A method for processing aircraft aerodynamic parameters based on reversible neural networks

CN122572271APending Publication Date: 2026-08-14UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Patent Information

Application Number
CN202610732301.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-05-26
Publication Date
2026-08-14

AI Technical Summary

Technical Problem

对于飞行器气动分析而言,这种单向映射方法虽然能够用于压力系数快速拟合,但在以下方面仍存在不足:其一,多数方法主要针对升力系数、阻力系数和俯仰力矩系数等低维标量气动参数展开建模,对于飞行器表面高维压力系数分布的表达能力有限;其二,即使能够预测压力分布,通常也只是完成由工况到响应的单向计算,难以进一步根据压力响应反推出对应工况参数;其三,当需要进行参数反演时,往往需要重新建立独立的逆向模型,或者采用迭代优化、搜索匹配等方法进行求解,存在实现流程复杂、计算开销较大、前后向结果一致性不足等问题;其四,对于飞行器气动问题,输入端通常为较低维的工况参数及测点位置信息,而输出端往往为压力响应,现有技术缺少一种能够在统一框架下同时处理该类维度不匹配问题并完成双向建模的方法

Benefits of technology

(1)基于可逆神经网络构建了双向映射框架,通过同一模型同时实现“工况参数→压力系数”的正向预测和“压力系数→工况参数”的逆向反演,有效拓展了气动模型的应用方式,避免了分别建立预测模型和反演模型所带来的结构重复和资源浪费。

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Abstract

This invention discloses a method for processing aircraft aerodynamic parameters based on a reversible neural network, belonging to the field of aircraft aerodynamic analysis and calculation technology. The method includes: constructing a training dataset containing operating parameters, surface measurement point coordinates, and corresponding pressure coefficients; expanding the dimensions of the operating parameters and measurement point coordinates to match the output dimension of the reversible neural network; constructing a reversible neural network model composed of multiple cascaded reversible modules, each module including an ActNorm normalization layer, a Real NVP affine coupling layer, and a random permutation layer; training the model using a joint loss function including forward prediction loss, inverse reconstruction loss, and latent variable distribution loss; and using the trained model to achieve forward prediction of pressure coefficients and inverse inversion of operating parameters. This invention simultaneously performs forward prediction and inverse inversion using the same reversible neural network model, solving the problems of complex bidirectional modeling and poor consistency in existing technologies.
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Description

Technical Field

[0001] This invention relates to the field of aircraft aerodynamics analysis and calculation technology, specifically to a method for processing aircraft aerodynamic parameters based on a reversible neural network. Background Technology

[0002] The surface pressure distribution of an aircraft changes significantly under different angles of attack, sideslip angles, Mach numbers, and control states. The surface pressure coefficient not only reflects the local flow state but also serves as fundamental data for further calculations of overall aerodynamic characteristics such as lift, drag, and pitching moment. Therefore, rapidly and accurately obtaining the aircraft's surface pressure coefficient under actual operating conditions is of great significance for aerodynamic layout design, shape optimization, wind tunnel testing and analysis, and flight condition assessment.

[0003] Currently, methods for acquiring aerodynamic parameters of aircraft mainly fall into two categories: traditional test-simulation methods and data-driven methods. Traditional test-simulation methods primarily rely on wind tunnel testing, high-fidelity numerical simulation, and aerodynamic databases built upon test or simulation results. The basic idea is to pre-acquire aerodynamic information such as pressure distribution, lift coefficient, drag coefficient, and pitch moment coefficient of the aircraft under multiple discrete operating conditions, and then estimate unknown operating conditions through interpolation, table lookup, or simplified mechanistic models. These methods typically have high accuracy, but generally suffer from long modeling cycles, high testing or computational costs, complex database maintenance, and limited ability to extrapolate operating conditions. Especially when the aircraft configuration is complex and the operating condition range is wide, traditional methods struggle to balance efficiency and flexibility. Data-driven methods, with the development of machine learning and deep learning, use surrogate models or neural networks to establish a mapping relationship between operating condition parameters and aerodynamic responses. For example, by using models such as multilayer perceptrons, convolutional neural networks, recurrent neural networks, or long short-term memory networks, and taking angle of attack, Mach number, geometric information, or measurement point coordinates as inputs, and outputting lift coefficient, drag coefficient, pitching moment coefficient, or surface pressure distribution, rapid prediction of aerodynamic parameters can be achieved. Compared with traditional wind tunnel tests and high-fidelity numerical simulations, this type of method can significantly reduce the cost of repetitive calculations and improve prediction speed, thus having high application value in rapid aerodynamic modeling of aircraft.

