Gibbs noise elimination method and device based on high-order discontinuous Galerkin method

Abstract

The present invention discloses a method and device for eliminating Gibbs noise based on a high-order discontinuous Galerkin method, which relates to the field of shock wave capture in computational fluid dynamics. The method can capture shock waves by eliminating Gibbs noise, ensuring smooth numerical calculations. The method includes: a server receiving flow field data to be processed from a client, the flow field data to be processed including flow field physical quantities and computational grid information; generating graph structure data based on the flow field physical quantities and computational grid information, and then constructing a training data sample library using the graph structure data; using a graph convolution filter to provide supervision information for the training data samples; training a deep learning model using the training data sample library; and using the trained deep learning model to remove Gibbs noise from the flow field physical quantities, and returning the denoising results to the client.

Description

Technical Field

[0001] The present invention relates to the technical field of shock wave capture in fluid mechanics research, and in particular to a method and device for eliminating Gibbs noise based on a high-order discontinuous Galerkin method. Background Art

[0002] Numerical accuracy is a key concern in all areas of computational science. Consequently, high-precision methods have attracted widespread attention and flourished within the CFD community. High-order discontinuous Galerkin schemes offer enhanced parallel computing efficiency, can flexibly achieve high-order accuracy for arbitrary geometries, and are more amenable to the application of techniques such as mesh adaptation. Therefore, among the numerous high-precision methods used in fluid mechanics research, high-order discontinuous Galerkin schemes are considered one of the most promising and academically valuable. However, during computation, high-order discontinuous Galerkin numerical schemes, like other high-order numerical schemes, can produce the Gibbs phenomenon at discontinuities. The term Gibbs phenomenon originally referred to the phenomenon of overfitting and underfitting near discontinuities when fitting functions with jump discontinuities using Fourier series sums, manifesting as oscillations. When using high-order discontinuous Galerkin methods for flow calculations, Gibbs noise accumulates near shock waves. This inaccurate and unstable nonphysical solution ultimately causes the calculation to stall. Eliminating this noise and ensuring smooth computation has become a bottleneck in the research of high-order discontinuous Galerkin methods.

[0003] Currently, in the field of high-order discontinuous Galerkin methods, three approaches are commonly used to address the problems caused by the Gibbs phenomenon: the first is the limiter, which has the disadvantage of severely affecting the accuracy of the global solution and, if the parameters are not properly selected, may increase the computational cost; the second is weighted substantially non-oscillatory reconstruction, which has the disadvantage of maintaining high-order accuracy but still being computationally expensive; and the third is artificial viscosity, which captures shock waves by introducing artificial dissipation into the governing equations. Artificial viscosity is more stable than the above two methods, but has the disadvantage of relying on empirical parameters, the selection of which may affect the accuracy and robustness of the underlying numerical method. Therefore, how to obtain a high-performance Gibbs noise elimination method at the lowest computational cost while ensuring high-precision flow field calculations has become a problem that needs further research and solution. Summary of the Invention

[0004] Embodiments of the present invention provide a method and device for eliminating Gibbs noise based on a high-order discontinuous Galerkin method, which can capture shock waves by eliminating Gibbs noise, ensuring smooth numerical calculations, thereby achieving Gibbs noise elimination at a minimal computational cost while ensuring high-precision flow field calculations.

[0005] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0006] In a first aspect, an embodiment of the present invention provides a method comprising:

[0007] The server receives flow field data to be processed sent by the client, wherein the flow field data to be processed includes: flow field physical quantities and computational grid information, wherein the flow field physical quantities include orthogonal components of velocity, density, pressure, and energy of the flow field, and the computational grid information includes the number of grid nodes and adjacency relationships between grid nodes;

[0008] Generate graph structure data according to the flow field data to be processed, and then use the graph structure data to build a training data sample library;

[0009] Training a deep learning model using the training data sample library;

[0010] The trained deep learning model is used to remove Gibbs noise from the flow field physical quantity, and the denoising result is returned to the client.

[0011] Specifically, S2 includes: generating a feature matrix X according to the flow field physical quantity; generating an adjacency matrix A and a degree matrix D according to the calculation grid information; using the graph structure data composed of the matrix X, A and D as sample data for training;

[0012] After S2, it also includes: using graph convolution filters to provide supervision information for training data samples.

[0013] The method of using a graph convolution filter to provide supervision information for a training data sample comprises: the server using a graph convolution filter to provide supervision information for the sample data, then forming an input-output data sample pair with the flow field physical quantity and the supervision information, and storing the input-output data sample as the sample data in the training data sample library; wherein the graph convolution filter is represents the adjacency matrix with self-loops added, express The degree matrix of express The inverse matrix of .

