A method, device, equipment and storage medium for inverse mapping of a reduced-order flow field

Abstract

The present application discloses an inverse mapping method, device, equipment and storage medium for a reduced-order flow field, which relates to the field of computational fluid dynamics, and includes: performing dimensionality reduction processing on the original output samples to obtain the reduced-order output samples corresponding to the input samples for training a flow field model to obtain a target reduced-order flow field model, and inputting the test samples into the target reduced-order flow field model to obtain the target low-dimensional output; determining the respective target distances between the target low-dimensional output and the reduced-order output samples, screening the reduced-order output samples based on the target distances to obtain the first target output samples, and determining the original output samples corresponding to the first target output samples as the second target output samples; determining the first weights of the first target output samples based on the target low-dimensional output, and determining the second weights of the second target output samples based on the first weights to perform inverse mapping on the target low-dimensional output to obtain the target high-dimensional output corresponding to the test samples. The present application realizes the inverse mapping of the reduced-order flow field to the original flow field.

Description

Technical Field

[0001] The present invention relates to the field of computational fluid dynamics, and particularly to a method, device, equipment and storage medium for inverse mapping of a reduced-order flow field. Background Art

[0002] The uncertainty quantification work of CFD (Computational Fluid Dynamics) has the characteristics of high-dimensional input, high-dimensional output and possible correlation, and has been more and more widely applied in heavy equipment engineering fields such as aerospace, energy power, and transportation. For example, the uncertainty quantification work of turbulence model coefficients needs to process about 10-dimensional uncertain input parameters. The output quantities not only include global integral quantities such as lift and drag coefficients, but sometimes also include time or space sequence-type responses such as the pressure distribution on the wall surface in airfoil simulation. There may be certain unknown correlations between these high-dimensional responses, and these high-dimensional output responses are sometimes dozens of dimensions, and some are even hundreds of dimensions. In particular, complex flow fields present typical multi-dimensional, correlated and strongly non-linear characteristics, so it is necessary to model the overall output. Although existing modeling methods (such as artificial neural networks) can model the overall high-dimensional output, the number of parameters to be estimated in the model is large, which affects the training time. Therefore, it is necessary to introduce a flow field reduction method, establish a prediction model between the model uncertain parameters and the reduced-order flow field, and then inverse map the reduced-order flow field response to the original flow field to finally obtain the corresponding prediction result. At present, the commonly used POD (Proper Orthogonal Decomposition) reduction method is mostly applicable to linear flow fields. For non-linear flow fields, it is necessary to introduce the KPOD (Kernel Proper Orthogonal Decomposition) reduction method. However, how to efficiently implement the inverse mapping from the reduced-order flow field to the original flow field is still an urgent problem to be solved. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a method, device, equipment and storage medium for inverse mapping of a reduced-order flow field, which can efficiently implement the inverse mapping from the reduced-order flow field to the original flow field. The specific scheme is as follows:

[0004] In the first aspect, the present application discloses a method for inverse mapping of a reduced-order flow field, including:

[0005] Obtaining training samples for training a flow field model, and performing dimensionality reduction processing on each original output sample corresponding to each input sample in the training samples to obtain each reduced-dimensional output sample corresponding to each input sample;

[0006] Training a flow field model based on each of the input samples and the corresponding reduced-dimension output samples to obtain a corresponding target reduced-order flow field model, and inputting test samples into the target reduced-order flow field model to perform corresponding low-dimensional output prediction based on the test samples by using the target reduced-order flow field model, so as to obtain a target low-dimensional output corresponding to the test samples;

[0007] Determining target distances between the target low-dimensional output and the reduced-dimension output samples, screening the reduced-dimension output samples based on the target distances to obtain corresponding first target output samples, and determining the original output samples corresponding to the first target output samples as second target output samples;

[0008] Using a preset optimization method to determine first weights corresponding to the first target output samples respectively based on the target low-dimensional output, and determining the first weights as second weights of the corresponding second target output samples respectively;

[0009] Performing inverse mapping on the target low-dimensional output based on the second target output samples and the corresponding second weights, so as to map the target low-dimensional output to a target high-dimensional space corresponding to the flow field model before reduction to obtain a target high-dimensional output corresponding to the test samples, thereby completing the corresponding output prediction.

[0010] Optionally, the dimension reduction processing of the original output samples corresponding to the input samples in the training samples to obtain the reduced-dimension output samples corresponding to the input samples includes:

[0011] Using a preset kernel function to determine a target matrix based on the original output samples corresponding to the input samples in the training samples, and performing mapping on the original output samples based on the target matrix to complete the dimension reduction processing, so as to obtain the reduced-dimension output samples corresponding to the input samples;

[0012] Wherein, the preset kernel function includes a Gaussian kernel function, a polynomial kernel function, and a Sigmoid kernel function.

[0013] Optionally, the using a preset kernel function to determine a target matrix based on the original output samples corresponding to the input samples in the training samples, and performing mapping on the original output samples based on the target matrix to complete the dimension reduction processing, so as to obtain the reduced-dimension output samples corresponding to the input samples includes:

[0014] Using a preset kernel function to determine a first target matrix based on the original output samples corresponding to the input samples in the training samples;

[0015] Performing centering processing on the first target matrix to obtain a second target matrix;

[0016] Diagonalize and reduce the dimension of the second target matrix based on a preset dimension reduction dimension to determine a third target matrix;

[0017] Map each of the original output samples based on the third target matrix to obtain each reduced-dimension output sample corresponding to each input sample;

[0018] Wherein, the preset dimension reduction dimension is less than the number of input samples, and the preset dimension reduction dimension is less than the dimension of the original output samples.

