Aircraft flow field prediction method and system based on multi-region physical driving neural network

Abstract

The invention discloses an aircraft flow field prediction method and system of a multi-region physical drive neural network, and the method comprises the steps: constructing a continuous region mask and high-dimensional physical parameter sampling system, carrying out the global sampling of high-dimensional physical parameters through employing a Latin hypercube sampling method, and carrying out the space division through combining with a KMeans clustering algorithm; inputting the space coordinates, the continuous area mask, the wall surface distance and the physical condition parameters into an AMPD model, and generating a boundary layer mask, an eddy current mask and a physical residual error; inputting the boundary layer mask and the eddy current mask into a physical constraint driven loss function system, and establishing a multi-target residual minimization loss function for training an AMPD model; based on the multi-target residual error minimization loss function and the physical residual error, training an AMPD model by adopting a course learning training strategy; wing surface flow field reconstruction is carried out through the trained AMPD model, aircraft flow field prediction is completed, and high-precision and high-efficiency intelligent prediction of wing streaming is achieved.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of computational fluid dynamics and artificial intelligence, specifically involving a method and system for predicting aircraft flow fields using multi-region physical-driven neural networks. Background Technology

[0002] In aerospace engineering, accurate prediction of airfoil flow characteristics is a crucial technological foundation for aircraft aerodynamic design, performance optimization, and safety assessment. Accurately understanding parameters such as flow field distribution, pressure distribution, and lift-drag characteristics under different operating conditions is of great significance for improving aircraft design efficiency and flight safety. While traditional computational fluid dynamics (CFD) methods can provide high prediction accuracy, they suffer from the following significant drawbacks: extremely high computational costs, with single flow field calculations typically requiring hours to days; complex mesh generation, necessitating remodeling for different airfoil geometries; and difficulty in meeting the engineering demands of real-time prediction and large-scale multi-condition optimization. In recent years, the application of deep learning technology in fluid mechanics has gradually increased, but existing methods face the following key technical challenges: (1) Lack of physical constraints leads to inconsistent predictions: Existing patents such as CN202411325265A use U-Net to directly predict flow field images, but its pure data-driven mode lacks explicit constraints on basic physical laws such as mass conservation, momentum conservation, and energy conservation. The prediction results may violate the basic principles of fluid mechanics, especially in strong gradient regions such as boundary layer, shock wave, and eddy current.

[0003] (2) Insufficient generalization ability of multiple airfoils: Patent CN202510266457 proposed an airfoil flow field prediction method based on multi-task learning. It partially solved the gradient conflict problem between airfoil surface and volume region prediction through multi-head decoder architecture and multi-task loss optimization strategy. However, its shared feature extraction layer is still limited by the geometric distribution of the training airfoil family, and its generalization ability to unseen airfoils is limited, making it difficult to adapt to airfoil changes with different thickness ratios and camber.

[0004] (3) The contradiction between computational complexity and accuracy: Patent CN202410781189A improves prediction accuracy by embedding Navier-Stokes equation constraints, but its multi-feature map joint processing mechanism leads to a significant increase in computational complexity and a large increase in the number of network parameters, which affects the feasibility of practical applications.

[0005] (4) Limited ability to handle complex flow phenomena: Patent CN202411622813A proposed a semi-supervised learning flow field prediction method based on Gaussian mixture model (GMM). Although the dependence on labeled data is reduced by pseudo-label generation and sample screening mechanism, the accuracy still needs to be improved when dealing with complex nonlinear flow phenomena such as flow separation, reattachment, and shock wave boundary layer interference.

[0006] (5) The multi-physical region processing mechanism is not perfect: Existing methods such as the machine learning model of CN202411065287A can capture the geometric evolution of the wake well, but its training data is limited to fixed airfoils, and it lacks an effective mechanism to distinguish and process the characteristics of different physical regions such as solid interior, wall, near-wall fluid, and free fluid.

[0007] Given the shortcomings of existing technologies, the following key technical issues urgently need to be addressed: Physical consistency guarantee: Establish a neural network architecture that integrates the conservation laws of fluid mechanics to ensure the physical rationality of the prediction results; Multi-airfoil adaptive capability: Develop a general modeling method with cross-airfoil generalization capability to reduce dependence on specific airfoil training data; Accurate capture of complex flow phenomena: Improve the prediction accuracy of models in complex regions such as shock waves, boundary layers, and flow separation; Multi-physical region coordinated processing: to achieve effective differentiation and unified modeling of the characteristics of different physical regions; Balancing computational efficiency and accuracy: Significantly improve computational efficiency while ensuring prediction accuracy, meeting the needs of real-time engineering applications.

[0008] Therefore, there is an urgent need to develop an intelligent flow field prediction technology that integrates prior physical knowledge, has multi-airfoil adaptability, and supports accurate prediction of complex flow phenomena, in order to break through the technical bottlenecks of existing methods and meet the practical application needs of aerospace engineering. Summary of the Invention

[0009] To address the aforementioned shortcomings in existing technologies, the present invention provides a multi-region physical-driven neural network-based aircraft flow field prediction method and system. By integrating physical conservation law constraints, multi-region adaptive modeling, and curriculum learning strategies, this method solves the technical problems existing in the physical consistency, multi-airfoil generalization ability, and capture of complex flow phenomena of existing methods.

[0010] To achieve the aforementioned objectives, the present invention employs the following technical solution: a multi-region physical-driven neural network-based method for predicting aircraft flow fields, comprising the following steps: S1. Obtain the wing geometry parameters, generate the airfoil profile through the airfoil parameterization equation, and divide the multi-physical region according to the continuous region mask; S2. The Latin hypercube sampling method is used to globally sample the high-dimensional physical parameters, and the KMeans clustering algorithm is combined to divide the parameter space into six representative sub-regions to obtain the physical condition parameters. S3. Input the spatial coordinates, continuous region mask, wall distance and physical condition parameters into the AMPD (Adaptive Multi-Region Physics-Driven Neural Network) model, and map them to a high-dimensional feature space through dilated convolution and linear transformation to generate boundary layer mask, eddy current mask and physical residual; S4. Input the boundary layer mask and eddy current mask into the loss function system driven by physical constraints, and establish a multi-objective residual minimization loss function based on the continuity equation, momentum conservation equation, energy equation and ideal gas state equation, which is used to train the AMPD model. S5. Based on the multi-objective residual minimization loss function and physical residual, the AMPD model is trained using a course learning training strategy. S6. Input the airfoil type, Mach number, Reynolds number, temperature and angle of attack into the trained AMPD model, and reconstruct the airfoil surface flow field through the trained AMPD model to complete the aircraft flow field prediction.

