Fluid migration prediction method and device based on uncertainty constraint

Abstract

The invention discloses a fluid migration prediction method and device based on uncertainty constraints, relates to the technical field of data processing, and mainly aims to solve the problems of poor accuracy and effectiveness of existing fluid migration prediction based on uncertainty constraints. Comprising the following steps: acquiring a noisy data set of a medium of the uranium-containing solution migrated underground, and constructing a convective diffusion physical control model for representing the convective diffusion process of the uranium-containing solution; constructing a joint posterior probability model based on the joint posterior distribution of the noisy data set, the physical consistency likelihood item of the convective diffusion physical control model and the physical residual item of the physical information neural network model; and solving the joint posterior probability model based on variational gradient descent to obtain a particle set of posterior distribution, and predicting the noisy data set according to the particle set and the physical information neural network model to obtain a fluid migration prediction result.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method and apparatus for predicting fluid transport based on uncertainty constraints. Background Technology

[0002] Porous media flow is the phenomenon of fluid seepage through tiny pores, widely existing in nature and engineering fields, especially in the transport of uranium-containing solutions in the nuclear industry. To predict and understand the flow of uranium-containing solutions, simulation methods are commonly used to predict the migration process of uranium-containing solutions in porous media in unknown environments.

[0003] Currently, existing fluid prediction methods typically employ numerical simulations, such as solving the flow-diffusion equations using finite difference or finite element methods. In these methods, parameters such as the velocity field and dispersion coefficient are usually assumed to be fixed values ​​to achieve the prediction objective. However, in practical engineering, these parameters often originate from limited monitoring data or inversion results, resulting in measurement errors and model uncertainties. When these uncertain parameters are directly substituted into the discrete numerical model, the errors accumulate over time, easily leading to shifts in the position of the uranium-containing solution contamination plume front, distortion of diffusion intensity, and even numerical oscillations or instability. Therefore, a fluid transport prediction method based on uncertainty constraints is urgently needed to address these problems. Summary of the Invention

[0004] In view of this, this application provides a method and apparatus for predicting fluid transport based on uncertainty constraints, the main purpose of which is to solve the problems of poor accuracy and effectiveness of existing fluid transport prediction based on uncertainty constraints.

[0005] According to one aspect of this application, a fluid transport prediction method based on uncertainty constraints is provided, comprising:

[0006] A noisy dataset of the medium transporting uranium-containing solution underground was obtained, and a convective diffusion physical control model characterizing the convective diffusion process of the uranium-containing solution was constructed. The noisy dataset includes formation physical parameters and fluid velocity field data with noise and uncertainty data. A joint posterior probability model is constructed based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model. The joint posterior probability model is used to describe the uncertainty distribution of the model parameters of the physical information neural network model. The joint posterior probability model is inferred and solved to obtain a set of particles with posterior distribution. Based on the set of particles and the physical information neural network model, the noisy dataset is predicted to obtain fluid migration prediction results. The fluid migration prediction results include uranium-containing solution concentration data at different times and spatial locations and the corresponding probability distributions.

[0007] Furthermore, before constructing the joint posterior probability model based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model, the method further includes: Based on Bayesian methods, a joint posterior distribution of the noisy dataset is constructed, which includes the prior distribution of model parameters, the prior distribution of physical parameters, and the data likelihood term. The physical consistency likelihood term of the convection-diffusion physical control model is determined based on the residuals and Gaussian noise of the convection-diffusion physical control model. The physical residual term is constructed based on the output differential term of the physical information neural network model.

[0008] Furthermore, the step of inferring and solving the joint posterior probability model to obtain the set of particles with the posterior distribution includes: The parameter particles of the physical information neural network model are iteratively evolved through the joint posterior probability model, and iteratively solved based on variational gradient descent during the iterative evolution process. Each pair of parameter particles corresponds to a set of model parameters and physical parameters. During the iterative solution process, if the parameter particles match the preset convergence conditions, the set of particles with the posterior distribution is determined.

[0009] Further, the step of predicting the noisy dataset based on the particle set and the physical information neural network model to obtain the fluid transport prediction result includes: In the process of using the physical information neural network model to predict the noisy dataset, the physical information neural network model is forward-predicted based on the particle set to obtain multiple sets of prediction results; The mean of the multiple sets of prediction results is statistically analyzed to obtain a deterministic prediction result, and the discrete distribution of the multiple sets of prediction results is statistically analyzed to obtain the reliability of the deterministic prediction result. The fluid transport prediction result is generated based on the deterministic prediction result and the confidence level.

[0010] Furthermore, the method also includes: Construct a physical information neural network model, which includes an input layer, an output layer, and at least one hidden layer; Calculate the differential derivatives of the output parameters of the output layer and the input parameters of the input layer, and construct the physical residual term of the physical information neural network model based on the differential derivatives and the convection-diffusion physical control model.

