Capillary wicking parameter calculation method and system based on physical information neural network

Abstract

The invention relates to the field of fluid mechanics, and provides a capillary wicking parameter calculation method and system based on a physical information neural network. The method comprises the following steps: carrying out space-time sampling on a capillary wicking physical domain to obtain a space-time coordinate set; constructing a multi-scale space-time encoder according to the space-time coordinate set, constructing a multi-scale space-time encoder based on time dependence and capillary enhancement, and obtaining an initial network model; performing multi-stage training optimization on the initial network model to obtain an optimized network model; and outputting to-be-calculated capillary wicking physical field parameters through the optimization network model to obtain a calculation result. According to the method, the staged physical behavior of the porous medium capillary wicking problem is simulated, and the accuracy of capillary wicking prediction is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fluid mechanics, and particularly relates to a capillary wicking parameter calculation method and system based on a physical information neural network. BACKGROUND

[0002] Capillary wicking phenomenon in porous media is widely present in many engineering fields such as textile materials, composite materials, soil science, and biomedical engineering. The wicking performance of fiber materials directly affects their functional characteristics, such as air permeability, thermal insulation, and liquid transport capacity. Accurate prediction and simulation of the wicking process are of great significance for material design and engineering applications.

[0003] For wicking modeling methods, Physics-Informed Neural Networks (PINN) as a new scientific computing method has shown great potential in solving partial differential equations and multi-physical field problems. PINN realizes the organic combination of data-driven and physical constraints by taking the governing equation as part of the loss function. However, the existing PINN model still has shortcomings in dealing with multi-time scale and multiphase flow problems: lack of network architecture design for specific physical phenomena, especially the dynamics of different time scales; lack of effective training strategies to balance the weights of different physical constraints, and the problem of insufficient precision in dealing with complex boundary conditions and initial conditions. SUMMARY

[0004] The present application provides a capillary wicking parameter calculation method and system based on a physical information neural network to solve the defects of the prior art.

[0005] The present application provides a capillary wicking parameter calculation method based on a physical information neural network, comprising:

[0006] S1: Spatiotemporal sampling of the capillary wicking physical domain is performed to obtain a set of spatiotemporal coordinates;

[0007] S2: A multi-scale spatiotemporal encoder is constructed according to the set of spatiotemporal coordinates, a multi-scale spatiotemporal encoder based on time dependence and capillary enhancement is constructed, and an initial network model is obtained;

[0008] S3: The initial network model is subjected to multi-stage training optimization to obtain an optimized network model;

[0009] S4: The optimized network model is used to output the capillary wicking physical field parameters to be calculated to obtain a calculation result.

[0010] The method comprises the following steps: S1, acquiring a set of space-time coordinates of a capillary wicking physical domain; S2, constructing a physical information neural network based on the set of space-time coordinates; S3, training the physical information neural network to obtain an initial network model; and S4, training the initial network model to obtain a final network model.

[0011] The method comprises the following steps: S1, acquiring a set of space-time coordinates of a capillary wicking physical domain; S2, constructing a physical information neural network based on the set of space-time coordinates; S3, training the physical information neural network to obtain an initial network model; and S4, training the initial network model to obtain a final network model.

[0012] S21: constructing a multi-scale space-time encoder, inputting the set of space-time coordinates into the multi-scale space-time encoder to obtain a basic space-time encoder;

[0013] S22: introducing a capillary enhancement module to correct capillary pressure in the multi-scale space-time encoder to obtain an optimized space-time encoder;

[0014] S23: introducing a self-adaptive viscosity field based on time evolution into a momentum equation loss to obtain an optimized momentum equation loss;

[0015] S24: establishing a physical constraint loss function based on the optimized momentum equation loss;

[0016] S25: training the optimized space-time encoder through the physical constraint loss function to obtain an initial network model.

[0017] The method comprises the following steps: S1, acquiring a set of space-time coordinates of a capillary wicking physical domain; S2, constructing a physical information neural network based on the set of space-time coordinates; S3, training the physical information neural network to obtain an initial network model; and S4, training the initial network model to obtain a final network model.

[0018]

[0019] wherein p is a corrected capillary pressure, C is a capillary coefficient, z is a wicking height direction, and ε2 is a regularization parameter for avoiding singular points. capillary cap

[0020] The expression of the self-adaptive viscosity field in step S23 is as follows:

[0021]

[0022] wherein φ is a phase field, t is time, is a self-adaptive viscosity field, μ is a dynamic viscosity of water, and μ is a dynamic viscosity of air. water air sigmoid is a function for simulating the viscosity increasing effect after saturation.

