Unsteady flow field reconstruction method, device and equipment for aircraft simulation and medium

Abstract

The application discloses an unsteady flow field reconstruction method, device and equipment for aircraft simulation and a medium, relates to the technical field of fluid mechanics, and comprises the following steps: constructing a training sample based on flow field physical quantity data; inputting the spatial coordinates of the grid points in the training sample into a current neural network to obtain target parameters, performing reparameterization on the original time coordinates corresponding to a time step based on the target parameters through rational quadratic spline mapping to obtain target time coordinates; jointly encoding the target time coordinates and the spatial coordinates, inputting the encoded coordinates into a current implicit neural representation network to obtain a prediction result of the flow field physical quantity; performing joint training on the current neural network and the current implicit neural representation network based on the mean square error between the prediction result and the flow field physical quantity data, a first constraint and a second constraint; and reconstructing the unsteady flow field based on a new implicit neural representation network and a new neural network. The unsteady flow field reconstruction, extrapolation and detail preservation capabilities are improved.

Description

Technical Field

[0001] This invention relates to the field of fluid mechanics, and in particular to a method, apparatus, equipment and medium for reconstructing unsteady flow fields for aircraft simulation. Background Technology

[0002] In computational fluid dynamics (CFD) numerical simulations, unsteady flow fields typically exhibit significant temporal evolution characteristics and spatial inhomogeneities. For example, in shear layers, mixing layers, boundary layer separation, vortex structure development, and multi-scale turbulent regions, the rate and complexity of physical quantities changing with time at different spatial locations are not consistent. For this type of data, if only a fixed time coordinate or a simple time encoding method is used for uniform modeling, the model is prone to underfitting in rapidly changing local regions and redundant fitting in slowly changing regions, thus affecting the reconstruction accuracy and temporal extrapolation stability.

[0003] Implicit Neural Representation (INR) maps continuous spatiotemporal coordinates to corresponding physical quantity values, enabling the expression of flow field data as a continuous function and supporting queries at arbitrary spatial and temporal locations. Compared to traditional discrete grid storage methods, INR shows great potential in super-resolution reconstruction, data compression, continuous interpolation, and sparse sampling reconstruction. However, existing INR methods still suffer from two prominent problems in unsteady flow field modeling: first, a unified temporal coordinate cannot adapt to the non-uniform evolution velocities of different spatial regions; second, relying solely on the direct concatenation of spatial and temporal coordinates makes it difficult to fully capture the coupling relationship between local high-frequency structures and global spatiotemporal dependencies in complex flow fields.

[0004] Currently, some methods enhance the ability of neural networks to represent high-frequency signals by using Fourier features, positional encoding, or periodic activation functions. However, these methods typically treat the time coordinate as a globally consistent input dimension and do not adaptively adjust the time representation according to the spatial location. Therefore, when the flow field structure undergoes nonlinear advancement, stretching, or mixing over time, problems such as time phase mismatch, local detail blurring, and increased target time step reconstruction error may still occur.

[0005] Therefore, how to construct an implicit neural reconstruction scheme for unsteady flow fields that can adaptively adjust the temporal coordinate representation according to the spatial region while taking into account both local high-frequency expression capability and global spatiotemporal correlation modeling capability is a problem that needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a method, apparatus, device, and medium for reconstructing unsteady flow fields in aircraft simulation, which can solve the problem that existing implicit neural representation methods are unable to simultaneously adapt to spatial non-uniform evolution, local high-frequency structure representation, and target time-step stable reconstruction when processing unsteady flow field data. The specific solution is as follows: In a first aspect, this application discloses a method for reconstructing unsteady flow fields for aircraft simulation, including: Acquire the flow field physical quantity data of the unsteady flow field of the target component at multiple time steps during the aircraft simulation, and construct training samples based on the flow field physical quantity data; The spatial coordinates of the grid points in the training samples are input into the current neural network to obtain target parameters. The original time coordinates corresponding to the time step are reparameterized based on the target parameters through rational quadratic spline mapping to obtain the target time coordinates. The target parameters are parameters used to control the deformation of the original time coordinates. The target parameters include width parameters, height parameters, and derivative parameters. The target time coordinates and spatial coordinates are jointly encoded, and the corresponding encoded coordinates are input into the current implicit neural representation network to obtain the prediction results of the flow field physical quantities of the unsteady flow field. Based on the mean square error between the prediction result and the flow field physical quantity data, the first constraint between the target time coordinate and the original time coordinate, and the second constraint of the rational quadratic spline mapping, the current neural network and the current implicit neural representation network are jointly trained to obtain a new implicit neural representation network and a new neural network. The unsteady flow field at the target time step and target spatial coordinates is reconstructed based on the new implicit neural representation network and the new neural network.

[0007] Optionally, the flow field physical quantity data includes one or more of the following: tracer, density, velocity, pressure, and temperature. Accordingly, constructing training samples based on the flow field physical quantity data includes: Spatial coordinates are generated based on a preset spatial resolution, and the time coordinates corresponding to each time step are normalized according to a preset time interval to obtain normalized time coordinates. Determine the neighborhood spatial coordinates and neighborhood flow field physical quantity values ​​corresponding to the neighboring grid points of the aforementioned grid point; Training samples are constructed based on the normalized time coordinates, spatial coordinates, flow field physical quantity data, neighborhood spatial coordinates, and neighborhood flow field physical quantity values ​​corresponding to each grid point.

[0008] Optionally, the current neural network includes a multilayer perceptron and a linear parameter mapping layer; the multilayer perceptron is used to extract features from the spatial coordinates to obtain a feature vector; the linear parameter mapping layer is used to determine target parameters based on the feature vector.