[0011] Furthermore, the acquisition of a noisy dataset of the medium in which uranium-containing solution migrates underground includes: The noisy data and the uncertain data are determined based on random variables that match a preset statistical distribution; The noise data and the uncertainty data are configured into the random noise, physical parameter measurement error and disturbance parameter in the fluid velocity field data to form the noisy dataset.

[0012] Furthermore, the construction of the convective diffusion physical control model characterizing the uranium-containing solution convective diffusion process includes: Define the initial physical conditions and boundary conditions; Based on the time derivative term, convection term, and diffusion or dispersive term, a convection-diffusion physical control model is constructed under the initial physical conditions and the boundary conditions.

[0013] According to another aspect of this application, a fluid transport prediction device based on uncertainty constraints is provided, comprising: The acquisition module is used to acquire a noisy dataset of the medium in which the uranium-containing solution migrates underground, and to construct a convective diffusion physical control model characterizing the convective diffusion process of the uranium-containing solution. The noisy dataset includes formation physical parameters and fluid velocity field data with noise data and uncertainty data. A construction module is used to construct a joint posterior probability model based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model. The joint posterior probability model is used to describe the uncertainty distribution of the model parameters of the physical information neural network model. The prediction module is used to infer and solve the joint posterior probability model to obtain the particle set of the posterior distribution, and to predict the noisy dataset based on the particle set and the physical information neural network model to obtain the fluid migration prediction result. The fluid migration prediction result includes uranium-containing solution concentration data at different times and spatial locations and the corresponding probability distribution.

[0014] Furthermore, the construction module is also used to construct a joint posterior distribution of the noisy dataset, which includes the prior distribution of model parameters, the prior distribution of physical parameters, and the data likelihood term, based on Bayesian methods; determine the physical consistency likelihood term of the convection-diffusion physical control model based on the residuals and Gaussian noise of the convection-diffusion physical control model; and construct the physical residual term based on the output differential term of the physical information neural network model.

[0015] Furthermore, the prediction module is specifically used to iteratively evolve the parameter particles of the physical information neural network model through the joint posterior probability model, and to iteratively solve the problem based on variational gradient descent during the iterative evolution process. Each pair of parameter particles corresponds to a set of model parameters and physical parameters. When the parameter particles match the preset convergence condition during the iterative solution process, the set of particles with the posterior distribution is determined.

[0016] Furthermore, the prediction module is specifically configured to, during the process of predicting the noisy dataset using the physical information neural network model, perform forward prediction on the physical information neural network model based on the particle set to obtain multiple sets of prediction results; perform mean statistics on the multiple sets of prediction results to obtain deterministic prediction results, and perform discrete distribution statistics on the multiple sets of prediction results to obtain the credibility of the deterministic prediction results; and generate the fluid transport prediction result based on the deterministic prediction results and the credibility.

[0017] Furthermore, the construction module is also used to construct a physical information neural network model, which includes an input layer, an output layer, and at least one hidden layer; calculate the differential derivatives of the output parameters of the output layer and the input parameters of the input layer, and construct the physical residual term of the physical information neural network model based on the differential derivatives and the convection-diffusion physical control model.

[0018] Furthermore, the acquisition module is specifically used to determine the noise data and the uncertainty data based on random variables that match a preset statistical distribution; and to configure the noise data and the uncertainty data into the random noise, physical parameter measurement error and disturbance parameter in the fluid velocity field data to form the noisy dataset.

[0019] Furthermore, the construction module is specifically used to define initial physical conditions and boundary conditions; and to construct a convection-diffusion physical control model under the initial physical conditions and the boundary conditions based on the time derivative term, the convection term, and the diffusion or dispersive term.

[0020] According to another aspect of this application, a storage medium is provided, wherein at least one executable instruction is stored therein, the executable instruction causing a processor to perform an operation corresponding to the above-described fluid transport prediction method based on uncertainty constraints.

[0021] According to another aspect of this application, a terminal is provided, comprising: a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other through the communication bus; The memory is used to store at least one executable instruction, which causes the processor to perform the operation corresponding to the above-described fluid transport prediction method based on uncertainty constraints.

[0022] By employing the above technical solutions, the technical solutions provided in the embodiments of this application have at least the following advantages: This application provides a method and apparatus for predicting fluid migration based on uncertainty constraints. Compared with the prior art, the embodiments of this application acquire a noisy dataset of the medium in which uranium-containing solution migrates underground, and construct a convective diffusion physical control model characterizing the convective diffusion process of the uranium-containing solution. The noisy dataset includes formation physical parameters and fluid velocity field data with noise and uncertainty data. Based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convective diffusion physical control model, and the physical residual term of the physical information neural network model, a joint posterior probability model is constructed. The joint posterior probability model is used to describe the uncertainty distribution of the model parameters of the physical information neural network model. The joint posterior probability model is inferred and solved to obtain the posterior distribution. A particle set is used to predict the noisy dataset based on the particle set and the physical information neural network model, resulting in fluid transport prediction results. The fluid transport prediction results include uranium-containing solution concentration data at different times and spatial locations, as well as the corresponding probability distributions. This achieves a quantitative characterization of physical consistency uncertainty and can quantitatively reflect the credibility range and uncertainty level of the prediction results under noisy conditions. By introducing a multi-particle cooperative evolution mechanism, a non-parametric approximation of the posterior distribution of neural network parameters is achieved, enabling uncertainty to propagate self-consistently with time and space evolution. This avoids the displacement of the uranium-containing solution plume front position and distortion of diffusion intensity, greatly reducing the occurrence of numerical oscillations or instability, thereby improving the stability and applicability of the physical model in complex engineering scenarios.

