A flow field noise reduction method, system and device based on Ginzburg-Landau theory

Abstract

The present invention provides a flow field denoising method, system, and device based on Ginzburg-Landau theory. The method comprises: obtaining wave function evolution data of the flow field and the corresponding velocity field according to the Schrödinger equation using the Klebbusch method to obtain an initial dataset of the velocity field and wave function; adding noise to the velocity field portion of the initial dataset to obtain a noisy dataset; constructing a neural network model and introducing the Ginzburg-Landau energy functional into the loss function of the neural network model; training the neural network model using the noisy dataset to obtain a trained neural network model; and using the trained neural network model to denoise a given noisy velocity field to obtain a denoised velocity field. By combining Ginzburg-Landau theory with a neural network, the present invention can find the corresponding wave function from the noisy velocity field, perform denoising, reconstruct the denoised velocity field data, and ensure that the denoised flow field conforms to physical laws and practical application requirements.

Description

Technical Field

[0001] The present invention belongs to the technical field of computational fluid dynamics, and relates to a flow field noise reduction method, system and device, and in particular to a flow field noise reduction method, system and device based on the Ginzburg-Landau theory. Background Art

[0002] Flow field denoising is an important and challenging task in computational fluid dynamics and related fields. It plays a central role in numerous applications, including weather forecasting, aerodynamics, and environmental modeling. However, when flow field data is sparse or contaminated by noise, traditional denoising methods (such as interpolation or optimization techniques) often struggle to maintain sufficient accuracy. Furthermore, the computational cost of high-fidelity, fine-resolution simulations is extremely high, making them difficult to apply to large-scale or real-time applications.

[0003] In recent years, data-driven methods based on deep learning have shown significant potential in solving noise problems in fluid dynamics. By utilizing large datasets, deep learning models can not only capture complex flow field patterns, but also provide efficient solutions to ill-posed inverse problems such as flow field denoising. However, most existing methods rely on large amounts of high-quality training data, which is often difficult to obtain in practical applications. In addition, these models usually lack the constraints of the basic physical laws of fluid dynamics, which limits their generalization ability when faced with noise interference or incomplete measurements. Therefore, although purely data-driven deep learning methods have made some progress in fluid denoising, they still have limitations in revealing the intrinsic physical properties of fluids.

[0004] To address the above challenges, it is urgent to explore new flow field noise reduction methods that not only have efficient noise reduction capabilities, but also must ensure that the flow field after noise reduction strictly complies with physical laws and meets practical application needs. Summary of the Invention

[0005] To address the above issues, the present invention proposes a flow field noise reduction method, system, and device based on the Ginzburg-Landau (GL) theory. The present invention can improve the accuracy of noise flow field noise reduction, thereby overcoming the challenges faced by existing technologies in the flow field noise reduction process.

[0006] The technical solution adopted in the present invention is as follows:

[0007] A flow field noise reduction method based on Ginzburg-Landau theory includes the following steps:

[0008] Based on the Klebbusch method and combined with the Schrödinger equation, the wave function evolution data of the flow field and the corresponding velocity field are obtained, and the initial data set of velocity field and wave function is obtained;

[0009] Add noise to the velocity field part of the initial data set to obtain a noisy data set;

[0010] Construct a neural network model and introduce the Ginzburg-Landau energy functional into the loss function of the neural network model;

[0011] Use the noise data set to train the neural network model to obtain a trained neural network model;

[0012] The trained neural network model is used to denoise the given noisy velocity field to obtain the denoised velocity field.

[0013] Furthermore, based on the Clebsch method,

[0014] The relationship between the wave function and the velocity field makes them satisfy physical constraints:

[0015] ,

[0016] in, is the velocity field, is a two-component wave function, , Two-component wave functions The real and imaginary parts of To control the parameters of vortex quantization, is an imaginary unit.

[0017] Furthermore, the velocity field and wave function initial data sets are obtained through testing or numerical solution methods.

[0018] Furthermore, the specific steps of the numerical solution method are:

[0019] Given the initial wave function and time step , according to the conversion formula of wave function and velocity field, the initial velocity field is obtained ;

[0020] The spectral method is used to solve the Schrödinger equation to obtain wave functions for several time steps that evolve over time. To maintain the stability of the numerical calculation, the wave function at each time step is normalized and then projected to complete the flow evolution calculation. Finally, the velocity field corresponding to each time step is calculated using the Klebbusch method.

[0021] The velocity field and wave function of each time step constitute a data pair sample, and the data pair samples of all time steps constitute the initial data set of velocity field and wave function.