[0009] Optionally, the step of reparameterizing the original time coordinates corresponding to the time step based on the target parameters using rational quadratic spline mapping to obtain the target time coordinates includes: The width parameter and the height parameter are normalized respectively to determine the interval width and interval height of multiple segmented intervals; The derivative parameter is positive-valued to determine the positive derivative at the endpoints of the spline segment; Based on the interval width, the interval height, and the positive derivative, the rational quadratic function value of the segmented interval corresponding to the original time coordinate is determined, and the rational quadratic function value is determined as the target time coordinate.

[0010] Optionally, the current implicit neural representation network includes a preset periodic activation residual encoding module, a preset multi-head attention module, and a preset output mapping module; the preset periodic activation residual encoding module includes multiple residual blocks; each residual block includes at least two linear layers; the preset periodic activation residual encoding module is used to perform feature encoding on the encoded coordinates based on a sinusoidal activation function to obtain target encoded coordinates; the preset multi-head attention module is used to determine the attention weight between any two target encoded coordinates, and perform feature fusion based on the attention weight to obtain fused features; the preset output mapping module is used to perform linear dimensionality reduction on the fused features to obtain the prediction results of the flow field physical quantities of the unsteady flow field.

[0011] Optionally, the step of jointly training the current neural network and the current implicit neural representation network based on the mean square error between the prediction result and the flow field physical quantity data, the first constraint between the target time coordinate and the original time coordinate, and the second constraint of the rational quadratic spline mapping, to obtain a new implicit neural representation network and a new neural network, includes: Determine the mean square of the difference between the target time coordinate and the original time coordinate, and use the mean square as the first constraint; Determine the logarithmic Jacobian determinant of the rational quadratic spline mapping, and use the square mean of the logarithmic Jacobian determinant as the second constraint; Determine the first product between the first constraint and the preset first constraint weight; Determine the second product between the second constraint and the preset second constraint weight; The mean square error between the prediction result and the flow field physical quantity data, and the sum of the first product and the second product are determined as the target loss function; Based on the target loss function, the current neural network and the current implicit neural representation network are jointly trained to obtain a new implicit neural representation network and a new neural network.

[0012] Optionally, the reconstruction of the unsteady flow field at the target time step and target spatial coordinates based on the new implicit neural representation network and the new neural network includes: The target spatial coordinates are input into a new neural network to obtain new target parameters; The new target time coordinates are obtained by reparameterizing the new time coordinates corresponding to the target time step based on the new target parameters using rational quadratic spline mapping. The new target time coordinates and the target spatial coordinates are jointly encoded, and the corresponding new encoded coordinates are input into a new implicit neural representation network to obtain new prediction results of the flow field physical quantities of the unsteady flow field. Based on the new prediction results, the unsteady flow field at the target time step and target spatial coordinates is reconstructed.

[0013] Optionally, after reconstructing the unsteady flow field at the target time step and target spatial coordinates based on the new implicit neural representation network and the new neural network, the method further includes: The normalized prediction results of the flow field physical quantities obtained after reconstructing the unsteady flow field at the target time step and target spatial coordinates are inversely normalized to the physical quantity values. The physical quantity values ​​are restored to the target flow field based on a preset grid order; the target flow field is a two-dimensional flow field or a three-dimensional flow field. The target flow field is visualized.

[0014] Secondly, this application discloses an unsteady flow field reconstruction device for aircraft simulation, comprising: The training sample construction module is used to acquire the flow field physical quantity data of the unsteady flow field of the target component at multiple time steps during the aircraft simulation process, and to construct training samples based on the flow field physical quantity data. The target time coordinate acquisition module is used to input the spatial coordinates of grid points in the training samples into the current neural network to obtain target parameters. Based on the target parameters, the original time coordinates corresponding to the time step are reparameterized using rational quadratic spline mapping to obtain the target time coordinates. The target parameters are parameters used to control the deformation of the original time coordinates. The target parameters include width parameters, height parameters, and derivative parameters. The prediction result acquisition module is used to jointly encode the target time coordinates and the spatial coordinates, and input the corresponding encoded coordinates into the current implicit neural representation network to obtain the prediction results of the flow field physical quantities of the unsteady flow field. The training module is used to jointly train the current neural network and the current implicit neural representation network based on the mean square error between the prediction result and the flow field physical quantity data, the first constraint between the target time coordinate and the original time coordinate, and the second constraint of the rational quadratic spline mapping, so as to obtain a new implicit neural representation network and a new neural network. The reconstruction module is used to reconstruct the unsteady flow field at the target time step and target spatial coordinates based on the new implicit neural representation network and the new neural network.

[0015] Thirdly, this application discloses an electronic device, including: Memory, used to store computer programs; A processor is used to execute computer programs to implement the steps of the unsteady flow field reconstruction method for aircraft simulation as described above.

[0016] Fourthly, this application discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the aforementioned unsteady flow field reconstruction method for aircraft simulation.