[0019] Optionally, the target flow field reduced-order model is a Kriging model built based on a preset function type; the preset function type includes a trend function and a correlation function.

[0020] Optionally, the screening of the reduced-dimension output samples based on the target distance to obtain corresponding first target output samples includes:

[0021] Determine the minimum distance between the target low-dimensional output and the reduced-dimension output samples based on all the target distances;

[0022] Screen the reduced-dimension output samples based on a preset distance multiple and the minimum distance to determine the first target output samples;

[0023] Wherein, the target distance corresponding to the first target output sample is less than or equal to the product of the minimum distance and the preset distance multiple, and the target distance is the Euclidean distance.

[0024] Optionally, the use of a preset optimization method to determine the first weight corresponding to each of the first target output samples based on the target low-dimensional output includes:

[0025] Use a preset optimization function to determine the first weight corresponding to each of the first target output samples based on the target low-dimensional output;

[0026] Wherein, the first weight is the weighted weight corresponding to each of the first target output samples when each of the first target output samples satisfies a preset weight solving condition; the preset weight solving condition is that the difference between the weighted sum result of each of the first target output samples and the target low-dimensional output is the smallest.

[0027] Optionally, the inverse mapping of the target low-dimensional output based on each of the second target output samples and the corresponding second weight to map the target low-dimensional output to the target high-dimensional space corresponding to the flow field model before the order reduction to obtain the target high-dimensional output corresponding to the test sample includes:

[0028] Performing weighted summation on each of the second target output samples based on the second weight to obtain a corresponding weighted summation result;

[0029] Determining the weighted summation result as the reflection result corresponding to the target high-dimensional space of the flow field model before order reduction for the target low-dimensional output, and determining the reflection result as the target high-dimensional output corresponding to the test sample; wherein, the dimension of the reflection result is the same as that of the second target output sample.

[0030] In a second aspect, the present application discloses a reflection device for a reduced-order flow field, including:

[0031] A sample dimensionality reduction module, configured to obtain training samples for training a flow field model, and perform dimensionality reduction processing on each original output sample corresponding to each input sample in the training samples to obtain each reduced-dimensional output sample corresponding to each input sample;

[0032] A low-dimensional output acquisition module, configured to perform flow field model training based on each input sample and the corresponding reduced-dimensional output samples to obtain a corresponding target flow field reduced-order model, and input a test sample into the target flow field reduced-order model to perform corresponding low-dimensional output prediction based on the test sample by using the target flow field reduced-order model to obtain the target low-dimensional output corresponding to the test sample;

[0033] A sample screening module, configured to determine each target distance between the target low-dimensional output and each reduced-dimensional output sample, screen the reduced-dimensional output samples based on the target distance to obtain corresponding first target output samples, and determine each original output sample corresponding to each first target output sample as a second target output sample;

[0034] A weight determination module, configured to determine first weights respectively corresponding to each first target output sample based on the target low-dimensional output by using a preset optimization method, and determine each first weight as the second weight of the corresponding second target output sample;

[0035] A high-dimensional output prediction module, configured to perform reflection on the target low-dimensional output based on each second target output sample and the corresponding second weight to map the target low-dimensional output to the target high-dimensional space corresponding to the flow field model before order reduction to obtain the target high-dimensional output corresponding to the test sample, so as to complete corresponding output prediction.

[0036] In a third aspect, the present application discloses an electronic device, including:

[0037] A memory, configured to store a computer program;

[0038] A processor for executing the computer program to implement the foregoing inverse mapping method for the reduced-order flow field.

[0039] In a fourth aspect, the present application discloses a computer-readable storage medium for storing a computer program, wherein when the computer program is executed by a processor, the foregoing inverse mapping method for the reduced-order flow field is implemented.

[0040] In the present application, when implementing the inverse mapping from the reduced-order flow field to the original flow field, training samples for training the flow field model are obtained, and dimensionality reduction processing is performed on each original output sample corresponding to each input sample in the training samples to obtain each reduced-dimensional output sample corresponding to each input sample; based on each input sample and the corresponding reduced-dimensional output samples, the flow field model is trained to obtain a corresponding target flow field reduction model, and the test sample is input into the target flow field reduction model to use the target flow field reduction model to perform corresponding low-dimensional output prediction based on the test sample to obtain a target low-dimensional output corresponding to the test sample; each target distance between the target low-dimensional output and each reduced-dimensional output sample is determined, and based on the target distance, the reduced-dimensional output samples are screened to obtain corresponding first target output samples, and each original output sample corresponding to each first target output sample is determined as a second target output sample; a preset optimization method is used to determine a first weight corresponding to each first target output sample based on the target low-dimensional output, and each first weight is respectively determined as a second weight of the corresponding second target output sample; an inverse mapping is performed on the target low-dimensional output based on each second target output sample and the corresponding second weight to map the target low-dimensional output to a target high-dimensional space corresponding to the flow field model before dimensionality reduction, obtaining a target high-dimensional output corresponding to the test sample to complete the corresponding output prediction. It can be seen that in the present application, the reduced-dimensional output samples are obtained by performing dimensionality reduction on the original output samples corresponding to the known input samples, and a target flow field reduction model is built according to the known input samples and their corresponding reduced-dimensional output samples. After the building is completed, any new input given to the target flow field reduction model can obtain the corresponding low-dimensional output, thus realizing the reduction of the original flow field and reducing the difficulty of building the model between the input and output. After the test sample is input into the target flow field reduction model to obtain the target low-dimensional output, the second target output samples with a relatively close distance to the target low-dimensional output can be screened according to the target distances between the target low-dimensional output and each reduced-dimensional output sample. Finally, according to the second target output samples and the second weights, the inverse mapping of the target low-dimensional output to the target high-dimensional space corresponding to the flow field model before dimensionality reduction (i.e., the original flow field) is realized, obtaining the target high-dimensional output. At this time, the target high-dimensional output is consistent with the dimension of the original flow field, thus efficiently realizing the inverse mapping from the reduced-order flow field to the original flow field while ensuring the accuracy. Description of the Drawings

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to the provided drawings.

