CN111444614A - Flow field reconstruction method based on graph convolution - Google Patents
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Abstract
The invention discloses a flow field reconstruction method based on graph convolution, which converts basic information of a fluid domain into graph structure data by carrying out grid division on the research fluid domain, extracts a mapping relation between the basic information and the research flow field (such as temperature, pressure, speed, vorticity and the like) by adopting graph convolution, and completes the task of obtaining various flow fields from the basic information. The method has the advantages that on one hand, the method can rapidly reconstruct the internal flow field, improve the reconstruction efficiency, reduce the economic cost and facilitate the operation of personnel; on the other hand, the method breaks away from the dependence of flow field reconstruction on the grid data by processing the grid data into the form of graph structure data, breaks through the application scene of the flow field reconstruction, can realize the flow field reconstruction on the structured grid and the unstructured grid at the same time, is not limited by the geometric shape of the researched object, and has great advantages compared with other reconstruction methods.
Description
Technical Field
The invention belongs to the technical field of flow heat exchange, and particularly relates to a flow field reconstruction method based on graph convolution.
Background
In traditional experiments and industrial detection, a series of measuring devices are generally adopted to detect basic data. A contact measurement tool represented by a thermocouple, a pressure strain gauge, or the like can obtain single-point information only by one device, and a large number of measurement devices are distributed on the surface of a measurement object to obtain global information, and information in a fluid region cannot be measured. Non-contact measurement tools, represented by infrared radiation and optical measurement, can accomplish the task of obtaining area information by one device, but the obtained area information is also limited by the surface. To solve this problem, a large number of new measurement techniques emerge. The measurement technology represented by ultrasonic waves can meet the measurement requirement of the internal flow field of a research object through reasonable distribution of multiple devices, but the devices are expensive and have poor reconstruction effect under complex environment or geometric conditions.
In recent years, with the popularization and development of deep learning methods in various engineering fields, more and more researches begin to pay attention to the application of convolutional neural networks in flow field reconstruction. The convolutional neural network is good at highly extracting characteristics from a large amount of basic data, and can realize an end-to-end flow field reconstruction task. Although the convolutional neural network can greatly reduce manual intervention in flow field reconstruction and complete mapping from known information to a global flow field, the convolutional neural network requires that the investigated flow field information must be lattice data and processed into a flow field matrix which can be directly used. However, in actual practice, most of the research watershed geometries are complex, and usually require unstructured grid to be used for segmentation, which is difficult to process into a grid point matrix.
Disclosure of Invention
The invention aims to provide a flow field reconstruction method based on graph convolution, which does not depend on a lattice data format, extracts a mapping relation between basic information and research characteristics (such as temperature, pressure, speed, vorticity and the like) by converting the basic information of a fluid domain into graph structure data and adopting graph convolution, and completes the task of reconstructing a global flow field from the basic information.
The invention is realized by adopting the following technical scheme:
A flow field reconstruction method based on graph convolution comprises the following steps:
1) Establishing a research model, and dividing grids:
establishing calculation model of research object, dividing grids according to numerical value or experimental requirement, and recording grid information, and obtaining a set of grid information for each calculation model, wherein each set of grid information includes position information L of each grid node m,lAnd a mesh division mode A m,mwherein, M is 1,2,3, M is the total number of grid nodes of the calculation model and is different according to different grid divisions of the calculation model, L is 1,2,3, L sequentially represents the position variable of the calculation model, and L is the total number of known variables of the calculation model;
2) Setting boundary conditions:
Setting boundary conditions of a research object under each set of calculation model, and designing different working conditions according to actual conditions; boundary conditions fall into two categories: if the boundary condition is that the flow field information of a certain area is directly set, recording the flow field information as an initial flow field F 0 m,kWherein K is 1,2,3, K, which in turn represents the flow field variables of the study subject, and K is the total number of flow field variables of the study subject; if the boundary condition indirectly limits the flow field information of one area, the boundary self-encoder converts the indirect boundary condition B' m,hMapping as an indirect flow field B m,hWherein H1, 2,3, H, in turn, represents the indirect boundary condition variables of the subject, and H is the total number of indirect boundary condition variables of the subject;
3) Obtaining global flow field information:
Obtaining the global flow field information Y of the calculation model through numerical calculation or experiments according to the calculation model established in the step 1) and the step 2) m,kWherein K is 1,2,3, K, which in turn represents the flow field variables of the study subject, and K is the total number of flow field variables of the study subject;
4) Integrating and processing data:
firstly, integrating the information of each set of calculation model of the research object, and splicing the grid position information L m,lInitial flow field F 0 m,kAnd indirect flow field B m,hKnown information X of the composition research object under the calculation model m,gwherein G1, 2,3, G, and G L + K + H, is subject Each set of calculation models contains three major parts of data: known information X m,gMesh division method A m,mAnd global flow field Y m,k(ii) a Secondly, all calculation models of the research object are integrated, and the known information of the research object is { X m,g}nThe grid division mode is { A m,m}nThe global flow field is { Y m,k}nWherein N is 1,2,3, and N is the total number of calculation models of the study object; finally, normalization operation is carried out on the calculation model information, and the normalized data are respectively expressed as known information 
And a global flow field 
5) Constructing a flow field reconstruction network based on graph convolution
Firstly, data division is carried out; dividing the training set into training sets according to the ratio of 2:2:1 
Verification set 
And test set 
Wherein 
As reconstructed input information, and 
Is an output target of the network; in the training process, a training set is used as a training sample, a verification set is used for verifying the effectiveness of the reconstruction network based on graph convolution, and a test set is used for testing the reconstruction capability of the network after training is finished; next, an adjacency matrix is obtained, which is partitioned in a grid-wise manner { A } m,m}nBased on the graph convolution structure The processed adjacency matrix mark obtained by reprocessing 
Finally, a flow field reconstruction network GCN based on graph convolution is constructed on the basis of the adjacent matrix, and information transmission, aggregation and updating operations are carried out according to the adjacent matrix to obtain a reconstructed flow field;
6) Training a graph convolution-based flow field reconstruction network
7) And (3) performing flow field reconstruction on the research flow field by using a flow field reconstruction network based on graph convolution:
Firstly, designing a proper grid according to measurement requirements; secondly, processing the known information according to the steps 1) to 4) 
And obtaining a mesh division mode A m,m(ii) a Then the image is transmitted into a graph to be convolved with GCN to obtain a reconstructed flow field Y' m,g。
The invention further improves the connection mode A of the grid nodes in the step 1) m,mThe adjacency matrix in the graph structure data is used for representing the connection relationship between each node and all other nodes, and the specific meaning is as follows:
The further improvement of the present invention is that in step 1), the grids in each set of computational model may adopt different partitioning methods, including structured grids, unstructured grids and mixed grids, and the total number M of grid nodes is different according to different grid partitioning methods.
The invention has the further improvement that in the step 2), the boundary self-Encoder is divided into an Encoder Encoder and a Decoder Decoder; encoder Encoder employs deconvolution to construct from indirect boundary condition B' hTo the indirect flow field B m,hThe Decoder uses a convolution configuration to map the function from the indirect flow field B m,hTo indirect boundary condition B' hSolution of (2) A code mapping function; the loss function of the self-encoder is the difference value between the result of encoding and decoding each indirect boundary condition variable and the original indirect boundary condition variable:
The further improvement of the invention is that in step 4), normalization operation with 0 as the center is respectively carried out on each parameter, g is fixed, and the used calculation models are uniformly normalized:
Maxg＝Max({Xm,g}n|1≤m≤M,1≤n≤N)
Ming＝Min({Xm,g}n|1≤m≤M,1≤n≤N)
Global flow field data { Y m,k}nThe normalization operation of (a) is similar.
A further improvement of the invention is that in step 5) the graph convolution for flow field reconstruction uses any effective network architecture, including frequency domain as well as spatial domain.