[0004] Most existing data-driven methods still focus on forward prediction, primarily addressing the problem of "predicting aerodynamic response from operating parameters." While this one-way mapping method can be used for rapid pressure coefficient fitting in aircraft aerodynamic analysis, it has limitations in the following aspects: First, most methods primarily model low-dimensional scalar aerodynamic parameters such as lift, drag, and pitch moment coefficients, limiting their ability to represent the high-dimensional pressure coefficient distribution on the aircraft surface. Second, even when pressure distribution can be predicted, it typically only completes a one-way calculation from operating conditions to response, making it difficult to further deduce the corresponding operating parameters from the pressure response. Third, when parameter inversion is required, it often necessitates rebuilding an independent inverse model or using iterative optimization or search matching methods, resulting in complex implementation processes, high computational costs, and insufficient consistency between forward and backward results. Fourth, for aircraft aerodynamic problems, the input is usually low-dimensional operating parameters and measurement point location information, while the output is often the pressure response; current technology lacks a method that can simultaneously handle this type of dimensional mismatch problem and complete bidirectional modeling within a unified framework.

[0005] Because existing data-driven methods primarily predict pressure coefficients based on known operating conditions, they still cannot achieve the reverse derivation of operating parameters from pressure coefficients within the same model, nor can they naturally guarantee the consistency between forward prediction and reverse solution. When it is necessary to invert flight state or operating parameters based on the target pressure response, it is usually still necessary to design an additional independent inversion model or use an iterative search method to gradually approximate the result. This not only increases computational complexity but also leads to difficulties in model coupling and inconsistencies between forward and backward results. Summary of the Invention

[0006] The purpose of this invention is to provide a method for processing aircraft aerodynamic parameters based on reversible neural networks. Through a dimension alignment mechanism, the reversible neural network is successfully applied to aircraft aerodynamic modeling, and the same model is used to achieve the dual functions of pressure coefficient prediction and operating condition parameter inversion.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for processing aircraft aerodynamic parameters based on a reversible neural network includes the following steps: Step 1: Construct a training dataset; each sample in the training dataset includes the aircraft's operating parameters, surface measurement point coordinates, and the corresponding surface pressure coefficient; Step 2: Perform dimensional expansion on the operating parameters and surface measuring point coordinates to obtain expanded input variables; perform dimensional expansion on the surface pressure coefficient to obtain expanded output variables; Step 3: Construct a reversible neural network model, which includes an input layer, multiple cascaded reversible modules, and an output layer. Each reversible module includes an ActNorm normalization layer, a Real NVP affine coupling layer, and a random permutation layer connected in sequence. The reversible neural network model is used to establish a bidirectional reversible mapping between input variables and output variables. The ActNorm normalization layer is used to map input variables with different dimensions and distribution ranges to a scale space, and its forward transformation is as follows: inverse transformation ,in and These are the learnable scaling and translation parameters, respectively; ⊙ represents element-wise multiplication, and ⊘ represents element-wise division. The Real NVP affine coupling layer is used to divide the input features into two parts, perform an affine transformation on one part based on the other part, and maintain the invertibility of the transformation; its forward transformation is... , Inverse transformation to , , This indicates the first part, which remains unchanged. The second part represents the affine transformation performed under the conditions of the first part; the output features are... , For scaling function, It is a translation function; The random permutation layer is used to rearrange the feature channels, and its transformation is as follows: , Let be the permutation matrix; Step 4: Using the training dataset, train the reversible neural network model through a joint loss function to obtain a reversible aerodynamic response model; Step 5: Use the trained reversible neural network model to process the aerodynamic parameters of the aircraft. Based on the input operating parameters and the coordinates of the surface measuring points, predict the pressure coefficient in the forward direction, and / or, based on the input pressure coefficient, inversely derive the corresponding operating parameters.

