Research method for solving sub-channel equation based on physical information neural network

Abstract

The invention provides a research method for solving a sub-channel equation based on a physical information neural network, and belongs to the technical field of artificial intelligence. The method comprises the following steps: firstly, determining a to-be-calculated physical problem, collecting related data, screening the data, and carrying out data preprocessing; determining a control equation, boundary conditions and initial conditions of the system according to the system needing to be calculated; selecting a proper adaptation technology based on the data features and the equation features; designing a neural network architecture for solving, and determining input and output of the network and a network structure; according to the selected adaptation technology and problem features, defining adjustment variables in corresponding forms; designing a composite loss function exclusive to the model; training and optimizing the model to ensure that the precision of the model reaches the highest; and outputting a result and completing multi-scene verification solution. According to the method, in a pressurized water reactor sub-channel single-phase liquid coolant one-dimensional transient scene, a flow field can be solved with high precision and key parameters can be synchronously inverted based on a small amount of data, and meanwhile, the method can adapt to sub-channels with different geometrical characteristics and carry out friction parameter inversion in a targeted manner.

Description

Technical Field

[0001] This invention provides a research method for solving subchannel equations based on physical information neural networks, belonging to the field of artificial intelligence technology. Background Technology

[0002] Thermal-hydraulic analysis of nuclear reactor cores is a core component for ensuring nuclear safety and operational efficiency. Its core requirement is the accurate calculation of coolant flow and heat transfer characteristics, and subchannel analysis is the mainstream technical approach to achieving this. Currently, solving subchannel equations mainly relies on traditional subchannel codes (such as COBRA and FLICA) and computational fluid dynamics (CFD) methods. However, both technologies have inherent limitations that cannot be overcome, failing to meet the engineering requirements of "high precision, low cost, and strong adaptability" in core analysis. Specific problems are as follows: Traditional subchannel codes rely on discrete mesh generation and empirical correlations to solve the governing equations, but they have significant limitations: First, the computational accuracy is highly dependent on empirical formulas such as friction factor and lateral mixing coefficient. These formulas are mostly based on experimental fitting under specific working conditions. When faced with transient or non-standard geometric conditions that deviate from the fitting boundary, the error will be amplified sharply, requiring repeated manual parameter adjustments, which is inefficient. Second, for subchannels with different geometric features such as the center, edges, and corners of the reactor core, separate meshes need to be constructed and empirical formulas need to be corrected, resulting in a redundant design of "one geometry, one model," which leads to long code development cycles and high maintenance costs. At the same time, the discrete techniques used, such as finite difference or finite volume methods, require mesh generation of the channels. The discrete accuracy is limited by the mesh density and is prone to losing fine local features of the flow field.

[0003] While CFD methods can capture flow field details through fine meshes, they face significant engineering bottlenecks in core-level subchannel analysis: a reactor core typically contains hundreds to thousands of subchannels, and CFD requires three-dimensional meshing for each channel. Single-condition calculations often take several days to weeks, completely failing to meet the timeliness requirements of transient core analysis (such as rapid assessment of accident conditions). Furthermore, CFD calculation results require extensive experimental data verification, but core thermal experiments (such as single-phase flow experiments under high temperature and pressure) are extremely costly due to high equipment requirements, operational difficulties, and difficulty in obtaining sufficient data to support model calibration, leading to doubts about the reliability of the calculation results.

[0004] In recent years, although neural networks have been attempted to be used for flow field prediction, their "black box" nature makes them unsuitable for the needs of core thermal-hydraulic analysis: such models require tens of thousands of sets of labeled data to train a reliable model, while core thermal data is scarce and the cost of acquiring it far exceeds the engineering affordability; more importantly, the model only learns the correlation between parameters by fitting data, without incorporating fluid dynamics control equations such as momentum equations and continuity equations, and the prediction results may show situations that violate physical laws, such as negative pressure and sudden changes in flow velocity, making them unsuitable for core safety analysis.

[0005] In the field of nuclear reactor core thermal-hydraulic analysis, research on Physical Information Neural Networks (PINNs) has largely focused on conventional fluid scenarios such as pipe flow and simple two-dimensional flow domains. While this overcomes the "black box" problem of traditional neural networks, there is a lack of targeted research on solving subchannel equations. Currently, the problems solved by PINNs have relatively simple dimensions, flow characteristics, and constraints, making it difficult to directly transfer the technical approach to subchannel equation solving scenarios. For high-dimensional problems like subchannels, PINNs currently lack a clear technical path, and there is an urgent need to explore suitable solutions. Summary of the Invention

[0006] Based on this, this invention proposes a PINN technology solution specifically suitable for high-dimensional solutions of subchannel equations. The purpose of this invention is to provide a physical information neural network solution and parameter inversion technique adapted to subchannel equations. In a one-dimensional transient scenario with a single-phase liquid coolant in a pressurized water reactor subchannel, this technique can solve the flow field with high accuracy and simultaneously invert key parameters using only a small amount of data. Furthermore, it can be adapted to subchannels with different geometric features to perform targeted friction parameter inversion.

