Intelligent numerical calculation method and system based on data and model adaptive correction

Abstract

The invention discloses an intelligent numerical calculation method and system based on data and model adaptive correction. The method comprises the following steps: determining a physical problem to be calculated, collecting related data, determining a data type, and performing data preprocessing; determining a control equation, boundary conditions and initial conditions of the system according to the system needing to be calculated; based on the data features and the equation features, selecting a data adaptive correction technology and a model adaptive adjustment technology; designing a neural network architecture for solving; defining adjustment variables in corresponding forms; designing a loss function of the model; training and optimizing the model to ensure that the precision of the model reaches the highest; model parameters are output, and solving of the proposed physical problem is completed. According to the method, data noise is filtered out in the solving process, incomplete parameters in a simulation model are automatically found and corrected, and the accuracy of data processing and model prediction is improved by dynamically adjusting data or the model and optimizing matching between the data and the model.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent numerical calculation, and in particular to an intelligent numerical calculation method and system based on data and model adaptive correction. Background Art

[0002] Physical-informed neural networks effectively integrate physical equations and data by integrating both the residual term of the physical equations and the loss term of the data into the neural network's loss function. This dual-driven approach facilitates efficient solution of both direct and inverse problems of physical problems. In this process, data sources typically include experimental data, simulation results, and numerical calculations. Experimental data often exhibit sparsity and noise, which poses challenges to model accuracy. First, due to measurement equipment errors, environmental interference, and random measurement fluctuations, experimental data inevitably contain noise, introducing additional errors in modeling and analysis. Second, due to the complexity of experimental conditions and the limitations of measurement equipment, the precise measurement of boundary conditions, such as fluid velocity or temperature gradient, is extremely challenging. Measurement errors in boundary conditions lead to uncertainty in some key parameters. Furthermore, due to technical or cost constraints, data acquisition is typically limited to limited space or time points. The sparsity of experimental data increases model uncertainty, making it difficult to accurately describe the overall behavior of the system.

[0003] Simulations and numerical calculations, on the other hand, are often based on simplified physical models and rely on empirical parameters that are difficult to precisely determine. These parameters can vary significantly under different conditions, leading to increased errors in simulation results and, in turn, reduced model accuracy and robustness. For example, when solving complex physical models such as the Navier-Stokes equations, direct solutions consume significant computing resources. To improve computational efficiency, simplified models, such as the Reynolds-Averaged Navier-Stokes (RANS) model, are often used. This simplification often introduces significant model errors when dealing with nonlinear phenomena such as strong turbulence.

[0004] Therefore, current research focuses on achieving high-precision solutions in noisy data and effectively removing noise from the data. Furthermore, adaptively adjusting the equations based on available data, allowing for dynamic parameter correction during the solution process, thereby enabling the derivation of physical processes and high-precision solutions, is also a key research direction. Summary of the Invention

[0005] The purpose of the present invention is to provide an intelligent numerical calculation method and system based on adaptive correction of data and models, which filters out data noise during the solution process, automatically discovers and corrects incomplete parameters in the simulation model, and optimizes the matching between data and model by dynamically adjusting data or model, thereby improving the accuracy of data processing and model prediction.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] An intelligent numerical calculation method based on adaptive correction of data and model, comprising the following steps:

[0008] (1) Identify the physical problem to be calculated, collect relevant data, determine the data type, and perform data preprocessing;

[0009] (2) Determine the control equations, boundary conditions, and initial conditions of the system according to the system to be calculated;

[0010] (3) Based on the data characteristics in step (1) and the equation characteristics in step (2), a correction technique is selected, specifically including: when there is significant noise in the data and the equation and boundary conditions are relatively complete, a data adaptive correction technique is used, which neutralizes the noise in the data by introducing trainable variables; when the data is accurate but there are missing values or simplified errors in the equation, a model adaptive adjustment technique is used, which compensates for the missing values in the equation or corrects the neglected physical effects by introducing trainable variables;

[0011] (4) Design a neural network architecture for solving the problem, and clarify the input, output, and network structure of the neural network architecture;

[0012] (5) Define the appropriate form of the moderator variable based on the selected correction technique and problem characteristics;

[0013] (6) Design the model’s loss function based on the selected correction technique;

[0014] (7) Training the neural network architecture based on the collected data, boundary conditions, and physical equations modified by the correction technology until the model converges, and adjusting the neural network architecture and optimization function according to the training results to obtain the model with the best performance;

[0015] (8) Based on the model with the best performance, the model parameters are output to complete the solution of the physical problem proposed in step (1).

