fully connected layers, and then the configuration points, the first attention feature and the second attention feature are input into multiple layers of sequentially cascaded network layers, wherein the first network layer directly uses the configuration points as input to obtain the output feature through the fully connected layer, and in the remaining network layers, the output feature of the previous network layer is first passed through the fully connected layer to obtain the intermediate feature H, and then the first attention feature and the second attention feature are used to weight 1-H and H respectively and then add them to obtain the output feature of the current network layer.

[0011] As a preferred embodiment of the first aspect, in the total loss function of the liquid phase physical information neural network,

[0012] The loss term of the dimensionless liquid phase control equation is: the deviation of the dimensionless liquid phase continuity balance equation after conversion by the fixed stress splitting method from zero; the fixed stress splitting method conversion method is to replace the time derivative of the volume strain in the liquid phase continuity balance equation of the soil hydraulic coupled partial differential equation system with the time derivative of the mean volume stress;

[0013] The liquid phase initial condition loss term is the deviation between the predicted value and the true value of the pore water pressure at the initial time point;

[0014] The liquid boundary condition loss term is the sum of the deviation between the predicted and true pore water pressure on the Dirichlet boundary and the deviation between the predicted and true velocity on the Neumann boundary condition.

[0015] As a preferred embodiment of the first aspect, in the total loss function of the solid-phase physical information neural network,

[0016] The loss term of the dimensionless solid phase governing equation is: the deviation of the dimensionless stress-deformation equilibrium equation in the soil hydraulic coupled partial differential equations from zero;

[0017] The solid phase initial condition loss term is the deviation between the predicted value and the true value of soil deformation at the initial time point;

[0018] The solid boundary condition loss term is the sum of the deviation between the predicted and true soil deformation on the Dirichlet boundary and the deviation between the predicted and true stress on the Robin mixed boundary condition.

[0019] As a preferred embodiment of the above-mentioned first aspect, when alternately freezing the liquid-phase physical information neural network and the solid-phase physical information neural network and optimizing another unfrozen physical information neural network, it is necessary to first sample a first configuration point sample consisting of space points and time points from the complete spatial domain and time domain, sample time points from the complete time domain and form a second configuration point sample with the space points at the boundary of the simulation space, and sample space points from the complete spatial domain and form a third configuration point sample with the initial time points corresponding to the initial moment of the simulation. The three types of samples obtained by sampling are respectively input into the liquid-phase physical information neural network and the solid-phase physical information neural network to obtain the predicted value of the soil pore water pressure and the predicted value of the soil deformation; then, according to the total loss function corresponding to the unfrozen physical information neural network, the dimensionless control equation loss term in the total loss function is calculated by the predicted value of the first configuration point sample, the boundary condition loss term in the total loss function is calculated by the predicted value of the second configuration point sample, and the initial condition loss term in the total loss function is calculated by the predicted value of the third configuration point sample. Finally, the total loss function value is weighted and the network parameters of the unfrozen physical information neural network are updated by the gradient descent optimization algorithm.

[0020] As a preferred embodiment of the first aspect above, a gradient normalization adaptive loss balancing strategy is introduced in each round of iteration to adaptively adjust the weighted weights of the three loss terms in the total loss function.

[0021] In a second aspect, the present invention provides a soil-hydraulic coupling simulation system based on a physical information neural network, comprising:

[0022] The initial parameter setting module is used to obtain the simulation space domain, time domain, initial boundary conditions and soil parameters for the target site where soil-hydraulic coupling simulation is required;

[0023] A model and loss construction module is used to construct a liquid-phase physical information neural network for predicting pore water pressure in soil, and set the weighted sum of the liquid-phase dimensionless control equation loss term, the liquid-phase boundary condition loss term, and the liquid-phase initial condition loss term as the corresponding total loss function; a solid-phase physical information neural network is constructed for predicting deformation in soil, and set the weighted sum of the solid-phase dimensionless control equation loss term, the solid-phase boundary condition loss term, and the solid-phase initial condition loss term as the corresponding total loss function; wherein the liquid-phase dimensionless control equation loss term and the solid-phase dimensionless control equation loss term are constructed by transforming the soil hydraulic coupling partial differential equation group based on the fixed stress splitting method;

[0024] The model training and prediction module is used to alternately train the liquid-phase physical information neural network and the solid-phase physical information neural network in an iterative manner based on a sequential training strategy until the iteration termination condition is reached, and use the two trained networks to predict the pore water pressure and deformation of the soil; in each round of iteration, the liquid-phase physical information neural network and the solid-phase physical information neural network are alternately frozen, and the two physical information neural networks are input with sampling configuration points from the spatial domain and the time domain to obtain the predicted values of the pore water pressure and deformation; finally, the total loss function value corresponding to the unfrozen physical information neural network is calculated, and the network parameters of the unfrozen physical information neural network are updated by backpropagation according to the total loss function value.

[0025] In a third aspect, the present invention provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, can implement the soil-hydraulic coupling simulation method based on a physical information neural network as described in any one of the schemes of the first aspect above.

[0026] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the soil-hydraulic coupling simulation method based on a physical information neural network as described in any one of the schemes of the first aspect above can be implemented.