[0023] The expression of the physical constraint loss function in step S24 is as follows:​​​​

[0024] L total =L momentum +L continuity +L phase +λ b ·L boundary +λ i ·L initial ;

[0025] wherein, L total is a physical constraint loss function, L momentum is an optimization momentum equation loss, L continuity is a continuity equation loss, L phase is a phase field equation loss, λ b is a boundary condition weight coefficient, L boundary is a boundary condition loss, λ i is an initial condition weight coefficient, L initial is an initial condition loss.

[0026] According to the capillary wicking parameter calculation method based on the physical information neural network provided by the application, in step S3, the training phase for training optimization includes:

[0027] The first training phase, the physical phase of the capillary wicking process corresponding to the first training phase is the capillary dominant period;

[0028] The second training phase, the physical phase of the capillary wicking process corresponding to the second training phase is the transition period;

[0029] The third training phase, the physical phase of the capillary wicking process corresponding to the third training phase is the gravity dominant period.

[0030] According to the capillary wicking parameter calculation method based on the physical information neural network provided by the application, step S3 specifically includes:

[0031] When the training phase is the first training phase, the time resolution is set to 0.01s, and the loss weight in the loss function is set to: momentum equation weight coefficient 0.8, continuity equation weight coefficient 0.8, and phase field equation weight coefficient 0.2;

[0032] When the training phase is the second training phase, the time resolution is set to 1s, and the loss weight in the loss function is set to: momentum equation weight coefficient 0.5, continuity equation weight coefficient 0.5, and phase field equation weight coefficient 0.5;

[0033] When the training phase is the third training phase, the time resolution is set to 100s, and the loss weight in the loss function is set to: momentum equation weight coefficient 0.2, continuity equation weight coefficient 0.2, and phase field equation weight coefficient 0.8.

[0034] The method further comprises the following step S3:

[0035] The theoretical reference solution is used to verify the training and optimization of the initial network model.

[0036] The method further comprises the following step S4:

[0037]

[0038] wherein h theory is the theoretical reference solution, t is time, r is the equivalent capillary radius, γ is the surface tension, θ is the contact angle, and μ is the chemical potential in the governing equation of the wicking problem.

[0039] The method further comprises the following step S4:

[0040] The method further comprises the following step S4:

[0041] The sampling module is configured to perform space-time sampling on the capillary wicking physical domain to obtain a set of space-time coordinates.

[0042] The construction module is configured to construct a multi-scale space-time encoder based on the set of space-time coordinates, and to construct a multi-scale space-time encoder based on time dependence and capillary enhancement to obtain an initial network model.

[0043] The training module is configured to perform multi-stage training and optimization on the initial network model to obtain an optimized network model.

[0044] The output module is configured to output the capillary wicking physical field parameter to be calculated based on the optimized network model obtained by the training module, and to obtain a calculation result.

[0045] The application provides a capillary wicking parameter calculation method and system based on a physical information neural network, which first performs accurate sampling, and a four-dimensional space-time coordinate set obtained can comprehensively capture complex space-time evolution characteristics in a porous medium, providing a high-quality data basis for subsequent neural network training and avoiding the problem of loss of calculation accuracy caused by improper grid division in traditional numerical methods; secondly, a multi-scale space-time encoder is constructed, which fully considers the physical characteristics of different time scales in the capillary wicking process, a time-dependent modulator can adaptively adjust the response strength of the network to the physical behavior of different time periods, and a capillary enhancement module realizes accurate modeling of the capillary force effect through capillary pressure correction, which significantly improves the stability and convergence of the PINN network when dealing with multi-time scale coupling problems; subsequently, a composite physical constraint is established, which can effectively avoid the defect that the traditional gradient descent method is easy to fall into a local optimal solution, and through the use of second-order information of the quasi-Newton method, the loss function is quickly converged, so that the network can meet the constraint conditions of multiple physical conservation laws; in addition, in the training stage, a three-stage training strategy is proposed, which is time-division according to the physical characteristics of the capillary wicking process, high-time-resolution sampling is adopted in the capillary dominant period to accurately capture the rapid capillary rise process in the initial stage, medium-resolution sampling in the transition period balances the calculation efficiency and accuracy requirement, and sparse sampling in the gravity dominant period focuses on the long-time-scale gravity balance state, so that the artificial intelligence algorithm can be optimized according to the characteristics of different physical stages, and the learning ability and generalization performance of the network for complex physical processes are significantly improved; in the overall training, the momentum equation loss function, the continuity equation loss function and the phase field equation loss function are optimized, so that the network prediction result strictly meets the physical conservation law, and the constraint mechanism based on physical information enables the artificial intelligence algorithm to maintain high-precision prediction ability in the data-scarce engineering application scene, overcoming the shortcomings of the pure data-driven method in physical consistency.