[0016] Furthermore, the step (1) specifies the physical problem to be calculated, collects relevant data, determines the data type, and performs data preprocessing, specifically including:

[0017] Clarify the nature and scope of the physical problem to be solved;

[0018] Collect data related to the physical problem and perform preliminary analysis to identify data characteristics and determine whether there is noise in the data. If noise is found, make assumptions about the noise model based on the actual situation and feasibility;

[0019] The noise model is assumed, including: establishing a noise model based on the results of data analysis, assuming the noise type, and estimating the noise threshold and its distribution characteristics.

[0020] Furthermore, the step (2) determines the control equations, boundary conditions and initial conditions of the system according to the system to be calculated, specifically including:

[0021] Identify the governing equations that describe the system's behavior, evaluate whether there are missing values or simplifying assumptions in the equations, and consider how these factors affect the system's accuracy;

[0022] According to the existing data and actual conditions, the initial conditions and boundary conditions of the system are set to ensure the accuracy and applicability of the model.

[0023] Furthermore, the step (3) selects a suitable correction technique based on the data characteristics in step (1) and the equation characteristics in step (2), specifically including:

[0024] When there is significant noise in the data and the equations and boundary conditions are relatively complete, data adaptive correction technology is used. Data adaptive correction technology neutralizes the noise in the data by introducing trainable variables;

[0025] When the data is accurate but there are missing values or simplification errors in the equation, model adaptive adjustment technology is used. Model adaptive adjustment technology introduces trainable variables to make up for the missing values in the equation or correct neglected physical effects.

[0026] Furthermore, the step (4) designs a neural network architecture for solving the problem, and clarifies the input, output, and network structure of the neural network architecture, specifically including:

[0027] Design the neural network architecture and select the optimization algorithm based on the selected correction technique;

[0028] Define the input and output of the neural network to ensure that the network can process and improve all aspects of the physical equations. The network output calculates the data loss and the loss of the control equation directly or through transformation.

[0029] Furthermore, the step (5) defines the corresponding form of adjustment variables according to the selected correction technology and problem characteristics, specifically including:

[0030] If the selected correction technique is data-adaptive correction, a trainable variable with the same size as the noise data is introduced into the neural network. The trainable variable serves as a model parameter or output of the network layer to represent the noise in the data. Based on the existing noise information, the distribution of the trainable variable is set, and its threshold is specified in the solution to achieve more accurate correction and avoid over-correction.

[0031] If the selected correction technology is the model adaptive adjustment technology, a trainable variable related to model simplification is introduced into the neural network. The trainable variable is a single value or a value distribution, which is used to make up for the missing values in the equation or correct the neglected physical effects.

[0032] Furthermore, in step (6), based on the selected correction technique, a loss function of the model is designed;

[0033] Designing an internal data point loss function: This function is used to measure the difference between the model output and the actual data. For data adaptive correction technology, this function adds the physical quantity output by the neural network to a trainable noise variable. This trainable variable is used to neutralize the noise in the data, reducing the impact of noise on the data and thus achieving data correction.

[0034] Design boundary data point loss function to evaluate the performance of the model under boundary conditions;

[0035] An equation loss function is designed to evaluate the degree of conformity of the model to the control equation. For missing values in the equation, their locations are clearly identified, and corresponding trainable variables are introduced at these locations. For the overall difference between the data and the equation due to model simplification or computational errors, a unified adjustment parameter is defined at the end of the equation. The size of the adjustment parameter should be consistent with the size of the total training points to neutralize the equation error and quantify the difference between the data and the equation through data approximation.

[0036] Furthermore, the step (8) outputs the model parameters based on the model with the best performance to complete the solution of the physical problem proposed in step (1), specifically including:

[0037] Data denoising: Adaptive data correction technology determines the noise type and distribution based on the output variable used to neutralize data noise, and restores high-precision data based on the linear transformation of the variable and the original noise data;

[0038] Equation determination: Based on the equation adaptive adjustment technology, the missing values in the physical equation or the deviation between the data and the equation are determined according to the parameters iterated by the neural network, and corresponding corrections are made.