[0017] This application first acquires the flow field physical quantity data of the unsteady flow field of the target component at multiple time steps during aircraft simulation, and constructs training samples based on the flow field physical quantity data; the spatial coordinates of the grid points in the training samples are input into the current neural network to obtain target parameters; the original time coordinates corresponding to the time steps are reparameterized based on the target parameters through rational quadratic spline mapping to obtain target time coordinates; the target parameters are parameters used to control the deformation of the original time coordinates; the target parameters include width parameters, height parameters, and derivative parameters; the target time coordinates and the spatial coordinates are then... Joint encoding involves inputting the corresponding encoded coordinates into the current implicit neural representation network to obtain the predicted results of the flow field physical quantities of the unsteady flow field. Based on the mean square error between the predicted results and the flow field physical quantity data, the first constraint between the target time coordinate and the original time coordinate, and the second constraint of the rational quadratic spline mapping, the current neural network and the current implicit neural representation network are jointly trained to obtain a new implicit neural representation network and a new neural network. Based on the new implicit neural representation network and the new neural network, the unsteady flow field at the target time step and the target spatial coordinate is reconstructed. It is evident that this application does not simply concatenate the time coordinate as a common input dimension into the neural network, but rather first generates target parameters based on the spatial coordinates, and then uses a spline mapping that satisfies monotonicity, continuity, and differentiability to reparameterize the time coordinates. Therefore, without disrupting the temporal order, adaptive correction can be performed on the time progression speed, phase position, and evolution scale in local regions, reducing the time phase mismatch, local structural ambiguity, and extrapolation error accumulation that are prone to occur in complex unsteady flow fields when using fixed-time encoding. In this way, by reparameterizing time, the same original time coordinate can be transformed into different effective time coordinates at different spatial locations, which can better adapt to the spatially non-uniform temporal evolution of unsteady flow fields. Rational quadratic spline mapping is used to transform the time coordinates, achieving differentiable, invertible, and constrained local nonlinear time alignment while maintaining the temporal order. This application limits the amplitude of time transformation and the degree of local scaling through time constraints and rational quadratic spline mapping, making the time reparameterization process smoother and more stable, reducing abnormal distortions in the early stages of training and error amplification during target time step extrapolation. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] Figure 1 This is a flowchart of an unsteady flow field reconstruction method for aircraft simulation disclosed in this application; Figure 2 This is a schematic diagram of an unsteady flow field reconstruction device for aircraft simulation disclosed in this application. Figure 3 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Currently, some methods enhance the ability of neural networks to represent high-frequency signals through Fourier features, positional encoding, or periodic activation functions. However, these methods typically treat the time coordinate as a globally consistent input dimension and do not adaptively adjust the time representation according to spatial location. Therefore, when the flow field structure undergoes nonlinear progression, stretching, or mixing over time, problems such as time phase mismatch, local detail blurring, and increased target time step reconstruction error may still occur. To solve the above technical problems, this application discloses an unsteady flow field reconstruction method, device, equipment, and medium for aircraft simulation, which can solve the problem that existing implicit neural representation methods are unable to simultaneously adapt to spatial non-uniform evolution, local high-frequency structure representation, and stable reconstruction of the target time step when processing unsteady flow field data.

[0022] For ease of understanding, the following explanation uses the reconstruction of a tracer field in a two-dimensional unsteady shear flow or mixed-layer flow field around a target component of an aircraft as an example. In other embodiments, the physical quantities of the target flow field can also be density, velocity components, pressure, temperature, vorticity, or other scalar or vector fields obtained from CFD simulation. The target component can be any aircraft component such as a wing, fuselage, tail, control surfaces, or nacelle, and the spatial dimension can be extended from two-dimensional to three-dimensional. It should be understood that in the following embodiments, "current neural network" refers to the network used to generate time-reparameterized target parameters based on spatial coordinates (also known as a spatial condition parameter generation network), and "current implicit neural representation network" refers to the network used to predict flow field physical quantities from continuous spatiotemporal coordinates (also known as an implicit neural representation model). After joint training, the two are updated to "new neural network" and "new implicit neural representation network," respectively.

[0023] See Figure 1 As shown, this invention discloses a method for reconstructing unsteady flow fields for aircraft simulation, comprising: Step S11: Obtain the flow field physical quantity data of the unsteady flow field of the target component at multiple time steps during the aircraft simulation, and construct training samples based on the flow field physical quantity data.

[0024] In this embodiment, a flow field data file in HDF5 (Hierarchical Data Format version 5) format is read, and target flow field physical quantities are extracted from a specified data group, such as tracer field data. This data is then organized into a two-dimensional data matrix corresponding to the number of time steps and the number of spatial grid points. The flow field physical quantity data includes one or more of tracer, density, velocity, pressure, and temperature. Then, spatial coordinates are generated based on a preset spatial resolution. The time coordinates corresponding to each time step are normalized according to a preset time interval to obtain normalized time coordinates. The neighborhood spatial coordinates and neighborhood flow field physical quantity values ​​corresponding to the neighboring grid points of each grid point are determined so that the current implicit neural representation network can utilize local spatial neighborhood information during training to better represent local structures such as shear interfaces and hybrid layer boundaries. Finally, training samples are constructed based on the normalized time coordinates, spatial coordinates, flow field physical quantity data, neighborhood spatial coordinates, and neighborhood flow field physical quantity values ​​corresponding to each grid point.

[0025] Specifically, during aircraft simulation, unsteady flow field physical quantity data are acquired at multiple time steps around target components such as wings, fuselages, or control surfaces. This data can originate from computational fluid dynamics simulation results, experimental measurements, or a dataset combining both. Unsteady flow fields can be shear flow, mixed laminar flow, separated vortex fields, or wake fields, etc. For two-dimensional flow fields, each sampling point can be represented as (t, x, y); for three-dimensional flow fields, each sampling point can be represented as (t, x, y, z). The electronic device generates regular grids, irregular grids, or spatial coordinate points obtained through a sampling strategy for each target time step. The time step number or physical time is normalized to the original time coordinates within a preset time interval. These original time coordinates are then combined with the corresponding spatial coordinates to obtain spatiotemporal coordinate samples. Simultaneously, the flow field physical quantities at the corresponding sampling points are used as supervision labels to construct training samples. These training samples can be randomly sampled in batches to improve training efficiency and reduce memory usage. In addition, during the training phase, a preset number of sample points are randomly selected from the spatial grid points for each training time step to construct a small batch of training samples.

