Migration simulation method, device and equipment for uranium-containing fluid and storage medium

Abstract

The invention discloses a uranium-containing fluid migration simulation method, a uranium-containing fluid migration simulation device, uranium-containing fluid migration simulation equipment and a storage medium, and relates to the technical field of digital uranium mine mining and metallurgy. The information of the current time step and the information of the next time step can be jointly used in the time iteration process, and therefore high solving precision and stability are achieved. The method comprises the following steps: describing a migration process of uranium-containing fluid in underground water by using a nonlinear partial differential equation set; iteratively solving the nonlinear partial differential equation set by using a pre-constructed time discretization physical information neural network to obtain prediction solutions at different set moments, and taking the solution of the current time step as input and the prediction solution of the next time step as output by the time discretization physical information neural network; and according to the prediction solutions at different set moments, determining the migration change of the uranium-bearing fluid in each time period so as to carry out migration simulation on the uranium-bearing fluid.

Description

Technical Field

[0001] The present application relates to the field of digital uranium mining and metallurgy technology, and in particular to a migration simulation method, device, equipment and storage medium for uranium-containing fluids. Background Art

[0002] As an important strategic mineral resource, uranium plays an irreplaceable role in the fields of energy production and nuclear energy technology. However, during the uranium exploration process, natural radioactive elements in the geological environment of uranium mines may induce secondary enrichment effects through groundwater migration, thereby posing a potential threat to regional ecological security and water resource sustainability. On the other hand, the migration of uranium-containing fluids can be used to infer the location of uranium deposits, clarify the focus of exploration work, thereby greatly improving the efficiency of prospecting and facilitating the efficient acquisition of uranium resources. Therefore, it is crucial to accurately simulate the migration process of uranium-containing fluids in groundwater. By simulating the migration path and range of uranium-containing fluids under different geological conditions, it is also possible to effectively evaluate their possible impact on the surrounding environment, providing a key basis for the coordinated promotion of subsequent resource development and environmental protection.

[0003] In related technologies, the migration simulation of uranium-containing fluids is usually described by a set of linear partial differential equations. Due to the complexity and uncertainty of geological conditions, such equations need to rely on numerical methods to achieve approximate solutions. Commonly used numerical methods include but are not limited to the finite element method, the finite difference method, and the finite volume method. The core idea of these methods is to convert continuous problems into discrete forms through meshing and discretization, and then obtain numerical solutions through iterative calculations. Although the above methods have shown good applicability in many scenarios, when dealing with complex boundary conditions, heterogeneous geological structures, and highly nonlinear problems, the complex geological conditions, chemical reaction characteristics of uranium, and the uncertainty of pollution sources will increase the difficulty of solution, making the meshing process require additional computational costs, and it is difficult to take into account both solution accuracy and computational efficiency. Summary of the Invention

[0004] In view of this, the present application provides a migration simulation method, device, equipment and storage medium for uranium-containing fluids. The main purpose is to solve the problem in the existing technology that complex geological conditions, chemical reaction characteristics of uranium and uncertainty of pollution sources increase the difficulty of solution, making the grid division process require additional computing costs, and it is difficult to take into account both solution accuracy and computing efficiency at the same time.

[0005] In a first aspect, a method for simulating the migration of a uranium-containing fluid is provided, the method comprising:

[0006] A system of nonlinear partial differential equations is used to describe the migration of uranium-bearing fluids in groundwater.

[0007] Iteratively solving the nonlinear partial differential equations using a pre-constructed time-discretized physical information neural network to obtain predicted solutions at different set times, wherein the time-discretized physical information neural network takes the solution of the current time step as input and the predicted solution of the next time step as output;

[0008] According to the prediction solutions at different set times, the migration changes of the uranium-containing fluid at different set times are determined to perform migration simulation on the uranium-containing fluid.

[0009] Furthermore, before using the pre-constructed time discretized physical information neural network to iteratively solve the nonlinear partial differential equations to obtain prediction solutions at different set times, the method further includes:

[0010] solving the solution of the nonlinear partial differential equations at the initial time by an analytical program;

[0011] Accordingly, the pre-built time discretized physical information neural network is used to iteratively solve the nonlinear partial differential equations to obtain prediction solutions at different set times, including:

[0012] Determining a target time series for solving the nonlinear partial differential equation system according to a preset time step;

[0013] The solution at the initial moment is input into a pre-constructed time-discretized physical information neural network, and the nonlinear partial differential equations are iteratively solved according to the target time series to obtain prediction solutions at different set moments.

[0014] Furthermore, the solution at the initial moment is input into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equations are iteratively solved according to the target time series to obtain prediction solutions at different set moments, including:

[0015] The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain a predicted solution for the next time step;

[0016] According to the target time series, different time steps are repeatedly iterated and solved until the last time step, and the prediction solutions at different set moments are obtained.

[0017] Furthermore, in the process of repeated iterative solutions for different time steps, the predicted solution of the next time step is input as the solution of the current time step into a pre-constructed time-discrete physical information neural network, and the nonlinear partial differential equations are iteratively solved to obtain the predicted solution of the next time step.

[0018] Furthermore, before inputting the solution at the initial moment as the solution of the current time step into a pre-constructed time discretization physical information neural network and iteratively solving the nonlinear partial differential equation system to obtain a predicted solution for the next time step, the method further includes:

[0019] A loss function is set according to an implicit discrete numerical calculation method, wherein the loss function is used to evaluate the degree of deviation of the predicted solution output by the neural network from the physical equation;

[0020] Accordingly, the solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain the predicted solution for the next time step, including:

[0021] The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain an intermediate solution;

[0022] Calculating the loss value of the intermediate solution during the iterative solution process according to a preset loss function;

[0023] If the loss value is greater than a set threshold, the parameters of the time-discretized physical information neural network are adjusted, and the nonlinear partial differential equation group is repeatedly iteratively solved using the time-discretized physical information neural network after parameter adjustment until the loss value is less than or equal to the set threshold, and the corresponding intermediate solution is used as the predicted solution for the next time step.

[0024] Furthermore, after using the pre-constructed time discretized physical information neural network to iteratively solve the nonlinear partial differential equations to obtain prediction solutions at different set times, the method further includes:

[0025] For the nonlinear partial differential equation system, calculating analytical solutions at different set times;

[0026] The analytical solutions at different set moments are compared with the predicted solutions at the corresponding set moments to evaluate the prediction performance of the time discretized physical information neural network.