[0023] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0024] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A flowchart of a fluid transport prediction method based on uncertainty constraints provided in an embodiment of this application is shown; Figure 2 This illustration shows a schematic diagram of a fluid transport prediction method using noisy data as input, according to an embodiment of this application. Figure 3 This illustration shows a schematic diagram of a prediction and uncertainty calculation process based on a particle ensemble, provided in an embodiment of this application. Figure 4 This illustration shows a one-dimensional result display diagram provided in an embodiment of this application; Figure 5 This illustration shows a two-dimensional result display diagram provided in an embodiment of this application; Figure 6 This illustration shows a three-dimensional result display diagram provided in an embodiment of this application; Figure 7 This paper presents another three-dimensional result display diagram provided by an embodiment of this application; Figure 8 This illustration shows a schematic diagram of particle iterative evolution provided in an embodiment of this application; Figure 9 This illustration shows a schematic diagram of a neural network structure provided in an embodiment of this application; Figure 10 This paper shows a block diagram of a fluid transport prediction device based on uncertainty constraints provided in an embodiment of this application. Figure 11 A schematic diagram of the structure of a terminal provided in an embodiment of this application is shown. Detailed Implementation

[0025] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0026] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0027] Foundational technologies for artificial intelligence generally include sensors, dedicated AI chips, cloud computing, distributed storage, big data processing, operating / interactive systems, and mechatronics. AI software technologies mainly encompass computer vision, robotics, biometrics, speech processing, natural language processing, and machine learning / deep learning.

[0028] This application provides a fluid transport prediction method based on uncertainty constraints, such as... Figure 1 As shown, the method includes: 101. Obtain a noisy dataset of the medium in which the uranium-containing solution migrates underground, and construct a convective diffusion physical control model characterizing the convective diffusion process of the uranium-containing solution.

[0029] In this embodiment, the current execution end, as the execution subject for fluid migration prediction, can be either a server or a terminal, in order to obtain a noisy dataset of the medium in which uranium-containing solution migrates underground. Noisy datasets refer to noisy formation parameters and the fluid velocity field parameters calculated from them. The data includes formation physical parameters with noise and uncertainty data, and fluid velocity field data. The fluid velocity field data may include, but is not limited to, data such as velocity, position, diffusion coefficient, initial conditions or boundary conditions generated by the uranium-containing solution during the flow process. Correspondingly, the noisy dataset is obtained by adding noise and uncertainty data to the fluid velocity field data, including but not limited to random noise, measurement errors and uncertainty disturbance parameters. This application does not make specific limitations.

[0030] It should be noted that the convection-diffusion physical control model in this embodiment is characterized as a mathematical expression simulating the physical flow of uranium-containing solutions, used to describe the evolution of transport variables over time and space. In the specific embodiment of the migration process of uranium-containing solutions in porous media, the convection-diffusion physical control model is preferably a convection-diffusion equation, which may include a time derivative term, a convection term, and a diffusion or dispersive term, and simultaneously defines initial conditions and boundary conditions, constructed through mathematical modeling.

[0031] 102. Construct a joint posterior probability model based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model.

[0032] In this embodiment, the joint posterior distribution of the noisy dataset refers to the joint posterior distribution of the noisy dataset established based on Bayesian methods; the physical consistency likelihood term of the convection-diffusion physical control model refers to transforming physical laws into a computable probability model for optimizing parameter estimation and prediction accuracy. In this embodiment, a likelihood function is constructed through the convection-diffusion physical control model, and then a Gaussian distribution is introduced to calculate the physical consistency likelihood term; the physical residual term of the physical information neural network model refers to the prior constraint term of the physical information neural network model. Since the physical information neural network model is constructed based on a neural network, the corresponding physical residual term can be constructed using input parameters and output parameters. The output parameters can be represented by partial differential equations in operator form and described by introducing unknown or uncertain parameters to obtain physical residual terms with uncertainty or unknowns.

[0033] It should be noted that, in order to perform fluid transport prediction using the physical information neural network model, the constructed joint posterior probability model is used to describe the uncertainty distribution of the model parameters of the physical information neural network model. In this case, the joint posterior probability model incorporates the joint posterior distribution, the physical consistency likelihood term, and the physical residual term into the Bayesian probability framework to obtain a joint posterior probability model for distinguishing deterministic physical information neural network predictions.

[0034] 103. The joint posterior probability model is inferred and solved to obtain the set of particles with posterior distribution, and the noisy dataset is predicted based on the set of particles and the physical information neural network model to obtain the fluid transport prediction result.