[0042] Figure 1 Flowchart of an inverse mapping method for a reduced-order flow field disclosed in the present application;

[0043] Figure 2 Box plot of quartiles of inverse mapping prediction error disclosed in the present application;

[0044] Figure 3 Structure diagram of an inverse mapping device for a reduced-order flow field disclosed in the present application;

[0045] Figure 4 Structure diagram of an electronic device disclosed in the present application. Detailed implementation manners

[0046] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0047] Existing modeling methods (such as artificial neural networks) can model the high-dimensional output as a whole, but the number of parameters to be estimated in the model is large, which affects the training time. Therefore, it is necessary to introduce a flow field reduction method to establish a prediction model between the uncertain parameters of the model and the reduced-order flow field, and then map the response of the reduced-order flow field back to the original flow field to finally obtain the corresponding prediction result. The commonly used POD reduction method at present is mostly applicable to linear flow fields. For non-linear flow fields, it is necessary to introduce the KPOD reduction method. However, how to efficiently implement the inverse mapping from the reduced-order flow field to the original flow field is still an urgent problem to be solved. To solve the above technical problems, the present application discloses an inverse mapping method for a reduced-order flow field, which can efficiently implement the inverse mapping from the reduced-order flow field to the original flow field.

[0048] See Figure 1 As shown, the embodiments of the present invention disclose an inverse mapping method for a reduced-order flow field, including:

[0049] Step S11: Obtain training samples for training a flow field model, and perform dimensionality reduction processing on each original output sample corresponding to each input sample in the training samples to obtain each reduced-dimensional output sample corresponding to each input sample.

[0050] In this embodiment, the training samples are sample data for training the flow field model. After obtaining the training samples, the KPOD method can be used to obtain the reduced-dimension output samples corresponding to the input samples. It should be noted that the flow field model to be trained in this application can be a wind tunnel flow field model used in the aircraft design process, or a flow field model involved in other application scenarios, such as the atmospheric circulation model in the meteorological prediction scenario, etc.

[0051] Perform dimensionality reduction processing on the original output samples corresponding to each input sample in the training samples to obtain the reduced-dimension output samples corresponding to each input sample. The specific process may include: determining a target matrix based on the original output samples corresponding to each input sample in the training samples using a preset kernel function, and performing mapping on each original output sample based on the target matrix to complete the dimensionality reduction processing, so as to obtain the reduced-dimension output samples corresponding to each input sample; wherein, the preset kernel function includes a Gaussian kernel function, a polynomial kernel function, and a Sigmoid kernel function.

[0052] In a specific implementation manner, the specific process of obtaining the reduced-dimension output samples by using the KPOD method includes: determining a first target matrix based on the original output samples corresponding to each input sample in the training samples using a preset kernel function; performing centering processing on the first target matrix to obtain a second target matrix; performing diagonal dimensionality reduction processing on the second target matrix based on a preset dimensionality reduction dimension to determine a third target matrix; performing mapping on each original output sample based on the third target matrix to obtain the reduced-dimension output samples corresponding to each input sample; wherein, the preset dimensionality reduction dimension is less than the number of input samples, and the preset dimensionality reduction dimension is less than the dimension of the original output samples. Specifically, if the input samples in the training samples are denoted as X and the original output samples are Y, the corresponding Gramm matrix G, that is, the first target matrix, is obtained according to Y using the kernel function, and each element in the matrix G satisfies the following conditions:

[0053] ;

[0054] where represents the element in the th row and th column of the matrix, represents the kernel function, and respectively represent the outputs of the th and th training samples, represents the kernel function parameter, and both represent the training sample numbers; represents the exponential function with the natural constant e as the base.

[0055] Then, centralize the Gramm matrix G, and we have:

[0056] ;

[0057] where represents the centralized Gramm matrix, that is, the second target matrix, represents the number of training samples, represents a row

[0058] Next, diagonalize and reduce the dimension of the matrix , and we have:

[0059] ;

[0060] where is the diagonal matrix of eigenvalues, is the eigenvector matrix, is the transpose matrix of represents the number of training samples; is eigenvalues, and there is ; Take the first columns of the eigenvector matrix , denoted as ; It can be understood that the dimension of the output of the training samples after dimensionality reduction is much smaller than the dimension of the output of the original training samples, and at the same time is also much smaller than the number of training samples , and the following formula needs to be satisfied:

[0061] ;

[0062] where is the precision set according to actual needs. After dimensionality reduction, we can get:

[0063] ;

[0064] where, represents the transpose of the matrix , and further, the th training sample mapped to the low-dimensional space is:

[0065] ;

[0066] ;

[0067] where, the third target matrix Z ( row The matrix of rows and columns represents the low-dimensional output of the training samples after dimensionality reduction, that is, the output samples after dimensionality reduction. represents the dimension of the output of the training samples after dimensionality reduction. represents the number of training samples. is the -th column of G. is 's -th column. represents a column vector of rows with all elements being 1. row is 's transpose. represents a matrix of rows and columns with all elements being 1. row column. represents the number of training samples.