[0027] Furthermore, determining the migration change of the uranium-containing fluid at different set times based on the prediction solutions at different set times to perform migration simulation on the uranium-containing fluid includes:

[0028] Determining the spatiotemporal variation information of physical quantities of the migration process of the uranium-containing fluid in the groundwater according to the prediction solutions at the different set moments;

[0029] The migration of the uranium-containing fluid is simulated based on the temporal and spatial variation information of the physical quantities during the migration of the uranium-containing fluid in the groundwater.

[0030] In a second aspect, a migration simulation device for a uranium-containing fluid is provided, the device comprising:

[0031] A description unit for describing the migration of uranium-bearing fluid in groundwater using a system of nonlinear partial differential equations;

[0032] a first solving unit, configured to iteratively solve the nonlinear partial differential equations using a pre-constructed time-discretized physical information neural network to obtain predicted solutions at different set moments, wherein the time-discretized physical information neural network takes the solution of the current time step as input and outputs the predicted solution of the next time step as output;

[0033] The determination unit is used to determine the migration changes of the uranium-containing fluid in each time period according to the prediction solutions at the different set moments, so as to perform migration simulation on the uranium-containing fluid.

[0034] Furthermore, the device further comprises:

[0035] a second solving unit, configured to solve the nonlinear partial differential equations at an initial time by an analytical program before iteratively solving the nonlinear partial differential equations by using the pre-constructed time discretized physical information neural network to obtain predicted solutions at different set times;

[0036] Accordingly, the first solving unit includes:

[0037] A determination module, configured to determine a target time series for solving the nonlinear partial differential equation system according to a preset time step;

[0038] A solution module is used to input the solution at the initial moment into a pre-built time-discretized physical information neural network, iteratively solve the nonlinear partial differential equations according to the target time series, and obtain predicted solutions at different set moments.

[0039] Furthermore, the solution module is specifically used to:

[0040] The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain a predicted solution for the next time step;

[0041] According to the target time series, different time steps are repeatedly iterated and solved until the last time step, and the prediction solutions at different set moments are obtained.

[0042] Furthermore, in the process of repeated iterative solutions for different time steps, the predicted solution of the next time step is input as the solution of the current time step into a pre-constructed time-discrete physical information neural network, and the nonlinear partial differential equations are iteratively solved to obtain the predicted solution of the next time step.

[0043] Furthermore, the first solving unit further includes:

[0044] a setting module for setting a loss function according to an implicit discrete numerical calculation method before inputting the solution at the initial moment as the solution of the current time step into a pre-constructed time-discretized physical information neural network and iteratively solving the nonlinear partial differential equation system to obtain a predicted solution for the next time step, wherein the loss function is used to evaluate the degree of deviation of the predicted solution output by the neural network from the physical equation;

[0045] Accordingly, the solution module is further configured to:

[0046] The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain an intermediate solution;

[0047] Calculating the loss value of the intermediate solution during the iterative solution process according to a preset loss function;

[0048] If the loss value is greater than a set threshold, the parameters of the time-discretized physical information neural network are adjusted, and the nonlinear partial differential equation group is repeatedly iteratively solved using the time-discretized physical information neural network after parameter adjustment until the loss value is less than or equal to the set threshold, and the corresponding intermediate solution is used as the predicted solution for the next time step.

[0049] Furthermore, the device further comprises:

[0050] a computing unit configured to calculate analytical solutions at different set times for the nonlinear partial differential equations after iteratively solving the nonlinear partial differential equations using the pre-constructed time-discretized physical information neural network to obtain predicted solutions at different set times;

[0051] A comparison unit is used to compare the analytical solutions at different set moments with the predicted solutions at corresponding set moments to evaluate the prediction performance of the time discretized physical information neural network.

[0052] Furthermore, the determining unit is specifically configured to:

[0053] Determining the spatiotemporal variation information of physical quantities of the migration process of the uranium-containing fluid in the groundwater according to the prediction solutions at the different set moments;

[0054] The migration of the uranium-containing fluid is simulated based on the temporal and spatial variation information of the physical quantities during the migration of the uranium-containing fluid in the groundwater.

[0055] In a third aspect, a storage medium is provided, on which a computer program is stored, and when the program is executed by a processor, the above-mentioned migration simulation method of uranium-containing fluid is implemented.

[0056] In a fourth aspect, a migration simulation device for uranium-containing fluid is provided, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, wherein the processor implements the above-mentioned migration simulation method for uranium-containing fluid when executing the program.

[0057] By leveraging the above-mentioned technical solution, the present application provides a method, apparatus, device, and storage medium for simulating the migration of uranium-containing fluids. Compared to current numerical methods for simulating the migration of uranium-containing fluids, the present application uses a system of nonlinear partial differential equations to describe the migration of uranium-containing fluids in groundwater. A pre-constructed time-discretized physical information neural network is used to iteratively solve the nonlinear partial differential equations to obtain predicted solutions at different set times. The time-discretized physical information neural network uses the solution at the current time step as input and the predicted solution at the next time step as output. Based on the predicted solutions at different set times, the migration changes of the uranium-containing fluid within each time period are determined to simulate the migration of the uranium-containing fluid. The entire process dynamically solves the predicted solutions of the nonlinear partial differential equations at different times using the time-discretized physical information neural network. Because the time-discretized physical information neural network model has second-order accuracy, it can combine information from the current and next time steps in the time iteration process, thereby achieving high solution accuracy and stability. Here, the time-discretized physical information neural network directly uses the solution of the current time step as input, without the need for additional loss terms to enforce the initial conditions. It then iterates the calculations on this basis to achieve progressive solutions for multiple time steps, effectively reducing the computational burden and effectively capturing changes in the equation solution during the time evolution process, thereby improving computational efficiency.