[0026] Step S12: Input the spatial coordinates of the grid points in the training samples into the current neural network to obtain the target parameters. Reparameterize the original time coordinates corresponding to the time step based on the target parameters through rational quadratic spline mapping to obtain the target time coordinates. The target parameters are parameters used to control the deformation of the original time coordinates. The target parameters include width parameters, height parameters, and derivative parameters.

[0027] In this embodiment, the spatial coordinates of grid points in the training samples are input into the current neural network. The current neural network outputs target parameters corresponding to the spatial location based on the spatial coordinates. These target parameters control the deformation of the original time coordinates and include a width parameter for determining the width of each segment within the time domain, a height parameter for determining the height of each segment within the transformed domain, and a derivative parameter for determining the derivative at the endpoints of each segment. Specifically, the current neural network is a spatial condition parameter generation network, including a multilayer perceptron and a linear parameter mapping layer. The multilayer perceptron maps the spatial coordinates into high-dimensional latent variables and extracts features from the spatial coordinates to obtain feature vectors. The linear parameter mapping layer determines the target parameters based on the feature vectors and outputs the parameter increments of the rational quadratic spline mapping. The parameter increments include width parameter increments, height parameter increments, and derivative parameter increments. By adding the parameter increments to the basic spline parameters, a set of time reparameterization parameters corresponding to each spatial location can be obtained.

[0028] In this embodiment, during reparameterization, the width and height parameters are normalized to determine the interval width and height of multiple segmented intervals; the derivative parameter is positive-valued to determine the positive derivative at the endpoints of the spline segments; based on the interval width, interval height, and positive derivative, the rational quadratic function value of the segmented interval corresponding to the original time coordinate is determined, and the rational quadratic function value is used as the target time coordinate. Specifically, the width parameter is normalized to obtain the width of multiple spline segments, the height parameter is normalized to obtain the height of multiple spline segments, and the derivative parameter is positive-valued to obtain the positive derivative at the endpoints of each segment. The target time coordinate is calculated using the rational quadratic function of the corresponding segment based on the segment containing the original time coordinate. Since the derivative at the endpoints of each segment is positive, and the segment width and height are positive, this time reparameterization mapping remains monotonic, thus not disrupting the temporal order of the unsteady flow field. In other words, this application uses the target parameter as the control parameter and reparameterizes the original time coordinates corresponding to the time step through rational quadratic spline mapping to obtain the target time coordinates. Since this time reparameterization is controlled by spatial coordinate conditions, the same original time coordinate can be mapped to different target time coordinates at different spatial locations. Therefore, different time stretching, compression, or alignment methods can be formed for shear layers, mixing layers, vortex kernels, and relatively stable regions. When the rational quadratic spline mapping uses K segments, the linear parameter mapping layer can output a parameter vector of length 3K+1, which includes K width parameter increments, K height parameter increments, and K+1 derivative parameter increments. These parameter increments are combined with globally learnable basic width parameters, basic height parameters, and basic derivative parameters to form a set of target parameters related to spatial location. Through this method, the current neural network can learn both the global time transformation trend and the local time transformation differences based on different spatial locations. Furthermore, the weights and biases of the last layer parameters of the current neural network, namely the linear parameter mapping layer, can be initialized with zero or near-zero initialization, thus making the time reparameterization in the initial training stage approach an identity mapping. This setting can prevent excessive time distortion in the early stages of training when the model has not yet learned a reliable flow field structure, thereby improving training stability.

[0029] Step S13: Jointly encode the target time coordinates and the spatial coordinates, and input the corresponding encoded coordinates into the current implicit neural representation network to obtain the prediction results of the flow field physical quantities of the unsteady flow field.

[0030] In this embodiment, the target time coordinates obtained after spatial conditional time reparameterization are jointly encoded with the corresponding spatial coordinates. For example, the target time coordinates are concatenated with the first and second spatial coordinates to form an input vector, and the corresponding encoded coordinates are input into the current implicit neural representation network. The current implicit neural representation network is used to learn the function mapping from continuous spatiotemporal coordinates to flow field physical quantities, and its output is the prediction result of one or more target flow field physical quantities, such as tracer concentration, density, velocity component, pressure, or temperature. In a specific implementation, the target time coordinates, the first and second spatial coordinates are concatenated into a three-dimensional input vector and input into the periodic activation residual encoding module. The periodic activation residual encoding module uses a sinusoidal activation function to perform high-frequency feature mapping on the continuous coordinates and extracts local high-frequency structural features through multi-layer residual blocks. Subsequently, a multi-head attention module is used to model the global correlation between samples, and the corresponding predicted values ​​of flow field physical quantities are obtained through the output mapping module. The current implicit neural representation network includes a preset periodic activation residual encoding module, a preset multi-head attention module, and a preset output mapping module. The preset periodic activation residual encoding module includes multiple residual blocks; each residual block includes at least two sinusoidal linear layers. When the input and output dimensions of a residual block are different, a sinusoidal linear transformation is used to transform the dimensions of the residual branches, and the outputs of the main branches and the residual branches are weighted and fused. The preset periodic activation residual encoding module is used to perform feature encoding on the encoded coordinates based on a sinusoidal activation function to obtain target encoded coordinates. The preset multi-head attention module is used to determine the attention weights between any two target encoded coordinates, and to perform feature fusion based on the attention weights to obtain fused features. The multi-head attention module includes a first multi-head attention unit, a first residual encoding unit, a second multi-head attention unit, a second residual encoding unit, and a third multi-head attention unit arranged sequentially to alternately update feature representations between local periodic feature encoding and global spatiotemporal dependency modeling. The preset output mapping module is used to perform linear dimensionality reduction on the fused features to obtain the prediction results of the flow field physical quantities of the unsteady flow field. The sinusoidal linear layer takes the linear transformation result as input and applies sinusoidal activation. Through the sinusoidal activation function, the model can better represent local high-frequency variations in the flow field, such as steep interface changes, fine-scale vortex structures, and mixing layer boundaries. Optionally, the sinusoidal linear layer can be a sinusoidal layer with a frequency factor, so that the features after linear transformation are mapped by a sinusoidal function before entering subsequent network layers. Through the combination of the frequency factor and residual connections, the model can express fine-scale structures such as vortex kernels, shear interfaces, and mixing layer boundaries while maintaining gradient propagation stability.