[0027] In a fifth aspect, the present invention provides a computer electronic device comprising a memory and a processor;

[0028] The memory is used to store computer programs;

[0029] The processor is used to implement the soil-hydraulic coupling simulation method based on physical information neural network as described in any one of the solutions of the first aspect above when executing the computer program.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1) The present invention provides a soil-hydraulic coupling simulation method based on a physical information neural network. It uses a sequential training strategy and a fully connected neural network with an attention mechanism to improve the traditional physical information neural network, thereby enhancing prediction accuracy and training stability. The trained physical information neural network can be used as a proxy model for pore water pressure and deformation prediction. Compared with the traditional finite element method, the present invention has the advantages of being mesh-free and data-driven, and is more physically interpretable than a purely data-driven black box model. Based on this method, inverse analysis and proxy models can be further established to estimate unknown soil parameters and constitutive models. It can also be used as a hybrid model that embeds physical information and data-driven to predict soil responses in unexplored spatiotemporal domains, showing great application potential.

[0032] 2) The sequential training strategy introduced in this paper avoids simultaneous training of solid-phase and liquid-phase networks, and approaches the true solution through iterative training. This training method reduces the difficulty of network optimization, makes it easier to find the optimal solution, and thus achieves higher accuracy. Traditional collaborative training methods, on the other hand, optimize both solid-phase and liquid-phase networks simultaneously, which inevitably increases the training difficulty and reduces the accuracy of the solution found.

[0033] 3) Drawing inspiration from the neural attention mechanism commonly used in computer vision, this paper introduces two additional mapping networks into a traditional fully connected neural network. These two additional networks map input variables into a high-dimensional feature space as attention weight features. These networks also improve the forward propagation process within the hidden layers of the traditional fully connected neural network, reducing the maximum eigenvalue of the Hessian matrix during training and thereby improving training stability.

[0034] 4) The present invention can also introduce an adaptive loss balancing strategy during the training process, so that the model can consider various loss terms more evenly during the training process, achieve back propagation gradient balance of various loss terms, and thus improve training accuracy and generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of the steps of the soil-hydraulic coupling simulation method based on physical information neural network;

[0036] Figure 2 Schematic diagram of sequential training strategy

[0037] Figure 3 This is a schematic diagram of the module composition of the soil-hydraulic coupling simulation system based on physical information neural network;

[0038] Figure 4 It is a schematic diagram of the structure of computer electronic equipment;

[0039] Figure 5 Schematic diagram of the model of one-dimensional saturated soil under overburden load. DETAILED DESCRIPTION

[0040] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. The technical features in the various embodiments of the present invention can be combined accordingly without conflicting with each other.

[0041] like Figure 1 As shown, in a preferred embodiment of the present invention, a soil hydraulic coupling simulation method based on physical information neural network is provided, and the specific steps are as follows:

[0042] S1: For the target site where soil-hydraulic coupling simulation is required, obtain the simulation space domain, time domain, initial and boundary conditions, and soil parameters.

[0043] It should be noted that the target site in the present invention refers to an object that requires soil hydraulic coupling simulation, such as natural or artificial structures such as slopes, foundation pits, dams, etc., and the specific object is not limited. In addition, the spatial domain, time domain and initial and boundary conditions of the simulation can be determined according to the simulation plan, and the soil parameters are determined according to the actual situation of the site. The spatial domain refers to the three-dimensional spatial range of the simulation object, and the time domain refers to the time range of the simulation, that is, the time interval from the initial moment to the end moment. The spatial domain and the time domain can be discretized into a series of spatial points and time points, and a configuration point is composed of a spatial point and a time point. The initial and boundary conditions refer to the initial conditions and boundary conditions. The specific initial conditions and boundary conditions need to be determined according to the actual simulation conditions.

[0044] S2. Construct a liquid-phase physical information neural network for predicting pore water pressure in soil, and set the weighted sum of the liquid-phase dimensionless control equation loss term, the liquid-phase boundary condition loss term, and the liquid-phase initial condition loss term as the corresponding total loss function; construct a solid-phase physical information neural network for predicting deformation in soil, and set the weighted sum of the solid-phase dimensionless control equation loss term, the solid-phase boundary condition loss term, and the solid-phase initial condition loss term as the corresponding total loss function; wherein, the liquid-phase dimensionless control equation loss term and the solid-phase dimensionless control equation loss term are constructed in a dimensionless manner after converting the soil hydraulic coupling partial differential equation group by the fixed stress splitting method.

[0045] In an embodiment of the present invention, both the liquid-phase physical information neural network and the solid-phase physical information neural network adopt the same improved fully-connected network with an attention mechanism. The improved fully-connected neural network draws inspiration from the neural attention mechanism commonly used in computer vision, and introduces two additional fully-connected layers as mapping networks in the traditional fully-connected neural network. These two additional mapping networks map the input variables to a high-dimensional feature space and improve the forward propagation process within the hidden layer of the traditional fully-connected neural network.