[0022] Furthermore, the noise added to the velocity field part of the initial data set is Gaussian noise, etc. Taking Gaussian noise as an example, it specifically includes:

[0023] According to the Gaussian distribution law, Gaussian noise is randomly generated:

[0024] ,

[0025] in, is the probability density function of the Gaussian distribution, is a random variable, is the mean of the Gaussian distribution, is the standard deviation of the Gaussian distribution;

[0026] The Gaussian noise obeys the Gaussian distribution law:

[0027] ,

[0028] in, For the samples of Gaussian noise, is the probability density function of the Gaussian distribution.

[0029] For each sample , for the velocity field Add Gaussian noise to each element in :

[0030] ,

[0031] ,

[0032] in, is the velocity field The velocity field in the x direction, is the velocity field The velocity field in the y direction, It's data The result after adding noise, It's data The result after adding noise.

[0033] Furthermore, the neural network model includes three residual neural networks with the same structural body, wherein the input of the first residual neural network is the noise velocity field, and the output is the noise wave function; the input of the second residual neural network is the noise wave function output by the first residual neural network, and the output is the noise reduction wave function; the input of the third residual neural network is the noise reduction wave function output by the second residual neural network, and the output is the noise reduction velocity field.

[0034] Furthermore, the residual neural network structure includes an encoder and a decoder; the encoder extracts high-level features and reduces spatial resolution through convolution and downsampling, and then increases the number of channels through a residual block sequence; the decoder restores spatial resolution through deconvolution upsampling, and then adjusts the number of channels through a residual block sequence.

[0035] Furthermore, the loss function of the first residual neural network is for:

[0036] ,

[0037] ,

[0038] ,

[0039] in, is the mean square error function, represents the total number of samples, Indicates the samples, Indicates the The wave function of a sample, Indicates the The noise wave function of samples, is the Ginzburg-Landau energy functional constraint, Indicates the The velocity field of samples;

[0040] Loss functions for the second and third residual neural networks for:

[0041] .

[0042] A flow field noise reduction system based on Ginzburg-Landau theory, comprising:

[0043] Data acquisition module: used to obtain the wave function evolution data of the flow field and the corresponding velocity field based on the Schrödinger equation using the Klebbusch method, and obtain the initial data set of the velocity field and wave function;

[0044] Data processing module: adding noise to the velocity field part of the initial data set to obtain a noisy data set;

[0045] Model building module: Build a neural network model and introduce the Ginzburg-Landau energy functional into the loss function of the neural network model;

[0046] Model training module: Use the noise data set to train the neural network model to obtain a trained neural network model;

[0047] Flow field prediction module: Use the trained neural network model to reduce the noise velocity field and obtain the reduced-noise velocity field.

[0048] A computer device, comprising:

[0049] one or more processors;

[0050] a memory for storing one or more programs;

[0051] When the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned flow field denoising method based on the Ginzburg-Landau theory.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention is based on the Ginzburg-Landau theory and combines the wave function and velocity field to construct an energy functional. Together with the mean square error, it serves as the loss function in the first residual neural network. It can find the corresponding wave function from the noisy velocity field. At the same time, through the subsequent residual neural network, it can reconstruct the denoised velocity field data and ensure that the denoised flow field conforms to the physical laws and the needs of practical applications, thereby improving the accuracy of the results. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Flowchart of the method in an embodiment of the present invention.

[0055] Figure 2 1 and 2 represent the real flow field, the noisy flow field, and the flow field after model noise reduction in an embodiment of the present invention. The left and right columns represent the velocity field in the x-direction and the velocity field in the y-direction, respectively.

[0056] Figure 3 This is a comparison diagram of the flow field denoised by the Gaussian filter and the model in the embodiment of the present invention, representing the denoising result of the velocity field in the x-direction.

[0057] Figure 4 This is a comparison diagram of the flow field denoised by the Gaussian filter and the model in the embodiment of the present invention, representing the denoising result of the velocity field in the y direction. DETAILED DESCRIPTION

[0058] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0059] like Figure 1 As shown, a flow field noise reduction method based on the Ginzburg-Landau theory includes the following steps:

[0060] S1. Based on the Klebbusch method and combined with the Schrödinger equation, the wave function evolution data of the flow field and the corresponding velocity field are obtained to obtain the initial data set of velocity field and wave function.

[0061] Determined based on the Clebsch method

[0062] The relationship between the wave function and the velocity field makes them satisfy physical constraints:

[0063] ,

[0064] in, is the velocity field, is a two-component wave function, , Two-component wave functions The real and imaginary parts of To control the parameters of vortex quantization, is an imaginary unit.