[0031] Step S14: Based on the mean square error between the prediction result and the flow field physical quantity data, the first constraint between the target time coordinate and the original time coordinate, and the second constraint of the rational quadratic spline mapping, the current neural network and the current implicit neural representation network are jointly trained to obtain a new implicit neural representation network and a new neural network.

[0032] In this embodiment, the mean square of the difference between the target time coordinate and the original time coordinate is determined, and the mean square is used as the first constraint; the logarithmic Jacobian determinant of the rational quadratic spline mapping is determined, and the mean square of the logarithmic Jacobian determinant is used as the second constraint; a first product between the first constraint and a preset first constraint weight is determined; a second product between the second constraint and a preset second constraint weight is determined; the mean square error between the prediction result and the flow field physical quantity data, and the sum of the first product and the second product are used as the target loss function; based on the target loss function, the current neural network and the current implicit neural representation network are jointly trained to obtain a new implicit neural representation network and a new neural network. This application uses the mean square error between the predicted results and the actual flow field physical quantities as the data reconstruction error term. It employs a first constraint between the target time coordinate and the original time coordinate to suppress unnecessary time distortion, and a second constraint using rational quadratic spline mapping to limit the local scaling of the time transformation. These three constraints are combined to construct the target loss function. End-to-end joint training is then performed on the current neural network and the current implicit neural representation network to obtain a new neural network and a new implicit neural representation network. By jointly training the current neural network and the current implicit neural representation network, time reparameterization and flow field physical quantity prediction can be coordinated and optimized synergistically.

[0033] The data reconstruction error can be represented by the mean squared error, used to constrain the predicted physical quantity to be close to the true physical quantity; the time identity constraint can be represented by the mean squared difference between the target time coordinate and the original time coordinate, used to suppress unnecessary time distortion; the Jacobian constraint can be represented by the mean squared difference of the logarithm of the monotonic spline mapping, the Jacobian determinant, used to constrain the local scaling of the time transformation. Therefore, the overall training loss can be expressed as the weighted sum of the data reconstruction error, the time identity constraint, and the Jacobian constraint. Specifically, the training objective satisfies the following form: L=L_data+λ_id×L_id+λ_jac×L_jac; Where L is the objective loss function; L_data represents the data reconstruction error; L_id represents the identity constraint (i.e., the first constraint); L_jac represents the Jacobian constraint (i.e., the second constraint); and λ_id and λ_jac represent the weights of the identity constraint and the Jacobian constraint, respectively. The data reconstruction error can also be the mean absolute error, the relative L2 error, or a combination thereof, and the second constraint can also be a local scaling penalty term. Hyperparameters are set during training to control the weights of the first and second constraints. When the flow field's temporal evolution is relatively stable, the weights of the first and second constraints can be increased to make the temporal reparameterization closer to the identity mapping; when the flow field exhibits significant nonlinear propagation, local accelerated evolution, or phase differences in different regions, the weights of the first and second constraints can be appropriately decreased to give the model stronger spatial adaptive temporal alignment capabilities.

[0034] Step S15: Reconstruct the unsteady flow field at the target time step and target spatial coordinates based on the new implicit neural representation network and the new neural network.

[0035] In this embodiment, the target spatial coordinates are input into a new neural network to obtain new target parameters; the new time coordinates corresponding to the target time step are reparameterized based on the new target parameters using rational quadratic spline mapping to obtain new target time coordinates; the new target time coordinates and the target spatial coordinates are jointly encoded, and the corresponding newly encoded coordinates are input into a new implicit neural representation network to obtain new prediction results for the flow field physical quantities of the unsteady flow field; the unsteady flow field at the target time step and target spatial coordinates is reconstructed based on the new prediction results. After training, the parameters of the new neural network and the new implicit neural representation network are loaded, and continuous queries are performed on any target time step and target spatial coordinates. The target time step can be an existing time step in the training set, an unobserved intermediate time step in the training set, or an extrapolated time step located near the training time range; the target spatial coordinates can be original grid points, refined grid points, or any continuous spatial coordinate points. For complete flow field reconstruction, all spatial grid points on the target time step can be traversed, and the prediction results can be restored to a two-dimensional or three-dimensional flow field array, thereby realizing the reconstruction of the unsteady flow field at the target time step and target spatial coordinates.

[0036] Furthermore, after reconstructing the unsteady flow field at the target time step and target spatial coordinates based on the new implicit neural representation network and the new neural network, the normalized prediction results of the flow field physical quantities obtained after reconstructing the unsteady flow field at the target time step and target spatial coordinates are denormalized into physical quantity values; the physical quantity values ​​are restored to the target flow field based on a preset grid order; the target flow field is a two-dimensional flow field or a three-dimensional flow field; and the target flow field is visualized. Specifically, the normalized prediction results obtained from the reconstruction are denormalized into physical quantity values; the physical quantity values ​​are restored to a two-dimensional or three-dimensional flow field according to a preset grid order; the reconstruction results are evaluated based on at least one of the following indicators: relative L2 error, structural similarity, gradient relative L2 error, and mixing layer width error; and the reconstruction results are output as a visualization file or a simulation post-processing file.