[0068] Step S12: Based on each of the input samples and the corresponding output samples after dimensionality reduction, perform flow field model training to obtain a corresponding target flow field reduced-order model, and input the test samples into the target flow field reduced-order model to use the target flow field reduced-order model to perform corresponding low-dimensional output prediction based on the test samples, so as to obtain the target low-dimensional output corresponding to the test samples.

[0069] In this embodiment, after obtaining the output samples after dimensionality reduction corresponding to each input sample by using each original output sample, the sample data can be used for flow field model training to obtain a corresponding target flow field reduced-order model, and then the test samples (a set of new input samples) can be input into the target flow field reduced-order model, so as to obtain the low-dimensional target output corresponding to the test samples. In a specific implementation manner, the target flow field reduced-order model is a Kriging model built based on a preset function type, and the preset function type includes a quadratic trend function and a Gaussian correlation function. It should be noted that the preset function type is not fixed, and the preset function type also includes other trend functions and correlation functions such as constants, first-order trend functions, and exponential correlation functions, and the trend functions and correlation functions can be selected according to actual needs to build the Kriging model. In addition, since the output samples after dimensionality reduction have fewer dimensions than the original output samples, compared with the conventional method of overall modeling of input samples and original output samples, the target flow field reduced-order model has fewer parameters to be estimated, shorter training time, and lower modeling difficulty.

[0070] Step S13: Determine the target distances between the target low-dimensional output and the output samples after dimensionality reduction, screen the output samples after dimensionality reduction based on the target distances to obtain corresponding first target output samples, and determine the original output samples corresponding to each of the first target output samples as second target output samples.

[0071] In this embodiment, the target low-dimensional output is the low-dimensional output prediction result of the target flow field reduction model obtained in the foregoing steps for the test sample. The target distance between the target low-dimensional output and each reduced-dimensional output sample can be the Euclidean distance between them. After obtaining all the target distances, the minimum distance between the target low-dimensional output and the reduced-dimensional output sample is determined from all the target distances according to the magnitude relationship of each target distance. Then, based on a preset distance multiple and the minimum distance, the reduced-dimensional output samples are screened to determine the first target output samples. The target distance corresponding to the first target output sample is less than or equal to the product of the minimum distance and the preset distance multiple, thereby screening out the reduced-dimensional output samples with a relatively large distance from the target low-dimensional output, improving the accuracy of the subsequent mapping result and reducing the error. The preset distance multiple N can be selected according to actual needs, such as selecting N = 10, etc. After screening out the first target output samples, the original output samples corresponding to each of the first target output samples can be determined according to the correspondence between the reduced-dimensional output samples and the original output samples, and these screened original output samples are determined as the second target output samples.

[0072] Step S14: Use a preset optimization method to determine the first weight corresponding to each of the first target output samples based on the target low-dimensional output, and determine each of the first weights as the second weight of the corresponding second target output sample.

[0073] In this embodiment, after determining the first target output samples and the second target output samples, it is necessary to use a preset optimization method to determine the first weight corresponding to each of the first target output samples based on the target low-dimensional output, which may specifically include: using a preset optimization function to determine the first weight corresponding to each of the first target output samples based on the target low-dimensional output. Among them, the first weight is the weighted weight corresponding to each of the first target output samples when each of the first target output samples satisfies the preset weight solution condition. The preset weight solution condition is that the difference between the weighted sum result of each of the first target output samples and the target low-dimensional output is the smallest. Specifically, the preset optimization function can be the fmincon function in Matlab. This function is an optimization tool for solving the minimum value of a constrained nonlinear multivariable function. When using the fmincon function, its constrained nonlinear multivariable function is that the difference between the target low-dimensional output and the weighted sum of the selected first target output samples (i.e., the low-dimensional output corresponding to the training samples) is the smallest. After obtaining the first weight, according to the correspondence between the first weight and the first target output sample, and the correspondence between the first target output sample and the second target output sample, each of the first weights corresponding to the first target output samples is determined as the second weight corresponding to the corresponding second target output sample.

[0074] Step S15: Based on each of the second target output samples and the corresponding second weights, perform an inverse mapping on the target low-dimensional output to map the target low-dimensional output to the target high-dimensional space corresponding to the flow field model before reduction, so as to obtain the target high-dimensional output corresponding to the test sample, and complete the corresponding output prediction.

[0075] In this embodiment, after determining the second weights corresponding to each second target output sample, an inverse mapping can be performed on the target low-dimensional output based on each second target output sample and the corresponding second weights to map the target low-dimensional output to the target high-dimensional space corresponding to the flow field model before reduction, so as to obtain the target high-dimensional output corresponding to the test sample. Specifically, it may include: performing weighted summation on each second target output sample based on the second weights to obtain the corresponding weighted summation result; determining the weighted summation result as the inverse mapping result corresponding to the target low-dimensional output in the target high-dimensional space corresponding to the flow field model before reduction, and determining the inverse mapping result as the target high-dimensional output corresponding to the test sample. It can be understood that since the inverse mapping result is obtained by performing weighted summation on the second target output samples (i.e., a part of the original output samples), the inverse mapping result has the same dimension as the second target output samples. That is to say, through the foregoing process, the target high-dimensional output corresponding to the test sample can be obtained, and the corresponding output prediction can be completed.