[0035] In this embodiment, after obtaining the joint posterior probability model, inference can be performed using Markov chain Monte Carlo, Hamiltonian Monte Carlo, variational inference, or Stein variational gradient descent. Preferably, the Stein variational gradient descent method is used to approximate the joint posterior probability model, resulting in a particle set with a posterior distribution, which is the probability distribution estimate output by the physical information neural network model. Finally, the fluid transport process is predicted based on the particle set and the physical information neural network model. Specifically, forward computation can be performed using the physical information neural network model corresponding to each particle in the particle set to obtain the prediction results of the transport process at different times and spatial locations. That is, the fluid transport prediction results include uranium-containing solution concentration data at different times and spatial locations, and the corresponding probability distributions, such as... Figure 2 As shown. Finally, the prediction results of multiple particles are statistically analyzed to obtain the predicted mean of the transport variables, which is then used as the output of the deterministic simulation results of the transport process.

[0036] For example, in a specific scenario, the input parameters are (X, t), where X is the spatial coordinate. t is a time variable. For natural datasets in the spatial domain, such as Figure 3 The diagram shown illustrates the prediction and uncertainty calculation process based on particle ensembles, as follows: Figure 4 The one-dimensional result display diagram shown is as follows: Figure 5 The two-dimensional result display diagram shown is as follows: Figure 6-7 The three-dimensional result is shown in the diagram.

[0037] In another embodiment of this application, for further definition and explanation, before constructing the joint posterior probability model based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model, the method further includes: Based on Bayesian methods, a joint posterior distribution of the noisy dataset is constructed, which includes the prior distribution of model parameters, the prior distribution of physical parameters, and the data likelihood term. The physical consistency likelihood term of the convection-diffusion physical control model is determined based on the residuals and Gaussian noise of the convection-diffusion physical control model. The physical residual term is constructed based on the output differential term of the physical information neural network model.

[0038] To construct a joint posterior probability model that uses uncertainty noise as a physical constraint, thereby improving the effectiveness and accuracy of fluid transport prediction, we first construct a joint posterior distribution of a noisy dataset based on Bayesian methods, including the prior distributions of model parameters, physical parameters, and data likelihood terms. Specifically, we define the noisy dataset... Construct the joint posterior distribution based on Bayes' theorem:

[0039] Where x and u are the velocity fields in the horizontal and vertical directions, respectively, and N is a natural number. These are the prior distributions of the model parameters and the physical parameters, respectively. Here, to characterize the uncertainty, the parameters of the neural network... and physical parameters (The unknown or uncertain parameters, representing the convective-diffusion physical control model, are set as random variables, and expressed as follows after introducing a prior distribution.) .in addition, The data likelihood term measures the degree of match between the model's predictions and the observed data. Under the assumption that the observation error follows a Gaussian distribution, the data likelihood term can be expressed as: ,in, This represents the standard deviation of the observation error.

[0040] Furthermore, to incorporate physical consistency into the Bayesian formula in probabilistic form to obtain a joint posterior probability model, the current execution end determines the physical consistency likelihood term based on the residuals and Gaussian noise of the convection-diffusion physical control model when determining the physical consistency likelihood term. Specifically, this is done at multiple discrete physical sampling points. Above, M is a natural number. The residuals of the convection-diffusion physical control model are treated as random variables, and the Gaussian noise assumption is introduced, expressed as: ; Let be the standard deviation of the physical residuals, representing the uncertainty of the residuals in the flow-diffusion physical control model. From this, the corresponding physical consistency likelihood term is obtained, expressed as: ; Furthermore, by unifying the data likelihood term and the physical consistency likelihood term, we obtain the joint likelihood function, expressed as: ; Finally, the constructed joint posterior probability model, which incorporates observation errors and physical constraints, is expressed as follows: .

[0041] It should be noted that the physical information neural network model in this embodiment is constructed using a neural network. In order to model the uncertain parameters as random variables, the current execution end can receive the basic variables used to describe the physical problem, namely fluid velocity field data, at least including spatial coordinates, into the input layer of the neural network. and time variables Neural networks are used to approximate physical field variables, and their output function can be expressed as: ; in, The output of the neural network, Let be the parameters of the neural network. Then, using partial differential equations, the output of the neural network is differentiated, explicitly introducing the convection-diffusion physical control model and its boundary conditions, which serve as the physical control equations, into the model. The partial differential equations can be expressed as: Boundary conditions or initial conditions are expressed as: Furthermore, the physical residual term constructed based on the neural network output is expressed as follows: .

[0042] In another embodiment of this application, for further definition and explanation, the step of inferring and solving the joint posterior probability model to obtain the particle set of the posterior distribution includes: The parameter particles of the physical information neural network model are iteratively evolved through the joint posterior probability model, and iteratively solved based on variational gradient descent during the iterative evolution process. Each pair of parameter particles corresponds to a set of model parameters and physical parameters. During the iterative solution process, if the parameter particles match the preset convergence conditions, the set of particles with the posterior distribution is determined.