[0037] In summary, this application does not simply concatenate the time coordinates as ordinary input dimensions directly into the neural network. Instead, it first generates target parameters based on spatial coordinates, and then reparameterizes the time coordinates using spline mapping that satisfies monotonicity, continuity, and differentiability. This allows for adaptive correction of the time progression rate, phase position, and evolution scale in local regions without disrupting the temporal order, reducing the temporal phase mismatch, local structural ambiguity, and extrapolation error accumulation that easily occur with fixed-time encoding in complex unsteady flow fields. Thus, through time reparameterization, the same original time coordinates can form different effective time coordinates at different spatial locations, better adapting to the spatially non-uniform temporal evolution patterns in unsteady flow fields. The rational quadratic spline mapping is used to transform the time coordinates, achieving differentiable, invertible, and constrained local nonlinear time alignment while maintaining the temporal order. This application limits the amplitude of time transformation and the degree of local scaling through time constraints and rational quadratic spline mapping constraints, making the time reparameterization process smoother and more stable, reducing abnormal distortions in the early training stages and error amplification during target time step extrapolation.

[0038] This embodiment further explains the spatial conditional time reparameterization module. This module is used to transform the original time coordinate t into the target time coordinate τ. Unlike globally shared time transformations, the time transformation in this embodiment is controlled by spatial coordinate conditions, i.e., τ=f(t|x,y). Therefore, different spatial locations can have different time stretching, compression, or local alignment methods.

[0039] In one specific implementation, the spatial condition parameter generation network receives spatial coordinates x and y, concatenates them, and inputs them into a multilayer perceptron Φ. The multilayer perceptron outputs spatial condition latent variables, and a linear parameter mapping layer maps these latent variables into a parameter vector of length 3K+1, where K is the number of spline segments. This parameter vector includes K width parameter increments, K height parameter increments, and K+1 derivative parameter increments.

[0040] To stabilize the training process, the basic width and height parameters can be initialized to zero, and the basic derivative parameter can be initialized to a constant that makes the derivative close to one. Simultaneously, the weights and biases of the last layer of the spatial condition parameter generation network can be initialized to zero. Thus, the model's temporal reparameterization mapping in the initial training phase approximates an identity mapping. As training progresses, the model gradually learns local temporal transformations based on the reconstruction needs of different spatial regions.

[0041] During time reparameterization, the width parameter is Softmax normalized and a minimum segment width is added to ensure that the width of all time segments is positive; the height parameter is Softmax normalized and a minimum segment height is added to ensure that the height of all value range segments is positive; the derivative parameter is Softplus processed and a minimum derivative is added to ensure that the endpoint derivatives are positive. Subsequently, rational quadratic spline values ​​are calculated based on the segments containing the original time coordinates to obtain the target time coordinate τ.

[0042] In this way, monotonic spline mapping can maintain the temporal order and avoid time folding; and the spatial condition parameters enable the model to learn more detailed time alignment in rapidly changing regions such as shear layers, vortex kernels, and hybrid interfaces, while maintaining a near-identical time mapping in stable regions.

[0043] Furthermore, the implicit neural representation model is explained in more detail. This model is used to learn the mapping relationship from continuous spatiotemporal coordinates to flow field physical quantities. The model input is a concatenated vector of the target time coordinate τ and spatial coordinates x and y, and the output is the flow field physical quantity value at the corresponding location.

[0044] In one specific implementation, the model first performs feature encoding using multiple periodic activation residual blocks. Each periodic activation residual block includes at least two sinusoidal linear layers, which take the linear transformation result as input and apply sinusoidal activation. Through the sinusoidal activation function, the model can better represent local high-frequency variations in the flow field, such as steep interface changes, fine-scale vortex structures, and mixing layer boundaries.

[0045] To avoid degradation during deep network training, periodically activated residual blocks fuse the output of the main branch with the input of the residual branch. When the input and output dimensions are inconsistent, a dimension transformation layer can be set on the residual branch to make the feature dimensions of the two branches consistent.

[0046] After periodically activating residual encoding, the model establishes global dependencies between sample points through a multi-head attention module. Specifically, multiple multi-head attention units can be inserted between different residual encoding stages, allowing the model to alternately update features between local high-frequency encoding and global correlation modeling. The multi-head attention module is beneficial for capturing the co-evolutionary relationships of the flow field structure at different spatial locations.

[0047] Finally, the model maps high-dimensional features to predicted values ​​of target flow field physical quantities through an output mapping module. For scalar field reconstruction, the output dimension can be one; for vector field reconstruction such as velocity fields, the output dimension can be two, three, or more.

[0048] Furthermore, when jointly optimizing the spatial condition parameter generation network and the implicit neural representation model using the AdamW optimizer, for each training batch, the time coordinates, spatial coordinates, and actual flow field physical quantities are read. The time coordinates and spatial coordinates are input into the model to obtain the predicted flow field physical quantities, the target time coordinates, and the logarithmic Jacobian determinant of the monotonic spline mapping. In one specific implementation, the training loss includes three parts: the first part is the mean square error between the predicted and actual flow field physical quantities; the second part is the squared mean of the difference between the target and original time coordinates; and the third part is the squared mean of the logarithmic Jacobian determinant. The electronic device performs backpropagation based on the weighted sum of the loss terms and updates the model parameters.