[0039] The present invention further provides an intelligent numerical calculation system based on data and model adaptive correction, which is applied to the above-mentioned intelligent numerical calculation method based on data and model adaptive correction, including:

[0040] The data processing module is used to identify the physical problem to be calculated, collect relevant data, determine the data type, and perform data preprocessing;

[0041] An equation determination module is used to determine the control equations, boundary conditions and initial conditions of the system according to the system to be calculated;

[0042] A correction technology selection module is used to select an appropriate correction technology based on data characteristics and equation characteristics;

[0043] The network architecture design module is used to design the neural network architecture for solving problems and clarify the input, output and network structure of the neural network architecture;

[0044] A regulating variable definition module is used to define regulating variables of corresponding forms according to the selected correction technology and problem characteristics;

[0045] The loss function design module is used to design the loss function of the model based on the selected correction technology;

[0046] The model training module is used to train the neural network architecture based on the collected data, boundary conditions, and physical equations modified by the correction technology until the model converges. The neural network architecture and optimization function are adjusted according to the training results to obtain the model with the best performance;

[0047] The problem solving module is used to output model parameters based on the model with the best performance and complete the solution to the physical problem proposed in step (1).

[0048] In addition, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program executes the above-mentioned intelligent numerical calculation method based on adaptive correction of data and model when the computer program is running.

[0049] In addition, the present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and is characterized in that when the processor runs the computer program, it executes the above-mentioned intelligent numerical calculation method based on adaptive correction of data and models.

[0050] According to the specific embodiments provided by the present invention, the intelligent numerical calculation method based on adaptive correction of data and models provided by the present invention discloses the following technical effects:

[0051] 1. Improve model accuracy and reliability:

[0052] When solving physical problems by integrating data with physical models, the compatibility of the data with the physical equations is crucial to the model's predictive accuracy. When the data and equations do not match, the mutual constraints between them make it difficult for the solution process to converge, and thus, it is difficult to achieve high-precision results. To address this issue, this paper proposes data adaptive correction technology and model adaptive adjustment technology. By introducing correction variables, these technologies mitigate the negative impact of the discrepancy between data and equations on the solution.

[0053] Specifically, when data contains significant noise and the physical equations and boundary conditions are relatively complete, data adaptive correction technology neutralizes the noise by introducing trainable variables. Within the constraints of the physical equations and boundary conditions, this technology can achieve high-precision solutions and data corrections. In contrast, when data is relatively accurate but the physical equations contain missing or simplified errors, model adaptive adjustment technology introduces trainable variables to compensate for missing or neglected physical effects in the equations. This method uses data to modify the model's governing equations.

[0054] Through these two technologies, we can effectively avoid the impact of data noise or incomplete and simplified equations, avoid the mutual constraints between data and equations, and thus achieve high-precision solutions.

[0055] 2. Noise determination and model equation optimization

[0056] Adaptive data correction technology enables high-precision training in high-noise environments, effectively filtering out noise from the data. This technology reduces the impact of noise by introducing data correction variables, based on the equations and boundary conditions of the physical model. The corrected model output accurately determines the distribution characteristics of the noise, and through a linear transformation of this correction variable with the original noisy data, higher-precision data is restored.

[0057] When physical models are simplistic or incomplete, model adaptive adjustment technology compensates for these deficiencies by dynamically adjusting variables in the model equations. This technology can deduce physical processes and modify physical equations based on the output values of the adjustment variables, providing a reliable method for studying complex physical phenomena.

[0058] This paper demonstrates the development of adaptive data correction and model adjustment technologies that can filter out data noise during the solution process and automatically detect and correct incomplete parameters in simulation models. This will help expand the application of data and model fusion technology, improve model accuracy and robustness, and provide a more reliable tool for solving complex engineering problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0060] Figure 1 Schematic diagram of the flow of an intelligent numerical calculation method based on adaptive correction of data and models according to an embodiment of the present invention;

[0061] Figure 2 This is a neural network algorithm architecture based on digital adaptive correction technology in an embodiment of the present invention;

[0062] Figure 3 This is a neural network algorithm architecture based on model adaptive adjustment technology in an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0064] The purpose of the present invention is to solve the problem of noise in data and the problem of parameter uncertainty in the model based on data adaptive correction technology and model adaptive adjustment technology of physical information neural network.