[0043] To enable inference and solution of the joint posterior probability model, and to incorporate uncertainties into the solution process, thereby improving the accuracy of fluid transport prediction through posterior inference, the current execution end initializes multiple neural network parameter particles during inference and solution. Each particle corresponds to a set of network parameters. The particle update direction is calculated based on the gradient information of the posterior probability. Then, a kernel function is introduced to realize the interaction between particles, so that the particles maintain distribution diversity while moving towards high-probability regions. Finally, the particles are updated repeatedly until the preset convergence condition is met. This step obtains a particle set to represent the posterior distribution of the parameters. At this time, the number of particles and the form of the kernel function can be adjusted according to the computing resources. This application embodiment does not make specific limitations.

[0044] In this embodiment, the Stein variational gradient descent method can be used to infer and solve the joint posterior probability model. In this case, the parameter particles of the physical information neural network model are first iteratively evolved using the joint posterior probability model. Specifically, the parameters... Represented as a group of particles Each particle corresponds to a set of neural network parameters and physical parameters. Furthermore, by performing parallel evolution on multiple particles, the joint posterior distribution is approximated. , The physical residual term represents the degree of dissatisfaction with the physical equations, ensuring that particles in the posterior distribution not only cluster in regions where the data fits well but also in physically reasonable parameter space regions. During the iterative evolution process, iterative solutions are performed based on variational gradient descent. Each pair of parameter particles corresponds to a set of model parameters and physical parameters. In each iteration, each particle evolves according to the update rule, as shown below: ; in, For the iteration step size, update the direction. The Stein variational gradient is expressed as: ; in, This is the driving term, used to propel particles towards regions with higher posterior probability density. This is a repulsion term used to maintain diversity among particles and prevent them from collapsing into a single mode, such as... Figure 8 As shown. Kernel function The preferred method is a radial basis function kernel, and the bandwidth parameter can be determined by the median heuristic method. This application does not impose specific limitations on the embodiments.

[0045] In addition, the log gradient of the joint posterior distribution It is calculated using the negative logarithmic posterior function, and its expression is: .

[0046] in, , These correspond to the error term of the observation data and the residual term of the convection-diffusion physical control model, respectively. , This is the prior regularization term for the neural network parameters and physical parameters.

[0047] Finally, during the iterative solution process, if the parameter particles match the preset convergence condition, the particle set representing the posterior distribution is determined. The preset convergence condition can be set based on different solution requirements, and this embodiment does not impose specific limitations. By repeatedly executing the particle update process until the preset convergence condition is met, the particle set representing the posterior distribution of neural network parameters and physical parameters is finally obtained.

[0048] In this application embodiment, in addition to Stein variational gradient descent for inference, variational inference methods, sampling-based Markov chain Monte Carlo methods, and other particle or sample-driven approximate Bayesian inference methods can also be selected. This application embodiment does not impose specific limitations. Furthermore, the number of particles in this application can be multiple or reduced to a smaller scale to obtain a basic estimate of the uncertainty.

[0049] In another embodiment of this application, for further definition and explanation, the step of predicting the noisy dataset based on the particle set and the physical information neural network model to obtain the fluid transport prediction result includes: In the process of using the physical information neural network model to predict the noisy dataset, the physical information neural network model is forward-predicted based on the particle set to obtain multiple sets of prediction results; The mean of the multiple sets of prediction results is statistically analyzed to obtain a deterministic prediction result, and the discrete distribution of the multiple sets of prediction results is statistically analyzed to obtain the reliability of the deterministic prediction result. The fluid transport prediction result is generated based on the deterministic prediction result and the confidence level.

[0050] To achieve prediction and uncertainty quantification analysis of the transmission process based on particle ensembles within a framework of physical constraints and Bayesian inference, enabling the model to simultaneously output prediction results and their uncertainty information, specifically, during the prediction of the noisy dataset using the physical information neural network model, forward prediction is performed on the physical information neural network model based on particle ensembles to obtain multiple sets of prediction results. Specifically, for any given time and spatial location... Each particle The corresponding physical information neural network model performs forward computation to obtain a set of prediction results, represented as follows: ; Furthermore, by performing averaging on the above multi-particle prediction results, a deterministic prediction result is obtained, expressed as: ; At this point, the predicted mean can be output as a deterministic simulation result of the transmission process. Simultaneously, discrete distribution statistics can be performed on the multiple sets of prediction results to obtain the reliability of the deterministic prediction result. That is, by statistically analyzing the discrete distribution of the particle prediction results, the uncertainty measure of the prediction result can be calculated, which can be expressed by variance: The results can also be represented by standard deviation and confidence intervals; however, this application does not impose specific limitations on these representations. Furthermore, the fluid transport prediction results can be numerical results, graphical results, spatial distribution maps, or time series curves; this application does not impose specific limitations on these representations.