[0046] Overall, the application combines the physical nature of capillary wicking in porous media, and through the organic fusion of the powerful nonlinear fitting ability of deep learning and physical constraints, not only solves the calculation bottleneck of traditional CFD methods in complex geometry and multi-scale problems, but also greatly improves the accuracy and calculation efficiency of capillary wicking prediction in engineering applications, providing an important theoretical basis and practical tool for the technical progress of porous media heat and mass transfer, microfluidic chip design, paper material engineering and other fields. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the present application or the prior art, the accompanying drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative effort.

[0048] Figure 1 A physical information neural network-based capillary wicking parameter calculation method flowchart provided for an embodiment of the present application;

[0049] Figure 2 A physical information neural network-based capillary wicking parameter calculation system structure schematic diagram provided for an embodiment of the present application;

[0050] Figure 3 A geometric model and boundary condition schematic diagram of a capillary wicking problem provided for an embodiment of the present application;

[0051] Figure 4 A loss change curve schematic diagram provided for an embodiment of the present application;

[0052] Figure 5 A capillary height comparison schematic diagram provided for an embodiment of the present application;

[0053] Figure 6 A continuous-time capillary height prediction schematic diagram provided for an embodiment of the present application;

[0054] Figure 7 A 3D phase field parameter schematic diagram provided for an embodiment of the present application. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described clearly and completely in the following with reference to the drawings in the present application. Obviously, the described embodiments are some embodiments of the present application, and should not be understood as limiting the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present application. In the description of the present application, it should be understood that the terms used are only for the purpose of description, and should not be understood as indicating or implying relative importance.

[0056] In order to better understand the present application, the research background of the present application will be explained in detail first.

[0057] Traditional wicking modeling methods are mainly based on the classic Washburn equation, which assumes that the capillary is an ideal cylinder and the liquid moves in one dimension under the driving of constant capillary pressure. However, the Washburn equation has obvious limitations: first, the actual porous medium has a complex three-dimensional geometric structure, which is different from the ideal capillary model; second, the wicking process involves multi-time scale dynamics, including the initial capillary-dominated rapid climb (0-60s), the intermediate capillary-gravity equilibrium transition stage (1-10min) and the late gravity-dominated saturation state (>10min); finally, the actual wicking process is accompanied by complex multiphase flow and interface phenomena, which is difficult to accurately describe with a simplified one-dimensional model.

[0058] Traditional numerical calculation methods such as finite element method, finite difference method and finite volume method, although they can handle complex geometry and multi-physical field coupling problems, still face major challenges in wicking modeling. First, the complex microstructure of the porous medium poses high requirements for grid division, which is prone to grid distortion and numerical instability; second, the multi-time scale characteristics of the wicking process require extremely fine time steps, resulting in low computational efficiency; finally, the dynamic evolution of the gas-liquid interface requires special interface capturing techniques, increasing the algorithm complexity and computational cost.

[0059] In recent years, Physics-Informed Neural Networks (PINN) as a new scientific computing method has shown great potential in solving partial differential equations and multi-physical field problems. PINN realizes the organic combination of data-driven and physical constraints by taking the control equation as part of the loss function.

[0060] However, existing PINN models still have deficiencies in dealing with multi-time scale and multiphase flow problems: lack of network architecture design for specific physical phenomena, making it difficult to accurately capture the dynamics of different time scales; lack of effective training strategies to balance the weights of different physical constraints; and lack of precision in dealing with complex boundary conditions and initial conditions.

[0061] The embodiments of the present application are described below in conjunction with the drawings.

[0062] As shown in Figure 1 The present application provides a capillary wicking parameter calculation method based on a physics-informed neural network, comprising:

[0063] S1: Spatiotemporal sampling of the capillary wicking physical domain to obtain a set of spatiotemporal coordinates.

[0064] Further, the time-space sampling algorithm is used to sample the capillary wicking physical domain in step S1 to obtain a four-dimensional time-space coordinate set containing internal points, boundary points and initial points. Specifically, the geometric boundary of the capillary wicking physical domain is first defined, which includes the fiber structure, pore space and fluid interface of the porous medium. Then, a structured grid generation method is used to divide the three-dimensional physical domain according to the preset grid density to generate uniformly distributed spatial nodes. The spatial coordinate system uses the Cartesian coordinate system, in which the x-axis and y-axis define the horizontal direction, and the z-axis defines the vertical wicking height direction.