[0076] In this embodiment, Figure 2 the quartile box plot corresponding to Method 1 in Figure 2 is the prediction error obtained by predicting the high-dimensional output corresponding to the test sample using the inverse mapping method of the reduced-order flow field disclosed in this embodiment. Method 2 is to predict the high-dimensional output corresponding to the test sample using the commonly used POD reduction method, and Method 3 is to predict the high-dimensional output corresponding to the test sample using the KPOD method of the Voronoi diagram. By comparing the corresponding prediction errors of each method in

[0077] it can be seen that in the problem of reducing the order of the flow field with high-dimensional related responses, compared with the commonly used POD reduction method and the method of performing KPOD inverse mapping by screening the outputs of some training samples using the Voronoi diagram, the prediction error of predicting the high-dimensional output corresponding to the test sample in this embodiment is smaller and the accuracy is higher. In practical applications, after constructing the target flow field reduction model (i.e., the prediction model between the model uncertain parameters and the reduced-order flow field) using this embodiment, parameters can be input into the target flow field reduction model according to actual needs to obtain the corresponding flow field response, and the high-dimensional output response corresponding to the flow field response in the original flow field can be solved using this embodiment, so as to complete the corresponding output prediction.

[0078] It can be seen that in this application, the original output samples corresponding to the known input samples are dimensionally reduced to obtain the dimensionally reduced output samples, and the target flow field reduced-order model is constructed based on the known input samples and their corresponding dimensionally reduced output samples. After the construction is completed, giving a new input to the target flow field reduced-order model arbitrarily can obtain the low-dimensional output corresponding to this input, thus realizing the reduction of the original flow field and reducing the difficulty of constructing the model between the input and output. After inputting the test samples into the target flow field reduced-order model to obtain the target low-dimensional output, the second target output samples with a relatively close distance to the target low-dimensional output can be selected according to the target distances between the target low-dimensional output and each dimensionally reduced output sample. Finally, based on the second target output samples and the second weights, the target low-dimensional output is mapped back to the target high-dimensional space corresponding to the flow field model before reduction (i.e., the original flow field) to obtain the target high-dimensional output. At this time, the dimension of the target high-dimensional output is the same as that of the original flow field, so as to efficiently realize the inverse mapping from the reduced-order flow field to the original flow field while ensuring the accuracy.

[0079] Based on the previous embodiment, it can be known that this application discloses a method for inverse mapping of a reduced-order flow field, which can efficiently realize the inverse mapping from the reduced-order flow field to the original flow field while ensuring the accuracy. Next, the specific inverse mapping process of the reduced-order flow field will be described.

[0080] Taking the one-dimensional advection-diffusion problem as an example, the research example is as follows:

[0081] ;

[0082] Among them, the input parameters are , , , which can represent the position, which can represent the time, which can represent the flow velocity. The physical quantity to be solved can be the concentration or temperature, etc. at the position at the time . Let the diffusion coefficient , the velocity , be the first-order partial derivative of in the direction, represents in the direction, be the second-order partial derivative of in the direction. The parameter space is discretized into 2000 uniform intervals, then the sample output The dimension is 1999 (excluding the boundary positions). The specific process of implementing the inverse mapping of the reduced-order flow field for this example is as follows:

[0083] First, obtain the training samples. Denote the input of the training samples as (where ), where to can take the velocity , and the time ; to can take the velocity , and the time ; to can take the velocity , and at the same time, the time value can be set to ; Denote the output of the training samples as (where ). Use the KPOD method to obtain the low-dimensional output (where ), and the superscript indicates that the obtained matrix is a column matrix. Among them, the kernel function selects the Gaussian kernel function, and the kernel function parameter takes 0.01, takes 0.99.

[0084] Then, establish a Kriging model between the training sample input and the low-dimensional output . Given 50 test sample inputs, denoted as , where , can take the velocity , and the time ; Denote the test sample output as , . Based on the Kriging model prediction, give the corresponding low-dimensional output (where ), where the Kriging model selects the quadratic trend function and the Gaussian correlation function, is the output dimension of the low-dimensional output.

[0085] Next, calculate the Euclidean distance between the low-dimensional output of the -th test sample and all the low-dimensional outputs of the training samples, take the minimum value among all the distances, denoted as , and filter out the low-dimensional outputs of the training samples that are less than , where , where , the corresponding high-dimensional output is , , is the number of low-dimensional outputs selected.

[0086] Finally, the fmincon function in Matlab is used to obtain the weights of the low-dimensional outputs selected from the th test sample , and use this as the weight of its corresponding high-dimensional output, and then sum the high-dimensional outputs of the selected training samples weighted, so as to obtain the predicted output of the th given test sample by Method 1 as:

[0087] ;

[0088] where, .

[0089] At the same time, the predicted outputs of the given 50 test samples are obtained by the POD method (Method 2), where the trend function and correlation function of the Kriging model are the same as those of the Kriging model in KPOD, and the reduction criterion of POD is the same as that of KPOD (taking 0.99); in addition, based on the Voronoi diagram method (Method 3), the th test sample in the polygon where it is located and the training samples in the adjacent polygons low-dimensional outputs and their corresponding high-dimensional outputs are selected, and the fmincon function in Matlab is used to obtain the weights of the low-dimensional outputs , and use this as the weight of its corresponding high-dimensional output, and then sum the selected high-dimensional outputs weighted to obtain the predicted output of the th given test sample as:

[0090] ;

[0091] where, , , , .