[0058] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0060] Figure 1 1 is a flow chart of a method for simulating migration of uranium-containing fluid in one embodiment of the present application;

[0061] Figure 2 is a schematic flow chart of a method for simulating migration of uranium-containing fluid in another embodiment of the present application;

[0062] Figure 3 yes Figure 2 A schematic flow chart of a specific implementation of step 203;

[0063] Figure 4 yes Figure 2 Another specific implementation flow diagram of step 203;

[0064] Figure 5 This is a structural block diagram of a time-discretized physical information neural network in one embodiment of the present application;

[0065] Figure 6 A schematic flow chart of a method for simulating migration of uranium-containing fluids in another embodiment of the present application;

[0066] Figure 7 Figure 1 A schematic flow chart of a specific implementation of step 103;

[0067] Figure 8 1 is a schematic structural diagram of a migration simulation device for uranium-containing fluid in one embodiment of the present application;

[0068] Figure 9 The figure is a schematic diagram of the device structure of a computer device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0069] The present application will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be noted that, unless there is a conflict, the embodiments and features in the embodiments of the present application can be combined with each other.

[0070] In related technologies, the migration simulation of uranium-containing fluids is usually described by a set of linear partial differential equations. Due to the complexity and uncertainty of geological conditions, such equations need to rely on numerical methods to achieve approximate solutions. Commonly used numerical methods include but are not limited to the finite element method, the finite difference method, and the finite volume method. The core idea of these methods is to convert continuous problems into discrete forms through meshing and discretization, and then obtain numerical solutions through iterative calculations. Although the above methods have shown good applicability in many scenarios, when dealing with complex boundary conditions, heterogeneous geological structures, and highly nonlinear problems, the complex geological conditions, chemical reaction characteristics of uranium, and the uncertainty of pollution sources will increase the difficulty of solution, making the meshing process require additional computational costs, and it is difficult to take into account both solution accuracy and computational efficiency.

[0071] In order to solve this problem, this embodiment provides a migration simulation method of uranium-containing fluid, such as Figure 1 As shown, the following steps are included:

[0072] 101. Use a set of nonlinear partial differential equations to describe the migration process of uranium-containing fluid in groundwater.

[0073] The migration of uranium-containing fluids in groundwater is generally complex. On one hand, the migration process involves factors such as uranium adsorption and desorption, as well as chemical reactions, which are nonlinearly related to factors such as concentration. Furthermore, the heterogeneity of the subsurface medium leads to different fluid flow and solute transport characteristics in different regions, and fluid flow and solute transport are mutually coupled. These nonlinear factors involve multiple interrelated physical quantities and complex physicochemical mechanisms, requiring a system of nonlinear partial differential equations to accurately describe the migration process and reflect the complex temporal and spatial variations of these physical quantities.

[0074] Specifically, the migration of uranium-bearing fluids is controlled by multiscale seepage dynamics, with their migration paths governed by differential permeability within the fracture network. Particularly within the well-developed interlayer oxidation zones, the viscosity changes triggered by phase transitions lead to significant spatiotemporal characteristics in the migration rate, meaning that the flow velocity of the uranium-bearing fluid can be simplified as u(x, t). Furthermore, the migration of uranium-bearing fluids is also constrained by the three-dimensional pore structure. Under the combined effects of capillary forces and displacement pressure, the flow of uranium-bearing fluids within the sandstone pores within this block exhibits non-Darcy flow characteristics, which can be described using nonlinear partial differential equations. Under one-dimensional conditions, this nonlinear partial differential equation can be described using a 2-meter region within the block where the velocity variation is most pronounced, with two segments marked as -1 m and 1 m, representing the starting and ending points of the uranium-bearing fluid flow within this region. At the initial time t = 0 s, the velocity distribution of the uranium-bearing fluid can be described by the sine function -sin(πx). The velocity is always zero in both segments of the uranium-bearing fluid, which can be described using boundary conditions.

[0075] Accordingly, the seepage process of uranium-bearing fluid in this area can be described by the following equations:

[0076]

[0077] In the above equations, the one-dimensional nonlinear partial differential equation consists of two parts, including the convection term and diffusion terms u(x, t) represents the flow velocity of the uranium-containing fluid at time t and spatial position x, and the viscosity coefficient ν is taken as 0.01π to characterize the diffusion effect.

[0078] 102. Utilize a pre-built time-discretized physical information neural network to iteratively solve the nonlinear partial differential equations to obtain prediction solutions at different set times.

[0079] A physical-information neural network is a neural network method that incorporates physical information and is widely used to solve linear and nonlinear partial differential equations and other problems involving physical constraints. By incorporating physical laws as constraints into the network's loss function, the network's output not only conforms to the data characteristics but also follows physical laws. Unlike traditional numerical methods, this method avoids reliance on complex grids and can effectively solve nonlinear partial differential equations without meshing. Specifically, the core idea of a physical-information neural network is to introduce physical laws into the neural network's loss function, which typically includes the residual term, boundary conditions, and initial condition loss terms for the nonlinear partial differential equations. By training the network to minimize the loss function, the physical-information neural network can learn the solution to the nonlinear partial differential equations.

[0080] It should be noted that the above-mentioned method uses iterative advancement to achieve multi-step time evolution prediction, and can maintain high accuracy and numerical stability at long time step sizes. This not only improves computational efficiency but also effectively handles the problem of solving nonlinear partial differential equations. However, the above-mentioned numerical method requires the use of a high number of stages for iterative solution. Considering the high requirements of the iterative advancement process on the generalization ability of the network, high-order methods lack practical value in engineering applications, resulting in a waste of computational resources. In practical application scenarios, implicit discretization numerical methods can be selected to solve nonlinear partial differential equations. The implicit discretization numerical method here has high stability and second-order accuracy in the process of solving nonlinear partial differential equations. Combining the advantages of explicit and implicit numerical methods, it can provide more accurate numerical solutions.

[0081] In this embodiment, the time-discretized physical information neural network is equivalent to applying the implicit discrete numerical method to the physical information neural network to solve the nonlinear partial differential equation problem. Here, the implicit discrete numerical method can use the Crank-Nicolson implicit discrete method, and the corresponding time-discretized physical information neural network is a physical information neural network constructed based on the Crank-Nicolson discrete format.

[0082] For the general form of nonlinear partial differential equations, the implicit discretization numerical method can be expressed as follows after discretizing time:

[0083]

[0084] Among them, u n and u n+1 Respectively represent the time t n and tn+1 The solution on , Δt is the time step, λ is the parameter of the nonlinear partial differential equation, is the nonlinear differential operator corresponding to the parameter λ at the nth time step, which can be regarded as the known term on the right side of the equation. is the nonlinear differential operator with the parameter λ corresponding to the n+1th time step, which can be considered as the known term on the right side of the equation. When solving nonlinear partial differential equations, taking the intermediate differences of the time derivatives and combining the solutions at the current and next moments can yield a more accurate solution. The above formula can be expressed as follows:

[0085]

[0086] It can be understood that the implicit discretization numerical method is second-order accurate, can approximate the actual solution with a certain accuracy, and has numerical stability. It can maintain stability at a large time step, avoiding the stability limitations of the explicit method.