[0051] Furthermore, standard deviation, confidence interval, or other uncertainty indicators can be obtained to quantitatively characterize the reliability of the transport process simulation results under noisy conditions. Finally, the fluid transport prediction results are generated based on the deterministic prediction results and the reliability. In a specific embodiment, uncertainty is non-uniformly distributed in spatial and temporal dimensions and can propagate as the transport process evolves, used to identify high-risk or high-uncertainty regions.

[0052] In another embodiment of this application, for further definition and explanation, the steps also include: Construct a physical information neural network model; Calculate the differential derivatives of the output parameters of the output layer and the input parameters of the input layer, and construct the physical residual term of the physical information neural network model based on the differential derivatives and the convection-diffusion physical control model.

[0053] To achieve prediction based on a physical information neural network model, the current execution end pre-constructs a physical information neural network model, which includes an input layer, an output layer, and at least one hidden layer, and can employ a fully connected feedforward network structure. In some embodiments, the neural network built from the physical information neural network model can be a residual neural network, a multi-branch neural network, or a network structure with shared parameters or skip connections, etc., and this application embodiment does not impose specific limitations. Furthermore, the activation function of the neural network can be a hyperbolic tangent function, or it can be ReLU, Sigmoid, Swish, or a combination thereof, as long as it can achieve function approximation. The number of layers and the number of neurons per layer of the neural network can be adjusted according to the complexity of the problem to reduce or increase the network size while still achieving basic simulation effects; this application embodiment does not impose specific limitations.

[0054] It should be noted that the current execution end calculates the differential derivatives of the output parameters of the output layer and the input parameters of the input layer, such as... Figure 9 As shown, the physical residual term of the physical information neural network model is constructed based on the differential derivative and the convection-diffusion physical control model.

[0055] In another embodiment of this application, for further definition and explanation, the step of obtaining a noisy dataset of the medium in which uranium-containing solution migrates underground includes: The noisy data and the uncertain data are determined based on random variables that match a preset statistical distribution; The noise data and the uncertainty data are configured into the random noise, physical parameter measurement error and disturbance parameter in the fluid velocity field data to form the noisy dataset.

[0056] To incorporate noise or uncertainty data into fluid transport prediction, noise data is used to describe random disturbances following a Gaussian distribution. Therefore, noise data can be random variables such as uniformly distributed noise, Laplace distributed noise, empirically distributed noise, or mixed-distribution noise. Similarly, the same random variable can be used as uncertainty data, and this application embodiment does not impose specific limitations. Furthermore, the noise data and the uncertainty data are configured in the random noise, physical parameter measurement error, and disturbance parameter in the fluid velocity field data to form a noisy dataset. In some embodiments, noise is a random variable following a preset statistical distribution for subsequent Bayesian inference modeling. In this case, simplification can be made according to the data acquisition situation of the actual problem. When there is no measured data, simulation can be performed using only physical constraints, and this application embodiment does not impose specific limitations.

[0057] In another embodiment of this application, for further definition and explanation, the step of constructing a convective diffusion physical control model characterizing the uranium-containing solution convective diffusion process includes: Define the initial physical conditions and boundary conditions; Based on the time derivative term, convection term, and diffusion or dispersive term, a convection-diffusion physical control model is constructed under the initial physical conditions and the boundary conditions.

[0058] To further simulate and predict the flow of uranium-containing liquids, the initial physical conditions can be represented by the initial position and initial concentration of the simulated uranium-containing solution. The boundary conditions can be the boundary positions of the uranium-containing solution during flow, and can be set based on different simulation requirements. For example, at the initial moment... This indicates that at the initial moment, there is no uranium-free solution present underground except at the source location; left boundary condition point. At this location, the initial concentration of the uranium-containing solution is constant. ,Right now The right boundary condition is at the far end. At this point, the concentration gradient of pollutants tends to 0, that is... The embodiments in this application are not specifically limited. Furthermore, based on the time derivative term, convection term, and diffusion or dispersive term, the convection-diffusion physical control model under the initial physical conditions and the boundary conditions can be constructed as follows: ; in, Indicates solute concentration. and They are respectively and velocity field in the direction, It is a constant diffusion coefficient, preferably a dispersion coefficient. It is a two-dimensional spatial region.

[0059] This application provides a fluid transport prediction method based on uncertainty constraints, which realizes a quantitative characterization of physical consistency uncertainty. It can quantitatively reflect the credibility range and uncertainty level of the prediction results under noisy conditions. By introducing a multi-particle cooperative evolution mechanism, it achieves non-parametric approximation of the posterior distribution of neural network parameters, so that uncertainty can propagate self-consistently with the evolution of time and space, avoids the position shift of the uranium-containing solution plume front and the distortion of diffusion intensity, and greatly reduces the occurrence of numerical oscillations or instability, thereby improving the stability and applicability of the physical model in complex engineering scenarios.