[0008] Further, in step 2, the dimensional expansion includes: The operating parameters and surface measuring point coordinates are expanded by zero-padding, and the input variables are... , , For the angle of attack, Sideslip angle, Mach number, The coordinates of the measuring points on the surface of the aircraft; The surface pressure coefficient is expanded by incorporating latent variables that characterize underlying features, resulting in an output variable. ; , The surface pressure coefficient of the aircraft. These are latent variables.

[0009] Furthermore, in step 3, the reversible neural network model introduces a multi-scale splitting mechanism to progressively output latent variables at different levels of the network in order to extract features at different scales. First-stage transformation output Divide it into two parts , The latent variable representing the output at the current scale. Continue to the next reversible module; second-level transformation The third-order transformation is The final latent variable .

[0010] Furthermore, in step 3, the reversible neural network model describes the latent variable distribution in conditional probability form, and the joint probability distribution of the latent variables... ,in, These are intermediate features before the second-level transformation.

[0011] Furthermore, in step 4, the joint loss function ;in, To reconstruct the loss term in reverse, For the input variables to be predicted, The variables are the actual input variables, and N is the total number of input variables; For positive prediction of loss, To predict the surface pressure coefficient, To predict the surface pressure coefficient. Latent variable distribution loss term, As a latent variable, For the true probability distribution, This represents the predicted probability distribution. , , These are the weighting coefficients for the reverse reconstruction loss term, the forward prediction loss term, and the latent variable distribution loss term, respectively.

[0012] Compared with the prior art, the present invention has the following beneficial effects: (1) A bidirectional mapping framework was constructed based on a reversible neural network. The positive prediction of "operating parameters → pressure coefficient" and the reverse inversion of "pressure coefficient → operating parameters" were realized simultaneously through the same model. This effectively expanded the application of aerodynamic models and avoided the structural duplication and resource waste caused by establishing prediction models and inversion models separately.

[0013] (2) By utilizing the reversibility design of the reversible neural network, the forward and reverse processes share the same mapping framework, ensuring the inherent consistency of the bidirectional mapping. Verification by the implementation examples shows that the reconstruction accuracy of the operating parameters matches the prediction accuracy of the pressure coefficient, and the model exhibits good bidirectional consistency.

[0014] (3) A dimension alignment mechanism was added. By padding the input with zeros and introducing hidden variables, the input and output were extended to the same dimension space. The reversible neural network was successfully applied to the field of aircraft aerodynamic modeling, providing an implementation path for the application of reversible modeling methods in aerodynamic problems.

[0015] (4) Introducing a multi-scale splitting mechanism, latent variables are output step by step at different levels of the network to realize multi-scale feature expression from coarse-grained to fine-grained; at the same time, the distribution of latent variables is described in the form of conditional probability, which more accurately portrays the dependency relationship between features at different scales and can accurately characterize the changing law of pressure response on the surface of the aircraft.

[0016] (5) The trained, verified and tested model can directly and quickly predict the pressure coefficient based on the given operating conditions, or quickly invert the operating condition parameters based on the target pressure response, without repeating the experiment or simulation calculation. At the same time, it serves a variety of application scenarios such as aircraft shape design optimization, test data analysis, state identification and inverse problem solving, providing a data-driven tool for aircraft aerodynamic analysis and significantly improving the efficiency and flexibility of aerodynamic analysis. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the reversible neural network model constructed in this invention.