[0014] The deep learning model includes: the network input layer and the network middle layer of the model are arranged in the order of graph convolution layer, graph attention layer and activation layer, the graph convolution layer contains six layers of convolution, the graph attention layer contains three layers of deconvolution and three layers of convolution, and the activation layer selects the Elu activation function; the graph convolution layer and the graph attention layer are used to extract the structural features of the flow field; the activation layer is used for network learning.

[0015] The convolution kernel of the graph convolution layer is represents the adjacency matrix with self-loops added, express The 1 / 2 power of the inverse matrix, where the implicit output dimensions are 5, 16, 64, 128, 64, and 16 respectively; the convolution kernel of the graph convolution layer is α, α represents the attention coefficient, and the implicit output dimensions are 16, 64, 128, 64, 16, and 5 respectively.

[0016] The convolution kernel of the graph convolution layer The process of aggregating feature information is in, Indicates that each node on the graph has a self-loop adjacency matrix added, X is the characteristic matrix of the graph, yes The 1 / 2 power of the inverse matrix; the process of solving the convolution kernel α of the graph attention layer is to first calculate the similarity coefficient e between its adjacent nodes and itself: e ij =a(WH i ||WH j ), j∈Neighbour(i), where the weight W and mapping a(·) are learned through a single-layer feedforward neural network training, and mapping a(·) is used to map features to the real field. ·||· represents the merging of tensors, H i and H j Represents the features of node i and node j in the current layer. Then, the attention coefficient α is calculated using the similarity coefficient e:

[0017] Among them, normalization is achieved through softmax, and the activation function σ(·) uses LeakyReLU.

[0018] The graph convolutional network layer aggregates the node’s own information and the information of neighboring nodes through an aggregation function to update the features of the lower-layer nodes: Where L is the number of layers in the neural network, H is the features of all nodes in the network layer, W is the weight of each layer, that is, the parameters that the network needs to learn, and σ(·) represents the activation function. The graph attention network layer uses the attention coefficient α as the node aggregation method through the aggregation function to update the features of the nodes in the lower layer: Among them, H is the feature of all nodes in the network layer, W is the weight of each layer, that is, the parameter that the network needs to learn, and σ(·) represents the activation function.

[0019] The LeakyReLU activation function is: x represents the input data to be activated; the Elu activation function is: x represents the input data to be activated; the loss function used to supervise the training of the deep learning model is L=L1+L2, including a first loss function L1 and a second loss function L2.

[0020] The first loss function L1 is: The second loss function L2 is: Among them, y d represents the true value of the d-th node in the grid, represents the predicted value of the dth node in the grid, and D represents the sample set size of the sample data.

[0021] In a second aspect, an embodiment of the present invention provides a device comprising:

[0022] A data receiving module is used to receive the flow field data to be processed sent by the client, wherein the flow field data to be processed includes: flow field physical quantities and calculation grid information;

[0023] A data processing module is configured to generate graph structure data according to the flow field data to be processed, and then use the graph structure data to construct a training data sample library;

[0024] A supervision information providing module is used to provide supervision information for training data samples using graph convolution filters;

[0025] A training module, configured to train a deep learning model using the training data sample library;

[0026] Noise removal module, used to remove Gibbs noise from flow field physical quantities using the trained deep learning model;

[0027] The data sending module is used to send the denoising result to the client.

[0028] The embodiments of the present invention provide a method and apparatus for removing Gibbs noise based on the high-order discontinuous Galerkin method. Using flow field quantities and computational grid information provided by a client, the server performs data processing on the server to construct a training data sample library. A graph convolution filter is then used to provide supervision information for the training data samples. A deep learning model is then trained, and the trained model is used to remove Gibbs noise from the flow field quantities. The denoised results are ultimately returned to the client. The deep learning model involved in this solution is easy to implement. Once trained, the model can be used to directly remove Gibbs noise from the flow field quantities, eliminating the need for CFD simulations to consume additional computing resources and labor costs to capture shock waves. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0030] Figure 1A schematic diagram of the system architecture provided by an embodiment of the present invention;

[0031] Figure 2 A flow chart of a method provided by an embodiment of the present invention;

[0032] Figure 3 A schematic diagram of a deep learning model provided by an embodiment of the present invention;

[0033] Figure 4 A schematic diagram of the framework of the Gibbs noise elimination method implemented in the present invention;

[0034] Figure 5 A schematic diagram of the device structure provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0035] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments of the present invention will be described in detail below, with examples of the embodiments illustrated in the accompanying drawings. Throughout, identical or similar reference numerals represent identical or similar elements or elements having identical or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and intended only to explain the present invention and are not to be construed as limiting the present invention. Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a," "an," "said," and "the" used herein may also include the plural forms. It should be further understood that the term "comprising" as used in the description of the present invention refers to the presence of the stated features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when an element is referred to as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or intervening elements may be present. Furthermore, "connected" or "coupled" as used herein may include wireless connections or couplings. The term "and / or" as used herein includes any and all combinations of one or more associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and will not be interpreted in an idealized or overly formal sense unless defined as such herein.