[0087] Specifically, the time-discretized physical information neural network uses the solution of the current time step as input and the predicted solution of the next time step as output during the iterative solution of a system of nonlinear partial differential equations. This allows the time-discretized physical information neural network to directly use the solution corresponding to the spatial coordinates at the initial moment as part of the network, eliminating the need for additional loss terms to constrain the initial conditions, thereby effectively reducing the computational burden. The predicted solution of the previous time step is then input into the time-discretized physical information neural network as the solution for the current time step. Iterative calculations are then performed on this basis, achieving progressive solutions for multiple time steps and obtaining predicted solutions at different set moments. This not only enables the network to make predictions across multiple time steps, but also effectively captures changes in the equation solution over time.

[0088] 103. Determine the migration changes of the uranium-containing fluid in each time period based on the prediction solutions at the different set moments, so as to perform migration simulation on the uranium-containing fluid.

[0089] In this embodiment, the set time can be customized, corresponding to the time setting of the time step within the time interval. For example, if the time interval starts at t = 0.0s and the total time span is 1s, then for solving 20 time steps, the set time of the time step is 0.05s. In other words, by setting different time steps for the nonlinear partial differential equation system, predicted solutions at different set times can be obtained. Accordingly, the migration of the uranium-containing fluid within the corresponding time period can be simulated based on the predicted solutions at different set times.

[0090] Specifically, the prediction solutions at different set times allow us to obtain physical quantity data related to the uranium-containing fluid, such as concentration and velocity, corresponding to each spatial grid point. These physical quantity data corresponding to each spatial grid point are then arranged in chronological order to construct a physical quantity dataset for the uranium-containing fluid. Furthermore, based on this physical quantity dataset, a migration simulation of the uranium-containing fluid is performed. This migration simulation involves two aspects: first, analyzing the migration position of the uranium-containing fluid based on the physical quantity dataset; second, analyzing the concentration distribution of the uranium-containing fluid based on this physical quantity dataset.

[0091] The aforementioned migration position analysis process can utilize a centroid calculation method. Specifically, for each time point, the centroid position can be calculated based on the concentration distribution of the uranium-containing fluid. By comparing the centroid positions, the overall migration direction and velocity of the uranium-containing fluid can be determined. Alternatively, a boundary tracking method can be employed. Specifically, a concentration threshold is set. When the concentration of a grid point exceeds this threshold, the point is considered to be within the uranium-containing fluid range. The boundary grid points of the uranium-containing fluid region at each time point are identified. By connecting these boundary points, the boundary contour of the uranium-containing fluid is obtained. By comparing the boundary contours at different times, changes in the migration range of the uranium-containing fluid can be determined.

[0092] Statistical analysis can be used during the aforementioned concentration distribution analysis. Specifically, concentration data at each time point is analyzed to calculate statistical quantities such as the mean, median, and standard deviation. The mean reflects the overall concentration level, while the standard deviation reflects the dispersion of concentration. By observing the changes in these statistics over time, the overall trend and fluctuation of the uranium-bearing fluid concentration can be determined. Concentration profile analysis can also be used. Specifically, a specific profile, such as a horizontal or vertical profile, can be selected and concentration curves plotted at different time points along that profile. This allows for a visual visualization of the concentration distribution along that profile and its evolution over time, such as the shift in the concentration peak and changes in the concentration gradient. Concentration contour plotting can also be used. Specifically, specialized plotting software can be used to create concentration contour maps based on concentration data at different time points. Concentration contours connect points of equal concentration. By observing the shape, density, and position of these contours, the spatial distribution of the uranium-bearing fluid concentration and its temporal evolution can be clearly determined.

[0093] It should be noted that the migration simulation method of uranium-containing fluid provided in the embodiment of the present invention has the advantages of grid-free, physical constraints and time discrete accuracy. It is suitable for groundwater and solute migration modeling scenarios under strong nonlinear coupling and multi-scale conditions, and is particularly suitable for environmental impact assessment and safety prediction in the process of in-situ leaching uranium mining.

[0094] The migration simulation method for uranium-containing fluids provided in the embodiments of the present application, compared to the current method of solving uranium-containing fluid migration simulations using numerical methods, uses a system of nonlinear partial differential equations to describe the migration process of uranium-containing fluids in groundwater. A pre-constructed time-discretized physical information neural network is used to iteratively solve the nonlinear partial differential equations to obtain predicted solutions at different set times. The time-discretized physical information neural network uses the solution of the current time step as input and the predicted solution of the next time step as output. Based on the predicted solutions at different set times, the migration changes of the uranium-containing fluid in each time period are determined to simulate the migration of the uranium-containing fluid. The entire process dynamically solves the predicted solutions of the nonlinear partial differential equations at different times using the time-discretized physical information neural network. Because the time-discretized physical information neural network model has second-order accuracy, it can combine the information of the current time step and the next time step in the time iteration process, thereby achieving high solution accuracy and stability. Here, the time-discretized physical information neural network directly uses the solution of the current time step as input, without the need for additional loss terms to enforce the initial conditions. It then iterates the calculations on this basis to achieve progressive solutions for multiple time steps, effectively reducing the computational burden and effectively capturing changes in the equation solution during the time evolution process, thereby improving computational efficiency.

[0095] In practical application scenarios, considering that the time-discretized physical information neural network uses the solution of the current time step as input to iteratively solve the nonlinear partial differential equations, for the initial time step, the analytical solution obtained by data derivation and calculation can be input into the time-discretized physical information neural network as the solution at the initial moment. Further, as Figure 2 As shown, before step 102, the method further includes the following steps:

[0096] 201. Solve the solution of the nonlinear partial differential equations at the initial time by an analytical program.

[0097] Accordingly, step 102 includes the following steps:

[0098] 202. Determine a target time series for solving the nonlinear partial differential equation system according to a preset time step.