[0018] Figure 2 This is a graph showing the changes in model training loss and validation loss in an embodiment of the present invention.

[0019] Figure 3 This is a comparison chart of the actual pressure coefficient and the predicted pressure coefficient in an embodiment of the present invention.

[0020] Figure 4 This is a scatter plot comparing the actual and predicted values ​​of the pressure coefficient in an embodiment of the present invention.

[0021] Figure 5 This is a distribution diagram of the pressure coefficient prediction error in an embodiment of the present invention. Detailed Implementation

[0022] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0023] This embodiment provides a method for processing aircraft aerodynamic parameters based on a reversible neural network, including the following steps: Step 1: Data Construction and Preprocessing; aircraft surface measuring points , This refers to the spatial coordinate data of measurement points on the surface of the aircraft.

[0024] aircraft surface pressure coefficient , This refers to the local pressure at a measuring point on the aircraft surface. For free-flowing environmental static pressure, For free-flowing air density, The free flow velocity.

[0025] Flight state parameter vector , For the angle of attack, Sideslip angle, It is the Mach number.

[0026] Input parameters Output target Pressure coefficient at measuring point .

[0027] Therefore, the aerodynamic prediction problem is expressed as: , , where the function It is a complex nonlinear aerodynamic response function.

[0028] This embodiment constructs a training dataset using aerodynamic numerical simulation data of an aircraft. Specifically, it obtains the aircraft's angle of attack, sideslip angle, Mach number, and spatial coordinates of measurement points, along with the surface pressure coefficient at those points, through simulation. The dataset in this embodiment includes 7000 samples, with an input feature dimension of 6 (…). The output dimension is 1-dimensional ( To ensure the reliability of model training, validation, and testing, the training dataset was divided into training, validation, and testing sets in a 7:1:2 ratio. The training set contains approximately 4900 samples, the validation set approximately 700 samples, and the testing set approximately 1400 samples. This dataset covers various flight conditions and measurement points at different surface locations, and can effectively characterize the nonlinear behavior of the aerodynamic pressure coefficient of an aircraft as a function of flight conditions and spatial location.

[0029] Step 2: Dimensional alignment processing; Since reversible neural networks require the input and output to satisfy the same dimension mapping, and in this embodiment the input is low-dimensional operating parameters and coordinate information, and the output is the pressure coefficient and its potential description, it is necessary to extend the input to the same dimension.

[0030] Let the expanded input variables be... , is the input variable; 0 is the zero-padding vector used to expand the input dimension to be consistent with the output side.

[0031] Output variables , The target output is the surface pressure coefficient. These are latent variables used to characterize potential feature information in the original input that is not explicitly included but contributes to the mapping.

[0032] The bidirectional reversible relationship established in this embodiment is as follows: , ; Right now: , ; The bidirectional reversibility ensures that the model can perform both forward prediction and inverse inversion.

[0033] Step 3: Constructing the reversible neural network model R-INN; like Figure 1 As shown, the reversible neural network model constructed in this embodiment includes an input layer, multiple cascaded reversible modules, and an output layer, wherein the reversible modules are connected sequentially to form the overall network structure.

[0034] Each of the reversible modules sequentially includes: an ActNorm normalization layer for reversible scaling of the input features; an affine coupling layer based on a Real NVP structure for nonlinear reversible mapping of features; and a random permutation layer for rearranging feature dimensions to enhance feature interaction capabilities. In a preferred embodiment, each reversible module further includes a multi-scale splitting structure for separating some features into latent variable outputs, with the remaining features continuing to be input into the next reversible module. Through the cascading combination of the above structures, the model can achieve multi-scale modeling of the complex nonlinear relationship of the aerodynamic pressure coefficient of an aircraft while maintaining reversibility.