[0046] The specific network structure of the improved fully connected network is described below. In the improved fully connected network, the network input is the spatial points collected in the spatial domain. x and the time points collected in the time domain t Configuration points , the configuration points are mapped into the first attention feature and the second attention feature respectively through two additional fully connected layers, and then the configuration points, the first attention feature and the second attention feature are input into the multi-layer cascade network layer, where the first network layer directly takes the configuration points as input and obtains the output feature through the fully connected layer. In the remaining network layers, the output feature of the previous network layer is first passed through the fully connected layer to obtain the intermediate feature H, and then the first attention feature and the second attention feature are used to weight 1-H and H respectively and then add them to obtain the output feature of the current network layer. In order to distinguish, the variable l To express the number of the network layer, l The intermediate feature H corresponding to the network layer is expressed as , the specific forward propagation process can be expressed as follows:

[0047]

[0048] Where, x and t are the input spatial point coordinates and time point coordinates, Express x and t Perform splicing operations; Represents the output features of the lth network layer; W and b are weights and biases, and their respective superscripts are used to distinguish different network layers; is an activation function, and in the embodiment of the present invention, the tanh activation function is preferably used; ⊙ represents element-by-element multiplication. Compared with the traditional fully connected neural network, the improved fully connected neural network can reduce the maximum eigenvalue of the Hessian array during training, thereby improving the stability of training.

[0049] In addition, it should be noted that both the liquid-phase physical information neural network and the solid-phase physical information neural network require a total loss function for network training. When training each physical information neural network, the corresponding total loss function must be called to calculate the total loss value. The loss function forms of the two physical information neural networks are similar, and both are weighted by three loss terms: the dimensionless control equation loss term, the boundary condition loss term, and the initial condition loss term. However, since one physical information neural network predicts the solid phase (deformation) and the other predicts the liquid phase (pore water), the control equations, boundary conditions, and initial conditions of the two are different.

[0050] In an embodiment of the present invention, the total loss function for liquid phase physical information neural network training is expressed as:

[0051]

[0052] Where: 、 、 They are the loss term of the dimensionless liquid phase control equation, the loss term of the liquid phase boundary condition and the loss term of the liquid phase initial condition, all of which are related to and related; 、 、 are the weights of the corresponding loss terms, and are the network parameters of the solid-phase physical information neural network and the liquid-phase physical information neural network, respectively.

[0053] In an embodiment of the present invention, the total loss function for solid-state physical information neural network training is expressed as:

[0054]

[0055] Where, 、 、 They are respectively the solid phase dimensionless control equation loss term, the solid phase boundary condition loss term and the solid phase initial condition loss term, all of which are related to and related; 、 、 are the weights of the corresponding loss terms, and are the network parameters of the solid-phase physical information neural network and the liquid-phase physical information neural network, respectively.

[0056] The specific forms of the two total loss functions described above depend on the selected set of coupled soil-hydraulic partial differential equations and the corresponding initial and boundary conditions. Based on the selected set of coupled soil-hydraulic partial differential equations, the dimensionless governing equation loss terms for the liquid and solid phases are established using the fixed stress splitting method. The boundary conditions and initial conditions in the initial and boundary conditions are then combined to establish the two additional loss terms for the liquid and solid phases, ultimately constructing the total loss function.

[0057] In an embodiment of the present invention, the total loss function of the liquid phase physical information neural network is The specific calculation methods of the three loss terms are as follows:

[0058] Loss term of dimensionless liquid phase governing equation is: the deviation of the dimensionless liquid phase continuity balance equation after conversion by the fixed stress splitting method from zero; the fixed stress splitting method conversion method is to replace the time derivative of the volume strain in the liquid phase continuity balance equation of the soil hydraulic coupled partial differential equation system with the time derivative of the mean volume stress;

[0059] Liquid initial condition loss term is the deviation between the predicted value and the true value of the pore water pressure at the initial time point;

[0060] Liquid boundary condition loss term It is formed by adding the deviation between the predicted and true pore water pressure on the Dirichlet boundary and the deviation between the predicted and true flow velocity on the Neumann boundary condition.

[0061] Similarly, the total loss function of the solid-state physical information neural network is The specific calculation methods of the three loss terms are as follows:

[0062] Solid-phase dimensionless control equation loss term is: the deviation of the dimensionless stress-deformation equilibrium equation in the soil hydraulic coupled partial differential equations from zero;

[0063] Solid phase initial condition loss term is the deviation between the predicted value and the true value of soil deformation at the initial time point;

[0064] Solid boundary condition loss term It is formed by the sum of the deviation between the predicted value and the true value of soil deformation on the Dirichlet boundary and the deviation between the predicted value and the true value of stress on the Robin mixed boundary condition.

[0065] In order to better understand the specific form of the above total loss function, the following is a set of partial differential equations of soil hydraulic coupling (including the liquid phase continuity balance equation and stress-deformation equilibrium equation ), specifically gives the method of transforming the equation and dimensionless operation using the fixed stress splitting method.

[0066] In an embodiment of the present invention, the fixed stress splitting method refers to replacing the time derivative of the volume strain in the liquid phase continuity balance equation with the time derivative of the average volume stress , without considering water compression, water source and body force, the liquid phase continuity equilibrium equation converted by the fixed stress splitting method is and stress-deformation equilibrium equation The expression is as follows:

[0067]

[0068] Where, K is the soil permeability tensor, P is the pore water pressure, is the unit weight of water, h is the elevation head, n is the porosity, S w is saturation, c is the hydraulic coupling coefficient, is the three-dimensional drained bulk modulus, v is the mean overall stress, "and" ” are the gradient and divergence operators, and is the Lamé constant, u i and x i is i Deformation and spatial point position in the direction (i.e., the x, y, and z directions in three-dimensional space), is the volume strain, is the Laplace operator.