[0011] Furthermore: In S1, the method for dividing multiple physical regions based on continuous region masks is as follows: Multiphysics regions are determined based on spatial distance and topology. The mask value for the airfoil interior region is 1, the mask value for the airfoil wall region is 2, the mask value for the near-wall fluid region is 3.0 to 4.0, the mask value for the external fluid region is 4, the mask value for the inlet region is 5, the mask value for the outlet region is 6, and the mask value for the free boundary region is 7. Among them, the near-wall fluid region mask S ( x The sigmoid function is used to describe the smooth transition from 3.0 to 4.0; In the formula, The distance to the wall is a point. x The closest distance to the airfoil wall, To adapt to the near-wall region scale, For smooth transition band parameters, This is the sigmoid function.

[0012] The beneficial effects of the above-mentioned further solutions are as follows: This invention proposes a continuous region masking mechanism to achieve smooth division and adaptive processing of multiple physical regions such as solids, walls, near-wall fluids, and free fluids.

[0013] Furthermore: In S2, the objective function of the KMeans clustering algorithm The specific expression is: In the formula, It is the first One cluster, It is a cluster center. For physical parameters, The square of the Euclidean distance; The high-dimensional physical parameters sampled are normalized to ensure that each physical parameter has the same scale during training. In the formula, Physical parameters The mean, Physical parameters standard deviation These are the normalized physical parameters.

[0014] Furthermore: In S3, the AMPD model includes an input embedding layer, a feature fusion backbone, and a physical constraint and explicit residual module connected in sequence; Input embedding layer: Input spatial coordinates, continuous region masks, wall distances, and physical condition parameters. Spatial coordinates are extracted using a dilated convolution module for multi-scale feature extraction and mapped to a 32-dimensional feature space, with dilation rates of 1, 2, and 4, generating spatial coordinate features. Continuous region masks and wall distances are embedded into a 16-dimensional feature space through independent linear transformations, generating region mask features and wall distance features, respectively. Physical condition parameters are encoded into physical condition vectors using a multilayer perceptron, which are used to train the AMPD model using the course learning training strategy. Feature fusion backbone: Spatial coordinate features, region mask features and wall distance features are combined to form a 64-dimensional fusion feature. The fusion feature is then input into the residual backbone network and attention mechanism module to obtain flow field data, including velocity field, density field, temperature field and pressure field. The residual backbone network consists of six stacked residual neural blocks. Each residual neural block includes a bilinear transform layer, layer normalization, Leaky ReLU activation function, and residual connections. The attention mechanism module is used to dynamically adjust the weights of features at different spatial locations and improve the model's ability to represent complex flow fields through deep feature fusion. The physical constraint and explicit residual module includes a gradient feature extraction unit, a physical region identification unit, a residual calculation unit, and a boundary condition enforcement unit; Gradient feature extraction unit: Input flow field data and calculate the spatial gradient, gradient magnitude and higher-order derivative features of vorticity of each physical quantity through adaptive finite difference method; Physical region identification unit: Dynamically identifies key physical regions in the flow field based on gradient characteristics, calculates boundary layer masks and eddy current masks, and provides region prior information for subsequent physical constraints; Residual calculation unit: Calculates physical residuals using the basic governing equations of fluid mechanics. Physical residuals include residuals of the continuity equation, momentum equation, energy equation, and ideal gas law equation. Boundary condition enforcement unit: Receives flow field data, physical residuals, continuous region mask, boundary layer mask, and eddy current mask. Inputs the spatial gradient, gradient magnitude, and higher-order derivative features of vorticity of each physical quantity calculated by the gradient feature extraction unit. Dynamically calculates gradients and divergences using an adaptive finite difference method, and enhances the physical residuals using an adaptive weight network. Corrects systemic biases in density, velocity, temperature, and pressure through residual calculations, and enforces corresponding physical constraints in different boundary regions. Based on the different physical regions corresponding to the continuous region mask values—inside the airfoil, on the airfoil wall, near-wall fluid, external fluid, inlet, outlet, and free boundary—it enforces corresponding constraints for no-slip boundary conditions, specified inflow conditions, pressure or velocity gradient conditions, and far-field boundary conditions, adjusting the flow field data and outputting the corrected flow field data.

[0015] The beneficial effects of the above-mentioned further solutions are as follows: the present invention constructs a physical constraint-driven neural network architecture, and ensures the physical consistency of flow field prediction through explicit residual correction.

[0016] Further: In S3, the boundary layer mask is calculated. The specific expression is: In the formula, For the velocity gradient, For gradient threshold, For characteristic attenuation length, d The distance to the solid boundary, k This is a gradient sensitivity parameter; Calculate the eddy current mask The specific expression is: In the formula, For the preset threshold, The clustering label is 1 for valid clusters and 0 for others. In the process of dynamically calculating the gradient using the adaptive finite difference method, the following formula is used: In the formula, and For grid spacing, and For grid node indexing, f Let be the physical field function to be differentiated. For grid points ( The function value at () For grid points ( The function value at () For grid points ( The function value at () For grid points ( The function value at (). Laplace operator The second derivative is approximated using a five-point scheme: The specific expressions for the boundary condition enforcement element that enforces the corresponding physical constraints in different boundary regions are as follows: In the formula, The velocity field within the solid region. This is the velocity field at the wall boundary, ensuring no-slip conditions between the solid surface and the wall.

[0017] Furthermore: In S4, the multi-objective residual minimization loss function of the physical constraint-driven loss function system. The specific expression is: In the formula, This refers to the loss term that encompasses continuity loss, momentum loss, energy loss, ideal gas state loss, inlet region loss, boundary condition constraints, and penalty loss. For the gradient norm regularization term of the physical quantity, For parameter weights, Loss due to constraint on the rate of change of physical quantities. The weight parameters are constrained by the rate of change. These are the gradient regularization weight parameters; Continuous loss The specific expression is: In the formula, An adaptive weighting function is calculated based on the key region weights of continuous region masking, near-wall distance, and physical shock waves. This represents the total number of sampling points within the fluid domain. For the first One sampling point, For the fluid computation domain, For the first The continuity equation residuals at each sampling point For the first Spatial coordinates of each sampling point; The velocity vector in response to the prediction is The density is The temperature is The pressure is P Spatial coordinates are Then the residual of mass conservation The specific expression is: In the formula, The sign of the partial derivative. x for x Axis coordinates y for y Axis coordinates u for x Directional velocity component, v for y Directional velocity component; Momentum loss includes x Momentum loss in the axial direction and y Momentum loss in the axial direction ; In the formula, and The standard deviation of the momentum residual. for x Momentum residual in the axial direction for y Momentum residual in the axial direction; In the formula, For the Laplace operator, and This is the viscous stress divergence term; In the formula, For fluid dynamic viscosity; Energy loss The specific expression is: In the formula, The normalization coefficient is... For numerically stable regularization terms, For the first The energy conservation equation residuals at each sampling point; Energy conservation equation residual The specific expression is: In the formula, For isobaric specific heat capacity, Thermal conductivity, This is a viscous dissipation term; In the formula, It is the bulk viscosity coefficient; Ideal gas state loss The specific expression is: In the formula, The residuals of the ideal gas law; In the formula, R Let be the ideal gas constant. For position x Density value at that location, It is the product of the ideal gas constant and temperature. For position x Predicted pressure value at the location; entrance area loss The specific expression is: In the formula, For standard inlet physical parameters, Number of entry nodes This is the entrance boundary area. q Set of physical quantity variables A single physical quantity in it. For the first Predicted physical quantity values ​​at each entry node; Boundary condition constraints are weighted by continuous values ​​generated through the tanh activation function to smoothly reflect the relative importance of each node in the anomalous physical region. The specific expression is: In the formula, For shock wave region weighting coefficients, This refers to the weighting coefficient for the eddy current region. The weighting coefficient for the sheared region. For shock wave identification mask, For eddy current identification mask, Identify the mask for the shear layer; Punishment loss The specific expression is: In the formula, As a safety threshold, As a penalty factor, This is the ReLU activation function.