[0035] The ActNorm normalization layer is used to map aerodynamic input variables with different dimensions and distribution ranges to a scale space more suitable for network training, while maintaining the invertibility of the transformation; this reduces the impact of differences in input variable distribution on the training process. The ActNorm normalization layer output... , and These represent the learnable scaling parameter and the translation parameter, respectively, and ⊙ denotes element-wise multiplication. The input features are used. Its inverse transform... ;⊘ indicates element-wise division.

[0036] The Real NVP affine coupling layer is used to divide the input features into two parts. , This indicates the first part, which remains unchanged. The second part represents the affine transformation performed under the conditions of the first part; the output characteristics of the Real NVP affine coupling layer. During the forward process, , , For scaling function, Both are translation functions, learned by neural networks. In the reverse process, , The Real NVP affine coupling layer has an explicit analytic inverse, thus ensuring the overall bidirectional invertibility of the network. It maintains the ability to express complex nonlinearities while efficiently calculating and inverting the Jacobian matrix.

[0037] The random permutation layer is used to rearrange the feature channels, enabling subsequent coupling layers to continue modeling different dimensional combinations, thereby enhancing the model's ability to learn complex coupling relationships between aerodynamic parameters. This solves the problem of only some variables being updated in a single coupling layer and enhances information interaction between different dimensions. A permutation matrix is ​​set. The random permutation layer outputs features .

[0038] The reversible flow module constructs a bidirectional reversible mapping such that the input variables and output variables satisfy the following condition: The input variables, after expansion, are represented as follows: ,middle, This represents the original input variables, including flight state parameters and spatial coordinates of the measurement points. This represents the zero-padding vector used for dimension alignment. The output variable is represented as: ,in, The surface pressure coefficient of the aircraft. These are latent variables, used to characterize potential feature information not explicitly represented in the input variables. Therefore, this reversible flow module establishes the following bidirectional reversible relationship. And it satisfies the inverse mapping: The above structure enables the model to have both forward prediction and backward inversion capabilities, thus ensuring that forward mapping and backward mapping are uniformly implemented in the same model.

[0039] To further enhance the model's ability to represent multi-scale aerodynamic features, a multi-scale splitting mechanism is introduced based on the traditional invertible neural network model INN. This mechanism is used to progressively output latent variables at different levels of the network to extract features at different scales. Let the output of the first-level transformation be... Then it is divided into two parts. , The latent variable representing the output at the current scale. Proceed to the next reversible flow module. Similarly, the second-stage transformation... The third-order transformation is The final latent variable Multi-scale structures can progressively extract features at different levels. Shallow latent variables tend to describe the coarse-grained relationship between operating parameters and spatial location, while deep latent variables tend to describe the fine-grained pattern of local pressure coefficient changes. This approach corresponds to the basic idea of ​​"layer-by-layer split latent" in R-INN.

[0040] This embodiment uses conditional probability to describe the distribution of latent variables, and the latent variables obtained after multi-scale splitting... Their joint probability distribution , The intermediate features before the second-level transformation; the joint probability distribution The solution can more accurately describe the dependencies between latent variables at different scales, and shallow latent variables. It tends to describe the coarse-grained relationship between operating parameters and spatial location, and its prior distribution conforms to a standard Gaussian distribution; middle-level latent variables exist Modeling is performed under these conditions to capture feature dependencies at intermediate scales and deep latent variables. exist Under specific conditions, modeling is performed to capture fine-grained patterns of local pressure coefficient variations. This conditional probabilistic modeling approach can more accurately describe the multi-scale characteristics of aerodynamic response distributions and enhance the model's ability to model complex nonlinear aerodynamic response distributions.