[0036] The embodiment of the present invention provides a method for eliminating Gibbs noise in a high-order discontinuous Galerkin numerical format, such as Figure 2 Shown, including:

[0037] Step 1: The server receives client data sent by the client. The client data includes flow field physical quantities and computational grid information. The flow field physical quantities include the orthogonal velocity components u and v, density ρ, pressure p, and energy E. The computational grid information includes the number of grid nodes and the adjacency relationship between grid nodes.

[0038] Step 2: Generate graph structure data based on the flow field physical quantities and computational grid information in a manner suitable for deep learning model training, and then use the graph structure data to build a training data sample library.

[0039] Step 3: Use graph convolution filters to provide supervision information for training data samples.

[0040] Step 4: Use the training data sample library to build a deep learning network structure and train the deep learning model. Figure 3 The deep learning network structure refers to the specific building blocks of the deep learning model.

[0041] Step 5: Use the trained deep learning model to remove Gibbs noise from the flow field physical quantities, such as Figure 4 The Gibbs noise removal method for the high-order discontinuous Galerkin numerical format is shown, and the denoising results are returned to the client. Gibbs noise removal is performed based on the flow field physical quantities provided by the client and the trained deep learning model, and the denoised flow field physical quantities output by the deep learning model are then returned to the client.

[0042] The method flow of this embodiment can be applied to Figure 1 In the scenario architecture shown, the client provides flow field physical quantities and computational grid information; the server uses the information provided by the client to complete data processing, thereby constructing a training data sample library; a graph convolution filter is used to provide supervision information for the training data samples, and then a deep learning model is trained; finally, the server uses the trained deep learning model to eliminate Gibbs noise based on the flow field physical quantities provided by the client, and returns the denoising results to the client.

[0043] In this embodiment, step 2 includes:

[0044] The server generates graph-structured data based on the flow field physical quantities and computational grid information, and then uses this graph-structured data to construct a training data sample library. This data is then used to generate a feature matrix X based on the flow field physical quantities, and an adjacency matrix A and a degree matrix D based on the computational grid information. These graph-structured data are then stored in the training data sample database. The feature matrix X serves as input to the deep learning model, while the adjacency matrix A and degree matrix D are used in the graph convolution filter and graph convolution operations within the learning model.

[0045] In this embodiment, step 3 includes:

[0046] The server uses a graph convolution filter to provide supervision information for the training data sample, and then forms an input-output data sample pair with the flow field physical quantity and the supervision information, and stores the input-output data sample pair in the training data sample library. represents the adjacency matrix with self-loops added, express The degree matrix of express The inverse matrix of .

[0047] In this embodiment, in step 4, the constructed deep learning network structure is as follows Figure 3 Shown, including:

[0048] The graph convolution layer, graph attention layer, and activation layer are used. The graph convolution layer contains six convolution layers, the graph attention layer contains three deconvolution layers and three convolution layers, and the activation layer uses the Elu activation function. The graph convolution layer and graph attention layer are used to extract the structural features of the flow field, and the activation layer is used to help the network learn.

[0049] Specifically, the deep learning network structure is arranged as graph convolution layer, graph attention layer and activation layer in the network input layer and the network middle layer, and no activation layer is set in the network output layer, and a total of twelve convolution operations are performed. Among them, the convolution kernel of the graph convolution layer is represents the adjacency matrix with self-loops added, express The 1 / 2 power of the inverse matrix, the implicit output dimensions are 5, 16, 64, 128, 64, 16 respectively; the convolution kernel of the graph convolution layer is α, α represents the attention coefficient, and the implicit output dimensions are 16, 64, 128, 64, 16, 5 respectively; the convolution kernel of the graph convolution layer The process of aggregating feature information is in, Indicates that each node on the graph has a self-loop adjacency matrix added, X is the characteristic matrix of the graph, yes The 1 / 2 power of the inverse matrix; the process of solving the convolution kernel α of the graph attention layer is to first calculate the similarity coefficient e between its adjacent nodes and itself: e ij =a(WH i ||WH j ), j∈Neighbour(i), where the weight W and mapping a(·) are learned through a single-layer feedforward neural network training, and mapping a(·) is used to map features to the real field. ·||· represents the merging of tensors, H i and H j Represents the features of node i and node j in the current layer. Then, the attention coefficient α is calculated using the similarity coefficient e:

[0050] Among them, normalization is achieved through softmax, and the activation function σ(·) uses LeakyReLU.