[0049] During the verification process, the model can be queried on the complete spatial grid at a specified time step, and the prediction results can be inversely transformed from the normalized numerical range back to the physical quantity range, and restored into a two-dimensional flow field according to the preset grid order. Subsequently, indicators such as relative L2 error, structural similarity, gradient relative L2 error, and mixing layer width error can be calculated to evaluate the reconstruction results from multiple aspects such as numerical error, structural preservation, gradient details, and physical feature scale.

[0050] Finally, in terms of output, the reconstruction results can be written to Tecplot format, VTK (Visualization Toolkit) format, HDF5 format, or other visualization post-processing formats to further observe the flow field structure, mixing layer width, vortex structure location, or other physical characteristics.

[0051] See Figure 2 As shown, this embodiment of the invention discloses an unsteady flow field reconstruction device for aircraft simulation, comprising: The training sample construction module 11 is used to acquire the flow field physical quantity data of the unsteady flow field of the target component at multiple time steps during the aircraft simulation process, and to construct training samples based on the flow field physical quantity data. The target time coordinate acquisition module 12 is used to input the spatial coordinates of grid points in the training samples into the current neural network to obtain target parameters, and to reparameterize the original time coordinates corresponding to the time step based on the target parameters through rational quadratic spline mapping to obtain the target time coordinates; the target parameters are parameters used to control the deformation of the original time coordinates; the target parameters include width parameters, height parameters, and derivative parameters; The prediction result acquisition module 13 is used to jointly encode the target time coordinates and the spatial coordinates, and input the corresponding encoded coordinates into the current implicit neural representation network to obtain the prediction results of the flow field physical quantities of the unsteady flow field. Training module 14 is used to jointly train the current neural network and the current implicit neural representation network based on the mean square error between the prediction result and the flow field physical quantity data, the first constraint between the target time coordinate and the original time coordinate, and the second constraint of the rational quadratic spline mapping, so as to obtain a new implicit neural representation network and a new neural network. The reconstruction module 15 is used to reconstruct the unsteady flow field at the target time step and target spatial coordinates based on the new implicit neural representation network and the new neural network.

[0052] Since the embodiments of the device part correspond to the embodiments described above, please refer to the embodiments described in the method part for the embodiments of the device part, and will not be repeated here.

[0053] In summary, this application does not simply concatenate the time coordinates as ordinary input dimensions directly into the neural network. Instead, it first generates target parameters based on spatial coordinates, and then reparameterizes the time coordinates using spline mapping that satisfies monotonicity, continuity, and differentiability. This allows for adaptive correction of the time progression rate, phase position, and evolution scale in local regions without disrupting the temporal order, reducing the temporal phase mismatch, local structural ambiguity, and extrapolation error accumulation that easily occur with fixed-time encoding in complex unsteady flow fields. Thus, through time reparameterization, the same original time coordinates can form different effective time coordinates at different spatial locations, better adapting to the spatially non-uniform temporal evolution patterns in unsteady flow fields. The rational quadratic spline mapping is used to transform the time coordinates, achieving differentiable, invertible, and constrained local nonlinear time alignment while maintaining the temporal order. This application limits the amplitude of time transformation and the degree of local scaling through time constraints and rational quadratic spline mapping constraints, making the time reparameterization process smoother and more stable, reducing abnormal distortions in the early training stages and error amplification during target time step extrapolation.

[0054] Furthermore, embodiments of this application also disclose an electronic device, Figure 3 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application.

[0055] Figure 3 This is a schematic diagram of the structure of an electronic device 20 provided in an embodiment of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the unsteady flow field reconstruction method for aircraft simulation disclosed in any of the foregoing embodiments. Alternatively, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0056] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0057] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0058] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the unsteady flow field reconstruction method for aircraft simulation executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0059] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned unsteady flow field reconstruction method for aircraft simulation. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0060] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0061] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0062] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0063] Finally, it should be noted that in this paper, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0064] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for reconstructing unsteady flow fields for aircraft simulation, characterized in that, include: Acquire the flow field physical quantity data of the unsteady flow field of the target component at multiple time steps during the aircraft simulation process, and construct training samples based on the flow field physical quantity data; The spatial coordinates of the grid points in the training samples are input into the current neural network to obtain target parameters. The original time coordinates corresponding to the time step are reparameterized based on the target parameters through rational quadratic spline mapping to obtain the target time coordinates. The target parameters are parameters used to control the deformation of the original time coordinates. The target parameters include width parameters, height parameters, and derivative parameters. The target time coordinates and spatial coordinates are jointly encoded, and the corresponding encoded coordinates are input into the current implicit neural representation network to obtain the prediction results of the flow field physical quantities of the unsteady flow field. Based on the mean square error between the prediction result and the flow field physical quantity data, the first constraint between the target time coordinate and the original time coordinate, and the second constraint of the rational quadratic spline mapping, the current neural network and the current implicit neural representation network are jointly trained to obtain a new implicit neural representation network and a new neural network. The unsteady flow field at the target time step and target spatial coordinates is reconstructed based on the new implicit neural representation network and the new neural network.

2. The unsteady flow field reconstruction method for aircraft simulation according to claim 1, characterized in that, The flow field physical quantity data includes one or a combination of tracer, density, velocity, pressure, and temperature; Accordingly, constructing training samples based on the flow field physical quantity data includes: Spatial coordinates are generated based on a preset spatial resolution, and the time coordinates corresponding to each time step are normalized according to a preset time interval to obtain normalized time coordinates. Determine the neighborhood spatial coordinates and neighborhood flow field physical quantity values ​​corresponding to the neighborhood grid points of the grid point; Training samples are constructed based on the normalized time coordinates, spatial coordinates, flow field physical quantity data, neighborhood spatial coordinates, and neighborhood flow field physical quantity values ​​corresponding to each grid point.