The further improvement of the invention is that in the step 5), the loss function of the flow field reconstruction network based on graph convolution is divided into two parts, wherein one part is the flow field loss F _ loss, and the purpose is to reduce the difference between the reconstructed flow field and the real flow field; the other part is gradient loss G _ loss, which aims to improve the smoothness of the flow field and reduce the difference between the reconstructed flow field and the real flow field, and the total loss function T _ loss is the weighted expression of the flow field loss F _ loss and the gradient loss G _ loss as follows:
T_loss＝w1×F_loss+w2×G_loss
Wherein the content of the first and second substances, 
To reconstruct the flow field, { G' m,m,k}nTo reconstruct the gradient information of the flow field, { G m,m,k}nThe gradient information of the real flow field is interpolation of each node and adjacent nodes; gradient information with real flow field G m,m,k}nFor example, the gradient information is calculated by fixing each parameter, i.e. fixing k and n, under each calculation model as follows:
Wherein operation [. ] ]Meaning that the row vectors of the left matrix are multiplied by the corresponding elements of the right vector, the operation 
Means that the column vector of the left-hand matrix is multiplied by the corresponding element of the right-hand vector; for the kth flow field parameter of the nth calculation model, if the ith node is not adjacent to the jth node, { A } m,m}n·{Ym,k}nAnd 
The element in the ith row and the j column is 0; if adjacent, then { A } m,m}n·{Ym,k}nWherein the element is { Y i,k}n，
Wherein the element is { Y j,k}nThe specific expression is as follows:
Wherein, a iRepresentation matrix { A m,m}nIth row vector, a' iRepresentation matrix { A m,m}nThe ith column vector is specifically expressed as follows:
Reconstructing gradient information { G 'of flow field' m,m,k}nThe calculation method is the same as that of the real flow field, and specifically comprises the following steps:
The invention is further improved in that in step 6), in the process of training the network, firstly, the optimizer is set to Adam, the initial learning rate is set to be 0.005, the minimum learning rate is 0.0001, and the learning rate is gradually reduced in the process of training.
The invention has at least the following beneficial technical effects:
The invention provides a flow field reconstruction method based on graph convolution, which converts basic information of a fluid domain into graph structure data by performing grid division on the fluid domain to be researched, extracts a mapping relation between the basic information and the flow field to be researched (such as temperature, pressure, speed, vorticity and the like) by adopting graph convolution, and completes the task of obtaining all global flow fields from the basic information. The method has the advantages that on one hand, the method can rapidly reconstruct the internal flow field, improve the reconstruction efficiency, reduce the economic cost and facilitate the operation of personnel; in another aspect, the method breaks away from the dependence of flow field reconstruction on lattice point data by processing the grid data into the form of graph structure data, breaks through the application scene of flow field reconstruction, and can simultaneously realize the flow field reconstruction of structured grids, unstructured grids and mixed grids.
Drawings
FIG. 1 is a flow chart of a flow field reconstruction method based on graph convolution according to the present invention;
FIG. 2 is a schematic diagram of a structured grid partitioning of the present invention;
FIG. 3 is a schematic diagram of the unstructured meshing of the present invention;
FIG. 4 is a schematic diagram of a graph convolution-based flow field reconstruction network according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples in accordance with the summary of the invention. The following is an application of the present invention, but not limited thereto, and the implementation personnel can modify the parameters thereof according to specific situations, and the implementation process is as shown in fig. 1.
As shown in fig. 1, the flow field reconstruction method based on graph convolution provided by the present invention includes the following steps:
the method comprises the steps of firstly, establishing a research model, dividing grids, establishing a calculation model of a research object, dividing the grids according to numerical values or experimental requirements, and recording grid information m,lAnd a mesh division mode A m,mwherein M is 1,2,3, M is the total number of grid nodes of the computational model and is different according to different grid divisions of the computational model, L is 1,2,3, L sequentially represents the position variable of the computational model, and L is the total number of known variables of the computational model.
As shown in fig. 2-3, the connection mode a of the grid nodes m,mThe adjacency matrix in the graph structure data is used for representing the connection relationship between each node and all other nodes, and the specific meaning is as follows:
The grids in each set of calculation model can adopt different division methods, including structured grids, unstructured grids, mixed grids and the like, and the total number M of grid nodes can be different according to different grid division modes.
And secondly, setting boundary conditions. Is provided with And determining the boundary conditions of the research object under each set of calculation model, and designing different working conditions according to actual conditions. Boundary conditions can be divided into two categories: if the boundary condition is that the flow field information of a certain area is directly set, recording the flow field information as an initial flow field F 0 m,kWhere K is 1,2,3, K, which in turn represents the flow field variables of the subject, and K is the total number of flow field variables for that subject. If the boundary condition indirectly limits the flow field information of a certain area, such as gradient and the like, the boundary self-encoder converts the indirect boundary condition B' hMapping as an indirect flow field B m,hWhere H1, 2,3, H, in turn, represents the indirect boundary condition variables of the subject, and H is the total number of indirect boundary condition variables for the subject.
