A discriminant regression flow field prediction method based on semi-supervised learning

Abstract

The present invention discloses a discriminant regression flow field prediction method based on semi-supervised learning, comprising the following steps: obtaining a semi-supervised flow field prediction data set; constructing a deep flow field prediction model based on a neural network; obtaining a preliminarily converged deep flow field prediction model through a preheating strategy; using the memory effect of a neural network to divide the difficult sample and simple sample data sets; using a discriminant regression method to train and optimize the deep flow field prediction model; using the deep flow field prediction model to perform predictions and obtain regression test results. The present invention uses the memory utility of a neural network to implement a discriminant regression prediction method to alleviate the problem of overfitting in semi-supervised learning for flow field prediction; by mixing pseudo-labeled and real-labeled samples, and using GMM to divide samples into difficult and easy samples, it is beneficial to subsequently adopt different learning strategies to enhance the discriminability of the model, thereby improving performance; at the same time, the optimized deep flow field prediction model is used to calculate the predicted value of the sample and obtain regression test results.

Description

Technical Field

[0001] The present invention belongs to the technical field of flow field prediction, and in particular relates to a discriminant regression flow field prediction method based on semi-supervised learning. Background Art

[0002] Flow field prediction aims to characterize the flow through control points and then predict the flow field. The core lies in how to achieve regression prediction of flow field properties based on control point characterization. Traditional computational fluid dynamics (CFD) requires the use of solving software to iteratively calculate and perform high-precision numerical simulations, such as solving the Euler equations, Reynolds-averaged Navier-Stokes (RANS) equations, etc. However, this requires a huge amount of computing power.

[0003] With the development of deep learning, neural networks are used to construct regression prediction models to automatically learn high-dimensional potential mapping relationships and achieve rapid prediction of flow fields. This can approximate the numerical simulation results of the solution software to a certain extent, thus providing convenience for researchers. However, existing deep learning methods require a large amount of training data, and the acquisition and source of data often require huge computing power and time costs due to the solution. Although the construction of a semi-supervised learning paradigm reduces the demand for large-scale training data sets in existing deep flow field prediction methods, saving computing power and time costs, a small number of training samples often easily cause deep models to overfit. Therefore, using a semi-supervised learning paradigm with a small amount of data to achieve prediction performance similar to that of a large amount of data training model has important research significance and application value for existing flow field prediction. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a discriminant regression flow field prediction method based on semi-supervised learning, which reduces the dependence of existing deep prediction models on large-scale training data and alleviates the problem of overfitting of semi-supervised learning in flow field prediction.

[0005] In order to solve the above technical problems, the present invention is implemented in the following ways:

[0006] A discriminant regression flow field prediction method based on semi-supervised learning includes the following steps:

[0007] S1. Obtain a semi-supervised flow field prediction dataset;

[0008] S2. Construct a deep flow field prediction model based on neural network;

[0009] S3, obtaining a preliminarily converged deep flow field prediction model through a warm-up strategy;

[0010] S4, using the memory effect of neural networks to divide difficult sample and simple sample data sets;

[0011] S5. Using discriminant regression method to train and optimize the deep flow field prediction model;

[0012] S6. Execute prediction using the deep flow field prediction model to obtain regression test results.

[0013] Furthermore, the semi-supervised flow field prediction dataset H in step S1 is expressed as follows:

[0014] HI=L∪U

[0015] in, represents a labeled dataset, represents an unlabeled dataset, x i Represents the coordinates of the control point of the i-th sample of the labeled data set, y i represents the flow field prediction value of the i-th sample of the labeled data set, N l represents the size of the labeled dataset, x j represents the coordinates of the control point of the jth sample of the unlabeled dataset, N u Represents the size of the unlabeled dataset.

[0016] Furthermore, in step S2, the deep flow field prediction model f(·, Θ), where Θ represents the model parameters, is a neural network model based on a multi-layer perceptron, consisting of an input layer, multiple hidden layers and an output layer, and is trained by weights and activation functions; for any control point coordinate x i ∈L∪U, the predicted value is expressed as f(x i ).

[0017] Furthermore, the specific method of step S3 is as follows:

[0018] Use the labeled data set to train the deep flow field prediction model to implement the preheating training of the model and reach the initial convergence state. When the preheating loss value is less than the specified threshold, the preheating process is judged to be converged. The preheating loss function expression of the preheating model is as follows:

[0019]

[0020] The specific expression of parameter optimization during the preheating process is as follows:

[0021]

[0022] Among them, AdamOptimizer represents the parameter optimizer.