[0065] The time-space coordinate set in step S1 includes internal point coordinates, boundary point coordinates and initial point coordinates of the capillary wicking physical domain, and the dimension of the time-space coordinate set includes spatial coordinates and time coordinates.

[0066] Further, the internal point coordinates are generated according to the equal interval principle inside the physical domain, the boundary point coordinates include the solid boundary, fluid inlet boundary and outlet boundary of the porous medium, the identification of the boundary point is realized by a geometric judgment algorithm, and the judgment condition is whether the node is located on the boundary surface of the physical domain, and the initial point coordinates correspond to the position of all spatial nodes at time 0. The time discretization process divides the entire time process of capillary wicking into multiple time steps, and the time coordinate t starts from the initial time 0 and increases according to the set time step Δt.

[0067] The finally obtained four-dimensional time-space coordinate set is a combination of three-dimensional spatial coordinates and one-dimensional time coordinates, which includes spatial coordinates (x, y, z) and time coordinates t, the spatial domain is defined as x∈[-0.005, 0.005]m, y∈[-0.005, 0.005]m, z∈[0, 0.06]m, the time domain is defined as t∈[0, 1800]s, and the total number of the time-space coordinate set is the product of the number of spatial nodes and the number of time steps.

[0068] S2: Constructing a multi-scale time-space encoder according to the time-space coordinate set, constructing a multi-scale time-space encoder based on time dependence and capillary enhancement to obtain an initial network model.

[0069] Further, step S2 further includes:

[0070] S21: Constructing a multi-scale time-space encoder, inputting the time-space coordinate set into the multi-scale time-space encoder to obtain a basic time-space encoder.

[0071] Further, the multi-scale space-time encoder established by the present application adopts a hierarchical neural network architecture, including an input layer, multiple hidden layers and an output layer. The input layer receives four-dimensional space-time coordinate data, each coordinate component as an independent input node, and the multi-scale feature extraction is realized through a parallel branch structure, each branch using different activation functions and network depths to process space-time features of different scales. Specifically, the first branch uses a tanh activation function to process low-frequency space-time changes, with 128 neurons and a network depth of 4 layers, the second branch uses a ReLU activation function to process medium-frequency space-time changes, with 256 neurons and a network depth of 6 layers, and the third branch uses a Swish activation function to process high-frequency space-time changes, with 512 neurons and a network depth of 8 layers. Feature fusion is realized through a weighted summation operation, and the weight coefficients are controlled by trainable parameters. The output layer uses a linear activation function to ensure the continuity of physical quantities.

[0072] S22: introducing a capillary enhancement module to correct the capillary pressure in the multi-scale space-time encoder to obtain an optimized space-time encoder.

[0073] In step S22, the expression for correcting the capillary pressure in the capillary enhancement module is:

[0074]

[0075] where p capillary is the corrected capillary pressure, C cap is the capillary coefficient, z is the wicking height direction, and ε2 is a regularization parameter to avoid singular points.

[0076] Further, the capillary enhancement module introduced by the present application specifically processes the nonlinear characteristics of capillary pressure, and calculates the corrected capillary pressure through a capillary pressure correction formula. In the above expression, the capillary coefficient is calculated from the physical parameters of the porous medium, and the regularization parameter controls the spatial variation gradient of the capillary pressure, with a numerical range of 0.01 to 1.0, which is adjusted adaptively through the network training process. The optimized space-time encoder adds a capillary enhancement branch to the original basic space-time encoder, which contains a 3-layer fully connected neural network with 64, 32 and 16 neurons respectively in each layer, and uses LeakyReLU as the activation function. The output is a single capillary pressure correction value. The overall data flow is as follows: coordinate input → capillary enhancement branch → capillary pressure correction value → addition of basic pressure → corrected pressure output.

[0077] S23: introducing an adaptive viscosity field based on time evolution to the momentum equation loss to obtain an optimized momentum equation loss.

[0078] In step S23, the expression for the adaptive viscosity field is:

[0079]

[0080] wherein, φ is the phase field, t is time, μ is the adaptive viscosity field, μ water μ is the dynamic viscosity of water, μ air μ is the dynamic viscosity of air, sigmoid is a function used to simulate the effect of viscosity increase after saturation.