[0099] 203. Input the solution at the initial moment into a pre-constructed time-discretized physical information neural network, iteratively solve the nonlinear partial differential equations according to the target time series, and obtain prediction solutions at different set moments.

[0100] In this embodiment, the analytical program is equivalent to a method or process for solving a system of nonlinear partial differential equations. The analytical program may not be a set of specific codes, but a series of steps and operations based on mathematical principles and logic, with the purpose of finding the solution to the system of equations through specific algorithms and methods.

[0101] It's understandable that when solving nonlinear partial differential equations, the target time series, as each tiny time step of the discretized time variable, can transform a continuous time problem into a problem to be solved in a series of discrete time steps. The more time steps in the target time series, the more iterations are required, and the corresponding set time is larger.

[0102] Specifically, in the above embodiment, Figure 3 As shown, step 203 includes the following steps:

[0103] 301. The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equations are iteratively solved to obtain a predicted solution for the next time step.

[0104] 302. According to the target time series, the iterative solution is repeated for different time steps until the last time step, and the prediction solution for different set moments is obtained.

[0105] In the process of repeatedly iteratively solving different time steps, this embodiment uses the predicted solution of the next time step as the solution of the current time step and inputs it into a pre-constructed time-discretized physical information neural network, and iteratively solves the nonlinear partial differential equation group to obtain the predicted solution of the next time step.

[0106] For example, in the process of solving the first time step, the analytical solution u0 is input into the time-discretized physical information neural network, and the nonlinear partial differential equation group is iteratively solved to obtain the predicted solution u1 of the second time step. Then, in the process of solving the second time step, the predicted solution u1 is input into the time-discretized physical information neural network, and the nonlinear partial differential equation group is iteratively solved to obtain the predicted solution u2 of the third time step. In the process of solving the third time step, the predicted solution u2 is input into the time-discretized physical information neural network, and the nonlinear partial differential equation group is iteratively solved to obtain the predicted solution u2 of the fourth time step. And so on, until the iterative time step reaches the set time step, the predicted solutions for different set times are obtained according to the predicted solution of the next time step corresponding to the set time step.

[0107] Taking into account the consistency between the time-discretized physical information neural network and the actual physical behavior, the loss value calculated by the loss function can be used to reflect the accuracy of the time-discretized physical information neural network, and the parameters of the time-discretized physical information neural network can be adjusted according to the gradient of the loss function, so that the time-discretized physical information neural network can more accurately approximate the analytical solution of the nonlinear partial differential equation system in the subsequent iterative process. Further, as Figure 4As shown, before step 301, the method further includes the following steps:

[0108] 401. Set the loss function according to the implicit discrete numerical calculation method.

[0109] Accordingly, step 301 includes the following steps:

[0110] 402. The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equations are iteratively solved to obtain an intermediate solution.

[0111] 403. Calculate the loss value of the intermediate solution during the iterative solution process according to a preset loss function.

[0112] 404. If the loss value is greater than a set threshold, the parameters of the time-discretized physical information neural network are adjusted, and the nonlinear partial differential equations are repeatedly solved iteratively using the time-discretized physical information neural network after parameter adjustment until the loss value is less than or equal to the set threshold, and the corresponding intermediate solution is used as the predicted solution for the next time step.

[0113] In this embodiment, a loss function is used to evaluate the degree of deviation of the predicted solution output by the neural network from the physical equation. Specifically, during the training process of each time step, the parameters of the time-discretized physical information neural network can be optimized by minimizing the loss function. If the loss value is greater than a set threshold, it means that the intermediate solution output at the current time step does not meet the equation residual requirements, and the parameters of the time-discretized physical information neural network need to be adjusted. The time-discretized physical information neural network with adjusted parameters is used to repeat the process of iteratively solving the nonlinear partial differential equation system until the loss value is less than or equal to the set threshold, and the corresponding intermediate solution is used as the predicted solution for the next time step.

[0114] For example, in the current time step, the loss value is calculated based on the intermediate solution output by the first iteration. If the loss value calculated by the first iteration is greater than the set threshold, the parameters of the time-discretized physical information neural network are adjusted, and the nonlinear partial differential equation is repeatedly solved for the second iteration. Then, the loss value is calculated based on the intermediate solution output by the second iteration. If the loss value calculated by the second iteration is still greater than the set threshold, the parameters of the time-discretized physical information neural network are continued to be adjusted, and the nonlinear partial differential equation is repeatedly solved for the third iteration. Then, the loss value is calculated based on the intermediate solution output by the third iteration. If the loss value calculated by the third iteration is less than the set threshold, the intermediate solution output by the third iteration is used as the predicted solution for the next time step.

[0115] In practical application scenarios, the structure of the time-discrete physical information neural network is as follows: Figure 5As shown, in Figure 5 In the example, the loss function set for the time-discretized physical information neural network can be expressed as: loss = MSE n , where MSE n is the residual of the equation, which can be expressed as follows:

[0116]

[0117]

[0118] Where n is the number of samples, i is the spatial coordinate x i The index of u n，i and u n+1，i Respectively represent the time t n and t n+1 The solution on , Δt is the time step, λ is the parameter of the nonlinear partial differential equation, is the nonlinear differential operator corresponding to the parameter λ at the nth time step, which can be regarded as the known term on the right side of the equation. is the nonlinear differential operator corresponding to the parameter λ at the n+1th time step, which can be regarded as the known term on the right side of the equation.

[0119] Correspondingly, after the training is completed, the predicted solution output by the time-discretized physical information neural network will serve as the new input for the next time step. In this way, the training and prediction of multi-step time evolution can be realized through transfer learning and iterative advancement, so that the time-discretized physical information neural network not only completes the single-step solution, but also realizes the complete dynamic solution through the progressive time step.

[0120] It is understandable that the time-discrete physical information neural network usually incorporates physical information into the model. In order to ensure that the solution conforms to the physical laws, the analytical solution obtained by theoretical derivation can be compared with the predicted solution to verify whether the time-discrete physical information neural network has correctly learned and utilized this physical information. Figure 6 As shown, after step 102, the method further includes the following steps:

[0121] 501. Calculate analytical solutions at different set times for the nonlinear partial differential equations.

[0122] 502. Compare the analytical solutions at different set moments with the predicted solutions at corresponding set moments to evaluate the prediction performance of the time discretized physical information neural network.