[0018] Furthermore: In S5, the specific method for training the AMPD model using the course-based learning training strategy is as follows: Phase 1: Angle of attack range limited to 20% of the total range, Reynolds number capped at 5×10. 5 Mach number upper limit 0.3, geometric sample size 15, physical condition size 5; Phase 2: Angle of attack range expanded to 40%, Reynolds number capped at 6×10 5 Mach number upper limit 0.5, geometric sample number 18, physical condition number 6; Phase 3: Angle of attack range expanded to 60%, Reynolds number capped at 7×10 5 Mach number upper limit 0.7, geometric sample size 20, physical condition size 7; Phase 4: Angle of attack range expanded to 80%, Reynolds number capped at 8×10 5 The upper limit of Mach number is 0.85, the number of geometric samples is 23, and the number of physical conditions is 8. Phase 5: Angle of attack range reaches 100%, Reynolds number cap 10. 6 The upper limit of Mach number is 0.95, the number of geometric samples is 25, and the number of physical conditions is 10. Each stage has a loss threshold, initially set at 500, which decreases to 10 as the training cycle increases. In each stage, the next stage begins when the verification loss is below the loss threshold and the training cycle is at least 20.

[0019] The beneficial effects of the above-mentioned further solutions are as follows: the present invention designs a course learning and training strategy to gradually improve the model's ability to predict complex flow phenomena.

[0020] A multi-region physics-driven neural network-based aircraft flow field prediction system, comprising: The data preprocessing module is used to generate airfoil profiles, construct continuous region masks, and perform high-dimensional physical parameter sampling. The neural network training module includes the AMPD model architecture, a physical constraint-driven loss function system, and a course learning and training strategy. The flow field prediction module includes a pre-trained AMPD model. Inputs include airfoil type, Mach number, Reynolds number, temperature, and angle of attack, and output complete flow field distribution data. The results visualization module provides display methods for velocity vector maps, pressure cloud maps, density cloud maps, velocity amplitude maps, and surface pressure coefficient curves.

[0021] The beneficial effects of this invention are as follows: (1) This invention provides a method and system for predicting aircraft flow fields using a multi-region physical-driven neural network. It proposes a continuous region mask and a high-dimensional physical parameter sampling system, and achieves smooth division of multiple physical regions through the sigmoid function. It establishes a Latin hypercube sampling and KMeans clustering strategy to perform global sampling and spatial division of parameters such as Mach number, Reynolds number, and temperature. It constructs an AMPD model that includes an input embedding layer, a feature fusion backbone, and physical constraints and explicit residual modules. It designs a loss function system driven by physical constraints and strengthens key flow regions by combining an adaptive weighting mechanism. It implements a five-stage incremental complexity course learning training strategy. By integrating physical constraints, multi-region adaptive modeling, and course learning, this invention solves the technical problems of existing methods in terms of physical consistency, multi-airfoil generalization ability, and capture of complex flow phenomena. It achieves high-precision and high-efficiency intelligent prediction of wing flow, which is more than 3,000 times faster than traditional CFD methods, and the prediction accuracy meets the requirements of engineering applications.

[0022] (2) The adaptive multi-region physical-driven neural network method of the present invention exhibits excellent prediction performance under various airfoils and different flow conditions: Prediction accuracy: The average error of the pressure coefficient distribution is <3%, and the error of the lift and drag coefficient is <5%, which meets the requirements of engineering applications; Physical consistency: It strictly satisfies the conservation laws of fluid mechanics and has no non-physical phenomena; Computational efficiency: More than 3,000 times faster than traditional CFD methods, with a single prediction time of less than 10 seconds; Highly adaptable: Supports various airfoil geometries and a wide range of operating conditions, with outstanding generalization ability; Complex flow capture: accurately predicts complex flow phenomena such as separation and shock waves, with significant technological advancements.

[0023] The method of this invention provides an efficient, accurate, and intelligent solution for rapid flow field analysis in the aerospace field, and has significant engineering application value. Attached Figure Description

[0024] Figure 1 This is a flowchart of the aircraft flow field prediction method using a multi-region physical-driven neural network according to the present invention.

[0025] Figure 2 This is a schematic diagram of the aircraft flow field prediction method using a multi-region physical-driven neural network according to the present invention.

[0026] Figure 3 This invention relates to a multi-region physics-driven neural network-based aircraft flow field prediction system. Detailed Implementation

[0027] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0028] like Figure 1 and Figure 2 As shown, in one embodiment of the present invention, the aircraft flow field prediction method using a multi-region physics-driven neural network includes the following steps: S1. Obtain the wing geometry parameters, generate the airfoil profile through the airfoil parameterization equation, and divide the multi-physical region according to the continuous region mask; S2. The Latin hypercube sampling method is used to globally sample the high-dimensional physical parameters, and the KMeans clustering algorithm is combined to divide the parameter space into six representative sub-regions to obtain the physical condition parameters. S3. Input the spatial coordinates, continuous region mask, wall distance and physical condition parameters into the AMPD model, and map them to a high-dimensional feature space through dilated convolution and linear transformation to generate boundary layer mask, eddy current mask and physical residual; S4. Input the boundary layer mask and eddy current mask into the loss function system driven by physical constraints, and establish a multi-objective residual minimization loss function based on the continuity equation, momentum conservation equation, energy equation and ideal gas state equation, which is used to train the AMPD model. S5. Based on the multi-objective residual minimization loss function and physical residual, the AMPD model is trained using a course learning training strategy. S6. Input the airfoil type, Mach number, Reynolds number, temperature and angle of attack into the trained AMPD model, and reconstruct the airfoil surface flow field through the trained AMPD model to complete the aircraft flow field prediction.