The invention further improves that in the step 2), the boundary self-Encoder is divided into an Encoder Encoder and a Decoder Decoder. Encoder Encoder employs deconvolution to construct from indirect boundary condition B' hTo the indirect flow field B m,hThe Decoder uses a convolution configuration to map the function from the indirect flow field B m,hTo indirect boundary condition B' hDecoding the mapping function. The loss function of the self-encoder is the difference value between the result of encoding and decoding each indirect boundary condition variable and the original indirect boundary condition variable:
And thirdly, obtaining the global flow field information. Obtaining the global flow field information Y of the calculation model through numerical calculation or experiments according to the calculation model established in the step 1) and the step 2) m,kWhere K is 1,2,3, K, which in turn represents the flow field variables of the subject, and K is the total number of flow field variables for that subject.
integrating and processing data, firstly, integrating information of each set of calculation model of the research object, and splicing grid position information L m,lInitial flow field F 0 m,kAnd indirect flow field B m,hKnown information X of the composition research object under the calculation model m,gWherein g is 1,2,3... G, and G ═ L + K + h, then each set of computational models for the study contained three major components of data, known information X m,gMesh division method A m,mAnd global flow field Y m,k. Secondly, all the calculation models of the study object are integrated. The known information of the study object is X m,g}nThe grid division mode is { A m,m}nThe global flow field is { Y m,k}nWherein N is 1,2,3, and N is the total number of calculation models of the study object. Finally, normalization operation is carried out on the calculation model information, and the normalized data are respectively expressed as known information 
And a global flow field 
Respectively carrying out normalization operation with 0 as the center on each parameter, fixing g, and uniformly normalizing the used calculation models:
Maxg＝Max({Xm,g}n|1≤m≤M,1≤n≤N)
Ming＝Min({Xm,g}n|1≤m≤M,1≤n≤N)
Global flow field data { Y m,k}nThe normalization operation of (a) is similar.
And fifthly, building a flow field reconstruction network based on graph convolution. First, data division is performed. Dividing the training set into training sets according to the ratio of 2:2:1 
Verification set 
And test set 
Wherein 
As reconstructed input information, and 
Is the output target of the network. In the training process, a training set is used as a training sample, a verification set is used for verifying the effectiveness of the reconstruction network based on graph convolution, and a test set is used for testing the reconstruction capability of the network after training is finished. Next, a adjacency matrix is obtained. The adjacency matrix is divided in a grid mode (A) m,m}nBased on the graph convolution structure, and marking the processed adjacent matrix as 
Wherein the processing method comprises adding self-loop, normalizing, standardizing and the like. And finally, constructing a flow field reconstruction network GCN based on graph convolution on the basis of the adjacent matrix, wherein the graph convolution network structure adopts GraphSage, and information transmission, aggregation, updating and other operations are carried out according to the adjacent matrix to obtain a reconstructed flow field. A flow field reconstruction network based on graph convolution is shown in fig. 4.
The loss function of the flow field reconstruction network based on graph convolution is divided into two parts, wherein one part is flow field loss F _ loss, and the purpose is to reduce the difference between a reconstructed flow field and a real flow field; the other part is the gradient loss G _ loss, which aims to improve the smoothness of the flow field and reduce the difference between the reconstructed flow field and the real flow field. The total loss function T _ loss is a weighted representation of the flow field loss F _ loss and the gradient loss G _ loss as follows:
T_loss＝w1×F_loss+w2×G_loss
Wherein the content of the first and second substances, 
To reconstruct the flow field, { G' m,m,k}nTo reconstruct the gradient information of the flow field, { G m,m,k}nThe gradient information of the real flow field is interpolation of each node and adjacent nodes. Gradient information with real flow field G m,m,k}nFor example, the gradient information is calculated by fixing each parameter, i.e. fixing k and n, under each calculation model as follows:
Wherein operation [. ] ]Meaning that the row vectors of the left matrix are multiplied by the corresponding elements of the right vector, the operation 
Meaning that the column vector of the left-hand matrix is multiplied by the corresponding element of the right-hand vector. For the kth flow field parameter of the nth calculation model, if the ith node is not adjacent to the jth node, { A } m,m}n·{Ym,k}nAnd 
The element in the ith row and the j column is 0; if adjacent, then { A } m,m}n·{Ym,k}nWherein the element is { Y i,k}n，
Wherein the element is { Y j,k}n. The specific expression is as follows:
Wherein, a iRepresentation matrix { A m,m}nIth row vector, a' iRepresentation matrix { A m,m}nThe ith column vector is specifically expressed as follows:
Reconstructing gradient information { G 'of flow field' m,m,k}nThe calculation method is the same as that of the real flow field, and specifically comprises the following steps:
And sixthly, training a flow field reconstruction network based on graph convolution. In the process of training the network, firstly, setting the optimizer as Adam, setting the initial learning rate to be 0.005, setting the minimum learning rate to be 0.0001, and reducing the learning rate in a step-by-step mode in the training process.