[0123] In this embodiment, numerical comparison can be used to compare the analytical solutions at different set times with the predicted solutions at the corresponding set times. If the predicted solution is not only numerically close to the analytical solution but also physically conforms to the relevant physical laws and constraints, it indicates that the integration of physical information is effective. Conversely, if the predicted solution is not numerically close to the analytical solution, it indicates that the prediction process violates the laws of physics. It is necessary to check whether the integration of physical information is correct and whether the time-discretized physical information neural network has a misunderstanding of physical concepts.

[0124] In this embodiment, the comparison of the analytical solutions at different set times with the predicted solutions at the corresponding set times may be a statistical comparison of physical quantities. For example, statistical quantities such as the mean and variance of the analytical solution and the predicted solution at different time points may be calculated. By comparing the means, the average level of the analytical solution and the predicted solution can be determined, and by comparing the variances, the degree of dispersion of the analytical solution and the predicted solution can be determined.

[0125] In actual application scenarios, referring to the content in step 101, the migration process of uranium-containing fluid in groundwater can be described as the following nonlinear partial differential equations:

[0126]

[0127] In the above system of equations, since the one-dimensional nonlinear partial differential equation contains both nonlinear convection and linear diffusion terms, it can describe the changes in the concentration and flow rate of uranium-containing fluids. It is particularly suitable for scenarios considering the dual effects of convection and diffusion. The corresponding analytical solution can be expressed as follows:

[0128]

[0129] Here, η is the integral variable of the spatially varying quantity. The analytical solution here shows that the waveform of the solution changes over time and is influenced by both initial and boundary conditions. This analytical solution provides a reference for the subsequent training and solution of the time-discretized physical information neural network. Accordingly, after applying the time-discretized physical information neural network for numerical solution, the predicted solution can be compared with the analytical solution to evaluate the accuracy and stability of the time-discretized physical information neural network.

[0130] Specifically, the time-discretized physical information neural network can learn the solution of one-dimensional nonlinear partial differential equations through the input initial conditions and boundary conditions. In this way, by minimizing the loss function to optimize the parameters of the time-discretized physical information neural network, a numerical solution that conforms to the laws of physics can be obtained.

[0131] Specifically, in this embodiment, Figure 7 As shown, step 103 includes the following steps:

[0132] 601. Determine the spatiotemporal variation information of physical quantities of the migration process of the uranium-containing fluid in the groundwater based on the prediction solutions at the different set moments.

[0133] 602. Perform migration simulation on the uranium-containing fluid based on the spatiotemporal variation information of physical quantities during the migration of the uranium-containing fluid in the groundwater.

[0134] In this embodiment, the physical quantities of the migration process of uranium-containing fluid in groundwater may include but are not limited to the concentration of uranium-containing fluid, groundwater flow rate, pressure, temperature and other spatiotemporal variation information, including spatial variation information and temporal variation information of the physical quantities of the migration process of uranium-containing fluid in groundwater.

[0135] The spatial variation information of the physical quantities of the migration process of specific uranium-containing fluids in groundwater can be used to simulate the migration of uranium-containing fluids through spatial distribution mapping, contour analysis and specific position detection.

[0136] During spatial distribution mapping, the predicted solution at each set moment can be visualized, with the distribution of physical quantities visualized using color coding to represent their magnitudes. By plotting the graphs at different time points, the diffusion range of uranium-bearing fluids in the underground space and the location of high and low concentration zones can be determined.

[0137] During contour analysis, contour lines of physical quantities are drawn to connect points with identical values. By analyzing the shape, density, and positional movement of contour lines over time, the spatial trend and gradient distribution of the physical quantity can be determined. For example, areas with dense contour lines indicate dramatic changes in the physical quantity, possibly due to large concentration gradients or rapid changes in flow rate.

[0138] During the detection process at specific locations, key spatial locations can be selected, such as the entrance and exit of groundwater flow, near possible pollution sources, and areas with large changes in geological structure. The changes in physical quantities at these locations over time can be recorded. By comparing the values of physical quantities at these specific locations at different time points, the changing patterns of physical quantities in local areas, as well as the differences and connections in the changes of physical quantities between different locations, can be analyzed.

[0139] The time variation information of the physical quantities of the migration process of specific uranium-containing fluid in groundwater can be used to simulate the migration of uranium-containing fluid through time series analysis, change rate calculation and characteristic time analysis.

[0140] During time series analysis, for each spatial location or region, a sequence of changes in a physical quantity over time can be extracted. This can then be plotted as a time-varying curve, with time plotted on the horizontal axis and the value of the quantity plotted on the vertical axis. By observing the trajectory of this curve, characteristics such as the rate of change of the quantity at different time stages, its upward or downward trends, and the presence of periodic variations can be analyzed. For example, a concentration-time curve can be used to determine how uranium-containing fluids diffuse in groundwater over time, whether they gradually stabilize or exhibit fluctuations.

[0141] In the process of calculating the rate of change, the speed of change of a physical quantity between adjacent time points, i.e., the time derivative, can be calculated to determine the speed of change and the acceleration of the change. A larger rate of change may indicate that the physical process is more active at that time or location, such as the rapid dilution of uranium-bearing fluids by groundwater flow or the rapid dissolution of uranium-bearing minerals, resulting in dramatic concentration changes.

[0142] In the process of characteristic time analysis, the stages and timeliness of the migration process of uranium-containing fluids in groundwater can be described by finding the characteristic times in the process of changes in physical quantities. By comparing the characteristic times in different spatial locations, the differences in the progress speed of physical processes in different areas and the impact of such differences on the entire migration process can be determined.

[0143] Furthermore, as a specific implementation of the above method, the present application embodiment provides a migration simulation device for uranium-containing fluid, such as Figure 8 As shown, the device includes: a description unit 71, a first solving unit 72 and a determination unit 73.

[0144] A description unit 71 for describing the migration process of uranium-containing fluid in groundwater using a system of nonlinear partial differential equations;

[0145] a first solving unit 72 for iteratively solving the nonlinear partial differential equations using a pre-constructed time-discretized physical information neural network to obtain predicted solutions at different set moments, wherein the time-discretized physical information neural network takes the solution of the current time step as input and outputs the predicted solution of the next time step as output;

[0146] The determination unit 73 is configured to determine the migration changes of the uranium-containing fluid in each time period according to the prediction solutions at the different set moments, so as to perform migration simulation on the uranium-containing fluid.