[0029] S1 specifically refers to: Airfoil geometry generation and mesh discretization: Using the NACA series airfoil as the flow field geometry basis, its airfoil profile is defined by parametric equations. It is discretized in the generalized coordinate domain using a two-dimensional uniform mesh to generate a standardized spatial point cloud. The typical mesh size is 100×100 nodes. Precise division of multi-physics regions: For different angles of attack and geometric configurations, multi-region division is achieved through spatial distance and topological discrimination. The specific allocation rules are shown in Table 1. Table 1 Mask Allocation Rules In S1, the method for dividing multiple physical regions based on continuous region masks is as follows: Multiphysics regions are determined based on spatial distance and topology. The mask value for the airfoil interior region is 1, the mask value for the airfoil wall region is 2, the mask value for the near-wall fluid region is 3.0 to 4.0, the mask value for the external fluid region is 4, the mask value for the inlet region is 5, the mask value for the outlet region is 6, and the mask value for the free boundary region is 7. Among them, the near-wall fluid region mask S ( x The sigmoid function is used to describe the smooth transition from 3.0 to 4.0; In the formula, The distance to the wall is a point. x The closest distance to the airfoil wall, To adapt to the near-wall region scale, For smooth transition band parameters, This is the sigmoid function.

[0030] This embodiment uses this mechanism to determine whether each node is close to the wall by introducing a smooth function form, thereby distinguishing between near-wall fluid and free fluid regions. Through a parameterized mask generation mechanism, it adaptively handles the geometric variations of different NACA series airfoils. For different airfoil parameters (maximum thickness, camber, camber position), it achieves precise adaptation of various airfoil geometries by dynamically adjusting the wall distance function and adaptive near-wall region scale.

[0031] In S2, the high-dimensional physical parameters are the basis for describing the physical properties of the flow field, as shown in Table 2: Table 2 Physical parameters and parameter ranges Implementation of the Latin hypercube sampling method: The Latin hypercube sampling method was used to... , and Sampling is performed to generate multiple sets of physical boundary condition samples to cover different flow field conditions.

[0032] in, The Reynolds number (Re) determines the intensity of compression effects such as shock waves and expansion waves in the flow field, and has a significant impact on flow separation and pressure distribution, especially at large angles of attack. Re represents the ratio of fluid inertial force to viscous force, directly affecting boundary layer behavior and eddy characteristics. From low to high Reynolds numbers, the viscous effects of the flow field and the formation of separated bubbles vary with Re. Indirectly modulate the compressibility and viscosity properties of the flow field, especially the thermodynamic behavior of gases at different temperatures.

[0033] The physical parameters were sampled using the Latin hypercube sampling method: 50 Mach numbers were sampled in the range [0.3, 0.95]; the Reynolds number was sampled in the range [1×10⁻⁶]. 4 1×10 6 Fifty values ​​were sampled within the range of [250K, 350K]; thirty values ​​were sampled for the free-flow temperature within the range of [250K, 350K], generating a total of 75,000 operating condition combinations. The KMeans clustering algorithm was used to divide the parameter space into six representative sub-regions, with the cluster centers corresponding to typical flow states such as low speed and low Reynolds number, medium speed and medium Reynolds number, high speed and low Reynolds number, low speed and high Reynolds number, high speed and high Reynolds number, and transonic complex operating conditions.

[0034] The KMeans clustering algorithm is used to generate physical condition parameters. The objective function of the KMeans clustering algorithm is... The specific expression is: In the formula, It is the first One cluster, It is a cluster center. For physical parameters, The square of the Euclidean distance is used to divide the parameter space into six representative sub-regions, effectively covering the flow field behavior from laminar weak compressibility to turbulent strong compressibility, providing diverse training samples for the model. The high-dimensional physical parameters sampled are normalized to ensure that each physical parameter has the same scale during training. In the formula, Physical parameters The mean, Physical parameters standard deviation These are the normalized physical parameters.

[0035] The AMPD model consists of an input embedding layer, a feature fusion backbone, and a physical constraint and explicit residual module connected in sequence. Input embedding layer: Input spatial coordinates, continuous region mask, wall distance, and physical condition parameters; Spatial coordinates are extracted and mapped to a 32-dimensional feature space through a dilated convolution module with dilation rates of 1, 2 and 4. Local and global spatial information are fused through multi-scale receptive fields to generate spatial coordinate features. The continuous region mask is embedded into the 16-dimensional feature space through independent linear transformations, preserving the continuity features of different physical regions (solid, wall, near-wall fluid, free fluid); After normalization, the wall distance is embedded into the 16-dimensional feature space through linear transformation to provide geometric prior information for boundary layer recognition. Physical condition parameters are encoded into physical condition vectors through a multilayer perceptron, which are used to train the AMPD model using course learning training strategies, and guide the AMPD model to adapt to different working conditions. Feature fusion backbone: Spatial coordinate features, region mask features and wall distance features are combined to form a 64-dimensional fusion feature. The fusion feature is then input into the residual backbone network and attention mechanism module to obtain flow field data, including velocity field, density field, temperature field and pressure field. The residual backbone network consists of six stacked residual neural blocks. Each residual neural block includes a bilinear transformation layer (64→128→64 dimensions), layer normalization, Leaky ReLU activation function (negative slope 0.01), and residual connections. The residual connections solve the gradient vanishing problem in deep networks and improve the model's representation ability. The attention mechanism module is used to dynamically adjust the weights of features at different spatial locations, and improves the model's ability to represent complex flow fields through deep feature fusion. The physical constraint and explicit residual module ensures the physical consistency and rationality of the neural network prediction results by integrating fluid dynamics conservation law constraints. The physical constraint and explicit residual module includes a gradient feature extraction unit, a physical region identification unit, a residual calculation unit, and a boundary condition enforcement unit. In this embodiment, the physical constraint and explicit residual module calculates the spatial gradient and higher-order derivative characteristics of the physical field using the adaptive finite difference method. Based on the velocity gradient and DBSCAN clustering algorithm, it dynamically identifies key flow regions such as boundary layers and eddies. It uses the basic control equations of fluid mechanics to calculate the physical residuals of continuity, momentum, energy, and state equations, and enforces corresponding physical constraint conditions in different boundary regions to ensure that the prediction results strictly satisfy the conservation laws of fluid mechanics.

[0036] Gradient feature extraction unit: Input flow field data and calculate the spatial gradient, gradient magnitude and higher-order derivative features of vorticity of each physical quantity through adaptive finite difference method; In this embodiment, for any physical field Its gradient magnitude Calculated using the following formula: In the formula, the spatial partial derivatives and A numerical solution method based on local least squares is adopted, which solves the problem through a system of linear equations.

[0037] Physical region identification unit: Dynamically identifies key physical regions in the flow field based on gradient characteristics, calculates boundary layer masks and eddy current masks, and provides region prior information for subsequent physical constraints; Residual calculation unit: Calculates physical residuals using the basic governing equations of fluid mechanics. Physical residuals include residuals of the continuity equation, momentum equation, energy equation, and ideal gas law equation. In this embodiment, the control equations used by the residual calculation unit are consistent with the physical constraint equations defined in the loss function in S4, ensuring physical consistency between the training and inference processes. This unit identifies portions of the prediction results that violate physical laws through residual analysis, providing a quantitative basis for subsequent corrections.