[0069] According to the principle of liquid phase continuity balance and the principle of stress-deformation balance, the equation and equation The value of should theoretically be 0, that is, it satisfies:

[0070]

[0071] In order to avoid the influence of the dimension difference of different parameters on the final model training, the dimensionless factor is introduced to make the two equilibrium equations dimensionless, so that the input and output of the neural network are in the same order of magnitude, thereby improving the training effect and stability of the physical neural network. and stress-deformation equilibrium equation After non-dimensionalizing the equation ( and After dimensionless transformation, they are expressed as and ) is expressed as follows:

[0072]

[0073] In the formula, after adding a horizontal line “—” to the top of any parameter A, Represents the dimensionless form of the parameter A (here A is the general expression of the parameter symbol in the formula, not a specific parameter, the same below), specifically: 、 、 Represent the dimensionless gradient operator, divergence operator, and Laplace operator, respectively. 、 represent the dimensionless form of pore water pressure and time (i.e. the moment of simulation, determined according to the input time point), represents the elevation head in dimensionless form, represents the mean overall stress in dimensionless form, and respectively in i Deformation in dimensionless form in direction and position of a point in space, Express the volume strain in dimensionless form; and are characteristic length and characteristic pressure, in meters and Pascals respectively. and m is an intermediate parameter, and its value is:

[0074]

[0075] In the formula E and v are the elastic modulus and Poisson's ratio, respectively.

[0076] because and In fact, the above liquid phase continuity balance equation and stress-deformation equilibrium equation The dimensionless form of the liquid phase continuity balance equation is and stress-deformation equilibrium equation The theoretical value of is 0, so when optimizing the model, the dimensionless value should be guaranteed. and The value of is as close to 0 as possible, so according to the dimensionless control equations of the liquid and solid phases established, the loss term of the dimensionless control equation of the liquid phase used for the training of the two physical information neural networks is and the loss term of the solid-phase dimensionless governing equation They can be expressed as:

[0077]

[0078] In the formula N g is the number of configuration points used to calculate the loss term of the control equation; after adding an upper triangle mark on the top of any parameter A, Represents the predicted value of the parameter in the physical information neural network, that is, and The pore water pressure and deformation predicted by the liquid phase physical information neural network and the solid phase physical information neural network are respectively calculated according to their respective equilibrium equations. and .

[0079] In addition, in the embodiment of the present invention, the initial boundary conditions include initial conditions and boundary conditions. Different initial boundary conditions can be set for the liquid phase and the solid phase respectively, thereby constructing different initial condition loss terms and boundary condition loss terms.

[0080] In the embodiment of the present invention, the initial conditions of the liquid phase are is the constraint condition of pore water pressure, boundary condition Contains Dirichlet boundary conditions involving pore water pressure and Neumann boundary conditions involving flow velocity, initial conditions of the solid phase is the deformation constraint condition, solid boundary condition It includes Dirichlet boundary conditions involving deformation and Robin mixed boundary conditions involving stress. The initial and boundary condition expressions for the solid and liquid phases are as follows:

[0081]

[0082]

[0083] Where, N ini , N b The number of configuration points corresponding to the calculation initial conditions and boundary conditions respectively; i Representatives in i Stress in the direction; after adding a wavy line mark on the top of any parameter A, Represents the true value of the parameter (ground truth), specifically: is the pore water pressure P The true value of For i Deformation in direction ui The true value of For i Stress in the direction i The true value of . Correspondingly, is the pore water pressure P The predicted value of For i Deformation in direction u i The predicted value of For i Stress in the direction i The predicted value of .

[0084] S3. Based on the sequential training strategy, the liquid phase physical information neural network and the solid phase physical information neural network are trained alternately in an iterative manner until the iteration termination condition is reached, and the two trained networks are used to predict the pore water pressure and deformation of the soil; in each round of iteration, the liquid phase physical information neural network and the solid phase physical information neural network are frozen alternately, and the sampled configuration points in the spatial domain and the time domain are input into the two physical information neural networks to obtain the predicted values of pore water pressure and deformation. Finally, the total loss function value corresponding to the unfrozen physical information neural network is calculated, and the network parameters of the unfrozen physical information neural network are updated by backpropagation according to the total loss function value.

[0085] It should be noted that the sequential training strategy used to alternately train the liquid and solid phase physical information neural networks means first freezing the solid phase neural network parameters to train the liquid phase physical information neural network, then freezing the liquid phase neural network parameters and starting to train the solid phase physical information neural network, and finally alternately training for several rounds until the loss reaches convergence stability. This process can be seen in Figure 2 As shown, the liquid phase corrected fully connected neural network , solid-phase modified fully connected neural network That is, two physical information neural networks of liquid phase and solid phase. The training method of the present invention is not limited, and a stochastic gradient descent optimization algorithm can be used.