[0065] At the same time, the wave function satisfies the normalization and incompressibility conditions:

[0066]

[0067] in, is an imaginary unit, the inner product Defined as , The conjugate of 、 is a two-component wave function The real and imaginary parts of .

[0068] The velocity field and wave function initial data sets are obtained by testing or numerical solution methods, wherein the specific steps of obtaining them by numerical solution methods are:

[0069] Given the initial wave function and time step , according to the conversion formula of wave function and velocity field, the initial velocity field is obtained ; Use the spectral method to solve the Schrödinger equation to obtain the wave function of several time steps that evolve over time. In order to maintain the stability of the numerical calculation, the wave function of each time step is normalized and projected to complete the flow evolution calculation. Finally, the velocity field corresponding to each time step is calculated according to the Klebbusch method so that the wave function and the velocity field meet the physical constraints. By repeatedly iterating these steps, the solution is obtained. The result of the wave function for each time step , and calculate The result of the velocity field for each time step ,in, Indicates the The wave function of time steps, Indicates the The velocity field of each time step, , the velocity field and wave function of each time step constitute a data pair sample: , , the data pairs of all time steps constitute the initial data set of velocity field and wave function.

[0070] S2. Add noise to the velocity field of the initial dataset to obtain a noisy dataset. The specific steps are:

[0071] Add noise to the velocity field. Taking Gaussian noise as an example, Gaussian noise is randomly generated according to the Gaussian distribution law:

[0072] ,

[0073] in, is the probability density function of the Gaussian distribution, is a random variable, is the mean of the Gaussian distribution, which determines the center position of the noise; is the standard deviation of the Gaussian distribution; it determines the amplitude range of the noise and the width of the distribution.

[0074] when and When , the Gaussian distribution is a standard normal distribution, and the noise generated at this time is called zero-mean white Gaussian noise.

[0075] The Gaussian noise conforms to the Gaussian distribution law:

[0076] ,

[0077] in, For the samples of Gaussian noise, is the probability density function of the Gaussian distribution.

[0078] For each sample , for the velocity field Add Gaussian noise to each element in :

[0079] ,

[0080] ,

[0081] in, is the velocity field The velocity field in the x direction, is the velocity field The velocity field in the y direction, It's data The result after adding noise, It's data The result after adding noise.

[0082] S3. Build a neural network model and introduce the Ginzburg-Landau energy functional into the loss function of the neural network model.

[0083] The neural network model includes three residual neural networks with the same main structure. The first residual neural network takes as input a noise velocity field and outputs a noise wave function. The second residual neural network takes as input the noise wave function output by the first residual neural network and outputs a noise reduction wave function. The third residual neural network takes as input the noise reduction wave function output by the second residual neural network and outputs a noise reduction velocity field. The structure of the neural network model is described in detail below:

[0084] ,

[0085] ,

[0086] in, and Respectively represent the weight and bias parameters to be trained of the residual neural network model; is the initial input data, For the The neural network outputs data, For the The neural network input data, Indicates the A neural network.

[0087] Residual Neural Network It consists of two parts: encoder and decoder.

[0088] Encoder part:

[0089] The input is passed through convolution and downsampling operations to gradually extract high-level features:

[0090]

[0091]

[0092] in is the input of the network, For output, is the convolutional layer, is the normalization layer, is a nonlinear activation function, is the maximum pooling layer, Refers to the window size, is the step length, is the padding size.

[0093] Then, through the residual block sequence, the number of channels is increased:

[0094]

[0095] in is the residual block, is the input of the network, is the output of the network, is the number of input channels, is the number of output channels, is the discard rate.

[0096] The composition structure of the residual block is:

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] in For input, is the output and also the input of the next layer. The same is true for the other inputs and outputs. 、 and 、 are the parameters of the normalization layer.

[0104]

[0105] in is the output of the residual block.

[0106] Decoder part:

[0107] The feature size and spatial resolution are gradually restored through deconvolution and residual blocks:

[0108]

[0109]

[0110] in is the deconvolution operation.

[0111] Furthermore, the loss function of the first residual neural network is for:

[0112] ,

[0113] ,

[0114] ,

[0115] in, is the mean square error function, represents the total number of samples, Indicates the samples, Indicates the The wave function of a sample, Indicates the The noise wave function of samples, is the Ginzburg-Landau energy functional constraint, Indicates the The velocity field of samples;

[0116] Loss functions for the second and third residual neural networks for:

[0117] .