[0038] Boundary condition enforcement unit: Receives flow field data, physical residuals, continuous region mask, boundary layer mask, and eddy current mask. Inputs the spatial gradient, gradient magnitude, and higher-order derivative features of vorticity of each physical quantity calculated by the gradient feature extraction unit. Dynamically calculates gradients and divergences using an adaptive finite difference method, and enhances the physical residuals using an adaptive weight network. Corrects systematic biases in density, velocity, temperature, and pressure through residual calculations, and enforces corresponding physical constraints in different boundary regions. Based on the different physical regions corresponding to the continuous region mask values—inside the airfoil, on the airfoil wall, near-wall fluid, external fluid, inlet, outlet, and free boundary—it enforces corresponding constraints for no-slip boundary conditions, specified inflow conditions, pressure or velocity gradient conditions, and far-field boundary conditions, adjusting the flow field data and outputting corrected flow field data, including density, velocity, temperature, and pressure fields. This ensures that the physical constraints in each boundary region are met, eliminates systematic biases in flow field prediction, and improves the physical consistency and accuracy of the prediction results.

[0039] Gradients and divergences are dynamically calculated using an adaptive finite difference method, and the physical residuals are enhanced by an adaptive weighted network. The residual calculations correct for systematic biases in density, velocity, temperature, and pressure, and corresponding physical constraints are enforced in different boundary regions to adjust the flow field data, ensuring consistency across multiple physical regions, especially at the wall. Enforcing the no-slip condition at the boundary ( , , By applying velocity and pressure constraints at a certain point, a flow field prediction that conforms to physical laws is ultimately generated.

[0040] In S3, the boundary layer mask is calculated. The specific expression is: In the formula, For the velocity gradient, As the gradient threshold, this embodiment uses the 95th percentile. The characteristic attenuation length is estimated based on the flow field scale. d The distance to the solid boundary,k The gradient sensitivity parameter is used; the eddy current mask identifies potential eddy current points by identifying regions with high velocity gradient values ​​(above the 90th quantile), and applies the DBSCAN clustering algorithm (setting a neighborhood radius of 50 mm and a minimum sample size of 10) to group them into connected regions, thus calculating the eddy current mask. The specific expression is: In the formula, For the preset threshold, The clustering label is 1 for valid clusters and 0 for others. In this embodiment, these masks guide the model's attention to key flow regions through a weighting mechanism. Subsequently, these masks are used in a physically constrained loss function system, which amplifies the contributions of high-gradient regions such as shock waves, eddies, and boundary layers through adaptive weighted residual terms, thereby improving the model's performance in capturing extreme nonlinear phenomena.

[0041] The core numerical calculation methods employed in the Physical Constraints and Explicit Residuals module include the adaptive finite difference method, the Laplace operator, viscous stress divergence, and boundary region enforcement. These methods provide the numerical foundation for the accurate calculation of physical residuals, as detailed below: In the process of dynamically calculating the gradient using the adaptive finite difference method, the following formula is used: In the formula, and For grid spacing, and For grid node indexing, f Let be the physical field function to be differentiated. For grid points ( The function value at () For grid points ( The function value at () For grid points ( The function value at () For grid points ( The function value at (). Laplace operator The second derivative is approximated using a five-point scheme: The specific expressions for the boundary condition enforcement element that enforces the corresponding physical constraints in different boundary regions are as follows: In the formula, The velocity field within the solid region. This is the velocity field at the wall boundary, ensuring no-slip conditions between the solid surface and the wall.

[0042] Viscous stress divergence: The divergence of stress tensor components is calculated using the finite difference method. : In the formula, The shear stress component represents the stress acting on the plane perpendicular to the y-axis along the x-direction. The normal stress component represents the stress acting along the x-direction on a plane perpendicular to the x-axis. Let x be the stress vector in the x-direction; Through the synergistic effect of the above four methods, the physical constraint and explicit residual module can effectively identify key physical regions in the flow field, calculate accurate physical residuals, enforce boundary conditions, and finally output flow field prediction results that satisfy the basic laws of fluid mechanics, significantly improving the physical consistency and prediction accuracy of the model in predicting complex flow phenomena.

[0043] In S4, the multi-objective residual minimization loss function that constructs a loss function system driven by physical constraints includes: Continuous loss The specific expression is: In the formula, An adaptive weighting function is calculated based on the key region weights of continuous region masking, near-wall distance, and physical shock waves. This represents the total number of sampling points within the fluid domain. For the first One sampling point, For the fluid computation domain, For the first The continuity equation residuals at each sampling point For the first Spatial coordinates of each sampling point; The velocity vector in response to the prediction is The density is The temperature is The pressure is P Spatial coordinates are Then the residual of mass conservation The specific expression is: In the formula, The sign of the partial derivative. x for x Axis coordinates y for y Axis coordinatesu for x Directional velocity component, v for y Directional velocity component; Momentum loss includes x Momentum loss in the axial direction and y Momentum loss in the axial direction ; In the formula, and This is the standard deviation of the momentum residuals, used to normalize different physical quantity scales, avoid weight shifts in the loss term, and improve training stability. for x Momentum residual in the axial direction for y Momentum residual in the axial direction; In the formula, For the Laplace operator, and This is the viscous stress divergence term; In the formula, For fluid dynamic viscosity; Energy loss The specific expression is: In the formula, The normalization coefficient is... For numerically stable regularization terms, For the first The energy conservation equation residuals at each sampling point; Energy conservation equation residual The specific expression is: In the formula, For isobaric specific heat capacity, Thermal conductivity, This is a viscous dissipation term; In the formula, It is the bulk viscosity coefficient; Ideal gas state loss The specific expression is: In the formula, The ideal gas equation of state residuals and ideal gas state losses serve as constraints to ensure that the predicted state variables are physically reasonable. In the formula, R Let be the ideal gas constant. For position x Density value at that location, It is the product of the ideal gas constant and temperature. For position x Predicted pressure value at the location; entrance area loss The specific expression is: In the formula, For standard inlet physical parameters, Number of entry nodes This is the entrance boundary area. q Set of physical quantity variables A single physical quantity in it. For the first Predicted physical quantity values ​​at each entry node; Boundary condition constraints are weighted by continuous values ​​generated through the tanh activation function to smoothly reflect the relative importance of each node in the anomalous physical region. The specific expression is: In the formula, For shock wave region weighting coefficients, This refers to the weighting coefficient for the eddy current region. The weighting coefficient for the sheared region. For shock wave identification mask, For eddy current identification mask, A mask is used to identify the shear layer; this mechanism amplifies the residuals in key regions, enhancing the training's focus on eddies and boundary layers.

[0044] Punishment loss The specific expression is: In the formula, As a safety threshold, As a penalty factor, This is the ReLU activation function.

