CN117034721B - Method and device for predicting temperature field of graph neural network for core particle integrated design - Google Patents

Method and device for predicting temperature field of graph neural network for core particle integrated design Download PDF

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CN117034721B
CN117034721B CN202311289898.4A CN202311289898A CN117034721B CN 117034721 B CN117034721 B CN 117034721B CN 202311289898 A CN202311289898 A CN 202311289898A CN 117034721 B CN117034721 B CN 117034721B
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徐鸿博
戴雨洋
胡陈枢
曾令仿
陈�光
毛海荣
张帅
崔钰
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Abstract

The invention discloses a graph neural network temperature field prediction method and device for core particle integrated design, comprising the following steps: according to finite element meshing, the grid cells are regarded as nodes of the graph data, two adjacent grid cells are connected by edges, and the graph data of the package structure formed by the nodes and the edges is obtained; obtaining initial codes of nodes according to the vertex position information of the grid cells, the material properties, the initial value conditions and the edge value conditions of the simulation problems; designing a depth map neural network model, firstly obtaining projection of nodes and edges in a high-dimensional space, then enabling the nodes to aggregate edge information, enabling the edges to aggregate the node information, and finally decoding the node information into temperature values; designing a loss function according to a physical equation and training a model; predicting temperature distribution by using a trained model; and finally, calculating the temperature of each vertex by using an interpolation method for the temperature of the grid unit.