[0081] The adaptive viscosity field dynamically adjusts the fluid viscosity according to the phase field value and time, the expression is as above, the specific momentum equation loss function is based on the simplified Navier-Stokes equation, and the expression of the optimized momentum equation loss obtained by the adaptive viscosity field based on the application is:

[0082]

[0083] wherein, L momentum is the optimized momentum equation loss, w is the vertical velocity component, u is the east-west velocity component, z is the wicking height direction, and g is the gravitational acceleration constant.

[0084] S24: Establish a physical constraint loss function based on the optimized momentum equation loss.

[0085] wherein, the expression of the physical constraint loss function in step S24 is:

[0086] L total = L momentum + L continuity + L phase + λ b · L boundary + λ i · L initial ;

[0087] wherein, L total is the physical constraint loss function, L momentum is the optimized momentum equation loss, L continuity is the continuity equation loss, L phase is the phase field equation loss, λ b is the boundary condition weight coefficient, L boundary is the boundary condition loss, λ i is the initial condition weight coefficient, L initial is the initial condition loss.

[0088] wherein, the continuity equation loss function is:

[0089]

[0090] where (u, v, w) is the three-dimensional velocity vector, which ensures the mass conservation of the fluid.

[0091] where the phase field equation loss function is based on the Cahn-Hilliard equation:

[0092]

[0093] where μ is the chemical potential, M is the phase field mobility, and ε is the interface thickness parameter.

[0094] where the boundary condition loss function includes three types of boundaries:

[0095] Inlet capillary pressure boundary:

[0096]

[0097] Fiber surface no-slip boundary:

[0098] L walt = ||u|| 2 +||v|| 2 +||w|| 2 ;

[0099] Outlet pressure boundary:

[0100] L outlet =||p|| 2 ;

[0101] where p is the pressure field, r is the equivalent capillary radius, γ is the surface tension, and θ is the contact angle.

[0102] S25: training the optimization spatio-temporal encoder by the physical constraint loss function to obtain an initial network model.

[0103] Further, in step S25, the training process adopts a hybrid optimization strategy of Adam optimizer combined with L-BFGS optimization algorithm. First, the spatio-temporal coordinate set is input into the optimization spatio-temporal encoder based on forward propagation, and the physical quantity prediction value is calculated. Then, the total loss value is calculated according to the physical constraint loss function, including the weighted sum of each loss component. In the back propagation stage, the gradient of the loss function with respect to the network parameters is calculated by automatic differentiation technology, and the gradient calculation is recursively performed using the chain rule. In the parameter update stage, the Adam optimizer is used for coarse tuning first, and then the L-BFGS optimizer is switched to fine tuning. The L-BFGS algorithm approximates the Hessian matrix by the quasi-Newton method, and the optimal step size is determined by the Wolfe condition in the line search process, until the training termination condition is met.

[0104] S3: performing multi-stage training optimization on the initial network model to obtain an optimized network model.

[0105] In step S3, the training phase for training optimization includes: a first training phase, the physical phase of the wicking process corresponding to the first training phase is capillary dominant period; a second training phase, the physical phase of the wicking process corresponding to the second training phase is transition period; a third training phase, the physical phase of the wicking process corresponding to the third training phase is gravity dominant period.

[0106] In step S3, specifically: when the training phase is the first training phase, the time resolution is set to 0.01s, and the loss weight in the loss function is set to: momentum equation weight coefficient 0.8, continuity equation weight coefficient 0.8, and phase field equation weight coefficient 0.2; when the training phase is the second training phase, the time resolution is set to 1s, and the loss weight in the loss function is set to: momentum equation weight coefficient 0.5, continuity equation weight coefficient 0.5, and phase field equation weight coefficient 0.5; when the training phase is the third training phase, the time resolution is set to 100s, and the loss weight in the loss function is set to: momentum equation weight coefficient 0.2, continuity equation weight coefficient 0.2, and phase field equation weight coefficient 0.8.

[0107] Further, the three-stage training strategy is divided according to the physical characteristics of the wicking process: stage 1-capillary dominant period (0-2s): high time resolution Δt=0.01s is adopted, the flow field equation is focused on training, and the loss weight is momentum equation 0.8, continuity equation 0.8, and phase field equation 0.2. Stage 2-transition period (2-300s): medium resolution Δt=1s is adopted, the flow field and phase field coupling are balanced, and the loss weight is momentum equation 0.5, continuity equation 0.5, and phase field equation 0.5; stage 3-gravity dominant period (300-1800s): sparse sampling Δt=10-100s is adopted, preferably 100s, interface evolution is focused on, and the loss weight is momentum equation 0.2, continuity equation 0.2, and phase field equation 0.8.