[0118] S4. The neural network model is trained using the noise data set to obtain a trained neural network model. In this embodiment, the network is trained using the Adam optimizer until the loss function reaches a stable state.

[0119] S5. Use the trained neural network model to reduce the noise velocity field to obtain the reduced noise velocity field. The specific steps are:

[0120] Given velocity field data with noise, the neural network model is used to calculate the corresponding noise wave function, noise reduction wave function and noise reduction velocity field:

[0121] The method for calculating the corresponding noise wave function, noise reduction wave function and noise reduction velocity field is:

[0122]

[0123]

[0124]

[0125] in, represents the noisy wave function, represents the velocity field with noise, represents the wave function after network noise reduction, Represents the velocity field after network denoising.

[0126] Example 1

[0127] To illustrate the application process and prediction effect of the method in detail, the application of the present invention is described in detail below using a specific actual situation as an example.

[0128] Aiming at typical vortex-induced noise phenomena such as vortex structure noise induced by shear turbulence at the tail of the wing and acoustic pressure wave radiation noise generated by vortex shedding in the experimental cylindrical flow, this embodiment considers the evolution and Gaussian noise of two vortex tubes. The initial center coordinates of the two vortex tubes are and , the radius of the vortex tube is and , the shape function of the vortex tube is ,in , indicating the vortex tubes, the mean value of Gaussian noise is , the standard deviation is The following steps are used to perform noise reduction:

[0129] Step 1: Initialize the wave function by the center coordinates, radius and shape function of the vortex tube , generating the initial states of the two vortex tubes.

[0130] Step 2: Take the time step , Planck's constant = 0.1, and the fast Fourier transform, normalization, and projection operations are applied to the initial wave function repeatedly to solve the Schrödinger equation and generate 400-step results. The corresponding velocity field data are obtained through the wave function and velocity field conversion formula, and are paired into 400 groups of samples according to the time step.

[0131] Step 3: Add Gaussian noise to the velocity field data according to the Gaussian noise distribution formula to obtain noise data.

[0132] Step 4: Build a residual neural network , consists of an encoder and a decoder part, each residual block contains two convolutional layers, where the convolutional layer is followed by a batch normalization layer and an activation function.

[0133] Step 5: Train the neural network using the GL energy functional loss and mean squared error loss. The mean squared error of each component is symmetrically weighted. Use the Adam optimizer for 1500 rounds of training, with a batch size of 4, a learning rate of 0.00001, and a regularization coefficient of 0.0001. Record the training loss and accuracy using SummaryWriter.

[0134] Step 6: For the trained network, given any velocity field data with noise, the corresponding wave function and the noise-reduced velocity field are obtained after the noise reduction by the neural network model of the present invention. The result of the noise-reduced velocity field is as follows: Figure 2As shown in the figure, the left and right columns represent the velocity field in the x direction and the velocity field in the y direction respectively.

[0135] To illustrate the technical effect of the present invention, a conventional noise reduction method such as Gaussian filter is used to conduct experiments. The Gaussian filter library function is imported into the Python software. The noisy velocity field is used as input. By setting the size of the Gaussian kernel, the velocity field after noise reduction is obtained, as shown in the figure. Figure 3 and Figure 4 As shown, Figure 3 is the noise reduction effect of the velocity field in the x direction, Figure 4 The denoising effect of the velocity field in the y direction is shown in Figure 2. Compared with the denoising results of the present invention, the denoising results of the present invention are more consistent with physical laws, better preserve structural features, and are more accurate. The Gaussian filter loses detail fidelity and destroys the characteristics of the velocity field.

[0136] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0137] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0138] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0139] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0140] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the contents disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present application that follow the general principles of the present application and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered merely as exemplary, and the true scope and spirit of the present application are indicated by the claims.