3. The unsteady flow field reconstruction method for aircraft simulation according to claim 1, characterized in that, The current neural network includes a multilayer perceptron and a linear parameter mapping layer; the multilayer perceptron is used to extract features from the spatial coordinates to obtain a feature vector; the linear parameter mapping layer is used to determine the target parameters based on the feature vector.

4. The unsteady flow field reconstruction method for aircraft simulation according to claim 1, characterized in that, The step of reparameterizing the original time coordinates corresponding to the time step based on the target parameters using rational quadratic spline mapping to obtain the target time coordinates includes: The width parameter and the height parameter are normalized respectively to determine the interval width and interval height of multiple segmented intervals; The derivative parameter is positive-valued to determine the positive derivative at the endpoints of the spline segment; Based on the interval width, the interval height, and the positive derivative, the rational quadratic function value of the segmented interval corresponding to the original time coordinate is determined, and the rational quadratic function value is determined as the target time coordinate.

5. The method for reconstructing unsteady flow fields for aircraft simulation according to claim 1, characterized in that, The current implicit neural representation network includes a preset periodic activation residual encoding module, a preset multi-head attention module, and a preset output mapping module; The preset periodic activation residual coding module includes multiple residual blocks; each residual block includes at least two linear layers; the preset periodic activation residual coding module is used to perform feature coding on the encoded coordinates based on a sinusoidal activation function to obtain target encoded coordinates; the preset multi-head attention module is used to determine the attention weight between any two target encoded coordinates, and perform feature fusion based on the attention weight to obtain fused features; The preset output mapping module is used to perform linear dimensionality reduction on the fused features to obtain the prediction results of the flow field physical quantities of the unsteady flow field.

6. The method for reconstructing unsteady flow fields for aircraft simulation according to claim 1, characterized in that, The method of jointly training the current neural network and the current implicit neural representation network based on the mean square error between the prediction result and the flow field physical quantity data, the first constraint between the target time coordinate and the original time coordinate, and the second constraint of the rational quadratic spline mapping, to obtain a new implicit neural representation network and a new neural network, includes: Determine the mean square of the difference between the target time coordinate and the original time coordinate, and use the mean square as the first constraint; Determine the logarithmic Jacobian determinant of the rational quadratic spline mapping, and use the square mean of the logarithmic Jacobian determinant as the second constraint; Determine the first product between the first constraint and the preset first constraint weight; Determine the second product between the second constraint and the preset second constraint weight; The mean square error between the prediction result and the flow field physical quantity data, and the sum of the first product and the second product are determined as the target loss function; Based on the target loss function, the current neural network and the current implicit neural representation network are jointly trained to obtain a new implicit neural representation network and a new neural network.

7. The method for reconstructing unsteady flow fields for aircraft simulation according to claim 1, characterized in that, The reconstruction of the unsteady flow field at the target time step and target spatial coordinates based on the new implicit neural representation network and the new neural network includes: The target spatial coordinates are input into a new neural network to obtain new target parameters; The new target time coordinates are obtained by reparameterizing the new time coordinates corresponding to the target time step based on the new target parameters using rational quadratic spline mapping. The new target time coordinates and the target spatial coordinates are jointly encoded, and the corresponding new encoded coordinates are input into a new implicit neural representation network to obtain new prediction results of the flow field physical quantities of the unsteady flow field. Based on the new prediction results, the unsteady flow field at the target time step and target spatial coordinates is reconstructed.

8. The method for reconstructing unsteady flow fields for aircraft simulation according to any one of claims 1 to 7, characterized in that, After reconstructing the unsteady flow field at the target time step and target spatial coordinates based on the new implicit neural representation network and the new neural network, the method further includes: The normalized prediction results of the flow field physical quantities obtained after reconstructing the unsteady flow field at the target time step and target spatial coordinates are inversely normalized to the physical quantity values. The physical quantity values ​​are restored to the target flow field based on a preset grid order; the target flow field is a two-dimensional flow field or a three-dimensional flow field. The target flow field is visualized.

9. A device for reconstructing unsteady flow fields for aircraft simulation, characterized in that, include: The training sample construction module is used to acquire the flow field physical quantity data of the unsteady flow field of the target component at multiple time steps during the aircraft simulation process, and to construct training samples based on the flow field physical quantity data. The target time coordinate acquisition module is used to input the spatial coordinates of grid points in the training samples into the current neural network to obtain target parameters. Based on the target parameters, the original time coordinates corresponding to the time step are reparameterized using rational quadratic spline mapping to obtain the target time coordinates. The target parameters are parameters used to control the deformation of the original time coordinates. The target parameters include width parameters, height parameters, and derivative parameters. The prediction result acquisition module is used to jointly encode the target time coordinates and the spatial coordinates, and input the corresponding encoded coordinates into the current implicit neural representation network to obtain the prediction results of the flow field physical quantities of the unsteady flow field. The training module is used to jointly train the current neural network and the current implicit neural representation network based on the mean square error between the prediction result and the flow field physical quantity data, the first constraint between the target time coordinate and the original time coordinate, and the second constraint of the rational quadratic spline mapping, so as to obtain a new implicit neural representation network and a new neural network. The reconstruction module is used to reconstruct the unsteady flow field at the target time step and target spatial coordinates based on the new implicit neural representation network and the new neural network.

10. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing a computer program to implement the steps of the unsteady flow field reconstruction method for aircraft simulation as described in any one of claims 1 to 8.

11. A computer-readable storage medium, characterized in that, A computer program is stored on a computer-readable storage medium, which, when executed by a processor, implements the steps of the unsteady flow field reconstruction method for aircraft simulation as described in any one of claims 1 to 8.

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