[0147] The uranium-containing fluid migration simulation device provided in an embodiment of the present invention, compared to current methods of simulating the migration of uranium-containing fluids through numerical solutions, uses a system of nonlinear partial differential equations to describe the migration of uranium-containing fluids in groundwater. A pre-constructed time-discretized physical information neural network is used to iteratively solve the nonlinear partial differential equations to obtain predicted solutions at different set times. The time-discretized physical information neural network uses the solution at the current time step as input and the predicted solution at the next time step as output. Based on the predicted solutions at different set times, the migration changes of the uranium-containing fluid within each time period are determined to simulate the migration of the uranium-containing fluid. The entire process dynamically solves the predicted solutions of the nonlinear partial differential equations at different times through the time-discretized physical information neural network. Because the time-discretized physical information neural network model has second-order accuracy, it can combine information from the current and next time steps in the time iteration process, thereby achieving high solution accuracy and stability. Here, the time-discretized physical information neural network directly uses the solution of the current time step as input, without the need for additional loss terms to enforce the initial conditions. It then iterates the calculations on this basis to achieve progressive solutions for multiple time steps, effectively reducing the computational burden and effectively capturing changes in the equation solution during the time evolution process, thereby improving computational efficiency.

[0148] In a specific application scenario, the device further includes:

[0149] a second solving unit, configured to solve the nonlinear partial differential equations at an initial time by an analytical program before iteratively solving the nonlinear partial differential equations by using the pre-constructed time discretized physical information neural network to obtain predicted solutions at different set times;

[0150] Accordingly, the first solving unit includes:

[0151] A determination module, configured to determine a target time series for solving the nonlinear partial differential equation system according to a preset time step;

[0152] A solution module is used to input the solution at the initial moment into a pre-built time-discretized physical information neural network, iteratively solve the nonlinear partial differential equations according to the target time series, and obtain predicted solutions at different set moments.

[0153] In a specific application scenario, the solution module is specifically used to:

[0154] The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain a predicted solution for the next time step;

[0155] According to the target time series, different time steps are repeatedly iterated and solved until the last time step, and the prediction solutions at different set moments are obtained.

[0156] In a specific application scenario, in the process of repeated iterative solutions for different time steps, the predicted solution of the next time step is input as the solution of the current time step into a pre-constructed time-discrete physical information neural network, and the nonlinear partial differential equation group is iteratively solved to obtain the predicted solution for the next time step.

[0157] In a specific application scenario, the first solving unit further includes:

[0158] a setting module for setting a loss function according to an implicit discrete numerical calculation method before inputting the solution at the initial moment as the solution of the current time step into a pre-constructed time-discretized physical information neural network and iteratively solving the nonlinear partial differential equation system to obtain a predicted solution for the next time step, wherein the loss function is used to evaluate the degree of deviation of the predicted solution output by the neural network from the physical equation;

[0159] Accordingly, the solution module is further configured to:

[0160] The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain an intermediate solution;

[0161] Calculating the loss value of the intermediate solution during the iterative solution process according to a preset loss function;

[0162] If the loss value is greater than a set threshold, the parameters of the time-discretized physical information neural network are adjusted, and the nonlinear partial differential equation group is repeatedly iteratively solved using the time-discretized physical information neural network after parameter adjustment until the loss value is less than or equal to the set threshold, and the corresponding intermediate solution is used as the predicted solution for the next time step.

[0163] In a specific application scenario, the device further includes:

[0164] a computing unit configured to calculate analytical solutions at different set times for the nonlinear partial differential equations after iteratively solving the nonlinear partial differential equations using the pre-constructed time-discretized physical information neural network to obtain predicted solutions at different set times;

[0165] A comparison unit is used to compare the analytical solutions at different set moments with the predicted solutions at corresponding set moments to evaluate the prediction performance of the time discretized physical information neural network.

[0166] In a specific application scenario, the determining unit is specifically configured to:

[0167] Determining the spatiotemporal variation information of physical quantities of the migration process of the uranium-containing fluid in the groundwater according to the prediction solutions at the different set moments;

[0168] The migration of the uranium-containing fluid is simulated based on the temporal and spatial variation information of the physical quantities during the migration of the uranium-containing fluid in the groundwater.

[0169] Based on the above Figure 1-Figure 7 The method shown in FIG. 1 is a method for performing the above-mentioned operation. Accordingly, the embodiment of the present application further provides a storage medium on which a computer program is stored. When the program is executed by a processor, the above-mentioned operation is performed. Figure 1-Figure 7 The migration simulation method of uranium-containing fluid is shown.

[0170] Based on this understanding, the technical solution of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, USB flash drive, mobile hard disk, etc.), including a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute the methods described in each implementation scenario of the present application.

[0171] Based on the above Figure 1-Figure 7 The method shown, and Figure 8 In order to achieve the above-mentioned purpose, the embodiment of the virtual device shown in the embodiment of the present application also provides a physical device for simulating the migration of uranium-containing fluid, which can be a computer, a smart phone, a tablet computer, a smart watch, a server, or a network device, etc. The physical device includes a storage medium and a processor; the storage medium is used to store a computer program; the processor is used to execute the computer program to achieve the above-mentioned Figure 1-Figure 7 The migration simulation method of uranium-containing fluid is shown.

[0172] Optionally, the physical device may further include a user interface, a network interface, a camera, a radio frequency (RF) circuit, a sensor, an audio circuit, a Wi-Fi module, etc. The user interface may include a display, an input unit such as a keyboard, etc., and the optional user interface may also include a USB interface, a card reader interface, etc. The network interface may optionally include a standard wired interface, a wireless interface (such as a Wi-Fi interface), etc.

[0173] In an exemplary embodiment, see Figure 9The physical device includes a communication bus, a processor, a memory, and a communication interface. It may also include an input / output interface and a display device. The various functional units can communicate with each other via the bus. The memory stores a computer program, and the processor is configured to execute the program stored in the memory and perform the uranium-containing fluid migration simulation method described in the above embodiment.

[0174] Those skilled in the art will understand that the physical device structure for simulating the migration of uranium-containing fluid provided in this embodiment does not constitute a limitation on the physical device, and may include more or fewer components, or a combination of certain components, or different component arrangements.