[0108] In step S3, the three-stage training strategy is divided according to the physical characteristics of the wicking process: stage 1-capillary dominant period (0-2s): high time resolution Δt=0.01s is adopted, the flow field equation is focused on training, and the loss weight is momentum equation 0.8, continuity equation 0.8, and phase field equation 0.2. Stage 2-transition period (2-300s): medium resolution Δt=1s is adopted, the flow field and phase field coupling are balanced, and the loss weight is momentum equation 0.5, continuity equation 0.5, and phase field equation 0.5; stage 3-gravity dominant period (300-1800s): sparse sampling Δt=10-100s is adopted, preferably 100s, interface evolution is focused on, and the loss weight is momentum equation 0.2, continuity equation 0.2, and phase field equation 0.8.

[0109] A theoretical reference solution is established, and the training optimization of the initial network model is verified by the theoretical reference solution.

[0110] The expression of the theoretical reference solution is:

[0111]

[0112] In the formula, h theory is the theoretical reference solution, t is time, r is the equivalent capillary radius, γ is the surface tension, θ is the contact angle, and μ is the chemical potential.

[0113] Specifically, when verifying, first, the reference solution is calculated by Washburn theory, that is, the above expression, and then the relative error between the model prediction result and the theoretical solution is compared, if the error is within the 5% threshold, the PINN network model meets the engineering precision requirement, otherwise, the three-stage training is performed again.

[0114] S4: outputting the to-be-calculated capillary wicking physical field parameter through the optimized network model to obtain a calculation result.

[0115] The calculation result in step S4 includes a pressure field value, a velocity field value, and a phase field value.

[0116] Specifically, the input of the trained model is a four-dimensional space-time coordinate (x, y, z, t), and the output is five physical quantities: pressure p, three-dimensional velocity (u, v, w), and phase field The phase field is used to describe the distribution of the gas-liquid interface.

[0117] As Figure 2 shown, the application also provides a capillary wicking parameter calculation system based on a physical information neural network, which comprises:

[0118] A sampling module 100 is configured to perform space-time sampling on a capillary wicking physical domain to obtain a set of space-time coordinates.

[0119] A construction module 200 is configured to construct a multi-scale space-time encoder according to the set of space-time coordinates, to construct a multi-scale space-time encoder based on time dependence and capillary enhancement, and to obtain an initial network model.

[0120] A training module 300 is configured to perform multi-stage training and optimization on the initial network model to obtain an optimized network model.

[0121] An output module 400 is configured to the optimized network model obtained by the training module 300, and is configured to output a to-be-calculated capillary wicking physical field parameter to obtain a calculation result.

[0122] The device embodiments described above are only schematic, wherein the units shown as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, that is, they can be located in one place, or distributed on multiple network units. According to actual needs, part or all of the modules can be selected to achieve the purpose of the embodiment scheme. Those skilled in the art can understand and implement it without creative labor.

[0123] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0124] The following describes a method and system for calculating capillary wicking parameters based on a physical information neural network, in conjunction with specific embodiments of the present invention.

[0125] The PINN modeling method proposed in this invention can predict the capillary wicking behavior of fiber materials with high accuracy. The implementation process includes the following steps:

[0126] First, establish the wicking physical model. Set the fiber radius r. fiber =1×10 -6 m, equivalent capillary radius r eql =1×10 -6 m, contact angle θ = 30°, surface tension γ = 0.07 N / m, dynamic viscosity of water μ water =1×10 -3 Pa·s, density ρ water =1000kg / m 3 The total time is 1800 seconds. Figure 3 As shown, the capillary wicking problem of the obtained capillary wicking physical domain is defined by the geometric model shown in the figure, which is a cylindrical structure with a diameter of 680 μm and a height of 1000 μm.

[0127] Next, the PINN network was constructed. A 4-layer fully connected network was adopted, with 128 hidden layers and tanh activation function. Capillary enhancement and gravity compensation modules were integrated, and the total number of network parameters was approximately 65,000.

[0128] The three-stage training will be conducted again. Stage 1 consists of 1000 rounds of training with a learning rate of 1 x 10^10. -3 Phase 2 training consists of 1500 rounds, with a learning rate of 5 x 10^5. -4 Phase 3 training consists of 500 rounds, with a learning rate of 1×10⁻⁶. -4 The total training time is approximately 4 hours.