[0065] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0066] like Figure 1 As shown, the intelligent numerical calculation method based on data and model adaptive correction provided by the present invention includes the following steps:

[0067] (1) Identify the physical problem to be calculated, collect relevant data, determine the data type, and perform data preprocessing, including:

[0068] Steps 1a-1b, Problem Definition: Clarify the nature and scope of the physical problem to be solved;

[0069] Step 1c, Data Collection and Preliminary Analysis: Collect data relevant to the problem, perform preliminary analysis to identify data characteristics, and determine whether there is noise in the data. If noise is found, make assumptions about the noise model based on the actual situation and feasibility.

[0070] Among them, the noise model assumption is: based on the results of data analysis, a noise model is established, the noise type (such as Gaussian noise, salt and pepper noise, etc.) is assumed, and the noise threshold and its distribution characteristics are estimated.

[0071] (2) According to the system to be calculated, determine the system's control equations, boundary conditions, and initial conditions, including:

[0072] Governing equations: Determine the governing equations that describe the system behavior, evaluate whether there are missing values or simplifying assumptions in the equations, and consider how these factors affect the system accuracy;

[0073] Initial conditions and boundary conditions: Based on existing data and actual conditions, the initial conditions and boundary conditions of the system are set to ensure the accuracy and applicability of the model.

[0074] (3) Based on the data characteristics in step (1) and the equation characteristics in step (2), select an appropriate correction technique, specifically including:

[0075] Step 3a, data adaptive correction technology: When there is significant noise in the data and the equations and boundary conditions are relatively complete, data adaptive correction technology is used. This technology neutralizes the noise in the data by introducing trainable variables. Figure 2 As shown in the figure, the neural network algorithm architecture based on digital adaptive correction technology is introduced into the neural network to reduce the impact of noise on model performance.

[0076] Take the two-dimensional NS equation as an example:

[0077] a) Navier-Stokes equations

[0078] The basic form of the Navier-Stokes equations is:

[0079]

[0080] Where u represents the velocity vector, p represents the pressure, and ν represents the kinematic viscosity coefficient.

[0081] b) Introduction of stream functions

[0082] For two-dimensional incompressible flow problems, the stream function ψ can be introduced so that the velocity vector u can be expressed as:

[0083]

[0084] By introducing the stream function, the continuity equation is automatically satisfied Therefore, only the momentum equation needs to be calculated, which simplifies the calculation process, reduces the complexity of the problem, and facilitates the solution.

[0085] c) Dimensionless transformation of data and equations

[0086] Due to the complex operating conditions of the reactor core, the numerical values of variables such as flow field pressure, velocity, and density vary greatly, which affects the convergence of the neural network calculation. It is necessary to perform dimensionless processing on the flow field parameters, equations, and data. Definition of dimensionless variables:

[0087]

[0088] Where U is the characteristic velocity, L is the characteristic length, and x represents the position vector. After dimensionless processing, the NS equation can be expressed as:

[0089]

[0090] Here, Re = UL / ν is the Reynolds number, which represents the ratio of inertial force to viscous force. Dimensionless processing helps avoid large numerical differences that can make neural network convergence difficult.

[0091] d) Data adaptive correction technology: When there is significant noise in the data and the equations and boundary conditions are relatively complete, data adaptive correction technology is used. This technology neutralizes the noise in the data by introducing trainable variables. Figure 2 As shown in the figure, the neural network algorithm architecture based on digital adaptive correction technology is introduced into the neural network to reduce the impact of noise on model performance.

[0092] The data adaptive correction term is At this time, the data loss becomes:

[0093]

[0094] Among them, L data_u is the loss of speed u; represents the collected and processed data (with noise); represents a trainable correction term used to neutralize the influence of noise; Represents the velocity parameter predicted by the neural network. The meanings of the other physical quantities are the same as above.

[0095] The input of the PINNs model is the dimensionless spatial coordinates:

[0096] x * =(x * ,y * )

[0097] The output is the dimensionless stream function ψ * and pressure p * , the dimensionless velocity u is obtained by derivation of the convection function *:

[0098]

[0099] Finally, we get the solution and source terms

[0100] u=Uu * ,p=ρU 2 p * .

[0101] Step 3b, model adaptive adjustment technology: When the data is accurate, but the equation has missing values or simplification errors, the model adaptive adjustment technology is used. This technology introduces trainable variables to make up for the missing values in the equation or correct the neglected physical effects. Figure 3 The figure shows the neural network algorithm architecture based on the model adaptive adjustment technology. The accuracy of the boundary conditions is crucial for accurate prediction. In actual measurement, there are often errors in the boundary conditions, which leads to R e The data has deviations, which affects the prediction. In this case, equation correction terms can be added to PINNs to compensate for the resulting model deviations. Again, take the two-dimensional NS equation as an example:

[0102] a) Navier-Stokes equations

[0103] The basic form of the Navier-Stokes equations is:

[0104]

[0105] Where u represents the velocity vector, p represents the pressure, and ν represents the kinematic viscosity coefficient.