[0051] The graph convolutional network layer aggregates the node’s own information and the information of neighboring nodes through an aggregation function to update the features of the lower-layer nodes: Where L is the number of layers in the neural network, H is the features of all nodes in the network layer, W is the weight of each layer, that is, the parameters that the network needs to learn, and σ(·) represents the activation function. The graph attention network layer uses the attention coefficient α as the node aggregation method through the aggregation function to update the features of the nodes in the lower layer: Among them, H is the feature of all nodes in the network layer, W is the weight of each layer, that is, the parameter that the network needs to learn, and σ(·) represents the activation function.

[0052] The LeakyReLU activation function is:

[0053]

[0054] The Elu activation function:

[0055]

[0056] In this embodiment, the loss function L=L1+L2 for supervising the training of the deep learning model includes loss functions L1 and L2. The deep learning model is implemented in a computer language, and the training results are stored in a server for subsequent use.

[0057] Specifically, the L1 loss function is:

[0058]

[0059] The L2 loss function is:

[0060]

[0061] Among them, y d represents the true value of the d-th node in the grid, that is, the supervision information provided by the graph convolution filter, represents the predicted value of the dth node in the grid, and D represents the size of the data sample set.

[0062] In this embodiment, step 5 includes:

[0063] The flow field physical quantity and the grid node information are used to generate graph structure data and then input into the trained deep learning model, and the deep learning model outputs the denoised flow field physical quantity, such as Figure 4 FIG. 4 is a schematic diagram of a Gibbs noise elimination method framework, and the final denoising result is returned to the client.

[0064] This embodiment also provides a Gibbs noise elimination device for high-order discontinuous Galerkin numerical format. Specifically, the denoising device can be run on a server in the laboratory, such as Figure 5 As shown, the denoising device includes:

[0065] The data receiving module is used to receive the flow field physical quantities and calculation grid information sent by the client;

[0066] A data processing module is used to generate graph structure data using the flow field physical quantities and calculation grid information to construct a training data sample library;

[0067] A supervision information providing module is used to provide supervision information for training data samples using graph convolution filters;

[0068] A training module, configured to train a deep learning model using the sample database;

[0069] Noise removal module, used to remove Gibbs noise from flow field physical quantities using the trained deep learning model;

[0070] The data sending module is used to send the denoising result to the client.

[0071] The advantages of the implementation of the present invention are that the deep learning model involved in this solution is easy to implement. Once the model is trained, it can be used to directly eliminate Gibbs noise of flow field physical quantities, so that CFD simulation calculations do not need to consume additional computing resources and labor costs to capture shock waves.

[0072] The Gibbs noise elimination method and device for the high-order discontinuous Galerkin numerical format provided in the embodiment of the present invention can be applied to the calculation of high-order discontinuous Galerkin flow fields under different incoming flow conditions.

[0073] Specifically, numerical simulations were conducted on a NACA0012 airfoil under transonic and supersonic incoming flow conditions. A constructed Gibbs noise elimination model was embedded in the high-order discontinuous Galerkin calculation process. First, the noisy data was processed; then, a deep learning model was used to denoise the noise data. Ultimately, the Gibbs phenomenon was eliminated, effectively suppressing numerical oscillations at the shock wave.

[0074] Embodiments of the present invention provide a method and apparatus for removing Gibbs noise from a high-order discontinuous Galerkin numerical format. Using flow field quantities and computational grid information provided by a client, data processing is performed on the server to construct a training data sample library. A graph convolution filter is then used to provide supervision information for the training data samples. A deep learning model is trained, and the trained model is used to remove Gibbs noise from the flow field quantities. The denoised results are ultimately returned to the client. The deep learning model involved in this solution is easy to implement. Once trained, the model can be used to directly remove Gibbs noise from the flow field quantities, eliminating the need for CFD simulations to consume additional computing resources and labor costs to capture shock waves.

[0075] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited to this. Any changes or replacements that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A Gibbs noise elimination method based on a high-order discontinuous Galerkin method, characterized in that: include: The server receives the flow field data to be processed sent by the client, wherein the flow field data to be processed includes: flow field physical quantities and calculation grid information; Generate graph structure data according to the flow field data to be processed, and then use the graph structure data to build a training data sample library; Training a deep learning model using the training data sample library; The trained deep learning model is used to remove Gibbs noise from the flow field physical quantity, and the denoising result is returned to the client.