And seventhly, performing flow field reconstruction on the researched flow field by applying a flow field reconstruction network based on graph convolution. First, a suitable grid is designed according to the measurement needs. Secondly, processing the known information according to the steps 1) to 4) 
And obtaining a mesh division mode A m,m. Then the image is transmitted into a graph to be convolved with GCN to obtain a reconstructed flow field Y' m,g。
Claims (8)
1. A flow field reconstruction method based on graph convolution is characterized by comprising the following steps:
1) Establishing a research model, and dividing grids:
establishing calculation model of research object, dividing grids according to numerical value or experimental requirement, and recording grid information, and obtaining a set of grid information for each calculation model, wherein each set of grid information includes position information L of each grid node m,lAnd a mesh division mode A m,m(ii) a Wherein m is 1,2,3..., M is the total number of grid nodes of the calculation model and is different according to different grid divisions of the calculation model, L is 1, 2.
2) Setting boundary conditions:
Setting boundary conditions of a research object under each set of calculation model, and designing different working conditions according to actual conditions; boundary conditions fall into two categories: if the boundary condition is that the flow field information of a certain area is directly set, recording the flow field information as an initial flow field F 0 m,kWherein K is 1,2,3, K, which in turn represents the flow field variables of the study subject, and K is the total number of flow field variables of the study subject; if the boundary condition indirectly limits the flow field information of one area, the boundary self-encoder converts the indirect boundary condition B' m,hMapping as an indirect flow field B m,hWherein H1, 2,3, H, in turn, represents the indirect boundary condition variables of the subject, and H is the total number of indirect boundary condition variables of the subject;
3) Obtaining global flow field information:
Obtaining the global flow field information Y of the calculation model through numerical calculation or experiments according to the calculation model established in the step 1) and the step 2) m,kWherein K is 1,2,3, K, which in turn represents the flow field variables of the study subject, and K is the total number of flow field variables of the study subject;
4) Integrating and processing data:
firstly, integrating the information of each set of calculation model of the research object, and splicing the grid position information L m,lInitial flow field F 0 m,kAnd indirect flow field B m,hKnown information X of the composition research object under the calculation model m,gwhere G is 1,2,3, G, and G is L + K + H, each set of computational models of the study object contains three major parts of data, known information X m,gMesh division method A m,mAnd global flow field Y m,k(ii) a Secondly, all calculation models of the research object are integrated, and the known information of the research object is { X m,g}nThe grid division mode is { A m,m}nGlobal flow field Is { Y m,k}nWherein N is 1,2,3, and N is the total number of calculation models of the study object; finally, normalization operation is carried out on the calculation model information, and the normalized data are respectively expressed as known information 
And a global flow field 
5) Constructing a flow field reconstruction network based on graph convolution
Firstly, data division is carried out; dividing the training set into training sets according to the ratio of 2:2:1 
Verification set 
And test set 
Wherein 
As reconstructed input information, and 
Is an output target of the network; in the training process, a training set is used as a training sample, a verification set is used for verifying the effectiveness of the reconstruction network based on graph convolution, and a test set is used for testing the reconstruction capability of the network after training is finished; next, an adjacency matrix is obtained, which is partitioned in a grid-wise manner { A } m,m}nBased on the graph convolution structure, and marking the processed adjacent matrix as 
Finally, constructing the basis on the adjacency matrix The method comprises the following steps that a flow field reconstruction network GCN of graph convolution carries out information transmission, aggregation and updating operation according to an adjacent matrix to obtain a reconstructed flow field;
6) Training a graph convolution-based flow field reconstruction network
7) And (3) performing flow field reconstruction on the research flow field by using a flow field reconstruction network based on graph convolution:
Firstly, designing a proper grid according to measurement requirements; secondly, processing the known information according to the steps 1) to 4) 
And obtaining a mesh division mode A m,m(ii) a Then the image is transmitted into a graph to be convolved with GCN to obtain a reconstructed flow field Y' m,g。
2. The flow field reconstruction method based on graph convolution according to claim 1, characterized in that in step 1), the connection mode A of grid nodes m,mThe adjacency matrix in the graph structure data is used for representing the connection relationship between each node and all other nodes, and the specific meaning is as follows:
3. The method for reconstructing the flow field based on graph convolution according to claim 1), wherein in step 1), the mesh in each set of calculation model can be divided differently, including structured mesh, unstructured mesh and mixed mesh, and the total number M of mesh nodes is different according to different mesh division modes.