[0007] When constructing the PINN network adapted for solving subchannel equations, relevant thermal parameters are additionally introduced into the neural network input layer to achieve the mapping from equation parameters to the physical field to be solved. The core logic of this method is that the flow state within the subchannel is not only determined by its spatiotemporal location but is also closely related to the thermal properties of the coolant. Therefore, in addition to traditional spatiotemporal parameters such as location and time, key thermal parameters such as Reynolds number, mass flow rate, and coolant density are incorporated into the input layer to form multi-dimensional input features, enabling the network to directly learn the nonlinear relationship between thermal parameters and the flow field. To achieve integrated output of flow field solution and parameter inversion, flow field parameters and friction factor parameterization terms are simultaneously set in the output layer (satisfying... Meanwhile, friction loss terms are set for friction factor parameters A and B. To ensure the physicality of parameter inversion, an initial iteration interval is given based on engineering experience. Additionally, a logarithmic transformation is introduced into A within the network. This ensures non-negativity, allowing it to iterate and invert within a reasonable range.

[0008] The training process employs a dynamic weight adjustment combined with residual-guided sampling to efficiently support the solution of the entire flow field using a small number of sample points. In the initial stage, the network primarily uses data loss terms, rapidly establishing a basic mapping between thermal parameters and the flow field using sample points. At this stage, sample point selection focuses on locations with significant changes in the physical field gradient, outlining the flow field profile with limited data. As training iterates, the residuals of the equations across the entire flow domain are calculated in real-time, dynamically identifying regions with weak prediction accuracy. These high-residue regions undergo targeted, intensive sampling—without increasing the global sample size, only a small number of points are added locally to enhance the network's learning of key details. This allows the network to autonomously correct prediction biases in sparse sample regions based on physical laws, avoiding local overfitting caused by excessive reliance on limited data.

[0009] Based on the above design, the present invention is first applied to a single-channel scenario for feasibility verification to confirm the adaptability of the network architecture to a single geometric sub-channel; further, by introducing geometric feature encoding, the single-channel model is extended to multiple geometric scenarios to verify the model's general adaptability to different geometric feature sub-channels without reconstructing the network. Figure 2 The diagram shown above illustrates the entire process framework for solving subchannel equations based on physical information neural networks, clarifying the coupling logic and execution order of each key step.

[0010] The present invention is specifically implemented using the following technical solutions: This invention relates to a research method for solving subchannel equations based on physical information neural networks, comprising the following steps: (1) Define the physical problem to be calculated, collect relevant data, screen the data, and perform data preprocessing; (2) Determine the governing equations, boundary conditions and initial conditions of the system based on the system to be calculated; (3) Based on the data characteristics in step (1) and the equation characteristics in step (2), select an appropriate adaptation technology; (4) Design the neural network architecture for solving the problem, and define the network inputs, outputs and network structure; (5) Define appropriate adjustment variables based on the selected adaptation technology and problem characteristics; (6) Design a composite loss function specific to the model; (7) Train and optimize the model to ensure that the model accuracy reaches its maximum; (8) Output the results and complete the multi-scenario verification solution.

[0011] Preferably, the physical problem that this invention specifically aims to solve is the high-precision solution of the flow field and the friction factor (A, B, satisfying) under a one-dimensional transient scenario of a single-phase liquid coolant in a pressurized water reactor channel. Synchronous inversion, with a research scope covering sub-channels with different geometric features such as center, edge, and corner.

[0012] Data collection and filtering: Collect problem-related data, including spatiotemporal parameters and thermal parameters. Extract parameters from N locations, of which N / 3 of the data is used for flow field feature learning, and the remainder is used for model accuracy comparison.

[0013] Preferably, the governing equations are the core governing equations describing the one-dimensional transient flow in the subchannel, including the mass equation and the momentum conservation equation. Initial and boundary conditions: Based on existing data and actual conditions, initial and boundary conditions are set for the system to ensure the accuracy and applicability of the model.