[0129] Finally, the results are verified. Figure 4The PINN prediction result is compared with the theoretical experiment, wherein the abscissa is Epoch, indicating the training round, the model is trained for a total of 1500 epochs, the ordinate is the loss value, indicating the error between the model prediction value and the true value, in the initial stage (0-50 epochs), the loss value sharply decreases from a higher position, about 10 -2 orders of magnitude, indicating that the model quickly learns in the early training, the error converges rapidly, in the middle stage (50-500 epochs), the loss value continues to decrease but the speed slows down, the curve appears small fluctuations, which is a normal training process, in the later stage (500-1500 epochs), the loss value tends to be stable, and is maintained at 10 -5 orders of magnitude, the curve is basically flat, which shows that the model has converged, it can be seen from the curve that the model of the application does not appear overfitting phenomenon, and the final loss value reaches 10 -5 orders of magnitude, which shows that the prediction accuracy of the model for the wicking height is high.

[0130] Based on Figure 4 , the prediction accuracy of the application at the key time points is as follows: t=1s, experiment=1.5mm, prediction=1.4mm, error=0.1mm (3.6%); t=60s: experiment=13.8mm, prediction=14.5mm, error=0.7mm (5.0%); t=300s: experiment=32.5mm, prediction=32.1mm, error=0.4mm (1.1%); t=1800s: experiment=52.0mm, prediction=52.5mm, error=0.5mm (1.0%).

[0131] The experimental results show that the PINN method of the application maintains high-precision prediction in the whole time range, and successfully captures the multi-time scale physical characteristics of the wicking process, thereby providing a high-precision modeling tool for porous medium transmission phenomena.

[0132] Figure 5 Fig. 1 is a comparison diagram of the wicking height prediction of the application, Figure 6 Fig. 2 is a comparison diagram of the continuous-time wicking height prediction of the application, Figure 5 and Figure 6 Fig. 3 is a comparison diagram of the wicking height prediction of the application, Figure 5 It can be seen that the average error between the two is 0.4mm, and the maximum error is 0.7mm, Figure 6 which also shows that the error between the two is very small, and the experimental results show that the PINN method of the application is comparable to the traditional experimental measurement method, and has high accuracy.

[0133] Figure 7 Fig. 4 is a 3D phase field diagram of the application, Figure 7The middle left side figure is a 3D phase field surface projection schematic diagram, Figure 7 The middle right side figure is a velocity streamline schematic diagram.

[0134] The present application proposes a porous medium capillary wicking modeling method based on physical information neural network, which realizes high-precision numerical simulation of multi-time scale capillary wicking process. The present application first constructs a multi-scale space-time encoder, integrates a time-dependent modulator and a capillary enhancement module, and designs a special network architecture for the physical characteristics of the wicking process. By using an adaptive loss function to simultaneously solve the Navier-Stokes momentum equation, the continuity equation and the Cahn-Hilliard phase field equation, the organic coupling of multiple physical fields is realized, and an innovative three-stage training strategy is also adopted to optimize the physical behavior of the capillary dominant period, the transition period and the gravity dominant period, effectively solving the problem of multi-time scale modeling.

[0135] The PINN modeling method proposed by the present application has significant advantages compared with traditional numerical methods. First, the present application is meshless, avoiding the grid distortion problem of traditional numerical methods in complex geometry and multiphase flow problems. Secondly, through the soft constraint method of physical constraints, the difficulty of boundary treatment in traditional methods is avoided. Finally, the continuity of neural network ensures the smoothness and physical consistency of the solution.

[0136] The method of the present application performs outstandingly in prediction accuracy. The present application successfully captures multiple physical stages of the wicking process: early capillary-dominated rapid climbing, mid-term transition balance and late gravity-dominated saturation state. Overall, the average prediction error of the PINN method of the present application is controlled within 5% in the entire time range (1s-1800s), reaching the engineering application accuracy.

[0137] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for calculating capillary wicking parameters based on physical information neural networks, characterized by, The method comprises the following steps: S1: spatiotemporal sampling of the capillary wicking physical domain to obtain a set of spatiotemporal coordinates; S2: constructing a multi-scale spatiotemporal encoder based on the set of spatiotemporal coordinates to obtain an initial network model; S3: multi-stage training and optimization of the initial network model to obtain an optimized network model; S4: outputting a capillary wicking physical field parameter to be calculated by the optimized network model to obtain a calculation result.

2. The method of claim 1, wherein, The set of spatiotemporal coordinates in step S1 includes internal point coordinates, boundary point coordinates, and initial point coordinates of the capillary wicking physical domain, and the dimensions of the set of spatiotemporal coordinates include spatial coordinates and time coordinates.