[0045] To further enhance training robustness and convergence stability, a stepwise exponential moving average (EMA) mechanism is introduced to dynamically normalize the statistical values ​​of the loss, avoiding the influence of local extrema on training. Furthermore, for gradient anomaly regions such as shock zones, the residual variance is calculated as a loss stability indicator to prevent training from falling into distortion divergence. In summary, a multi-objective residual minimization loss function system driven by physical constraints is presented. The specific expression is: In the formula, This refers to the loss term that encompasses continuity loss, momentum loss, energy loss, ideal gas state loss, inlet region loss, boundary condition constraints, and penalty loss. For the gradient norm regularization term of the physical quantity, For parameter weights, Loss due to constraint on the rate of change of physical quantities. The weight parameters are constrained by the rate of change. These are the gradient regularization weight parameters; In S5, the specific method for training the AMPD model using the course-based learning training strategy is as follows: Phase 1: Angle of attack range limited to 20% of the total range, Reynolds number capped at 5×10. 5 Mach number upper limit 0.3, geometric sample size 15, physical condition size 5; Phase 2: Angle of attack range expanded to 40%, Reynolds number capped at 6×10 5 Mach number upper limit 0.5, geometric sample number 18, physical condition number 6; Phase 3: Angle of attack range expanded to 60%, Reynolds number capped at 7×10 5 Mach number upper limit 0.7, geometric sample size 20, physical condition size 7; Phase 4: Angle of attack range expanded to 80%, Reynolds number capped at 8×10 5 The upper limit of Mach number is 0.85, the number of geometric samples is 23, and the number of physical conditions is 8. Phase 5: Angle of attack range reaches 100%, Reynolds number cap 10. 6 The upper limit of Mach number is 0.95, the number of geometric samples is 25, and the number of physical conditions is 10. Each stage has a loss threshold, initially set at 500, which decreases to 10 as the training cycle increases. In each stage, the next stage begins when the verification loss is below the loss threshold and the training cycle is at least 20.

[0046] In this embodiment, the course learning and training strategy further includes: Phased early stop mechanism: Each phase sets a loss threshold (decreasing from 500 in the first phase to 10 in the fifth phase). When the validation loss is below the threshold and the training cycle is at least 20, a switch is triggered. The new phase retains some samples from the previous phase and dynamically adjusts the cycle according to the validation loss (extending by 2 cycles when the loss exceeds 500). Global early stop terminates training when the overall performance stagnates. Sample selection and refresh strategy: The training set and validation set are generated using different random seeds to avoid overlap; the geometric samples for each stage are uniformly sampled from the LHS results based on the angle of attack threshold, and the physical conditions are randomly selected from the candidate pool that meets the upper limits of Reynolds number and Mach number; the samples are refreshed every 5 cycles to prevent overfitting. Physical clustering collaborative optimization: The samples at each stage not only increase in difficulty, but also cover cluster diversity, avoiding overfitting under a single condition and enhancing the robustness of the model.

[0047] like Figure 3 As shown, a multi-region physics-driven neural network-based aircraft flow field prediction system is applied to the multi-region physics-driven neural network-based aircraft flow field prediction method. The system includes: The data preprocessing module is used to generate airfoil profiles, construct continuous region masks, and perform high-dimensional physical parameter sampling. The neural network training module includes the AMPD model architecture, a physical constraint-driven loss function system, and a course learning and training strategy. The flow field prediction module includes a pre-trained AMPD model. Inputs include airfoil type, Mach number, Reynolds number, temperature, and angle of attack, and output complete flow field distribution data. The results visualization module provides display methods for velocity vector maps, pressure cloud maps, density cloud maps, velocity amplitude maps, and surface pressure coefficient curves.

[0048] The neural network training module adopts a distributed deployment architecture, which specifically includes: Service Architecture: A microservice architecture based on RESTful APIs, providing flow field prediction service interfaces through standard HTTP / HTTPS protocols, supporting data exchange in JSON format, and facilitating integration with different client applications and third-party systems; Concurrency processing capability: Supports concurrent access by multiple users. A single server node can handle no less than 50 concurrent requests at the same time. The system response time is kept within 2 seconds through request queue management and asynchronous processing mechanism. Load balancing and fault tolerance: Configure an automatic load balancer to intelligently distribute requests based on server load. When a single node fails, it can automatically switch to a backup node within 30 seconds to ensure service continuity. The system has automatic monitoring and fault detection functions and supports automatic service restart and recovery. Scalable design: It adopts a containerized deployment approach, supports horizontal scaling based on load requirements, and can dynamically add or remove computing nodes to ensure stable service quality during peak periods.

[0049] To verify the flow field prediction results of the trained AMPD model, the following cases are provided, including the prediction performance of different airfoils under different operating conditions: Case 1: Select test condition: NACA 0012 airfoil, Ma = 0.5, Re = 3×10 5 α = 6° = 288K.

[0050] Prediction accuracy verification: Compared with CFD (Fluent solver, k-ω SST turbulence model) results, the average relative error of the pressure coefficient distribution is 2.1%; the surface friction coefficient error is less than 4.5%; the predicted lift coefficient CL is 0.667, the CFD reference value is 0.655, and the relative error is 1.8%; the predicted drag coefficient CD is 0.0089, the CFD reference value is 0.0085, and the relative error is 4.7%. Flow field feature capture: Successfully predicted the acceleration zone on the upper surface and the stagnation zone on the lower surface of the airfoil; accurately captured the leading-edge stagnation point and the trailing-edge wake region; the boundary layer thickness prediction is consistent with the theoretical calculation, with 99% of the boundary layer thickness errors <3%.

[0051] Computational efficiency: A single prediction takes 5.8 seconds, which is more than 3,700 times faster than the traditional CFD method (about 6 hours).

[0052] Case 2: This embodiment verifies the predictive performance of the NACA 2412 airfoil under different operating conditions. The airfoil has a maximum thickness of 12% and a maximum camber of 2% at 40% chord length.

[0053] The test conditions were set as follows: Mach number 0.6, Reynolds number 3 × 10⁻⁶. 5 The angle of attack was 6°, and the free-flow temperature was 288K. The training process followed a five-stage course learning strategy, with convergence losses of 428.7, 156.3, 78.9, 38.2, and 7.4 for each stage.

[0054] Comparison of the prediction results with wind tunnel experimental data shows that the average relative error of the airfoil surface pressure coefficient distribution is 2.8%; the prediction error of the lift coefficient is 1.5%; and the prediction error of the drag coefficient is 4.2%. At key locations such as the airfoil leading edge stagnation point, the upper surface pressure peak point, and the trailing edge, the prediction accuracy remains within 3%.

[0055] In terms of flow separation prediction, this method successfully captured the laminar separation bubble phenomenon near the trailing edge of the upper surface of the airfoil. The error of the separation point location compared with experimental observation is less than 2% of the chord length, and the error of the reattachment point location is less than 3% of the chord length.

[0056] Case 3: This embodiment tests the ability to predict complex flows under high angle-of-attack and large angle-of-attack conditions. The NACA 0012 airfoil was selected, with an angle of attack set at 15°, Mach number 0.4, and Reynolds number 5 × 10⁻⁶. 5 .