[0141] The above specific embodiments are used to illustrate the present invention rather than to limit the present invention. Any modifications and changes made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A flow field noise reduction method based on Ginzburg-Landau theory, characterized in that: The following steps are involved: Based on the Klebbusch method and combined with the Schrödinger equation, the wave function evolution data of the flow field and the corresponding velocity field are obtained, and the initial data set of velocity field and wave function is obtained; Add noise to the velocity field part of the initial data set to obtain a noisy data set; Construct a neural network model and introduce the Ginzburg-Landau energy functional into the loss function of the neural network model; Use the noise data set to train the neural network model to obtain a trained neural network model; The trained neural network model is used to reduce the noise velocity field and obtain the reduced noise velocity field. The neural network model includes three residual neural networks with the same main structure, wherein the input of the first residual neural network is a noise velocity field, and the output is a noise wave function; the input of the second residual neural network is the noise wave function output by the first residual neural network, and the output is a noise reduction wave function; the input of the third residual neural network is the noise reduction wave function output by the second residual neural network, and the output is a noise reduction velocity field; The loss function of the first residual neural network for: ， ， ， in, is the mean square error function, represents the total number of samples, Indicates the samples, Indicates the The wave function of a sample, Indicates the The noise wave function of samples, is the Ginzburg-Landau energy functional constraint, Indicates the Velocity field of samples; Loss functions of the second and third residual neural networks for: 。 2. The flow field noise reduction method based on the Ginzburg-Landau theory according to claim 1, characterized in that: The relationship between the wave function and the velocity field is determined based on the Klebbusch method, so that the two satisfy physical constraints: ， in, is the velocity field, is a two-component wave function, , Two-component wave functions The real and imaginary parts of To control the parameters of vortex quantization, is an imaginary unit.

3. The flow field noise reduction method based on Ginzburg-Landau theory according to claim 1, characterized in that: The velocity field and wave function initial data sets are obtained through testing or numerical solution methods.

4. The flow field noise reduction method based on the Ginzburg-Landau theory according to claim 3, characterized in that: The specific steps of the numerical solution method are: Given the initial wave function and time step , according to the conversion formula of wave function and velocity field, the initial velocity field is obtained ; The spectral method is used to solve the Schrödinger equation to obtain the wave functions of several time steps that evolve over time. The wave functions of each time step are normalized and then projected to complete the flow evolution calculation. Finally, the velocity field corresponding to each time step is calculated according to the Klebbusch method. The velocity field and wave function of each time step constitute a data pair sample, and the data pair samples of all time steps constitute the initial data set of velocity field and wave function.

5. The flow field noise reduction method based on Ginzburg-Landau theory according to claim 1, characterized in that: The noise added to the velocity field of the initial dataset is Gaussian noise, which includes: According to the Gaussian distribution law, Gaussian noise is randomly generated: ， in, is the probability density function of the Gaussian distribution, is a random variable, is the mean of the Gaussian distribution, is the standard deviation of the Gaussian distribution; The Gaussian noise obeys the Gaussian distribution: ， in, For the samples of Gaussian noise, is the probability density function of the Gaussian distribution; For each sample , for the velocity field Add Gaussian noise to each element in : ， ， in, is the velocity field The velocity field in the x direction, is the velocity field The velocity field in the y direction, It's data The result after adding noise, It's data The result after adding noise.

6. The flow field noise reduction method based on Ginzburg-Landau theory according to claim 1, characterized in that: The residual neural network structure includes an encoder and a decoder; the encoder extracts high-level features and reduces spatial resolution through convolution and downsampling, and then increases the number of channels through a sequence of residual blocks; The decoder restores the spatial resolution through deconvolution upsampling and then adjusts the number of channels through a sequence of residual blocks.

7. A flow field noise reduction system based on Ginzburg-Landau theory, characterized in that: include: Data acquisition module: used to obtain the wave function evolution data of the flow field and the corresponding velocity field based on the Schrödinger equation using the Klebbusch method, and obtain the initial data set of the velocity field and wave function; Data processing module: adding noise to the velocity field part of the initial data set to obtain a noisy data set; Model building module: Build a neural network model and introduce the Ginzburg-Landau energy function into the loss function of the neural network model; Model training module: Use the noise data set to train the neural network model to obtain a trained neural network model; Flow field prediction module: Use the trained neural network model to reduce the noise velocity field and obtain the reduced noise velocity field; The neural network model includes three residual neural networks with the same main structure, wherein the input of the first residual neural network is a noise velocity field, and the output is a noise wave function; the input of the second residual neural network is the noise wave function output by the first residual neural network, and the output is a noise reduction wave function; the input of the third residual neural network is the noise reduction wave function output by the second residual neural network, and the output is a noise reduction velocity field; The loss function of the first residual neural network for: ， ， ， in, is the mean square error function, represents the total number of samples, Indicates the samples, Indicates the The wave function of a sample, Indicates the The noise wave function of samples, is the Ginzburg-Landau energy functional constraint, Indicates the Velocity field of samples; Loss functions of the second and third residual neural networks for: 。 8. A computer device, characterized in that: The computer device comprises: one or more processors; a memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the flow field denoising method based on the Ginzburg-Landau theory as described in any one of claims 1 to 6.

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