[0092] Through the above process, it can be obtained that the prediction error of the 50 test samples by Method 1 is:

[0093] ;

[0094] The prediction error obtained by using Method 2 is:

[0095] ;

[0096] The prediction error obtained by using Method 3 is:

[0097] ;

[0098] Among them, .

[0099] Figure 2 is the box plot of the quartiles of the prediction errors of the three methods. Among them, in the abscissa, Method 1 represents the method of the present application, Method 2 represents the POD method, and Method 3 represents the method of weighted inverse mapping after screening some low-dimensional outputs based on the Voronoi diagram. The ordinate represents the prediction error. It can be seen from Figure 2 that compared with the POD method and the method based on Voronoi diagram screening, the method developed in this paper has the smallest prediction error and higher accuracy.

[0100] It can be seen that the present application reduces the dimension of the original output samples corresponding to the known input samples to obtain the reduced-dimensional output samples, and builds a target flow field reduced-order model according to the known input samples and their corresponding reduced-dimensional output samples. After the construction is completed, any new input is given to the target flow field reduced-order model, and the low-dimensional output corresponding to the input can be obtained, thereby realizing the reduction of the original flow field and reducing the difficulty of constructing the model between the input and output. After the test samples are input into the target flow field reduced-order model to obtain the target low-dimensional output, the second target output samples that are closer to the target low-dimensional output can be screened out according to the target distances between the target low-dimensional output and the reduced-dimensional output samples. Finally, according to the second target output samples and the second weights, the target low-dimensional output is inversely mapped to the target high-dimensional space corresponding to the flow field model before reduction (i.e., the original flow field) to obtain the target high-dimensional output. At this time, the dimension of the target high-dimensional output is the same as that of the original flow field, so as to efficiently realize the inverse mapping from the reduced-order flow field to the original flow field while ensuring the accuracy.

[0101] Refer to Figure 3 shown, the present application discloses a device for inverse mapping of a reduced-order flow field, including:

[0102] A sample dimension reduction module 11, configured to obtain training samples for training a flow field model, and perform dimension reduction processing on each original output sample corresponding to each input sample in the training samples to obtain each reduced-dimensional output sample corresponding to each input sample;

[0103] The low-dimensional output acquisition module 12 is configured to perform flow field model training based on each of the input samples and the corresponding output samples after dimensionality reduction, obtain a corresponding target reduced-order flow field model, and input a test sample into the target reduced-order flow field model, so as to perform corresponding low-dimensional output prediction based on the test sample by using the target reduced-order flow field model, and obtain a target low-dimensional output corresponding to the test sample;

[0104] The sample screening module 13 is configured to determine each target distance between the target low-dimensional output and each of the output samples after dimensionality reduction, screen the output samples after dimensionality reduction based on the target distance to obtain corresponding first target output samples, and determine each of the original output samples corresponding to each of the first target output samples as a second target output sample;

[0105] The weight determination module 14 is configured to determine a first weight corresponding to each of the first target output samples based on the target low-dimensional output by using a preset optimization method, and determine each of the first weights as a second weight of the corresponding second target output sample;

[0106] The high-dimensional output prediction module 15 is configured to perform inverse mapping on the target low-dimensional output based on each of the second target output samples and the corresponding second weights, so as to map the target low-dimensional output to a target high-dimensional space corresponding to the flow field model before dimensionality reduction, and obtain a target high-dimensional output corresponding to the test sample, so as to complete corresponding output prediction.

[0107] It can be seen that in this application, the output samples after dimensionality reduction are obtained by performing dimensionality reduction on the original output samples corresponding to the known input samples, and a target reduced-order flow field model is built according to the known input samples and the corresponding output samples after dimensionality reduction. After the building is completed, any new input given to the target reduced-order flow field model can obtain the low-dimensional output corresponding to the input, thereby realizing the reduction of the original flow field and reducing the difficulty of building a model between the input and output. After the test sample is input into the target reduced-order flow field model to obtain the target low-dimensional output, the second target output samples with a relatively close distance to the target low-dimensional output can be screened according to each target distance between the target low-dimensional output and each output sample after dimensionality reduction. Finally, based on the second target output samples and the second weights, the inverse mapping of the target low-dimensional output to the target high-dimensional space corresponding to the flow field model before dimensionality reduction (i.e., the original flow field) is realized, and the target high-dimensional output is obtained. At this time, the target high-dimensional output is consistent with the dimension of the original flow field, thereby realizing the inverse mapping from the reduced-order flow field to the original flow field efficiently while ensuring the accuracy.

[0108] In a specific embodiment, the sample dimensionality reduction module 11 may specifically include:

[0109] A sample dimensionality reduction sub-module, which is used to determine a target matrix based on each original output sample corresponding to each input sample in the training sample by using a preset kernel function, and map each of the original output samples based on the target matrix to complete dimensionality reduction processing, so as to obtain each dimensionality-reduced output sample corresponding to each input sample;

[0110] Among them, the preset kernel function includes a Gaussian kernel function, a polynomial kernel function, and a Sigmoid kernel function.