[0106] b) Introduction of stream functions

[0107] For two-dimensional incompressible flow problems, the stream function ψ can be introduced so that the velocity vector u can be expressed as:

[0108]

[0109] By introducing the stream function, the continuity equation is automatically satisfied Therefore, only the momentum equation needs to be calculated, which simplifies the calculation process, reduces the complexity of the problem, and facilitates the solution.

[0110] c) Dimensionless transformation of data and equations

[0111] Due to the complex operating conditions of the reactor core, the numerical values of variables such as flow field pressure, velocity, and density vary greatly, which affects the convergence of the neural network calculation. It is necessary to perform dimensionless processing on the flow field parameters, equations, and data. Definition of dimensionless variables:

[0112]

[0113] Where U is the characteristic velocity and L is the characteristic length. After dimensionless processing, the NS equation can be expressed as:

[0114]

[0115] Here, Re = UL / ν is the Reynolds number, which represents the ratio of inertial force to viscous force. Dimensionless processing helps avoid large numerical differences that can make neural network convergence difficult.

[0116] d) Trainable source terms

[0117] Introducing a correctable source term to correct the equation deviation, a trainable source term ν is introduced into the dimensionless NS equation f So that the equation can be expressed as:

[0118]

[0119] The source term is obtained through neural network training and can be adaptively adjusted to meet the characteristics and reconstruction requirements of different flow fields.

[0120] At this point the equation loss function becomes:

[0121]

[0122] The input of the PINNs model is the dimensionless spatial coordinates:

[0123] x * =(x * ,y * )

[0124] The output is the dimensionless stream function ψ * and pressure p * , through the convection function:

[0125]

[0126] Finally, we get the solution and the source term ν f :

[0127] u=Uu * ,p=ρU 2 p * .

[0128] (4) Design the neural network architecture for solving the problem, clarify the network input and output as well as the network structure, including:

[0129] Architecture selection: Designing a suitable neural network architecture and choosing an appropriate optimization algorithm to support the selected correction technique;

[0130] Input and output design: Define the input and output of the neural network to ensure that the network can process and improve all aspects of the physical equations. The network output should be able to calculate the data loss and the loss of the control equation directly or through transformation.

[0131] (5) Based on the selected correction technique and problem characteristics, define the corresponding form of the adjustment variable, including:

[0132] Step 5a, Data Adaptive Correction: Data adaptive correction introduces trainable variables into the neural network that are consistent with the noise data size. These variables can be model parameters or network layer outputs, intended to represent the noise in the data. Based on the existing noise information, the distribution of the trainable variables can be set, and their thresholds can be specified during the solution to achieve more accurate correction and avoid overcorrection.

[0133] Step 5b, model adaptive adjustment: Introduce trainable variables related to model simplification into the neural network. These variables can be single values or value distributions to make up for missing values in the equation or correct neglected physical effects.

[0134] (6) Based on the selected correction technique, design the loss function of the model, including:

[0135] Design a comprehensive loss function, which includes three main parts:

[0136] Internal data point loss function: This function measures the difference between the model output and the actual data. For data adaptive correction technology, since the physical quantity output by the neural network needs to be compared with noisy data, the trainable noise variable is added to the physical quantity output by the neural network to neutralize the noise in the data, thereby reducing the impact of noise on the data and achieving data correction.

[0137] Boundary data point loss function: evaluates the performance of the model under boundary conditions;

[0138] Equation loss function: Evaluates the degree of conformity of the model to the control equation; for missing values in the equation, its location is clarified and corresponding trainable variables are introduced at these locations. In addition, for the overall difference between the data and the equation due to model simplification or computational errors, a unified adjustment parameter can be defined at the end of the equation. The size of the adjustment parameter should be consistent with the size of the total training points to neutralize the equation error and quantify the difference between the data and the equation through data approximation.

[0139] (7) Train and optimize the model to ensure the highest accuracy, including:

[0140] The neural network is trained using data, boundary conditions, and adaptively modified physical equations until the model converges. Based on the training results, the neural network architecture and optimization function are adjusted to achieve optimal performance.