[0041] To enhance the model's expressive power, this embodiment cascades multiple reversible coupling layers; the reversible neural network contains K layers, and the network mapping... , This represents the k-th invertible layer. This structure can extract complex nonlinear features from the input variables layer by layer, thereby establishing a high-dimensional mapping relationship between flight state parameters and pressure coefficients. Overall transformation. Then the Jacobian matrix For an affine coupling layer, its Jacobian matrix is Therefore, its determinant simplifies to ,and then This property allows the network to perform probability density estimation without explicitly calculating complex matrix determinants, thereby improving training efficiency and stability. R-INN relies on this type of computable Jacobian structure to achieve probabilistic modeling and stable training.

[0042] Based on the variable transformation of the invertible module, the probability density of the original input variable Simplified to By mapping the original aerodynamic input to the latent variable space and combining it with Jacobian determinant compensation terms, a unified modeling of the input and output distributions can be achieved.

[0043] Step 4: Train the reversible neural network model; Using the training dataset, the reversible neural network model is trained using a joint loss function. The trained reversible neural network model is then validated and tested using the validation and test sets in both forward and reverse directions to obtain a reversible aerodynamic response model.

[0044] Joint loss function , , , These are the weighting coefficients for different loss terms. To reconstruct the loss term in reverse, For the input variables to be predicted, represents the actual input variables, and N represents the total number of input variables. For positive prediction of loss, To predict the surface pressure coefficient, To predict the surface pressure coefficient. Latent variable distribution loss term, As a latent variable, For the true probability distribution, This represents the predicted probability distribution.

[0045] like Figure 2 As shown, with the increase of training rounds, both training loss and validation loss exhibit a rapid decreasing trend and gradually stabilize. In the early stages of training, the loss value decreases rapidly, indicating that the constructed invertible neural network can effectively learn the nonlinear mapping relationship between aircraft operating parameters, measurement point coordinates, and pressure coefficients. As training continues, the gap between training loss and validation loss remains small, and no obvious bifurcation occurs, indicating that the model does not exhibit significant overfitting during training and has good generalization ability.

[0046] After training, the reversible neural network model can perform both forward prediction and inverse inversion.

[0047] Validation of positive prediction performance: like Figure 3 As shown, the actual pressure coefficient and the predicted pressure coefficient are compared after being sorted by numerical value. It can be seen that the two curves are highly consistent in their overall trend, exhibiting good tracking ability in the low pressure coefficient region, the intermediate transition region, and the high pressure coefficient region. This indicates that it can not only achieve accurate prediction at the single-point numerical level, but also maintain a good overall distribution and trend of the pressure coefficient.

[0048] like Figure 4 As shown, a scatter plot comparison of the actual pressure coefficient of the test samples and the model prediction results reveals that most sample points are distributed near the ideal diagonal, indicating a high degree of consistency between the predicted and actual values. The implementation results demonstrate high accuracy in pressure coefficient prediction tasks. The mean absolute error is 4.3652 × 10⁻⁶. -2 The root mean square error is 7.8738 × 10⁻⁶. -2 Coefficient of determination R 2 It is 0.9861.

[0049] like Figure 5 As shown, a statistical analysis of the pressure coefficient prediction error was performed. The error distribution reveals that the prediction error for most samples is concentrated near zero, indicating that the overall prediction results are relatively close to the actual values. The statistical results show that the mean error is -1.0952 × 10⁻⁶. -2 The value is close to zero, indicating that there is no significant systematic overestimation or underestimation in the overall forecasting process. Meanwhile, the standard deviation of the error is 7.7972 × 10⁻⁶. -2 This indicates that the prediction error distribution is relatively concentrated and the prediction stability is good.

[0050] Verification of the inverse inversion effect: After training, the model can be used based on the input pressure coefficient. and latent variables The corresponding operating parameters are reconstructed through the reverse propagation relationship. The accuracy of the reconstructed operating parameters matched the accuracy of the forward prediction, indicating that the model has good bidirectional consistency.