[0086] In the embodiment of the present invention, since the information required to calculate the three loss terms in the total loss function is different, different configuration points need to be sampled to calculate the respective loss terms. Specifically, when alternately freezing the liquid-phase physical information neural network and the solid-phase physical information neural network and optimizing another unfrozen physical information neural network, it is necessary to first sample a first configuration point sample consisting of space points and time points from the complete spatial domain and time domain, sample time points from the complete time domain and combine them with the space points at the boundary of the simulation space to form a second configuration point sample, and sample space points from the complete spatial domain and combine them with the initial time points corresponding to the initial moment of the simulation to form a third configuration point sample. The three types of samples obtained by sampling are respectively input into the liquid-phase physical information neural network and the solid-phase physical information neural network to obtain the predicted values of the soil pore water pressure and the predicted values of the soil deformation; then, according to the total loss function corresponding to the unfrozen physical information neural network, the dimensionless control equation loss term in the total loss function is calculated by the predicted value of the first configuration point sample, the boundary condition loss term in the total loss function is calculated by the predicted value of the second configuration point sample, and the initial condition loss term in the total loss function is calculated by the predicted value of the third configuration point sample. Finally, the total loss function value is weighted and the network parameters of the unfrozen physical information neural network are updated by the gradient descent optimization algorithm.

[0087] In addition, in the embodiment of the present invention, a gradient normalized adaptive loss balancing strategy can be introduced in each round of iteration to adaptively adjust the weights of the three loss terms in the total loss function. The adaptive loss balancing strategy using gradient normalization refers to automatically updating the weights corresponding to each loss term during the training process. The gradient normalization adaptive loss weight updating method mainly calculates the gradient vector of each loss term with respect to the network parameters. L 2 norm, and calculate the relative training degree of each loss term to update the weight. The gradient normalization adaptive loss balance strategy belongs to the prior art. In the embodiment of the present invention, the gradient normalization loss weight calculation method can be implemented according to the following steps:

[0088] (1) Any of the first k The current loss weight of the loss item ( k =1, 2, 3 correspond to the total loss function of the liquid phase mentioned above. 、 、 , or in the total solid loss function 、 、 ) is recorded as , calculate the effect of each loss term on the network parameters in the total loss function The gradient vector of L 2 norm, that is , where It is k The corresponding loss items L 2 norm, It is k The loss value of the loss item, k is the corresponding loss weight.

[0089] (2) Calculate all loss items L 2 Mean of the norm .

[0090] (3) Calculate the training degree of each loss term, that is , where Indicates the k The loss value of the initial training loss term.

[0091] (4) Calculate the relative training degree of each loss term, that is .

[0092] (5) Adjust the loss weight so that each loss item Approaching an average level , that is, the weight value used for the next round of total loss calculation after adjustment is:

[0093]

[0094] Where, satisfy ,in and are two hyperparameters.

[0095] This gradient normalized adaptive loss balancing strategy is suitable for balancing the gradients of multiple loss terms. Compared with fixed loss weights, this method can improve prediction accuracy.

[0096] In summary, the method of the present invention adopts a sequential training strategy, an improved fully connected neural network and an adaptive loss balance scheme to improve the traditional physical information neural network, thereby improving the prediction accuracy and training stability. At the same time, compared with the traditional finite element method, this method has the advantages of being grid-free and data-driven, and has physical interpretability compared to pure black box models such as pure data-driven. The physical information neural network trained by the present invention can be used for pore water pressure and deformation prediction. The hydraulic coupling behavior of the soil is mainly caused by two boundary conditions, the first is the rainfall boundary condition, and the second is the load boundary condition. The present invention can be applied to both boundary conditions to explore the seepage and deformation behavior of the soil under rainfall or overlying loads. According to this method, inverse analysis and proxy models can be further established to estimate unknown soil parameters and constitutive models, and as a hybrid model embedded with physical information and data-driven to predict soil responses in undetected spatiotemporal domains, it has great application potential.

[0097] It should be noted that the method steps shown in S1 to S3 above can essentially be implemented in the form of a computer program.

[0098] Therefore, based on the same inventive concept, Figure 3 As shown, the present invention further provides a soil-hydraulic coupling simulation system based on a physical information neural network, corresponding to the soil-hydraulic coupling simulation method based on a physical information neural network provided in the above embodiment, which includes:

[0099] The initial parameter setting module is used to obtain the simulation space domain, time domain, initial boundary conditions and soil parameters for the target site where soil-hydraulic coupling simulation is required;

[0100] A model and loss construction module is used to construct a liquid-phase physical information neural network for predicting pore water pressure in soil, and set the weighted sum of the liquid-phase dimensionless control equation loss term, the liquid-phase boundary condition loss term, and the liquid-phase initial condition loss term as the corresponding total loss function; a solid-phase physical information neural network is constructed for predicting deformation in soil, and set the weighted sum of the solid-phase dimensionless control equation loss term, the solid-phase boundary condition loss term, and the solid-phase initial condition loss term as the corresponding total loss function; wherein the liquid-phase dimensionless control equation loss term and the solid-phase dimensionless control equation loss term are constructed by transforming the soil hydraulic coupling partial differential equation group based on the fixed stress splitting method;

[0101] The model training and prediction module is used to alternately train the liquid-phase physical information neural network and the solid-phase physical information neural network in an iterative manner based on a sequential training strategy until the iteration termination condition is reached, and use the two trained networks to predict the pore water pressure and deformation of the soil; in each round of iteration, the liquid-phase physical information neural network and the solid-phase physical information neural network are alternately frozen, and the two physical information neural networks are input with sampling configuration points from the spatial domain and the time domain to obtain the predicted values of the pore water pressure and deformation; finally, the total loss function value corresponding to the unfrozen physical information neural network is calculated, and the network parameters of the unfrozen physical information neural network are updated by backpropagation according to the total loss function value.

