CN-121997708-A - Two-dimensional vorticity prediction method based on improved Fourier neural operator

CN121997708ACN 121997708 ACN121997708 ACN 121997708ACN-121997708-A

Abstract

A two-dimensional vorticity prediction method based on an improved Fourier neural operator is characterized in that parameters needed by different frequency components are processed by constructing and training a neural operator model with a multi-layer perceptron to carry out parameterization kernel integration operator and a uniform model, so that two-dimensional vorticity prediction is realized by adapting to any number of frequency components by a fixed number of parameters. The invention has lower relative error in the high frequency domain, and simultaneously has lower relative error in the low frequency domain due to the strong function fitting capability of the multi-layer perceptron.

Inventors

DENG ZHIJIE
Xiao Zipeng

Assignees

上海交通大学

Dates

Publication Date: 20260508
Application Date: 20241212

Claims (6)

1. The two-dimensional vorticity prediction method based on the improved Fourier neural operator is characterized in that parameters required by different frequency components are processed by a parameterized kernel integration operator and a uniform model through constructing and training a neural operator model with a multi-layer perceptron, so that the two-dimensional vorticity prediction is realized by adapting to any number of frequency components with a fixed number of parameters; The neural operator model fits the mapping between two function spaces through a neural network, so that partial differential equation solutions of different functions are obtained through a set of model parameters.
2. The method for predicting two-dimensional vorticity based on improved Fourier neural operator according to claim 1, wherein said parameterized kernel integration operator is when kernel function satisfies In the form, complex integration operations are converted into easier-to-calculate multiplications in fourier space using convolution theorem, specifically: Wherein: The fourier transform of the signal is performed, A kernel function on frequency after fourier transformation, As a function of the kernel, As a function of the degree of freedom and, in the discrete case, Obtained by parameterizing the values on the different frequency components.
3. The method for two-dimensional vorticity prediction based on improved Fourier neural operators according to claim 1, wherein the parameterization is to fit discrete frequency coordinates to the corresponding kernel function's mapping of values on the coordinates by using a multi-layer perceptron, specifically, values of a given frequency coordinate on a set of basis functions Two multi-layer perceptron And Calculating complex valued kernel functions for frequency after fourier transformation Wherein N is the number of basis functions, and k is the number of frequency coordinates.
4. The two-dimensional vorticity prediction method based on the improved Fourier neural operator according to claim 1, wherein the neural operator model comprises a linear layer unit, an activation function unit, a multi-layer perceptron operator unit and a kernel integration operator unit, wherein the linear layer unit performs linear change processing according to input vorticity function information to obtain a higher or lower-dimension function result, the activation function unit performs nonlinear change processing according to the function information to obtain a nonlinear mapped function result, the multi-layer perceptron unit performs orthogonal basis function calculation and nonlinear change processing according to frequency coordinate information to obtain a kernel function result in the kernel integration operator, and the kernel integration operator unit performs integration operator operation according to a kernel function and an input vorticity function to obtain a linear mapped function result.
5. The improved fourier neural operator-based two-dimensional vorticity prediction method as defined in claim 4, wherein the kernel result is calculated by a multi-layer perceptron, and comprises: step a, after obtaining the frequency coordinates of each value of the discrete vorticity value after Fourier change, calculating the value of a group of limited orthogonal basis functions on the group of coordinates; B, respectively inputting the values obtained in the step a into two multi-layer perceptron to fit the real part and the imaginary part of the kernel function to obtain the final kernel function value, specifically, the values of the given frequency coordinates on a group of basis functions Two multi-layer perceptron And By the formula Nonlinear variation of multi-layer perceptron to obtain kernel function after Fourier transformation 。
6. The improved fourier nerve operator-based two-dimensional vorticity prediction method according to any one of claims 1-5, comprising: Step 1, training data set acquisition, namely after a plurality of different initial vorticity values are randomly generated by a Gaussian process, solving by a numerical solution method, namely solving a speed field by solving a Poisson equation and solving the vorticity values at the subsequent moments under a fixed time step by using a Kelank-Nicolsen method; Step 2, constructing a nerve operator model and training by utilizing the data set obtained in the step 1, namely inputting vorticity of a plurality of previous moments into the nerve operator model, calculating a loss function according to the predicted vorticity of the next moment, and updating parameters of the nerve operator model; Step 3, hydrodynamic simulation, namely inputting the actual vorticity observed into the neural operator model trained in the step 2 to obtain a predicted value of the vorticity of time, wherein the predicted value of the vorticity of time is specifically obtained by inputting the actual observed vorticity data of 0s-T-1 s Inputting the trained neural operator model in the step 2 to obtain the vorticity data of the th second Inputting the obtained T second vorticity data and the 1 st to T-1 st second data into a nerve operator model to obtain a T+1st second vorticity result, and iterating until the subsequent time vorticity data is obtained, wherein the input time period during training is [0, T-1] second, and the spatial resolution is 。