[0051] Step 5: Using a reversible aerodynamic response model, achieve bidirectional prediction of "rapid prediction of pressure coefficient" and "inversion of operating condition parameters based on pressure coefficient" in aircraft aerodynamic analysis.

[0052] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for processing aircraft aerodynamic parameters based on a reversible neural network, characterized in that, Includes the following steps: Step 1: Construct the training dataset; Each sample in the training dataset includes the aircraft's operating parameters, surface measurement point coordinates, and the corresponding surface pressure coefficient. Step 2: Perform dimensional expansion on the operating parameters and surface measuring point coordinates to obtain expanded input variables; perform dimensional expansion on the surface pressure coefficient to obtain expanded output variables; Step 3: Construct a reversible neural network model, which includes an input layer, multiple cascaded reversible modules, and an output layer. Each reversible module includes an ActNorm normalization layer, a Real NVP affine coupling layer, and a random permutation layer connected in sequence. The reversible neural network model is used to establish a bidirectional reversible mapping between input variables and output variables. The ActNorm normalization layer is used to map input variables with different dimensions and distribution ranges to a scale space, and its forward transformation is as follows: inverse transformation ,in and These are the learnable scaling and translation parameters, respectively; ⊙ represents element-wise multiplication, and ⊘ represents element-wise division. The Real NVP affine coupling layer is used to divide the input features into two parts, perform an affine transformation on one part based on the other part, and maintain the invertibility of the transformation; its forward transformation is... , Inverse transformation to , , This indicates the first part, which remains unchanged. This represents the second part, which undergoes an affine transformation under the conditions of the first part. Output features , For scaling function, It is a translation function; The random permutation layer is used to rearrange the feature channels, and its transformation is as follows: , Let be the permutation matrix; Step 4: Using the training dataset, train the reversible neural network model through a joint loss function to obtain a reversible aerodynamic response model; Step 5: Use the trained reversible neural network model to process the aerodynamic parameters of the aircraft. Based on the input operating parameters and the coordinates of the surface measuring points, predict the pressure coefficient in the forward direction, and / or, based on the input pressure coefficient, inversely derive the corresponding operating parameters.

2. The method for processing aircraft aerodynamic parameters based on a reversible neural network according to claim 1, characterized in that, In step 2, the dimensional expansion includes: The operating parameters and surface measuring point coordinates are expanded by zero-padding, and the input variables are... , , For the angle of attack, Sideslip angle, Mach number, The coordinates of the measuring points on the surface of the aircraft; The surface pressure coefficient is expanded by incorporating latent variables that characterize underlying features, resulting in an output variable. ; , The surface pressure coefficient of the aircraft. These are latent variables.

3. The method for processing aircraft aerodynamic parameters based on a reversible neural network according to claim 1, characterized in that, In step 3, the reversible neural network model introduces a multi-scale splitting mechanism to progressively output latent variables at different levels of the network in order to extract features at different scales. First-stage transformation output Divide it into two parts , The latent variable representing the output at the current scale. Continue to the next reversible module; second-level transformation The third-order transformation is The final latent variable .

4. The method for processing aircraft aerodynamic parameters based on a reversible neural network according to claim 3, characterized in that, In step 3, the reversible neural network model describes the distribution of latent variables in the form of conditional probability, and the joint probability distribution of the latent variables... ,in, These are intermediate features before the second-level transformation.

5. The method for processing aircraft aerodynamic parameters based on a reversible neural network according to claim 1, characterized in that, In step 4, the joint loss function ;in, To reconstruct the loss term in reverse, For the input variables to be predicted, The variables are the actual input variables, and N is the total number of input variables; For positive prediction of loss, To predict the surface pressure coefficient, To predict the surface pressure coefficient. Latent variable distribution loss term, As a latent variable, For the true probability distribution, This represents the predicted probability distribution. , , These are the weighting coefficients for the reverse reconstruction loss term, the forward prediction loss term, and the latent variable distribution loss term, respectively.