[0102] In addition, based on the same inventive concept, Figure 4 As shown, the present invention also provides a computer electronic device corresponding to the soil hydraulic coupling simulation method based on physical information neural network provided in the above embodiment, which includes a memory and a processor;

[0103] The memory is used to store computer programs;

[0104] The processor is configured to implement the soil-hydraulic coupling simulation method based on physical information neural network as described above when executing the computer program;

[0105] Furthermore, the logic instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention.

[0106] Therefore, based on the same inventive concept, the present invention provides a computer-readable storage medium corresponding to a soil-hydraulic coupling simulation method based on a physical information neural network, and a computer program is stored on the storage medium. When the computer program is executed by a processor, it can realize the soil-hydraulic coupling simulation method based on a physical information neural network as described above.

[0107] Therefore, based on the same inventive concept, the present invention provides a computer program product, including a computer program / instruction, which, when executed by a processor, can implement the soil-hydraulic coupling simulation method based on physical information neural network as described above.

[0108] Specifically, in the computer-readable storage medium of the above three embodiments, the stored computer program is executed by the processor to perform the above steps S1 to S3.

[0109] It is understood that the storage medium may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Furthermore, the storage medium may be any medium capable of storing program code, such as a USB flash drive, a mobile hard drive, a magnetic disk, or an optical disk.

[0110] It is understandable that the above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, and discrete hardware components.

[0111] It should also be noted that those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working process of the system described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here. In the various embodiments provided in this application, the division of steps or modules in the system and method is only a logical function division. In actual implementation, there may be other division methods, for example, multiple modules or steps can be combined or integrated together, and a module or step can also be split.

[0112] The present invention will further demonstrate the detailed implementation process and technical effects of the soil-hydraulic coupling simulation method based on physical information neural network shown in the above steps S1 to S3 in a specific example scenario through a specific embodiment, so as to facilitate understanding of the essence of the present invention.

[0113] Example

[0114] The steps of this embodiment are the same as the soil-hydraulic coupling simulation method based on physical information neural network shown in the aforementioned steps S1 to S3. They will not be fully repeated here. The key steps, specific simulation scenarios, some specific parameter settings and implementation results of this embodiment will be mainly demonstrated.

[0115] In this embodiment, the overburden load boundary condition of one-dimensional saturated soil is taken as an example. The simulated structure is a soil column, and its three-dimensional sketch is shown in Figure 5 The soil mass satisfies the lateral constraint conditions, only the top surface is permeable, and the overburden pressure is 100kPa. The soil mass parameters are: a c = 1.0, E = 1.9 10 4 Kpa, v = 0.3, w = 9.8 kN / m 3 , and K sat = 3.47 10 -5 m / s. The parameters used to train the physical neural network are: sampling 4000 first configuration points to optimize the residual of the control equation, that is, N g is 4000, and the second and third configuration points for optimizing the boundary condition loss term and the initial condition loss term are 80 and 500 respectively, that is, N b is 80, N ini is 500. These points are randomly sampled in each round.

[0116] In addition, the liquid-phase physical information neural network and the solid-phase physical information neural network of this embodiment both adopt an improved fully connected network with an attention mechanism. In order to compare and show the effect between the improved fully connected network and the traditional fully connected network, and to prove the advantage of the adaptive loss balance strategy of the gradient normalization method for model training, this embodiment sets up a total of four models for comparison, as shown in Table 1: the first model M1 adopts the traditional fully connected neural network and the method of not updating the loss weight, the second model M2 adopts the traditional fully connected neural network and the adaptive loss balance strategy of the gradient normalization method, the third model M3 adopts the improved fully connected neural network and the method of not updating the loss weight, and the fourth model M4 adopts the improved fully connected neural network and the adaptive loss balance strategy of the gradient normalization method. By calculating the relative value between the predicted value and the analytical solution L 2 The performance of the model is determined by the relative L2 error. The smaller the relative L2 error, the more accurate the model. Each model is tested 10 times under different random seeds.

[0117] Table 1

[0118]

[0119] The traditional fully connected neural network uses five fully connected hidden layers, each with 128 neurons. The improved fully connected neural network uses the same five fully connected hidden layers (128 neurons per layer) and includes two additional fully connected layers as mapping networks. Each mapping network consists of a fully connected hidden layer with 128 neurons, which is used to map the original configuration points to the first and second attention features. The fully connected hidden layers in all network models use the Tanh activation function. In the sequential training strategy, the number of internal training rounds for the physical information neural networks of the aqueous and solid phases remains consistent, at 100,000. Because the total stress of the entire compressed column remains constant in one dimension, the number of external rounds is set to 1. The Adam optimizer is used for network parameter optimization.