[0141] (8) Output model parameters to complete the solution of the physical problem proposed in step (1), specifically including:

[0142] Step 8a, data denoising: For data adaptive correction technology, the noise type and noise distribution can be determined based on the output variable used to neutralize the data noise, and high-precision data can be restored based on the linear transformation of the variable and the original noise data;

[0143] Step 8b, equation determination: For the equation adaptive adjustment technology, the missing values in the physical equation or the deviation value between the data and the equation can be determined based on the parameters iterated by the neural network, and corresponding corrections can be made.

[0144] When dealing with the noise problem in the data, the present invention introduces trainable variables into the neural network to correct the data. This method uses trainable variables to approximate the noise distribution in the data, thereby fine-tuning the original data without modifying the physical model. Specifically, the data adaptive correction technology introduces trainable variables into the physical variables output by the neural network, assuming that the physical variables output by the neural network are noise-free data variables, and the trainable parameters represent the data noise. These trainable parameters are added to the physical variables output by the neural network to calculate the data loss term. In order to ensure the effectiveness of this process, it is necessary to clarify the initial conditions, boundary conditions and control equations of the physical problem so as to properly control the iterative process of the trainable parameters. The core of this method is to optimize the match between data and model by dynamically adjusting the data, thereby improving the accuracy of data processing and model prediction.

[0145] Corresponding to the data adaptive correction technology is the model adaptive adjustment technology for the problems of physical model simplification and equation incompleteness. This technology aims to make up for the incomplete values in the equation or correct the physical effects that are ignored in the process of model simplification by introducing trainable variables in the neural network. These trainable variables can be single values or numerical distributions. Specifically, the model adaptive adjustment technology incorporates these trainable variables into the physical equations to adapt to the different adjustment targets of the equations. By adjusting the position and form of the trainable variables, this technology can improve the existing model in combination with data constraints during the dynamic adjustment process of the model. The core of this method is to dynamically adjust the variables in the equation to supplement the incompleteness caused by parameter accuracy and model simplification, thereby improving the model's ability to describe actual physical phenomena and the accuracy of prediction.

[0146] Example:

[0147] The specific steps of applying the intelligent numerical calculation method based on data and model adaptive correction described in the present invention to fluid mechanics measurement are as follows:

[0148] Step 1: Identify the physical problem to be solved

[0149] Problem Description: In this example, the flow behavior of fluid within a reactor plate element is studied. The goal is to calculate the velocity field, temperature field, and pressure distribution of the fluid and analyze the flow characteristics of the fluid within the plate element flow channel.

[0150] Data collection: Obtain velocity, pressure, and temperature data of the fluid in the pipeline through experimental measurement and numerical simulation.

[0151] Step 2: Determine the system's governing equations, boundary conditions, and initial conditions

[0152] Governing equations: conservation of mass, momentum, and energy:

[0153]

[0154] Where ρ is density, u is velocity vector, p is pressure, τ is stress tensor, g is gravity; c p is the specific heat capacity at constant pressure, T is the temperature field, k is the thermal conductivity of the fluid, and Q is the volume heat source term.

[0155] Boundary conditions: Inlet: set the velocity distribution; Outlet: set the pressure boundary; Wall: use the no-slip condition (velocity is zero).

[0156] Step 3: Select the correction technology (taking data adaptive correction technology as an example)

[0157] Correction technology: To address the noise in experimental measurement data, data adaptive correction technology is used. Trainable variables are introduced into the neural network to estimate the noise distribution and perform data denoising.

[0158] Step 4: Design the Neural Network Architecture

[0159] Network type: fully connected neural network;

[0160] Input: location coordinates and time;

[0161] Output: corrected velocity field, temperature field and pressure distribution;

[0162] Network structure: Multi-layer fully connected layers are used to extract fluid features and predict correction amounts.

[0163] Step 5: Define the moderator variable

[0164] Adjustment variable: Introducing a trainable variable ε into the neural network to correct for noise in the measurement data;

[0165] Adjustment method: gradually correct the noise data under the solution of boundary conditions and control equations.

[0166] Step 6: Design a loss function

[0167] L=λ1L data +λ2L boundary +λ3L equation

[0168] Among them, the data loss L data : Measures the difference between the predicted value and the measured data; boundary loss L boundary :Ensure that the boundary conditions meet the physical constraints; the equation loss L equation : Evaluate the degree of conformity of the neural network solution to the NS equation; λ1, λ2, λ3 are weight factors, λ1+λ2+λ3=0.