Description

Method and device for predicting temperature field of graph neural network for core particle integrated design
Technical Field
The invention belongs to the field of chip package simulation, and particularly relates to a method and a device for predicting a temperature field of a graph neural network for core particle integrated design.
Background
With the rapid rise of artificial intelligence technology, the demand for chips with high computing power in the fields of intelligent manufacturing, intelligent computing, etc. is increasing. However, the advanced process gradually approaches to the physical limit, and the method of improving the computing performance and power consumption of the chip by the advanced process not only reduces the yield of the chip, but also greatly improves the cost of manufacturing the chip. To cope with the above problems, researchers have proposed a core integration technique. The technology manufactures the die of chips with different functions through a mature process technology, and then assembles the die into a complete chip based on a 2.5D/3D advanced packaging technology, so that the chip yield is improved while the cost is considered. Through silicon via technology (Through Silicon Via, TSV) for implementing multiple chip stack packages in a mid-level and 3D package in a 2.5D package, etc., makes the core package structure more and more complex. Therefore, the chip integrated design based on advanced packaging technology faces the problem of difficult heat dissipation caused by complex packaging structure, wherein the problem of device failure caused by temperature distribution and stress is receiving a lot of attention. Thus, it is necessary to perform a die package structure-thermal-stress simulation at the die integration design stage. The traditional finite element method is very time-consuming in solving the thermal and mechanical simulation problems of the complex packaging structure, so that the core particle integrated design efficiency is low, and in order to cope with the problems, a high-efficiency simulation method for the core particle integrated design is urgently needed. In view of the quick reasoning capability of machine learning, the method turns the gaze into machine learning, and improves the simulation efficiency while maintaining the simulation accuracy as much as possible through a machine learning method.
Unstructured grids are commonly used in finite element simulation because of the complexity and multiscale of advanced packaging structures. Therefore, the finite element simulation result cannot be directly used for training and reasoning of a machine learning model, data needs to be preprocessed first, and finite element simulation data is converted into a data type which can be used for machine learning according to simulation problems. Considering the multi-scale features in the core integrated design, such as the TSV and solder joint of the micron scale and the substrate and printed circuit board of the millimeter scale, however, when describing the geometry of the package structure with the three-dimensional tensor of smaller size, a great deal of geometric features of the micron scale device are lost, and when describing the package geometry with the tensor of larger size, the input and target output dimensions of the machine learning model are very large, which results in difficult model training. Therefore converting the unstructured grid directly into regular tensor data is not the optimal choice. Since the finite element mesh naturally has a graph structure described by nodes and edges, describing the package structure described by the finite element mesh data with graph data and implementing temperature-stress prediction with a graph neural network is a good choice.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a graph neural network temperature field prediction method and device for core particle integrated design, which can realize the rapid prediction of the temperature field in the core particle integrated design and overcome the problems of finite element unstructured grid, multiscale and the like.
The aim of the invention is realized by the following technical scheme: a graph neural network temperature field prediction method for core particle integrated design comprises the following steps:
(1) According to finite element meshing, mesh data are arranged into graph data, and the graph data are recorded as a graphThe method comprises the steps of carrying out a first treatment on the surface of the Wherein each grid unit is represented by a node, and all nodes form a node set of the graph data; adjacent two grid units are connected by edges, and all edges form a collection of edges of the graph data;
(2) Acquiring an initial code of a node;
(3) Obtaining the temperature of each vertex in each grid unit according to the finite element simulation result; obtaining the temperature of the grid unit by an interpolation method according to the position coordinates of the grid unit, the position coordinates and the temperature of each vertex of the grid unit;
(4) Designing a depth map neural network model: the method comprises the steps of obtaining projection of nodes and edges in a high-dimensional space by using a neural network, aggregating characteristics of the nodes and the edges by using a graph neural network, and finally decoding the characteristics of the nodes into temperature field distribution;
(5) According to the temperature field simulation problem, designing a loss function and taking the initial codes of the nodes and the temperatures of the grid units obtained in the step (2) and the step (3) as a depth map neural network model in the data set training step (4);
(6) Predicting the temperature of each grid cell by using a trained graph neural network;
(7) The temperature of each vertex is obtained by an interpolation algorithm according to the coordinates of the vertices in the finite element mesh and the temperature of the mesh unit.
Further, in the step (1), the mesh data includes a mesh unit number, a mesh unit corresponding material number, a mesh unit total vertex number, vertex position coordinates, a list of vertex numbers of each mesh unit, and a boundary value condition; and according to the vertex number list of each grid, sorting the number list of the grid unit to which each vertex belongs.
Further, in the step (1), the node is any point inside the grid unit, and the nodes of two adjacent grid units are connected to form an edge.
Further, in the step (2), initial codes of the nodes are obtained according to coordinates and material properties of all vertexes of the grid unit and edge value conditions in the temperature field simulation problem; the initial coding of the node is formed by splicing the position of the node, the material property of the grid unit and the boundary value condition;
for the transient thermal simulation problem, the initial coding of the nodes needs to code time variable and initial value conditions besides the positions of the nodes, the material properties of the grid cells and the edge value conditions;