[0120] Table 2 shows the relative performance of the four comparison models on pore water pressure and vertical displacement after training. L 2 The mean and standard deviation of the error, models M2 and M4 using the adaptive loss balance strategy have lower L 2 The error indicates that the prediction accuracy is improved, while the M3 and M4 using the improved fully connected neural network have reduced the L 2 The standard deviation of the error indicates improved training stability. Finally, the combination of an improved fully connected neural network and an adaptive loss balancing strategy achieves optimal prediction performance.

[0121] Table 2

[0122]

[0123] In addition, this embodiment also compares the model accuracy of the sequential training strategy and the traditional training strategy. The traditional training strategy refers to not using the fixed stress splitting method to process the fluid-solid coupling equilibrium equation, and using a collaborative training method to train the solid and liquid phase networks. In this comparison method, both models do not use the improved fully connected neural network and gradient normalized equilibrium method. By comparing the sequential training method using the fixed stress splitting method and the traditional collaborative training method, the results shown in Table 3 show that the mean values of the L2 error accuracy obtained for pore water pressure prediction are 0.0365 and 0.0405, respectively, with standard deviations of 0.00179 and 0.00256, and the mean values of the L2 error accuracy obtained for vertical deformation prediction are 0.0027 and 0.0045, respectively, with standard deviations of 0.00077 and 0.00121. It can be seen that the sequential training strategy of the fixed stress splitting method adopted in the present invention has smaller errors than the traditional collaborative training method, higher prediction accuracy, and stronger stability.

[0124] Table 3

[0125]

[0126] It should be noted that, although the sequential training strategy can be carried out based on the fixed strain splitting method and the fixed stress splitting method. If the liquid phase continuity balance equation in the fluid-solid coupling balance equation is not changed by the fixed stress splitting method, that is, the volume strain term is retained in the equation, it is suitable for the fixed strain splitting method. However, the reason why the present invention is based on the sequential training strategy of the fixed stress splitting method is that the fixed strain splitting method is extremely unstable in the solution, and it is easy to have trivial solutions and wrong solutions. In the liquid phase continuity balance equation of the fluid-solid coupling equation, the volume strain term is retained, which is suitable for the collaborative training strategy, that is, the solid phase and liquid limit networks are trained at the same time, so that the correct solution can be obtained. This method belongs to a traditional training method. The present invention is based on the sequential training strategy of the fixed stress splitting method, which can avoid the simultaneous training of the solid phase and liquid phase networks, and approximate the true solution in an iterative training manner. This training method reduces the difficulty of network optimization, makes it easier to find the optimal solution, and thus has higher accuracy. On the contrary, the traditional collaborative training method, which optimizes both the solid phase and liquid phase networks at the same time, inevitably increases the difficulty of training, and the accuracy of the solution is worse.

Claims

1. A soil-hydraulic coupling simulation method based on physical information neural network, characterized in that: include: S1: For the target site where soil-hydraulic coupling simulation is required, obtain the simulation space domain, time domain, initial and boundary conditions, and soil parameters; S2. Constructing a liquid-phase physical information neural network for predicting pore water pressure in soil, and setting the weighted sum of the liquid-phase dimensionless control equation loss term, the liquid-phase boundary condition loss term, and the liquid-phase initial condition loss term as the corresponding total loss function; constructing a solid-phase physical information neural network for predicting deformation in soil, and setting the weighted sum of the solid-phase dimensionless control equation loss term, the solid-phase boundary condition loss term, and the solid-phase initial condition loss term as the corresponding total loss function; wherein the liquid-phase dimensionless control equation loss term and the solid-phase dimensionless control equation loss term are constructed in a dimensionless manner after converting the soil hydraulic coupled partial differential equation group by the fixed stress splitting method; S3. Based on the sequential training strategy, the liquid phase physical information neural network and the solid phase physical information neural network are trained alternately in an iterative manner until the iteration termination condition is reached, and the two trained networks are used to predict the pore water pressure and deformation of the soil; in each round of iteration, the liquid phase physical information neural network and the solid phase physical information neural network are frozen alternately, and the sampled configuration points in the spatial domain and the time domain are input into the two physical information neural networks to obtain the predicted values of pore water pressure and deformation. Finally, the total loss function value corresponding to the unfrozen physical information neural network is calculated, and the network parameters of the unfrozen physical information neural network are updated by backpropagation according to the total loss function value.

2. The soil-hydraulic coupling simulation method based on physical information neural network according to claim 1, characterized in that: The liquid-phase physical information neural network and the solid-phase physical information neural network both use the same fully connected network with an attention mechanism. The network inputs are configuration points consisting of spatial points collected from the spatial domain and time points collected from the time domain. The configuration points are mapped into first attention features and second attention features respectively through two additional fully connected layers. Then, the configuration points, first attention features and second attention features are input into multiple layers of sequentially cascaded network layers, where the first network layer directly uses the configuration points as input to obtain output features through the fully connected layer. In the remaining network layers, the output features of the previous network layer are first passed through the fully connected layer to obtain the intermediate feature H. Then, the first attention feature and the second attention feature are used to weight 1-H and H respectively and then added to obtain the output features of the current network layer.