[0014] Preferably, step (4) involves designing the PINN network architecture for solving the problem, specifying the network's inputs, outputs, and structure, including: Architecture selection: Design a suitable neural network architecture and select appropriate optimization algorithms to support the nonlinear mapping of thermal parameters and flow field and the embedding of physical equation constraints. Input / output design: Define the input and output of the neural network to ensure that the network can integrate flow field solution and friction factor relationship inversion.

[0015] Preferably, the loss function designed based on the selected technology specifically includes: In addition to the three conventional loss terms of PINN—data, physics, and boundary—a friction parameter constraint term is introduced to ensure the physical rationality of the parameter inversion. A suitable dynamic weight allocation method is selected to adjust the various loss functions in stages, achieving synergistic optimization of data and physical laws.

[0016] Preferably, step (7) employs a residual adaptive sampling mechanism to intensively sample regions with poor training results, enhances feature learning, and adjusts the neural network architecture and optimization function based on the training results.

[0017] Preferably, the output model parameters, which complete the solution of the physical problem proposed in step (1), specifically include: Model core parameter output: Outputs all parameters of the PINN model after training convergence, providing basic support for subsequent model reuse and engineering applications.

[0018] Multi-scenario verification: Based on existing models and geometric feature encoding, adaptability verification is performed for different geometric feature sub-channels.

[0019] Compared with the prior art, the present invention has the following beneficial effects: 1. Integrated PINN modeling for adapting sub-channel solutions: In PINN modeling of subchannel equations, the deep integration of thermal properties and physical laws, and the synergy between flow field solution and parameter inversion, are crucial for the model's engineering adaptability. Conventional PINN modeling relies solely on spatiotemporal parameters, making it difficult to correlate the thermal effects of the coolant within the subchannel. Furthermore, flow field calculation and friction factor inversion are typically separate processes. Additionally, imbalances can easily arise between data fitting and physical constraints during training for high-dimensional problems, leading to low modeling efficiency and insufficient physical consistency. To address these issues, this invention proposes a modeling scheme that combines "thermal parameter embedding + integrated output + dynamic training optimization."

[0020] Specifically, in addition to traditional spatiotemporal parameters, key thermal parameters such as Reynolds number, mass flow rate, and coolant density are added to the network input layer to directly establish the correlation between thermal characteristics and flow field behavior. At the output layer, flow field parameters and friction factor parameterization terms are set simultaneously, and exponential and logarithmic transformations are used to ensure the physical rationality of the friction parameters, achieving integrated output of solution and inversion. The training process employs a two-stage dynamic weight adjustment strategy: initially, data loss is prioritized to quickly establish the basic mapping, while later, the weight of physical loss is gradually increased to guide the model to strictly adhere to the laws of mass and momentum conservation. Simultaneously, a residual adaptive point allocation strategy is introduced, calculating the residual of the physical equations across the entire flow domain every n iterations, and locally refining sampling in high residual regions, thus strengthening the fitting of weak regions without increasing the global sample size. This approach effectively avoids the problems of missing thermal effects, process fragmentation, and training imbalance in traditional modeling, enhancing the model's targeted adaptation to one-dimensional transient scenarios in pressurized water reactor channels.

[0021] 2. Design for Universal Adaptability Verification of Multi-Geometric Feature Sub-channels In the analysis of multiple geometric sub-channels in the reactor core, the geometric differences between the center, edge, and corner channels pose a core requirement for the model's universality. Traditional methods require modeling different geometric channels, which not only suffers from architectural redundancy and high parameter tuning costs, but also struggles to guarantee the consistency of multi-channel solution results, failing to efficiently adapt to scenarios where multiple geometries coexist within the small watershed of the reactor core. To address this issue, this invention proposes an adaptation and verification scheme based on "geometric feature encoding - channel parameter association."

[0022] Specifically, based on the single-channel PINN model, a new 1D geometric feature encoding is added to the input layer. Different geometric types are identified using specific values, and the encoding is implicitly correlated with characteristic parameters such as flow area and wetted perimeter of each channel, enabling the network to automatically identify geometric differences. Simultaneously, the network architecture, loss function, and training strategy remain consistent, eliminating the need to reconstruct the model for different geometries; adaptation to sub-channels with different geometric features can be achieved solely through encoding. This invention effectively avoids the problem of redundant design in traditional multi-model approaches, requiring only one model to complete the solution verification for different geometric sub-channels, ensuring that the results for each channel conform to physical laws, and providing support for efficient analysis of multi-geometric scenarios in reactor cores. Attached Figure Description

[0023] Figure 1 A flowchart illustrating the research method for solving subchannel equations based on physical information neural networks; Figure 2 This is a flowchart illustrating the entire process of solving subchannel equations using a physical information neural network. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the preferred embodiments of this invention will be described in further detail below with reference to the examples. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0025] Example 1 like Figure 1 As shown, the research method for solving sub-channel equations based on physical information neural networks is implemented according to the following steps: Step 1: Define the physical problem The core issues of solving the one-dimensional transient flow field of single-phase coolant in the pressurized water reactor channel and inverting the friction factor parameters are clarified, and the background and objectives of the problem are defined.