[0057] Under this condition, large-scale flow separation occurs on the upper surface of the airfoil, forming a distinct separation vortex structure. The prediction results show that this method accurately captures the separation point location (located at 45% chord length), with an error of less than 3% chord length compared to the CFD calculation results. The backflow phenomenon and vortex distribution within the separation region are also accurately predicted.

[0058] The predicted lift coefficient has an error of 3.7% compared with the experimental data. Considering the strong nonlinearity and instability of the flow under large angle of attack, this level of accuracy indicates that the method has a good ability to capture complex flows.

[0059] In terms of boundary layer prediction, this method accurately predicts the variation trend of boundary layer thickness along the chord length through precise division of continuous region masks, and the prediction error of 99% of the boundary layer thickness remains within 5%.

[0060] Case 4: This embodiment verifies the shock wave capture capability under near-transonic conditions. The test conditions are NACA 0012 airfoil, Mach number 0.85, Reynolds number 8 × 10⁻⁶. 5 Angle of attack 2°.

[0061] Under these conditions, a supersonic region forms on the upper surface of the airfoil, generating a normal shock wave at its rear. Predictions show the shock wave location is at 70% chord length, with an error of 1.8% chord length compared to experimental data. The pressure jump and density change before and after the shock wave were accurately predicted, with a pressure prediction error of less than 5%.

[0062] Shock boundary layer disturbances were also effectively captured, and shock-induced boundary layer thickening and possible local separation were reflected in the prediction results. This indicates that the method has good numerical stability and physical accuracy in handling shock-like discontinuities.

[0063] Through the verification of the above four cases, the adaptive multi-region physical-driven neural network method of the present invention exhibits excellent prediction performance under various airfoils and different flow conditions: (1) Prediction accuracy: The average error of the pressure coefficient distribution is <3%, and the error of the lift and drag coefficient is <5%, which meets the requirements of engineering applications; (2) Physical consistency: It strictly satisfies the conservation laws of fluid mechanics and has no non-physical phenomena; (3) Computational efficiency: It is more than 3,000 times faster than traditional CFD methods, and a single prediction takes less than 10 seconds; (4) High adaptability: Supports a variety of airfoil geometries and a wide range of operating conditions, with outstanding generalization ability; (5) Complex flow capture: accurately predicts complex flow phenomena such as separation and shock waves, with significant technological advancements.

[0064] The method of this invention provides an efficient, accurate, and intelligent solution for rapid flow field analysis in the aerospace field, and has significant engineering application value.

[0065] In the description of this invention, it should be understood that the terms "center," "thickness," "upper," "lower," "horizontal," "top," "bottom," "inner," "outer," and "radial," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying the relative importance or the number of technical features implicitly specified. Therefore, a feature defined by "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

Claims

1. A method for predicting aircraft flow field using a multi-region physics-driven neural network, characterized in that, Includes the following steps: S1. Obtain the wing geometry parameters, generate the airfoil profile through the airfoil parameterization equation, and divide the multi-physical region according to the continuous region mask; S2. The Latin hypercube sampling method is used to globally sample the high-dimensional physical parameters, and the KMeans clustering algorithm is combined to divide the parameter space into six representative sub-regions to obtain the physical condition parameters. S3. Input the spatial coordinates, continuous region mask, wall distance and physical condition parameters into the AMPD model, and map them to a high-dimensional feature space through dilated convolution and linear transformation to generate boundary layer mask, eddy current mask and physical residual; S4. Input the boundary layer mask and eddy current mask into the loss function system driven by physical constraints, and establish a multi-objective residual minimization loss function based on the continuity equation, momentum conservation equation, energy equation and ideal gas state equation, which is used to train the AMPD model. S5. Based on the multi-objective residual minimization loss function and physical residual, the AMPD model is trained using a course learning training strategy. S6. Input the airfoil type, Mach number, Reynolds number, temperature and angle of attack into the trained AMPD model, and reconstruct the airfoil surface flow field through the trained AMPD model to complete the aircraft flow field prediction.

2. The aircraft flow field prediction method using a multi-region physical-driven neural network according to claim 1, characterized in that, In S1, the method for dividing multiple physical regions based on continuous region masks is as follows: Multiphysics regions are determined based on spatial distance and topology. The mask value for the airfoil interior region is 1, the mask value for the airfoil wall region is 2, the mask value for the near-wall fluid region is 3.0 to 4.0, the mask value for the external fluid region is 4, the mask value for the inlet region is 5, the mask value for the outlet region is 6, and the mask value for the free boundary region is 7. Among them, the near-wall fluid region mask S ( x The sigmoid function is used to describe the smooth transition from 3.0 to 4.0; In the formula, The distance to the wall is a point. x The closest distance to the airfoil wall, To adapt to the near-wall region scale, For smooth transition band parameters, This is the sigmoid function.

3. The aircraft flow field prediction method using a multi-region physical-driven neural network according to claim 1, characterized in that, In S2, the objective function of the KMeans clustering algorithm is... The specific expression is: In the formula, It is the first One cluster, It is a cluster center. For physical parameters, The square of the Euclidean distance; The high-dimensional physical parameters sampled are normalized to ensure that each physical parameter has the same scale during training. In the formula, Physical parameters The mean, Physical parameters standard deviation These are the normalized physical parameters.

4. The aircraft flow field prediction method using a multi-region physical-driven neural network according to claim 1, characterized in that, In S3, the AMPD model consists of an input embedding layer, a feature fusion backbone, and a physical constraint and explicit residual module connected in sequence. Input embedding layer: Input spatial coordinates, continuous region masks, wall distances, and physical condition parameters. Spatial coordinates are extracted using a dilated convolution module for multi-scale feature extraction and mapped to a 32-dimensional feature space, with dilation rates of 1, 2, and 4, generating spatial coordinate features. Continuous region masks and wall distances are embedded into a 16-dimensional feature space through independent linear transformations, generating region mask features and wall distance features, respectively. Physical condition parameters are encoded into physical condition vectors using a multilayer perceptron, which are used to train the AMPD model using the course learning training strategy. Feature fusion backbone: Spatial coordinate features, region mask features and wall distance features are combined to form a 64-dimensional fusion feature. The fusion feature is then input into the residual backbone network and attention mechanism module to obtain flow field data, including velocity field, density field, temperature field and pressure field. The residual backbone network consists of six stacked residual neural blocks. Each residual neural block includes a bilinear transform layer, layer normalization, Leaky ReLU activation function, and residual connections. The attention mechanism module is used to dynamically adjust the weights of features at different spatial locations and improve the model's ability to represent complex flow fields through deep feature fusion. The physical constraint and explicit residual module includes a gradient feature extraction unit, a physical region identification unit, a residual calculation unit, and a boundary condition enforcement unit; Gradient feature extraction unit: Input flow field data and calculate the spatial gradient, gradient magnitude and higher-order derivative features of vorticity of each physical quantity through adaptive finite difference method; Physical region identification unit: Dynamically identifies key physical regions in the flow field based on gradient characteristics, calculates boundary layer masks and eddy current masks, and provides region prior information for subsequent physical constraints; Residual calculation unit: Calculates physical residuals using the basic governing equations of fluid mechanics. Physical residuals include residuals of the continuity equation, momentum equation, energy equation, and ideal gas law equation. Boundary condition enforcement unit: Receives flow field data, physical residuals, continuous region mask, boundary layer mask, and eddy current mask. Inputs the spatial gradient, gradient magnitude, and higher-order derivative features of vorticity of each physical quantity calculated by the gradient feature extraction unit. Dynamically calculates gradients and divergences using an adaptive finite difference method, and enhances the physical residuals using an adaptive weight network. Corrects systemic biases in density, velocity, temperature, and pressure through residual calculations, and enforces corresponding physical constraints in different boundary regions. Based on the different physical regions corresponding to the continuous region mask values—inside the airfoil, on the airfoil wall, near-wall fluid, external fluid, inlet, outlet, and free boundary—it enforces corresponding constraints for no-slip boundary conditions, specified inflow conditions, pressure or velocity gradient conditions, and far-field boundary conditions, adjusting the flow field data and outputting the corrected flow field data.