[0060] Furthermore, as a response to the above Figure 1 The implementation of the method shown in this application provides a fluid transport prediction device based on uncertainty constraints, such as... Figure 10 As shown, the device includes: The acquisition module 21 is used to acquire a noisy dataset of the medium in which the uranium-containing solution migrates underground, and to construct a convective diffusion physical control model characterizing the convective diffusion process of the uranium-containing solution. The noisy dataset includes formation physical parameters and fluid velocity field data with noise data and uncertainty data. Module 22 is used to construct a joint posterior probability model based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model. The joint posterior probability model is used to describe the uncertainty distribution of the model parameters of the physical information neural network model. The prediction module 23 is used to infer and solve the joint posterior probability model to obtain the particle set of the posterior distribution, and to predict the noisy dataset based on the particle set and the physical information neural network model to obtain the fluid migration prediction result. The fluid migration prediction result includes uranium-containing solution concentration data at different times and spatial locations and the corresponding probability distribution.

[0061] Furthermore, the construction module is also used to construct a joint posterior distribution of the noisy dataset, which includes the prior distribution of model parameters, the prior distribution of physical parameters, and the data likelihood term, based on Bayesian methods; determine the physical consistency likelihood term of the convection-diffusion physical control model based on the residuals and Gaussian noise of the convection-diffusion physical control model; and construct the physical residual term based on the output differential term of the physical information neural network model.

[0062] Furthermore, the prediction module is specifically used to iteratively evolve the parameter particles of the physical information neural network model through the joint posterior probability model, and to iteratively solve the problem based on variational gradient descent during the iterative evolution process. Each pair of parameter particles corresponds to a set of model parameters and physical parameters. When the parameter particles match the preset convergence condition during the iterative solution process, the set of particles with the posterior distribution is determined.

[0063] Furthermore, the prediction module is specifically configured to, during the process of predicting the noisy dataset using the physical information neural network model, perform forward prediction on the physical information neural network model based on the particle set to obtain multiple sets of prediction results; perform mean statistics on the multiple sets of prediction results to obtain deterministic prediction results, and perform discrete distribution statistics on the multiple sets of prediction results to obtain the credibility of the deterministic prediction results; and generate the fluid transport prediction result based on the deterministic prediction results and the credibility.

[0064] Furthermore, the construction module is also used to construct a physical information neural network model, which includes an input layer, an output layer, and at least one hidden layer; calculate the differential derivatives of the output parameters of the output layer and the input parameters of the input layer, and construct the physical residual term of the physical information neural network model based on the differential derivatives and the convection-diffusion physical control model.

[0065] Furthermore, the acquisition module is specifically used to determine the noise data and the uncertainty data based on random variables that match a preset statistical distribution; and to configure the noise data and the uncertainty data into the random noise, physical parameter measurement error and disturbance parameter in the fluid velocity field data to form the noisy dataset.

[0066] Furthermore, the construction module is specifically used to define initial physical conditions and boundary conditions; and to construct a convection-diffusion physical control model under the initial physical conditions and the boundary conditions based on the time derivative term, the convection term, and the diffusion or dispersive term.

[0067] This application provides a fluid transport prediction device based on uncertainty constraints, which realizes a quantitative characterization of physical consistency uncertainty. It can quantitatively reflect the credibility range and uncertainty level of the prediction results under noisy conditions. By introducing a multi-particle cooperative evolution mechanism, it achieves non-parametric approximation of the posterior distribution of neural network parameters, so that uncertainty can propagate self-consistently with the evolution of time and space, avoids the position shift of the uranium-containing solution plume front and the distortion of diffusion intensity, and greatly reduces the occurrence of numerical oscillations or instability, thereby improving the stability and applicability of the physical model in complex engineering scenarios.

[0068] According to one embodiment of this application, a storage medium is provided, the storage medium storing at least one executable instruction, which can execute the fluid transport prediction method and apparatus based on uncertainty constraints in any of the above method embodiments.

[0069] Figure 11 The diagram shows a structural schematic of a terminal according to one embodiment of the present application. The specific embodiments of the present application do not limit the specific implementation of the terminal.

[0070] like Figure 11 As shown, the terminal may include: a processor 302, a communications interface 304, a memory 306, and a communications bus 308.

[0071] The processor 302, communication interface 304, and memory 306 communicate with each other via communication bus 308.

[0072] Communication interface 304 is used to communicate with other network elements such as clients or other servers.

[0073] The processor 302 is used to execute program 310, specifically to execute the relevant steps in the above-described embodiment of the fluid transport prediction method and apparatus based on uncertainty constraints.

[0074] Specifically, program 310 may include program code that includes computer operation instructions.

[0075] Processor 302 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application. The terminal includes one or more processors, which may be processors of the same type, such as one or more CPUs; or they may be processors of different types, such as one or more CPUs and one or more ASICs.

[0076] Memory 306 is used to store program 310. Memory 306 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0077] Specifically, program 310 can be used to cause processor 302 to perform the following operations: A noisy dataset of the medium in which uranium-containing solution migrates underground is obtained, and a convective diffusion physical control model characterizing the convective diffusion process of the uranium-containing solution is constructed. The noisy dataset includes formation physical parameters and fluid velocity field data with noise and uncertainty data. A joint posterior probability model is constructed based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model. The joint posterior probability model is used to describe the uncertainty distribution of the model parameters of the physical information neural network model. The joint posterior probability model is inferred and solved to obtain a set of particles with posterior distribution. Based on the set of particles and the physical information neural network model, the noisy dataset is predicted to obtain fluid migration prediction results. The fluid migration prediction results include uranium-containing solution concentration data at different times and spatial locations and the corresponding probability distributions.