4. The method for reconstructing the flow field based on graph convolution according to claim 2, wherein in step 2), the boundary self-Encoder is divided into two parts, namely an Encoder Encoder and a Decoder Decode; encoder Encoder employs deconvolution to construct from indirect boundary condition B' hTo the indirect flow field B m,hEncoding mapping function of, and decoder Decoder uses convolution construction from indirect flow field B m,hTo indirect boundary condition B' hDecoding the mapping function of (a); the loss function of the self-encoder is the difference value between the result of encoding and decoding each indirect boundary condition variable and the original indirect boundary condition variable:
5. The flow field reconstruction method based on graph convolution according to claim 4, characterized in that in step 4), for each parameter, a normalization operation with 0 as a center is performed, g is fixed, and the used calculation models are uniformly normalized:
Maxg＝Max({Xm,g}n|1≤m≤M,1≤n≤N)
Ming＝Min({Xm,g}n|1≤m≤M,1≤n≤N)
Global flow field data { Y m,k}nThe normalization operation of (a) is similar.
6. The flow field reconstruction method based on graph convolution according to claim 5, wherein in step 5), the graph convolution used for flow field reconstruction adopts any effective network architecture including frequency domain and space domain.
7. The flow field reconstruction method based on graph convolution according to claim 6, characterized in that in step 5), the loss function of the flow field reconstruction network based on graph convolution is divided into two parts, one part is the flow field loss F _ loss, which aims to reduce the difference between the reconstructed flow field and the real flow field; the other part is gradient loss G _ loss, which aims to improve the smoothness of the flow field and reduce the difference between the reconstructed flow field and the real flow field, and the total loss function T _ loss is the weighted expression of the flow field loss F _ loss and the gradient loss G _ loss as follows:
T_loss＝w1×F_loss+w2×G_loss
Wherein the content of the first and second substances, 
To reconstruct the flow field, { G' m,m,k}nTo reconstruct the gradient information of the flow field, { G m,m,k}nThe gradient information of the real flow field is interpolation of each node and adjacent nodes; gradient information with real flow field G m,m,k}nFor example, the gradient information is calculated by fixing each parameter, i.e. fixing k and n, under each calculation model as follows:
Wherein operation [. ] ]Meaning that the row vectors of the left matrix are multiplied by the corresponding elements of the right vector, the operation 
Means that the column vector of the left-hand matrix is multiplied by the corresponding element of the right-hand vector; for the kth flow field parameter of the nth calculation model, if the ith node is not adjacent to the jth node, { A } m,m}n·{Ym,k}nAnd 
The element in the ith row and the j column is 0; if adjacent, then { A } m,m}n·{Ym,k}nWherein the element is { Y i,k}n，
Wherein the element is { Y j,k}nThe specific expression is as follows:
Wherein, a iRepresentation matrix { A m,m}nIth row vector, a' iRepresentation matrix { A m,m}nThe ith column vector is specifically expressed as follows:
Reconstructing gradient information { G 'of flow field' m,m,k}nThe calculation method is the same as that of the real flow field, and specifically comprises the following steps:
8. The flow field reconstruction method based on graph convolution according to claim 7, wherein in step 6), in the process of training the network, the optimizer is firstly set to Adam, the initial learning rate is set to 0.005, the minimum learning rate is 0.0001, and the learning rate gradually decreases in the process of training.
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