5. The aircraft flow field prediction method using a multi-region physical-driven neural network according to claim 4, characterized in that, In S3, the boundary layer mask is calculated. The specific expression is: In the formula, For the velocity gradient, For gradient threshold, For characteristic attenuation length, d The distance to the solid boundary, k This is a gradient sensitivity parameter; Calculate the eddy current mask The specific expression is: In the formula, For the preset threshold, The clustering label is 1 for valid clusters and 0 for others. In the process of dynamically calculating the gradient using the adaptive finite difference method, the following formula is used: In the formula, and For grid spacing, and For grid node indexing, f Let be the physical field function to be differentiated. For grid points ( The function value at () For grid points ( The function value at () For grid points ( The function value at () For grid points ( The function value at (). Laplace operator The second derivative is approximated using a five-point scheme: The specific expressions for the boundary condition enforcement element that enforces the corresponding physical constraints in different boundary regions are as follows: In the formula, The velocity field within the solid region. This is the velocity field at the wall boundary, ensuring no-slip conditions between the solid surface and the wall.

6. The aircraft flow field prediction method using a multi-region physical-driven neural network according to claim 5, characterized in that, In S4, the multi-objective residual minimization loss function of the physically constrained loss function system. The specific expression is: In the formula, This refers to the loss term that encompasses continuity loss, momentum loss, energy loss, ideal gas state loss, inlet region loss, boundary condition constraints, and penalty loss. For the gradient norm regularization term of the physical quantity, For parameter weights, Loss due to constraint on the rate of change of physical quantities. The weight parameters are constrained by the rate of change. These are the gradient regularization weight parameters; Continuous loss The specific expression is: In the formula, An adaptive weighting function is calculated based on the key region weights of continuous region masking, near-wall distance, and physical shock wave. This represents the total number of sampling points within the fluid domain. For the first One sampling point, For the fluid computation domain, For the first The continuity equation residuals at each sampling point For the first Spatial coordinates of each sampling point; The velocity vector in response to the prediction is The density is The temperature is The pressure is P Spatial coordinates are Then the residual of mass conservation The specific expression is: In the formula, The sign of the partial derivative. x for x Axis coordinates y for y Axis coordinates u for x Directional velocity component, v for y Directional velocity component; Momentum loss includes x Momentum loss in the axial direction and y Momentum loss in the axial direction ; In the formula, and The standard deviation of the momentum residual. for x Momentum residual in the axial direction for y Momentum residual in the axial direction; In the formula, For the Laplace operator, and This is the viscous stress divergence term; In the formula, For fluid dynamic viscosity; Energy loss The specific expression is: In the formula, The normalization coefficient is... For numerically stable regularization terms, For the first The energy conservation equation residuals at each sampling point; Energy conservation equation residual The specific expression is: In the formula, For isobaric specific heat capacity, Thermal conductivity, This is a viscous dissipation term; In the formula, It is the bulk viscosity coefficient; Ideal gas state loss The specific expression is: In the formula, The residuals of the ideal gas law; In the formula, R Let be the ideal gas constant. For position x Density value at that location, It is the product of the ideal gas constant and temperature. For position x Predicted pressure value at the location; entrance area loss The specific expression is: In the formula, For standard inlet physical parameters, Number of entry nodes This is the entrance boundary area. q Set of physical quantity variables A single physical quantity in it. For the first Predicted physical quantity values ​​at each entry node; Boundary condition constraints are weighted by continuous values ​​generated through the tanh activation function to smoothly reflect the relative importance of each node in the anomalous physical region. The specific expression is: In the formula, For shock wave region weighting coefficients, This refers to the weighting coefficient for the eddy current region. The weighting coefficient for the sheared region. For shock wave identification mask, For eddy current identification mask, Identify the mask for the shear layer; Punishment loss The specific expression is: In the formula, As a safety threshold, As a penalty factor, This is the ReLU activation function.

7. The aircraft flow field prediction method using a multi-region physical-driven neural network according to claim 1, characterized in that, In S5, the specific method for training the AMPD model using the course-based learning training strategy is as follows: Phase 1: Angle of attack range limited to 20% of the total range, Reynolds number capped at 5×10. 5 Mach number upper limit 0.3, geometric sample size 15, physical condition size 5; Phase 2: Angle of attack range expanded to 40%, Reynolds number capped at 6×10 5 Mach number upper limit 0.5, geometric sample number 18, physical condition number 6; Phase 3: Angle of attack range expanded to 60%, Reynolds number capped at 7×10 5 Mach number upper limit 0.7, geometric sample size 20, physical condition size 7; Phase 4: Angle of attack range expanded to 80%, Reynolds number capped at 8×10 5 The upper limit of Mach number is 0.85, the number of geometric samples is 23, and the number of physical conditions is 8. Phase 5: Angle of attack range reaches 100%, Reynolds number cap 10. 6 The upper limit of Mach number is 0.95, the number of geometric samples is 25, and the number of physical conditions is 10. Each stage has a loss threshold, initially set at 500, which decreases to 10 as the training cycle increases. In each stage, the next stage begins when the verification loss is below the loss threshold and the training cycle is at least 20.

8. A multi-region physical-driven neural network-based aircraft flow field prediction system, applied to the multi-region physical-driven neural network-based aircraft flow field prediction method as described in any one of claims 1 to 7, characterized in that the system... include: The data preprocessing module is used to generate airfoil profiles, construct continuous region masks, and perform high-dimensional physical parameter sampling. The neural network training module includes the AMPD model architecture, a physical constraint-driven loss function system, and a course learning and training strategy. The flow field prediction module includes a pre-trained AMPD model. Inputs include airfoil type, Mach number, Reynolds number, temperature, and angle of attack, and output complete flow field distribution data. The results visualization module provides display methods for velocity vector maps, pressure cloud maps, density cloud maps, velocity amplitude maps, and surface pressure coefficient curves.

Images