[0111] In a specific implementation manner, the sample dimensionality reduction sub-module may specifically include:

[0112] A first matrix determination unit, which is used to determine a first target matrix based on each original output sample corresponding to each input sample in the training sample by using a preset kernel function;

[0113] A second matrix determination unit, which is used to perform centering processing on the first target matrix to obtain a second target matrix;

[0114] A third matrix determination unit, which is used to perform diagonalization dimensionality reduction processing on the second target matrix based on a preset dimensionality reduction dimension to determine a third target matrix;

[0115] A sample dimensionality reduction unit, which is used to map each of the original output samples based on the third target matrix to obtain each dimensionality-reduced output sample corresponding to each input sample;

[0116] Among them, the preset dimensionality reduction dimension is less than the number of input samples, and the preset dimensionality reduction dimension is less than the dimension of the original output sample.

[0117] In a specific implementation manner, the sample screening module 13 may specifically include:

[0118] A minimum distance determination sub-module, which is used to determine the minimum distance between the target low-dimensional output and the dimensionality-reduced output sample based on all the target distances;

[0119] A sample screening sub-module, which is used to screen the dimensionality-reduced output samples based on a preset distance multiple and the minimum distance to determine a first target output sample;

[0120] Among them, the target distance corresponding to the first target output sample is less than or equal to the product of the minimum distance and the preset distance multiple, and the target distance is the Euclidean distance.

[0121] In a specific implementation manner, the weight determination module 14 may specifically include:

[0122] The first weight determination sub-module is configured to determine, based on the target low-dimensional output by using a preset optimization function, the first weights corresponding to the respective first target output samples.

[0123] Wherein, the first weight is the weighted weight corresponding to each of the first target output samples when each of the first target output samples meets a preset weight solution condition; the preset weight solution condition is that the difference between the weighted sum result of each of the first target output samples and the target low-dimensional output is the smallest.

[0124] In a specific embodiment, the high-dimensional output prediction module 15 may specifically include:

[0125] The weighted sum sub-module is configured to perform a weighted sum on each of the second target output samples based on the second weight to obtain a corresponding weighted sum result.

[0126] The high-dimensional output prediction sub-module is configured to determine the weighted sum result as the reflection result corresponding to the target high-dimensional space of the flow field model before order reduction of the target low-dimensional output, and determine the reflection result as the target high-dimensional output corresponding to the test sample; wherein, the dimension of the reflection result is the same as that of the second target output sample.

[0127] Furthermore, an embodiment of the present application also discloses an electronic device. Figure 4 It is a structural diagram of an electronic device 20 shown according to an exemplary embodiment. The content in the figure should not be regarded as any limitation on the scope of use of the present application.

[0128] Figure 4 It is a structural schematic diagram of an electronic device 20 provided by an embodiment of the present application. The electronic device 20 may specifically 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. Wherein, the memory 22 is used to store a computer program, and the computer program is loaded and executed by the processor 21 to implement the relevant steps in the reflection method of the reduced-order flow field disclosed in any of the foregoing embodiments. In addition, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0129] In this embodiment, the power supply 23 is used to provide a working 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 is any communication protocol applicable to the technical solution of the present application, and no specific limitation is imposed thereon herein; the input / output interface 25 is used to obtain external input data or output data to the outside, and the specific interface type thereof can be selected according to specific application needs, and no specific limitation is made herein.

[0130] In addition, as a carrier for storing resources, the memory 22 can be a read-only memory, a random access memory, a magnetic disk, an optical disk, etc. The resources stored thereon can include an operating system 221, a computer program 222, etc. The storage method can be transient storage or permanent storage.

[0131] Among them, the operating system 221 is used to manage and control each hardware device and the computer program 222 on the electronic device 20, and it can be Windows Server, Netware, Unix, Linux, etc. In addition to the computer program that can be used to complete the inverse mapping method of the reduced-order flow field executed by the electronic device 20 disclosed in any of the foregoing embodiments, the computer program 222 can further include computer programs that can be used to complete other specific tasks.

[0132] Furthermore, the present application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, the inverse mapping method of the reduced-order flow field disclosed above is implemented. For the specific steps of this method, reference can be made to the corresponding content disclosed in the foregoing embodiments, and details will not be repeated here.

[0133] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and reference can be made to the method part for related parts.

[0134] Those skilled in the art can further realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. To clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described according to functions in the above description. Whether these functions are executed in a hardware or software manner 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 to exceed the scope of the present application.

[0135] The steps of the method or algorithm described in combination with the embodiments disclosed herein can be directly implemented by hardware, a software module executed by a processor, or a combination of the two. The software module can be placed in a random access memory (RAM), internal 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 technical field.

[0136] Finally, it should also be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or device comprising the said element.

[0137] The technical solutions provided in this application have been introduced in detail above. Specific examples are used in this text to elaborate on the principles and implementation manners of this application. The descriptions of the above embodiments are only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to this application.

Claims

1. A method for inverse mapping of a reduced-order flow field, characterized in that: include: Acquire training samples for training the flow field model, and perform dimensionality reduction processing on each original output sample corresponding to each input sample in the training samples to obtain each dimensionality-reduced output sample corresponding to each input sample; Perform flow field model training based on each of the input samples and the corresponding output samples after dimensionality reduction to obtain a corresponding target flow field reduced-order model, and input a test sample into the target flow field reduced-order model to use the target flow field reduced-order model to perform corresponding low-dimensional output prediction based on the test sample to obtain a target low-dimensional output corresponding to the test sample; Determine each target distance between the target low-dimensional output and each of the dimensionality-reduced output samples, screen the dimensionality-reduced output samples based on the target distance to obtain corresponding first target output samples, and determine each of the original output samples corresponding to each of the first target output samples as a second target output sample; Determine the first weights corresponding to the first target output samples based on the target low-dimensional output using a preset optimization method, and determine the first weights as the second weights of the corresponding second target output samples; The target low-dimensional output is inversely mapped based on each of the second target output samples and the corresponding second weights to map the target low-dimensional output to the target high-dimensional space corresponding to the flow field model before reduction, and the target high-dimensional output corresponding to the test sample is obtained to complete the corresponding output prediction.