[0026] Step 2: Define the nature and scope of the problem Define the nature of the problem, determine the research scope of single-channel and multi-geometric feature sub-channels, and clarify the core research content.

[0027] Step 3: Determine the system's governing equations, boundary conditions, and initial conditions. Determine the mass and momentum conservation equations for the subchannels, assess the effects of equation simplification, and set initial and boundary conditions.

[0028] Step 4: Data Collection and Preliminary Analysis Collect spatiotemporal, thermal, and flow field data, filter data for learning and verification, and perform data preprocessing.

[0029] Step 5: Design the PINN network architecture adapted for sub-channel solving We selected the PINN architecture and optimization algorithm, designed the network input and output dimensions, and determined the hidden layer structure.

[0030] Step 6: Construct a multi-objective composite loss function Design a composite loss function that incorporates constraints from data, physics, boundary, and friction parameters, and employ dynamic weight allocation.

[0031] Step 7: Train and optimize the model The model is trained using a residual adaptive sampling and two-stage weight adjustment strategy, and the accuracy is monitored and optimized to output the model parameters.

[0032] Step 8: Single-channel verification and physics field solution Conduct single-channel feasibility verification, verify model accuracy, and output single-channel flow field distribution and friction factor inversion parameters.

[0033] Step 9: Multi-geometric feature sub-channel adaptation and solution Based on step 6, geometric feature encoding is introduced, and the encoding is associated with the geometric parameters of the sub-channel, thus extending the single-channel model into a multi-geometric adaptation model; Multi-geometric feature sub-channel scenario verification was carried out to confirm the model's adaptability to different geometric features, output the multi-channel flow field distribution and corresponding friction factor parameters, and complete the physical field solution for the entire scenario.

[0034] The embodiments described above are some, but not all, embodiments of the present invention. The detailed description of the embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A research method for solving subchannel equations based on physical information neural networks, characterized in that, Includes the following steps: (1) Define the physical problem to be calculated, collect relevant data, filter the data, and perform data preprocessing; (2) Determine the governing equations, boundary conditions and initial conditions of the system based on the system to be calculated; (3) Based on the data characteristics in step (1) and the equation characteristics in step (2), select an appropriate adaptation technology; (4) Design the neural network architecture for solving the problem, and define the network inputs, outputs and network structure; (5) Define appropriate adjustment variables based on the selected adaptation technology and problem characteristics; (6) Design a composite loss function specific to the model; (7) Train and optimize the model to ensure that the model accuracy reaches its maximum; (8) Output the results and complete the multi-scenario verification solution.

2. The research method for solving sub-channel equations based on physical information neural networks as described in claim 1, characterized in that, The identified physical problem to be solved is the high-precision solution of the flow field and the synchronous inversion of the friction factor in the one-dimensional transient scenario of the single-phase liquid coolant in the sub-channel of the pressurized water reactor. The research scope covers sub-channels with different geometric features such as the center, edge, and corner.

3. The research method for solving sub-channel equations based on physical information neural networks as described in claim 1, characterized in that, The relevant data collected in step (1) covers spatiotemporal parameters and thermal parameters, and parameters at N locations are extracted.

4. The research method for solving sub-channel equations based on physical information neural networks as described in claim 1, characterized in that, The governing equations mentioned in step (2) are the core governing equations for determining the one-dimensional transient flow in the subchannel, including the mass equation and the momentum conservation equation.

5. The research method for solving sub-channel equations based on physical information neural networks as described in claim 1, characterized in that, Step (4) involves designing the PINN network architecture for solving the problem, specifying the network's inputs, outputs, and structure, including: Architecture selection: Design a suitable neural network architecture and select appropriate optimization algorithms to support the nonlinear mapping of thermal parameters and flow field and the embedding of physical equation constraints. Input / output design: Define the input and output of the neural network to ensure that the network can integrate flow field solution and friction factor relationship inversion.

6. The research method for solving sub-channel equations based on physical information neural networks as described in claim 1, characterized in that, Step (7) employs a residual adaptive sampling mechanism to refine sampling in regions with poor training performance. Enhance feature learning and adjust the neural network architecture and optimization function based on the training results.

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