3. The method of claim 1, wherein the physical information neural network is a convolutional neural network. Step S2 further comprises the following steps: S21: constructing a multi-scale spatiotemporal encoder, inputting the set of spatiotemporal coordinates into the multi-scale spatiotemporal encoder to obtain a basic spatiotemporal encoder; S22: introducing a capillary enhancement module to correct the capillary pressure in the multi-scale spatiotemporal encoder to obtain an optimized spatiotemporal encoder; S23: introducing an adaptive viscosity field based on time evolution into a momentum equation loss to obtain an optimized momentum equation loss; S24: establishing a physical constraint loss function based on the optimized momentum equation loss; S25: training the optimized spatiotemporal encoder by the physical constraint loss function to obtain an initial network model.

4. The method of claim 3, wherein the physical information neural network is trained using a dataset comprising a plurality of training examples, each training example comprising a set of physical information and a corresponding set of capillary wicking parameters. The expression for correcting the capillary pressure by the capillary enhancement module in step S22 is: where p capillary is the corrected capillary pressure, C cap is the capillary coefficient, z is the wicking height direction, ε z is a regularization parameter to avoid singularities; The expression for the adaptive viscosity field in step S23 is: wherein, is a phase field, t is time, is an adaptive viscosity field, μ water is a dynamic viscosity of water, μ air is a dynamic viscosity of air, sigmoid is a function used to simulate the effect of viscosity increase after saturation; The expression for the physical constraint loss function in step S24 is: L total = L momentum + L continuity + L phase + λ b · L boundary + λ i · L initial ; where L total is the physical constraint loss function, L momentum is the optimization momentum equation loss, L continuity is the continuity equation loss, L phase is the phase field equation loss, λ b is the boundary condition weight coefficient, L boundary is the boundary condition loss, λ i is the initial condition weight coefficient, L initial is the initial condition loss.

5. The method of claim 1, wherein, In step S3, the training stages for training and optimization include: A first training stage, wherein the physical stage of the capillary wicking process corresponding to the first training stage is a capillary dominant period; A second training stage, wherein the physical stage of the capillary wicking process corresponding to the second training stage is a transition period; A third training stage, wherein the physical stage of the capillary wicking process corresponding to the third training stage is a gravity dominant period.

6. The method of claim 5, wherein the physical information neural network is trained using a dataset comprising a plurality of training examples, each training example comprising a set of physical information and a corresponding set of capillary wicking parameters. Step S3 specifically comprises the following steps: When the training stage is the first training stage, the time resolution is set to 0.01s, and the loss weights in the loss function are set as follows: momentum equation weight coefficient 0.8, continuity equation weight coefficient 0.8, and phase field equation weight coefficient 0.2; When the training stage is the second training stage, the time resolution is set to 1s, and the loss weights in the loss function are set as follows: momentum equation weight coefficient 0.5, continuity equation weight coefficient 0.5, and phase field equation weight coefficient 0.5; When the training stage is the third training stage, the time resolution is set to 100s, and the loss weights in the loss function are set as follows: momentum equation weight coefficient 0.2, continuity equation weight coefficient 0.2, and phase field equation weight coefficient 0.

8.

7. The method of claim 1, wherein the physical information neural network is a convolutional neural network. Step S3 further comprises the following steps: Establishing a theoretical reference solution to verify the training and optimization of the initial network model by the theoretical reference solution.

8. The method of claim 7, wherein the physical information neural network is trained using a dataset comprising a plurality of training examples, each training example comprising a set of physical information and a corresponding set of capillary wicking parameters. The expression for the theoretical reference solution is: where h theory is the theoretical reference solution, t is time, r is the equivalent capillary radius, γ is the surface tension, θ is the contact angle, and μ is the chemical potential in the governing equation of the wicking problem.

9. The method of claim 1, wherein, The calculation result in step S4 includes pressure field values, velocity field values, and phase field values.

10. A physical information neural network-based capillary wicking parameter calculation system, characterized by, The method comprises the following steps: A sampling module for spatiotemporal sampling of the capillary wicking physical domain to obtain a set of spatiotemporal coordinates; The construction module is configured to construct a multi-scale space-time encoder based on the set of space-time coordinates, and construct a multi-scale space-time encoder based on time dependence and capillary enhancement, to obtain an initial network model. The training module is configured to perform multi-stage training optimization on the initial network model to obtain an optimized network model. The output module is configured to output the optimized network model obtained by the training module, and output a capillary wicking physical field parameter to be calculated to obtain a calculation result.

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