[0023] Furthermore, the specific method of step S4 is as follows:

[0024] S41. Use the preheated model to calculate the predicted value of each control point sample in the unlabeled dataset U, and use the predicted value as the pseudo-labeled value of the unlabeled dataset. The expression is as follows:

[0025]

[0026] in, represents the predicted value calculated by the warm-up model;

[0027] S42, the model uses the labeled dataset L and the pseudo-labeled dataset It is used to retrain the model and reach preliminary convergence. When the loss value is less than the specified threshold, the training process is judged to have converged. The total loss function expression of the discriminant training is as follows:

[0028]

[0029] Among them, λ represents the equilibrium parameter;

[0030] S43, obtain the model retrained in step S42, and calculate the semi-supervised flow field prediction data set All sample loss values ​​​​of , and based on the neural network memory effect Divided into difficult sample and simple sample data sets; for The loss value of the j-th sample in is calculated as follows:

[0031]

[0032] Furthermore, all sample loss values ​​obtained are Feed the two-component Gaussian mixture model GMM(·) to classify all samples. The specific expression of the classification process is as follows:

[0033]

[0034] Among them, A j express The classification label of the jth sample in;

[0035] According to the classification label Re-divided into labeled sample sets and unlabeled sample sets, and reconstructed into a semi-supervised flow field prediction dataset The specific expression is as follows:

[0036]

[0037]

[0038] in, and Represents the re-divided labeled sample set and unlabeled sample set.

[0039] Furthermore, the specific method of step S5 is as follows:

[0040] The overall loss of discriminant regression is calculated using H divided in step S43. The loss calculation formula is as follows:

[0041]

[0042] in, and express and The number of samples in; using discriminant regression overall loss The specific expression of the process of optimizing model parameters is as follows:

[0043]

[0044] Among them, Θ represents the parameters of the deep flow field prediction model, and AdamOptimizer represents the parameter optimizer.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] The flow field prediction method proposed in the present invention utilizes the memory utility of a neural network to implement a discriminative regression prediction method, thereby alleviating the overfitting problem of semi-supervised learning in flow field prediction; by mixing pseudo-annotated and truly annotated samples, and using GMM to divide the samples into difficult and easy samples, it is beneficial to subsequently adopt different learning strategies to enhance the discriminability of the model, thereby improving performance; at the same time, the optimized deep flow field prediction model is used to calculate the predicted value of the sample to obtain the regression test result. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the flow field prediction method of the present invention. DETAILED DESCRIPTION

[0048] The specific implementation of the present invention is further described in detail below with reference to the accompanying drawings and specific examples.

[0049] like Figure 1 As shown, a discriminant regression flow field prediction method based on semi-supervised learning includes the following steps:

[0050] S1. Obtain a semi-supervised flow field prediction dataset. The semi-supervised flow field prediction dataset H is expressed as follows:

[0051] H=L∪U

[0052] in, represents the labeled data set, L is the control point coordinate data with data labels, represents an unlabeled dataset, x i Represents the coordinates of the control point of the i-th sample of the labeled data set, y i represents the flow field prediction value of the i-th sample of the labeled data set, N l represents the size of the labeled dataset, x j represents the coordinates of the control point of the jth sample of the unlabeled dataset, N u Represents the size of the unlabeled dataset.

[0053] S2. Construct a deep flow field prediction model based on a neural network and initialize its network parameters. The deep flow field prediction model f(·, Θ), where Θ represents the model parameters, is a neural network model based on a multi-layer perceptron, which is a feedforward neural network consisting of an input layer, multiple hidden layers, and an output layer. It is trained by weights and activation functions to perform predictions. For any control point coordinate x i ∈L∪U, the predicted value is expressed as f(x i ).

[0054] S3. Obtain a preliminarily converged deep flow field prediction model through a preheating strategy. The specific method is as follows:

[0055] The deep flow field prediction model is trained using a labeled data set to implement the preheating training of the model and reach a preliminary convergence state. When the preheating loss value is less than the specified threshold, the preheating process is judged to have converged. The threshold is set to 0.1. The preheating loss function expression of the preheating model is as follows:

[0056]

[0057] The specific expression of parameter optimization during the preheating process is as follows:

[0058]

[0059] Among them, AdamOptimizer represents the parameter optimizer.

[0060] S4. Use the memory effect of neural network to divide the difficult sample and simple sample data sets. The specific method is as follows:

[0061] S41. Use the preheated model to calculate the predicted value of each control point sample in the unlabeled dataset U, and use the predicted value as the pseudo-labeled value of the unlabeled dataset. The expression is as follows:

[0062]

[0063] in, represents the predicted value calculated by the preheating model; the supervised flow field prediction dataset H is redefined as

[0064] S42. In order to enhance the discriminability of the model in distinguishing between difficult and easy samples, the model uses the labeled dataset L and the pseudo-labeled dataset It is used to retrain the model and reach preliminary convergence. When the loss value is less than the specified threshold, the training process is judged to have converged. In the present invention, the threshold is set to 0.2. The total loss function expression of the discriminant training is as follows:

[0065]

[0066] Among them, λ represents the equilibrium parameter, and the specific expression of the process is as follows:

[0067]

[0068] S43, obtain the model retrained in step S42, and calculate the semi-supervised flow field prediction data set All sample loss values ​​​​of , and based on the neural network memory effect Divide the dataset into difficult samples and simple samples. The memory effect means that the neural network usually prioritizes learning the simple patterns of simple samples in early training, and then learns the patterns of difficult samples. For this reason, the dataset is divided into difficult samples and simple samples by warming up the model in the early stage.