[0175] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages the hardware and software resources of the physical device used for the uranium-containing fluid migration simulation, supporting the execution of information processing programs and other software and / or programs. The network communication module is used to facilitate communication between components within the storage medium and with other hardware and software within the physical information processing device.

[0176] Through the description of the above implementation methods, those skilled in the art can clearly understand that the present application can be implemented with the help of software plus the necessary general hardware platform, or it can be implemented through hardware. By applying the technical solution of the present application, compared with the current existing methods, the present application dynamically solves the predicted solutions of the nonlinear partial differential equations at different times through a time-discretized physical information neural network. Since the time-discretized physical information neural network model has second-order accuracy, it can combine the information of the current time step with the next time step in the time iteration process, thereby achieving higher solution accuracy and stability. Here, the time-discretized physical information neural network directly uses the solution of the current time step as input, without the need to force the initial conditions to be constrained by additional loss terms, and iterates the calculation on this basis to achieve progressive solution of multiple time steps, effectively reducing the computational burden, and can also effectively capture the changes in the equation solution during the time evolution process, thereby improving computational efficiency.

[0177] Those skilled in the art will understand that the accompanying drawings are only schematic diagrams of a preferred implementation scenario, and the modules or processes in the accompanying drawings are not necessarily required to implement the present application. Those skilled in the art will understand that the modules in the devices in the implementation scenario can be distributed in the devices of the implementation scenario according to the implementation scenario description, or can be changed accordingly and located in one or more devices different from the implementation scenario. The modules of the above-mentioned implementation scenario can be combined into one module, or can be further split into multiple sub-modules.

[0178] The serial numbers of the above application are for descriptive purposes only and do not represent the advantages or disadvantages of the implementation scenarios. The above disclosure only discloses several specific implementation scenarios of the present application, but the present application is not limited thereto. Any changes that can be conceived by those skilled in the art should fall within the scope of protection of the present application.

Claims

1. A method for simulating the migration of uranium-containing fluids, characterized in that: include: A system of nonlinear partial differential equations is used to describe the migration of uranium-bearing fluids in groundwater. Iteratively solving the nonlinear partial differential equations using a pre-constructed time-discretized physical information neural network to obtain predicted solutions at different set times, wherein the time-discretized physical information neural network takes the solution of the current time step as input and the predicted solution of the next time step as output; According to the prediction solutions at different set moments, the migration changes of the uranium-containing fluid in each time period are determined to perform migration simulation on the uranium-containing fluid.

2. The method according to claim 1, characterized in that Before using the pre-built time discretized physical information neural network to iteratively solve the nonlinear partial differential equations to obtain prediction solutions at different set times, the method further includes: solving the solution of the nonlinear partial differential equations at the initial time by an analytical program; Accordingly, the pre-built time discretized physical information neural network is used to iteratively solve the nonlinear partial differential equations to obtain prediction solutions at different set times, including: Determining a target time series for solving the nonlinear partial differential equation system according to a preset time step; The solution at the initial moment is input into a pre-constructed time-discretized physical information neural network, and the nonlinear partial differential equations are iteratively solved according to the target time series to obtain prediction solutions at different set moments.

3. The method according to claim 2, characterized in that The solution at the initial moment is input into a pre-built time discretization physical information neural network, and the nonlinear partial differential equations are iteratively solved according to the target time series to obtain prediction solutions at different set moments, including: The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain a predicted solution for the next time step; According to the target time series, different time steps are repeatedly iterated and solved until the last time step, and the prediction solutions at different set moments are obtained.

4. The method according to claim 3, characterized in that In the process of repeated iterative solutions for different time steps, the predicted solution of the next time step is input as the solution of the current time step into a pre-constructed time-discretized physical information neural network, and the nonlinear partial differential equations are iteratively solved to obtain the predicted solution for the next time step.

5. The method according to claim 3, characterized in that Before inputting the solution at the initial moment as the solution for the current time step into a pre-constructed time-discretized physical information neural network and iteratively solving the nonlinear partial differential equation system to obtain a predicted solution for the next time step, the method further includes: A loss function is set according to an implicit discrete numerical calculation method, wherein the loss function is used to evaluate the degree of deviation of the predicted solution output by the neural network from the physical equation; Accordingly, the solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain the predicted solution for the next time step, including: The solution at the initial moment is input as the solution of the current time step into a pre-constructed time discretization physical information neural network, and the nonlinear partial differential equation system is iteratively solved to obtain an intermediate solution; Calculating the loss value of the intermediate solution during the iterative solution process according to a preset loss function; If the loss value is greater than a set threshold, the parameters of the time-discretized physical information neural network are adjusted, and the nonlinear partial differential equation group is repeatedly iteratively solved using the time-discretized physical information neural network after parameter adjustment until the loss value is less than or equal to the set threshold, and the corresponding intermediate solution is used as the predicted solution for the next time step.

6. The method according to any one of claims 1 to 5, characterized in that After using the pre-constructed time-discretized physical information neural network to iteratively solve the nonlinear partial differential equations to obtain prediction solutions at different set times, the method further includes: For the nonlinear partial differential equation system, calculating analytical solutions at different set times; The analytical solutions at different set moments are compared with the predicted solutions at the corresponding set moments to evaluate the prediction performance of the time discretized physical information neural network.

7. The method according to any one of claims 1 to 5, characterized in that Determining the migration change of the uranium-containing fluid at different set times based on the predicted solutions at different set times to perform migration simulation on the uranium-containing fluid includes: Determining the spatiotemporal variation information of physical quantities of the migration process of the uranium-containing fluid in the groundwater according to the prediction solutions at the different set moments; The migration of the uranium-containing fluid is simulated based on the temporal and spatial variation information of the physical quantities during the migration of the uranium-containing fluid in the groundwater.

8. A migration simulation device for uranium-containing fluid, characterized in that: include: A description unit for describing the migration of uranium-bearing fluid in groundwater using a system of nonlinear partial differential equations; a first solving unit, configured to iteratively solve the nonlinear partial differential equations using a pre-constructed time-discretized physical information neural network to obtain predicted solutions at different set moments, wherein the time-discretized physical information neural network takes the solution of the current time step as input and outputs the predicted solution of the next time step as output; The determination unit is used to determine the migration changes of the uranium-containing fluid in each time period according to the prediction solutions at the different set moments, so as to perform migration simulation on the uranium-containing fluid.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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