2. The method according to claim 1, characterized in that The flow field physical quantities include the velocity orthogonal component of the flow field, the density of the flow field, the pressure of the flow field and the energy of the flow field. The computational grid information includes the number of grid nodes and the adjacency relationship between grid nodes.

3. The method according to claim 1 or 2, characterized in that Generating graph structure data according to the flow field data to be processed, and then using the graph structure data to construct a training data sample library, includes: Generate a characteristic matrix X according to the flow field physical quantity; Generate an adjacency matrix A and a degree matrix D according to the computational grid information; The graph structure data composed of matrices X, A and D is used as sample data for training; After using graph structure data to construct a training data sample library, it also includes: using graph convolution filters to provide supervision information for the training data samples.

4. The method according to claim 3, characterized in that The use of graph convolution filters to provide supervision information for training data samples includes: The server uses a graph convolution filter to provide supervision information for the sample data, then forms an input-output data sample pair with the flow field physical quantity and the supervision information, and stores the input-output data sample pair as the sample data in the training data sample library; Among them, the graph convolution filter is represents the adjacency matrix with self-loops added, express The degree matrix of express The inverse matrix of .

5. The method according to claim 4, characterized in that The deep learning model includes: the network input layer and the network intermediate layer of the model are arranged in the order of graph convolution layer, graph attention layer and activation layer, the graph convolution layer includes six layers of convolution, the graph attention layer includes three layers of deconvolution and three layers of convolution, and the activation layer selects Elu activation function; The graph convolution layer and graph attention layer are used to extract the structural features of the flow field; The activation layer is used for network learning.

6. The method according to claim 5, characterized in that The convolution kernel of the graph convolution layer is represents the adjacency matrix with self-loops added, express The 1 / 2 power of the inverse matrix, where the implicit output dimensions are 5, 16, 64, 128, 64, and 16 respectively; The convolution kernel of the graph attention layer is α, where α represents the attention coefficient, and the implicit output dimensions are 16, 64, 128, 64, 16, and 5 respectively.

7. The method according to claim 6, characterized in that The convolution kernel of the graph convolution layer The process of aggregating feature information: in, Indicates that each node on the graph has a self-loop adjacency matrix added, X is the characteristic matrix of the graph, yes The 1 / 2 power of the inverse matrix; The method of obtaining the convolution kernel α of the graph attention layer includes: first calculating the similarity coefficient e between the adjacent nodes and itself: e ij =a(WH i ||WH j ), j∈Neighbour(i), Neighbour(i) represents the neighbor node of the current node i, where the weight W and mapping a(·) are learned through a single-layer feedforward neural network training. Mapping a(·) is used to map features to the real number field, ·||· represents the merging of tensors, and H i and H j Represents the features of node i and node j in the current layer, and then calculates the attention coefficient α through the similarity coefficient e: Among them, normalization is achieved through softmax, and the activation function σ(·) uses LeakyReLU.

8. The method according to claim 6, characterized in that The graph convolutional network layer aggregates the node’s own information and the information of neighboring nodes through an aggregation function to update the features of the nodes in the lower layer: Where L is the number of layers in the neural network, H is the features of all nodes in the network layer, W is the weight of each layer, that is, the parameters that the network needs to learn, and σ(·) represents the activation function; The graph attention network layer uses the attention coefficient α as the node aggregation method through the aggregation function to update the features of the lower-layer nodes: Among them, W is the weight of each layer, that is, the parameter that the network needs to learn, and σ(·) represents the activation function.

9. The method according to claim 7, characterized in that The Elu activation function is: x represents the input data to be activated; The LeakyReLU activation function is: x represents the input data to be activated; The loss function used to supervise the training of the deep learning model is L=L1+L2, including a first loss function L1 and a second loss function L2; The first loss function L1 is: The second loss function L2 is: Among them, y d represents the true value of the d-th node in the grid, represents the predicted value of the dth node in the grid, and D represents the sample set size of the sample data.

10. A Gibbs noise elimination device based on a high-order discontinuous Galerkin method, characterized in that: include: A data receiving module is used to receive the flow field data to be processed sent by the client, wherein the flow field data to be processed includes: flow field physical quantities and calculation grid information; A data processing module is configured to generate graph structure data according to the flow field data to be processed, and then use the graph structure data to construct a training data sample library; A supervision information providing module is used to provide supervision information for training data samples using graph convolution filters; A training module, configured to train a deep learning model using the training data sample library; Noise removal module, used to remove Gibbs noise from flow field physical quantities using the trained deep learning model; The data sending module is used to send the denoising result to the client.

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