[0069] for The loss value of the j-th sample in is calculated as follows:

[0070]

[0071] Furthermore, all sample loss values ​​obtained are Feed the two-component Gaussian mixture model GMM(·) to classify all samples. The specific expression of the classification process is as follows:

[0072]

[0073] Among them, A j express The classification label of the jth sample in A j =1 or A j =0, the classification label result is a simple sample or a difficult sample;

[0074] According to the classification label Re-divided into labeled sample sets and unlabeled sample sets, and reconstructed into a semi-supervised flow field prediction dataset The specific expression is as follows:

[0075]

[0076]

[0077] in, and Represents the re-divided labeled sample set and unlabeled sample set, which are used for discriminant regression learning in step S5.

[0078] S5. Use the discriminant regression method to train and optimize the deep flow field prediction model. The specific method is as follows:

[0079] The overall loss of discriminant regression is calculated using H divided in step S43. The loss calculation formula is as follows:

[0080]

[0081] in, and express and The number of samples in; using discriminant regression overall loss The specific expression of the process of optimizing model parameters is as follows:

[0082]

[0083] Among them, Θ represents the parameters of the deep flow field prediction model, and AdamOptimizer represents the parameter optimizer.

[0084] S6. Execute prediction using the deep flow field prediction model to obtain regression test results.

[0085] The above description is only an implementation mode of the present invention. It is stated again that for ordinary technicians in this technical field, several improvements can be made to the present invention without departing from the principle of the present invention. These improvements are also included in the protection scope of the claims of the present invention.

Claims

1. A discriminant regression flow field prediction method based on semi-supervised learning, characterized by: The following steps are involved: S1. Obtain a semi-supervised flow field prediction dataset; S2. Construct a deep flow field prediction model based on neural network; S3, obtaining a preliminarily converged deep flow field prediction model through a preheating strategy; S4, using the memory effect of neural networks to divide difficult sample and simple sample data sets; S5. Using discriminant regression method to train and optimize the deep flow field prediction model; S6. Execute prediction using the deep flow field prediction model to obtain regression test results; The semi-supervised flow field prediction dataset H in step S1 is expressed as follows: H=L∪U in, represents a labeled dataset, represents an unlabeled dataset, x i Represents the coordinates of the control point of the i-th sample of the labeled data set, y i represents the flow field prediction value of the i-th sample of the labeled data set, N l represents the size of the labeled dataset, x j represents the coordinates of the control point of the jth sample of the unlabeled dataset, N u represents the size of the unlabeled dataset; The specific method of step S3 is as follows: Use the labeled data set to train the deep flow field prediction model to implement the preheating training of the model and reach the initial convergence state. When the preheating loss value is less than the specified threshold, the preheating process is judged to be converged. The preheating loss function expression of the preheating model is as follows: The specific expression of parameter optimization during the preheating process is as follows: Among them, AdamOptimizer represents the parameter optimizer, Θ represents the deep flow field prediction model parameters; The specific method of step S4 is as follows: S41. Use the preheated model to calculate the predicted value of each control point sample in the unlabeled dataset U, and use the predicted value as the pseudo-labeled value of the unlabeled dataset. The expression is as follows: in, represents the predicted value calculated by the warm-up model; S42, the model uses the labeled dataset L and the pseudo-labeled dataset It is used to retrain the model and reach preliminary convergence. When the loss value is less than the specified threshold, the training process is judged to have converged. The total loss function expression of the discriminant training is as follows: Among them, λ represents the equilibrium parameter; S43, obtain the model retrained in step S42, and calculate the semi-supervised flow field prediction data set All sample loss values ​​​​of , and based on the neural network memory effect Divided into difficult sample and simple sample data sets; for The loss value of the j-th sample in is calculated as follows: All sample loss values ​​obtained Feed the two-component Gaussian mixture model GMM(·) to classify all samples. The specific expression of the classification process is as follows: Among them, A j express The classification label of the jth sample in; According to the classification label Re-divided into labeled sample sets and unlabeled sample sets, and reconstructed into a semi-supervised flow field prediction dataset The specific expression is as follows: in, and represents the re-divided labeled sample set and unlabeled sample set, and express and The number of samples in .

2. The discriminant regression flow field prediction method based on semi-supervised learning according to claim 1 is characterized in that: The deep flow field prediction model f(·, Θ) in step S2, where Θ represents the model parameters, is a neural network model based on a multi-layer perceptron, consisting of an input layer, multiple hidden layers and an output layer, and is trained by weights and activation functions; for any control point coordinate x i ∈L∪U, the predicted value is expressed as f(x i ).

3. The discriminant regression flow field prediction method based on semi-supervised learning according to claim 1 is characterized in that: The specific method of step S5 is as follows: The overall loss of discriminant regression is calculated using H divided in step S43. The loss calculation formula is as follows: in, and express and The number of samples in; using discriminant regression overall loss The specific expression of the process of optimizing model parameters is as follows: Among them, Θ represents the parameters of the deep flow field prediction model, and AdamOptimizer represents the parameter optimizer.

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