[0078] Obviously, those skilled in the art should understand that the modules or steps of this application described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device. In some cases, the steps shown or described can be performed in a different order than those presented here, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, this application is not limited to any particular combination of hardware and software.

[0079] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A fluid transport prediction method based on uncertainty constraints, characterized in that, include: A noisy dataset of the medium in which uranium-containing solution migrates underground is obtained, and a convective diffusion physical control model characterizing the convective diffusion process of the uranium-containing solution is constructed. The noisy dataset includes formation physical parameters and fluid velocity field data with noise and uncertainty data. A joint posterior probability model is constructed based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model. The joint posterior probability model is used to describe the uncertainty distribution of the model parameters of the physical information neural network model. The joint posterior probability model is inferred and solved to obtain a set of particles with posterior distribution. Based on the set of particles and the physical information neural network model, the noisy dataset is predicted to obtain fluid migration prediction results. The fluid migration prediction results include uranium-containing solution concentration data at different times and spatial locations and the corresponding probability distributions.

2. The method according to claim 1, characterized in that, Before constructing the joint posterior probability model based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model, the method further includes: Based on Bayesian methods, a joint posterior distribution of the noisy dataset is constructed, which includes the prior distribution of model parameters, the prior distribution of physical parameters, and the data likelihood term. The physical consistency likelihood term of the convection-diffusion physical control model is determined based on the residuals and Gaussian noise of the convection-diffusion physical control model. The physical residual term is constructed based on the output differential term of the physical information neural network model.

3. The method according to claim 2, characterized in that, The set of particles whose posterior distribution is obtained by inferring and solving the joint posterior probability model includes: The parameter particles of the physical information neural network model are iteratively evolved through the joint posterior probability model, and iteratively solved based on variational gradient descent during the iterative evolution process. Each pair of parameter particles corresponds to a set of model parameters and physical parameters. During the iterative solution process, if the parameter particles match the preset convergence conditions, the set of particles with the posterior distribution is determined.

4. The method according to claim 1, characterized in that, The step of predicting the noisy dataset based on the particle set and the physical information neural network model to obtain fluid transport prediction results includes: In the process of using the physical information neural network model to predict the noisy dataset, the physical information neural network model is forward-predicted based on the particle set to obtain multiple sets of prediction results; The mean of the multiple sets of prediction results is statistically analyzed to obtain a deterministic prediction result, and the discrete distribution of the multiple sets of prediction results is statistically analyzed to obtain the reliability of the deterministic prediction result. The fluid transport prediction result is generated based on the deterministic prediction result and the confidence level.

5. The method according to claim 1, characterized in that, The method further includes: Construct a physical information neural network model, which includes an input layer, an output layer, and at least one hidden layer; Calculate the differential derivatives of the output parameters of the output layer and the input parameters of the input layer, and construct the physical residual term of the physical information neural network model based on the differential derivatives and the convection-diffusion physical control model.

6. The method according to claim 1, characterized in that, The acquisition of noisy datasets of uranium-containing solutions transported underground includes: The noisy data and the uncertain data are determined based on random variables that match a preset statistical distribution; The noise data and the uncertainty data are configured into the random noise, physical parameter measurement error and disturbance parameter in the fluid velocity field data to form the noisy dataset.

7. The method according to claim 1, characterized in that, The construction of the convective diffusion physical control model characterizing the uranium-containing solution convective diffusion process includes: Define the initial physical conditions and boundary conditions; Based on the time derivative term, convection term, and diffusion or dispersive term, a convection-diffusion physical control model is constructed under the initial physical conditions and the boundary conditions.

8. A fluid transport prediction device based on uncertainty constraints, characterized in that, include: The acquisition module is used to acquire a noisy dataset of the medium in which the uranium-containing solution migrates underground, and to construct a convective diffusion physical control model characterizing the convective diffusion process of the uranium-containing solution. The noisy dataset includes formation physical parameters and fluid velocity field data with noise data and uncertainty data. A construction module is used to construct a joint posterior probability model based on the joint posterior distribution of the noisy dataset, the physical consistency likelihood term of the convection-diffusion physical control model, and the physical residual term of the physical information neural network model. The joint posterior probability model is used to describe the uncertainty distribution of the model parameters of the physical information neural network model. The prediction module is used to infer and solve the joint posterior probability model to obtain the particle set of the posterior distribution, and to predict the noisy dataset based on the particle set and the physical information neural network model to obtain the fluid migration prediction result. The fluid migration prediction result includes uranium-containing solution concentration data at different times and spatial locations and the corresponding probability distribution.

9. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-7.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-7.

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