[0169] Step 7: Train and optimize the model

[0170] Optimization method: Gradient descent or Adam optimizer;

[0171] Goal: To maximize model accuracy through iterative training.

[0172] Step 8: Output model parameters

[0173] Output results: corrected fluid velocity field and pressure distribution as well as corrected parameters.

[0174] This paper, by incorporating data adaptive correction and model adaptive adjustment techniques, achieves high-precision simulation of incompressible fluid flow within reactor plate elements. This method effectively accounts for the effects of noise in experimental data while compensating for errors introduced by simplification or parameter uncertainty in the traditional NS equations. This approach provides more reliable numerical support for flow, heat transfer, and safety analysis within nuclear reactors.

[0175] The present invention further provides an intelligent numerical calculation system based on data and model adaptive correction, which is applied to the above-mentioned intelligent numerical calculation method based on data and model adaptive correction, including:

[0176] The data processing module is used to identify the physical problem to be calculated, collect relevant data, determine the data type, and perform data preprocessing;

[0177] An equation determination module is used to determine the control equations, boundary conditions and initial conditions of the system according to the system to be calculated;

[0178] A correction technology selection module is used to select an appropriate correction technology based on data characteristics and equation characteristics;

[0179] The network architecture design module is used to design the neural network architecture for solving problems and clarify the input, output and network structure of the neural network architecture;

[0180] A regulating variable definition module is used to define regulating variables of corresponding forms according to the selected correction technology and problem characteristics;

[0181] The loss function design module is used to design the loss function of the model based on the selected correction technology;

[0182] The model training module is used to train the neural network architecture based on the collected data, boundary conditions, and physical equations modified by the correction technology until the model converges. The neural network architecture and optimization function are adjusted according to the training results to obtain the model with the best performance;

[0183] The problem solving module is used to output model parameters based on the model with the best performance and complete the solution to the physical problem proposed in step (1).

[0184] In addition, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which executes the above-mentioned intelligent numerical calculation method based on adaptive correction of data and models when the computer program is run.

[0185] In addition, the present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and when the processor runs the computer program, it executes the above-mentioned intelligent numerical calculation method based on adaptive correction of data and models.

[0186] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the existing technology can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or certain parts of the embodiments.

[0187] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. An intelligent numerical calculation method based on adaptive correction of data and model, characterized in that: The following steps are involved: (1) Identify the physical problem to be calculated, collect relevant data, determine the data type, and perform data preprocessing; (2) Determine the control equations, boundary conditions, and initial conditions of the system according to the system to be calculated; (3) Based on the data characteristics in step (1) and the equation characteristics in step (2), a correction technique is selected, specifically including: when there is significant noise in the data and the equation and boundary conditions are relatively complete, a data adaptive correction technique is used, which neutralizes the noise in the data by introducing trainable variables; when the data is accurate but there are missing values or simplified errors in the equation, a model adaptive adjustment technique is used, which compensates for the missing values in the equation or corrects the neglected physical effects by introducing trainable variables; (4) Design a neural network architecture for solving the problem, and clarify the input, output, and network structure of the neural network architecture; (5) Define the appropriate form of the moderator variable based on the selected correction technique and problem characteristics; (6) Design the model’s loss function based on the selected correction technique; (7) Training the neural network architecture based on the collected data, boundary conditions, and physical equations modified by the correction technology until the model converges, and adjusting the neural network architecture and optimization function according to the training results to obtain the model with the best performance; (8) Based on the model with the best performance, the model parameters are output to complete the solution of the physical problem proposed in step (1).

2. The intelligent numerical calculation method based on data and model adaptive correction according to claim 1 is characterized in that: The step (1) specifies the physical problem to be calculated, collects relevant data, determines the data type, and performs data preprocessing, specifically including: Clarify the nature and scope of the physical problem to be solved; Collect data related to the physical problem and perform preliminary analysis to identify data characteristics and determine whether there is noise in the data. If noise is found, make assumptions about the noise model based on the actual situation and feasibility; The noise model is assumed, including: establishing a noise model based on the results of data analysis, assuming the noise type, and estimating the noise threshold and its distribution characteristics.