Description

Two-dimensional vorticity prediction method based on improved Fourier neural operator The application is a divisional application of application number [ 202411675131. X ] application date [2024/12/12] name [ fluid mechanics optimization simulation method based on improved Fourier neural operator ] applicant [ Shanghai university of traffic ]. Technical Field The invention relates to a technology in the field of neural networks, in particular to a two-dimensional vorticity prediction method based on an improved Fourier neural operator. Background The existing two-dimensional vorticity prediction technology depends on numerical methods, such as a finite element method, but huge calculation time is needed when the methods are simulated, the method based on deep learning is low in precision at present, and a used model needs a large number of parameters, so that the requirement on hardware is high. Disclosure of Invention Aiming at the problems that the prior Fourier neural operator needs independent parameters to process different frequency components and has overlarge parameter quantity and poor simulation accuracy during simulation, the invention provides a two-dimensional vorticity prediction method based on an improved Fourier neural operator, which processes the parameters needed by different frequency components through a neural network uniform model, the Fourier nerve operator can keep a lower parameter quantity, meanwhile, the simulation errors of the model under different frequency components are reduced, a uniformly-spread parameterized nerve operator model is realized, and the improvement of the hydrodynamic simulation field is realized based on the model. The invention is realized by the following technical scheme: The invention relates to a two-dimensional vorticity prediction method based on an improved Fourier neural operator, which comprises the steps of constructing and training a neural operator model with a multi-layer perceptron to carry out parameterization of a nuclear integral operator and processing parameters needed by different frequency components by a uniform model, thereby adapting any number of frequency components with a fixed number of parameters to realize two-dimensional vorticity prediction. The neural operator model fits the mapping between two function spaces through a neural network, so that partial differential equation solutions of different functions are obtained through a set of model parameters. The parameterized kernel integration operator refers to when the kernel function meets the following conditionsIn the form, complex integration operations are converted into easier-to-calculate multiplications in fourier space using convolution theorem, specifically: Wherein: The fourier transform of the signal is performed, A kernel function on frequency after fourier transformation,As a function of the kernel,As a function of the degree of freedom and, in the discrete case,Obtained by parameterizing the values on the different frequency components. The parameterization refers to fitting a discrete frequency coordinate to a corresponding kernel function's value mapping on the coordinate by using a multi-layer perceptron, specifically, the value of a given frequency coordinate on a set of basis functionsTwo multi-layer perceptronAndCalculating complex valued kernel functions for frequency after fourier transformationWherein N is the number of basis functions, and k is the number of frequency coordinates. Technical effects The invention utilizes a multi-layer perceptron and an orthogonal basis function to embed a kernel function in a fitting kernel integration operator. Lower hydrodynamic simulation errors compared to the prior art, including lower errors in all frequency domains. Drawings FIG. 1 is a flow chart of the present invention; FIG. 2 is a schematic diagram of a neural operator model; FIG. 3 is a schematic diagram of the effect of the embodiment. Detailed Description As shown in fig. 1, the present invention relates to a two-dimensional vorticity prediction method based on an improved fourier nerve operator, comprising: Step 1, training data set acquisition, namely, after a certain number of different initial vorticity values are randomly generated by using a Gaussian process, solving by using a numerical solution method, firstly, solving a speed field by solving a Poisson equation, and then, solving the vorticity values at the subsequent moments under a fixed time step by using a Kelank-Nicolsen method. And 2, constructing a nerve operator model, training by using the data set obtained in the step 1, namely inputting vorticity (the first 10 in the experiment) of the previous time into the nerve operator model, calculating a loss function according to the predicted vorticity of the next time, and updating parameters of the nerve operator model. As shown in FIG. 2, the nerve operator model comprises a linear layer unit, an activated function unit, a multi-layer perce