2. The inverse mapping method of reduced-order flow field according to claim 1, characterized in that: The performing dimensionality reduction processing on each original output sample corresponding to each input sample in the training sample to obtain each dimensionality reduced output sample corresponding to each input sample includes: Determine a target matrix based on each original output sample corresponding to each input sample in the training sample using a preset kernel function, and map each original output sample based on the target matrix to complete dimensionality reduction processing to obtain each reduced-dimensionality output sample corresponding to each input sample; Among them, the preset kernel function includes Gaussian kernel function, polynomial kernel function and Sigmoid kernel function.

3. The inverse mapping method of reduced-order flow field according to claim 2, characterized in that: The method of determining a target matrix based on each original output sample corresponding to each input sample in the training sample by using a preset kernel function, and mapping each original output sample based on the target matrix to complete the dimensionality reduction process to obtain each dimensionality-reduced output sample corresponding to each input sample, includes: Determine a first target matrix based on each original output sample corresponding to each input sample in the training samples using a preset kernel function; Centralizing the first target matrix to obtain a second target matrix; Performing diagonal dimension reduction processing on the second target matrix based on a preset dimension reduction dimension to determine a third target matrix; Mapping each of the original output samples based on the third target matrix to obtain each dimensionally reduced output sample corresponding to each of the input samples; The preset dimension reduction dimension is smaller than the number of the input samples, and the preset dimension reduction dimension is smaller than the dimension of the original output sample.

4. The inverse mapping method of reduced-order flow field according to claim 1, characterized in that: The target flow field reduced-order model is a Kriging model built based on a preset function type; the preset function type includes a trend function and a correlation function.

5. The inverse mapping method of reduced-order flow field according to claim 1, characterized in that: The step of screening the dimension-reduced output samples based on the target distance to obtain corresponding first target output samples includes: Determine the minimum distance between the target low-dimensional output and the output sample after dimensionality reduction based on all the target distances; Screening the output samples after dimension reduction based on a preset distance multiple and the minimum distance to determine a first target output sample; The target distance corresponding to the first target output sample is less than or equal to the product of the minimum distance and the preset distance multiple, and the target distance is a Euclidean distance.

6. The inverse mapping method of reduced-order flow field according to claim 1, characterized in that: The determining the first weights respectively corresponding to the first target output samples based on the target low-dimensional output using a preset optimization method includes: Determine first weights corresponding to the first target output samples based on the target low-dimensional output using a preset optimization function; Among them, the first weight is the weighted weight corresponding to each first target output sample when each first target output sample meets the preset weight solution condition; the preset weight solution condition is that the difference between the weighted sum of each first target output sample and the target low-dimensional output is the smallest.

7. The inverse mapping method of a reduced-order flow field according to any one of claims 1 to 6, characterized in that: The method of performing inverse mapping on the target low-dimensional output based on each of the second target output samples and the corresponding second weights to map the target low-dimensional output to a target high-dimensional space corresponding to the flow field model before order reduction to obtain a target high-dimensional output corresponding to the test sample includes: Performing weighted summation on each of the second target output samples based on the second weight to obtain a corresponding weighted summation result; The weighted summation result is determined as the inverse mapping result corresponding to the target high-dimensional space corresponding to the flow field model of the target low-dimensional output before reduction, and the inverse mapping result is determined as the target high-dimensional output corresponding to the test sample; wherein the inverse mapping result has the same dimension as the second target output sample.

8. A back-mapping device for a reduced-order flow field, characterized in that: include: A sample dimension reduction module is used to obtain training samples for training the flow field model, and perform dimension reduction processing on each original output sample corresponding to each input sample in the training sample to obtain each dimension-reduced output sample corresponding to each input sample; A low-dimensional output acquisition module is used to perform flow field model training based on each of the input samples and the corresponding output samples after dimensionality reduction to obtain a corresponding target flow field reduced-order model, and input a test sample into the target flow field reduced-order model to use the target flow field reduced-order model to perform a corresponding low-dimensional output prediction based on the test sample to obtain a target low-dimensional output corresponding to the test sample; A sample screening module, used to determine each target distance between the target low-dimensional output and each of the output samples after dimensionality reduction, screen the output samples after dimensionality reduction based on the target distance to obtain corresponding first target output samples, and determine each of the original output samples corresponding to each of the first target output samples as a second target output sample; A weight determination module, configured to determine first weights corresponding to the first target output samples based on the target low-dimensional output using a preset optimization method, and determine the first weights as second weights of the corresponding second target output samples; A high-dimensional output prediction module is used to reversely map the target low-dimensional output based on each of the second target output samples and the corresponding second weights, so as to map the target low-dimensional output to the target high-dimensional space corresponding to the flow field model before reduction, and obtain the target high-dimensional output corresponding to the test sample to complete the corresponding output prediction.

9. An electronic device, characterized in that: include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the inverse mapping method of the reduced-order flow field as claimed in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: Used to store a computer program, wherein when the computer program is executed by a processor, the inverse mapping method of the reduced-order flow field according to any one of claims 1 to 7 is implemented.

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