3. The soil-hydraulic coupling simulation method based on physical information neural network according to claim 1, characterized in that: In the total loss function of the liquid phase physical information neural network, The loss term of the dimensionless liquid phase control equation is: the deviation of the dimensionless liquid phase continuity balance equation after conversion by the fixed stress splitting method from zero; the fixed stress splitting method conversion method is to replace the time derivative of the volume strain in the liquid phase continuity balance equation of the soil hydraulic coupled partial differential equation system with the time derivative of the mean volume stress; The liquid phase initial condition loss term is the deviation between the predicted value and the true value of the pore water pressure at the initial time point; The liquid boundary condition loss term is the sum of the deviation between the predicted and true pore water pressure on the Dirichlet boundary and the deviation between the predicted and true velocity on the Neumann boundary condition.

4. The soil-hydraulic coupling simulation method based on physical information neural network according to claim 1, characterized in that: In the total loss function of the solid-phase physical information neural network, The loss term of the dimensionless solid phase governing equation is: the deviation of the dimensionless stress-deformation equilibrium equation in the soil hydraulic coupled partial differential equations from zero; The solid phase initial condition loss term is the deviation between the predicted value and the true value of soil deformation at the initial time point; The solid boundary condition loss term is the sum of the deviation between the predicted and true soil deformation on the Dirichlet boundary and the deviation between the predicted and true stress on the Robin mixed boundary condition.

5. The soil-hydraulic coupling simulation method based on physical information neural network according to claim 1, characterized in that: When alternately freezing the liquid-phase physical information neural network and the solid-phase physical information neural network and optimizing the other unfrozen physical information neural network, it is necessary to first sample a first configuration point sample consisting of space points and time points from the complete spatial domain and time domain, sample time points from the complete time domain and combine them with the space points at the boundary of the simulation space to form a second configuration point sample, and sample space points from the complete spatial domain and combine them with the initial time points corresponding to the initial moment of the simulation to form a third configuration point sample. The three types of samples obtained by sampling are respectively input into the liquid-phase physical information neural network and the solid-phase physical information neural network to obtain the predicted values of the soil pore water pressure and the predicted values of the soil deformation. Then, according to the total loss function corresponding to the unfrozen physical information neural network, the dimensionless control equation loss term in the total loss function is calculated by the predicted value of the first configuration point sample, the boundary condition loss term in the total loss function is calculated by the predicted value of the second configuration point sample, and the initial condition loss term in the total loss function is calculated by the predicted value of the third configuration point sample. Finally, the total loss function value is obtained by weighting and the network parameters of the unfrozen physical information neural network are updated using the gradient descent optimization algorithm.

6. The soil-hydraulic coupling simulation method based on physical information neural network according to claim 1, characterized in that: In each round of iteration, a gradient normalization adaptive loss balancing strategy is introduced to adaptively adjust the weights of the three loss terms in the total loss function.

7. A soil-hydraulic coupling simulation system based on physical information neural network, characterized in that: include: The initial parameter setting module is used to obtain the simulation space domain, time domain, initial boundary conditions and soil parameters for the target site where soil-hydraulic coupling simulation is required; A model and loss construction module is used to construct a liquid-phase physical information neural network for predicting pore water pressure in soil, and set the weighted sum of the liquid-phase dimensionless control equation loss term, the liquid-phase boundary condition loss term, and the liquid-phase initial condition loss term as the corresponding total loss function; a solid-phase physical information neural network is constructed for predicting deformation in soil, and set the weighted sum of the solid-phase dimensionless control equation loss term, the solid-phase boundary condition loss term, and the solid-phase initial condition loss term as the corresponding total loss function; wherein the liquid-phase dimensionless control equation loss term and the solid-phase dimensionless control equation loss term are constructed by transforming the soil hydraulic coupling partial differential equation group based on the fixed stress splitting method; The model training and prediction module is used to alternately train the liquid-phase physical information neural network and the solid-phase physical information neural network in an iterative manner based on a sequential training strategy until the iteration termination condition is reached, and use the two trained networks to predict the pore water pressure and deformation of the soil; in each round of iteration, the liquid-phase physical information neural network and the solid-phase physical information neural network are alternately frozen, and the two physical information neural networks are input with sampling configuration points from the spatial domain and the time domain to obtain the predicted values of the pore water pressure and deformation; finally, the total loss function value corresponding to the unfrozen physical information neural network is calculated, and the network parameters of the unfrozen physical information neural network are updated by backpropagation according to the total loss function value.

8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, it can implement the soil-hydraulic coupling simulation method based on physical information neural network as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that The storage medium stores a computer program, and when the computer program is executed by the processor, the soil-hydraulic coupling simulation method based on physical information neural network according to any one of claims 1 to 7 is implemented.

10. A computer electronic device, characterized in that: including memory and processor; The memory is used to store computer programs; The processor is configured to implement the soil-hydraulic coupling simulation method based on physical information neural network as described in any one of claims 1 to 7 when executing the computer program.

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