3. The intelligent numerical calculation method based on data and model adaptive correction according to claim 1 is characterized in that: The step (2) is to determine the control equations, boundary conditions and initial conditions of the system according to the system to be calculated, which specifically includes: Identify the governing equations that describe the system's behavior, evaluate whether there are missing values or simplifying assumptions in the equations, and consider how these factors affect the system's accuracy; According to the existing data and actual conditions, the initial conditions and boundary conditions of the system are set to ensure the accuracy and applicability of the model.

4. The intelligent numerical calculation method based on data and model adaptive correction according to claim 1 is characterized in that: The step (4) is to design a neural network architecture for solving the problem, clarify the input, output and network structure of the neural network architecture, and specifically include: Design the neural network architecture and select the optimization algorithm based on the selected correction technique; Define the input and output of the neural network to ensure that the network can process and improve all aspects of the physical equations. The network output is used directly or through transformation to calculate the data loss and the loss of the control equation.

5. The intelligent numerical calculation method based on data and model adaptive correction according to claim 1 is characterized in that: The step (5) defines the corresponding form of adjustment variables according to the selected correction technology and problem characteristics, specifically including: If the selected correction technique is data-adaptive correction, a trainable variable with the same size as the noise data is introduced into the neural network. The trainable variable serves as a model parameter or output of the network layer to represent the noise in the data. Based on the existing noise information, the distribution of the trainable variable is set, and its threshold is specified in the solution to achieve more accurate correction and avoid over-correction. If the selected correction technology is the model adaptive adjustment technology, a trainable variable related to model simplification is introduced into the neural network. The trainable variable is a single value or a value distribution, which is used to make up for the missing values in the equation or correct the neglected physical effects.

6. The intelligent numerical calculation method based on data and model adaptive correction according to claim 1 is characterized in that: Said step (6) is to design a loss function of the model based on the selected correction technique; Designing an internal data point loss function: This function is used to measure the difference between the model output and the actual data. For data adaptive correction technology, this function adds the physical quantity output by the neural network to a trainable noise variable. This trainable variable is used to neutralize the noise in the data, reducing the impact of noise on the data and thus achieving data correction. Design boundary data point loss function to evaluate the performance of the model under boundary conditions; Design an equation loss function to evaluate the model's compliance with the control equation. For missing values in the equation, identify their locations and introduce corresponding trainable variables at these locations. For the overall difference between the data and the equation due to model simplification or computational error, a unified adjustment parameter is defined at the end of the equation. The size of the adjustment parameter should be consistent with the size of the total training points to neutralize the equation error and quantify the difference between the data and the equation through data approximation.

7. The intelligent numerical calculation method based on data and model adaptive correction according to claim 1 is characterized in that: The step (8) outputs the model parameters based on the model with the best performance to complete the solution of the physical problem proposed in step (1), specifically including: Data denoising: Adaptive data correction technology determines the noise type and distribution based on the output variable used to neutralize data noise, and restores high-precision data based on the linear transformation of the variable and the original noise data; Equation determination: Based on the equation adaptive adjustment technology, the missing values in the physical equation or the deviation between the data and the equation are determined according to the parameters iterated by the neural network, and corresponding corrections are made.

8. An intelligent numerical calculation system based on data and model adaptive correction, applied to the intelligent numerical calculation method based on data and model adaptive correction according to any one of claims 1 to 7, characterized in that: include: The data processing module is used to identify the physical problem to be calculated, collect relevant data, determine the data type, and perform data preprocessing; An equation determination module is used to determine the control equations, boundary conditions and initial conditions of the system according to the system to be calculated; A correction technology selection module is used to select an appropriate correction technology based on data characteristics and equation characteristics; The network architecture design module is used to design the neural network architecture for solving problems and clarify the input, output and network structure of the neural network architecture; A regulating variable definition module is used to define regulating variables of corresponding forms according to the selected correction technology and problem characteristics; The loss function design module is used to design the loss function of the model based on the selected correction technology; The model training module is used to train the neural network architecture based on the collected data, boundary conditions, and physical equations modified by the correction technology until the model converges. The neural network architecture and optimization function are adjusted according to the training results to obtain the model with the best performance; The problem solving module is used to output model parameters based on the model with the best performance and complete the solution to the physical problem proposed in step (1).

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is running, the intelligent numerical calculation method based on adaptive correction of data and models according to any one of claims 1 to 7 is executed.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, wherein: When the processor runs the computer program, it executes the intelligent numerical calculation method based on adaptive correction of data and models according to any one of claims 1 to 7.

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