the positions of the nodes are obtained through the weighted summation of coordinates of all vertexes of the grid unit.
Further, in the step (4), the projection of the nodes and the edges in the high-dimensional space is obtained by using a neural network, specifically: for nodesFeatures in high-dimensional space, available fully connected networks +.>：
Wherein,representing the real number field, ++>Representing the dimension of the initial encoding of a node, +.>For the dimension of the high-dimensional space +.>Representing node->Features in high-dimensional space, +.>Is a fully connected network->Weight of->Is a fully connected network->Is offset from (a);
the edge is connected with two nodes, and the characteristics of the edge in the high-dimensional space are extracted according to the characteristics of the two nodes in the high-dimensional space.
Further, extracting the characteristics of the edges in a high-dimensional space by adopting a bilinear model or a single-layer full-connection network;
using bilinear models，/>
Using single-layer fully-connected networks，
Wherein,representing edge->Features in high-dimensional space, +.>Is any one of the non-linear activation functions,representing the node +.>And->Features in high-dimensional space->And->According to->Before->The subsequent sequences are spliced end to form a vector, which is marked with +.>Indicating transpose,/->And->The weights and offsets of the bilinear model respectively,and->Weights and biases for fully connected networks.
Further, in the step (4), the characteristics of the nodes and the edges are aggregated by using a graph neural network, and finally the nodes are encoded and decoded into temperature field distribution; the method comprises the following steps: features and graphs of nodes and edges in high-dimensional spaceUpdating the codes of the nodes and the edges as input of the graph neural network; the updating mode of the node code is that the average value of all edges directly connected with the node is taken, the node is +.>The secondary polymeric edge is characterized by:
there are two methods for edge aggregation node feature, the first, bilinear model in the form of residual errorSide->First->The secondary aggregation node is characterized in that:
second, a fully connected network in the form of a residual errorSide->First->The secondary aggregation node is characterized in that:
wherein the polymerization timesSatisfy->，/>；
After the aggregation for s times, the node is enabled to aggregate the edge characteristics again to obtain the final code of the nodeThen use the fully connected network +.>The node characteristics are decoded as the temperature of the node, i.e. the temperature of the grid cell:
further, in the step (5), the loss function is composed of two parts, namely a predicted loss of the model and a loss of the equation;
the predicted loss of the model is；
The loss of the equation is:;
loss function。
The temperature field prediction device of the graph neural network for the core particle integrated design comprises one or more processors, and is used for realizing the temperature field prediction method of the graph neural network for the core particle integrated design.
A computer readable storage medium having stored thereon a program which, when executed by a processor, is adapted to carry out the above described method of temperature field prediction for a graph neural network for a core particle-oriented integrated design.
The beneficial effects of the invention are as follows: on the one hand, the vertexes of the grid cells and the edges of the grid cells in the finite element grid data have the characteristics of graph data, and the grid data contain the multi-scale characteristics of the packaging structure, so that the graph data is used for describing the packaging structure, and the simulation data of the multi-scale model can be adapted. On the other hand, the core package contains a plurality of materials, and the presence of some vertices in the mesh data at interfaces of two or more materials presents difficulties in describing the material properties of the vertices. Considering that the finite element mesh cells are in one-to-one correspondence with the material properties, mesh cells are more suitable for nodes of the graph data than vertices of the mesh.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a finite element mesh cell abstracted to nodes in graph data; wherein (a) in fig. 1 is triangle mesh division, and (b) in fig. 1 is to abstract each mesh unit into a node, and (c) in fig. 1 only maintains a node set of relative position relation between the node and the mesh unit;
FIG. 2 is a flow chart of a method of constructing a set of edges in graph data from finite element mesh data; wherein (a) in fig. 2 marks one cell in the triangle mesh with a shadow, (b) in fig. 2 further marks a triangle mesh cell having a common side with the marked triangle cell, fig. 2 (c) abstracts all meshes as nodes, and (d) in fig. 2 connects nodes corresponding to two mesh cells having a common side with an edge;
FIG. 3 is an overall flow chart of a depth map neural network;
FIG. 4 is a general flow chart of the present invention;
FIG. 5 is a positional relationship between grid cells and nodes;
fig. 6 is a hardware configuration diagram of the present invention.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings. The features of the examples and embodiments described below may be combined with each other without conflict.
The invention discloses a graph neural network temperature field prediction method for core particle integrated design, which is shown in fig. 4 and comprises the following steps:
step 1: according to the grid division of the finite element, obtaining graph data of a packaging structure consisting of nodes and edges, and recording the graph asWherein the node set->Contains->Personal node->Expressed in terms ofIs the starting point +.>Directed edges of the end point, +.>Representing a set of edges. The node set is constructed in the manner shown in fig. 1, and the edge set is constructed in the manner shown in fig. 2. The structure map data based on the finite element mesh division will be described in detail below by taking a two-dimensional triangle mesh as an example.
For the construction of the node set, as shown in fig. 1, the dotted line in (a) in fig. 1 is an edge of the grid cell, and the dot is a vertex of the grid cell. Considering that each grid cell has only one material property, each grid cell is regarded as a node in the graph data, and the number of the node directly takes the number of the grid cell, namely, the firstPersonal node->And->The grid cells correspond and the relative positional relationship between the grid cells needs to be preserved. Thus, as shown in fig. 1 (b), the nodes of the graph data may be represented by one point inside the grid cell, and the set of nodes in the graph data after the grid is removed is shown in fig. 1 (c).
For the construction of the collection of edges, as shown in FIG. 2. First, the adjacency relation between grid cells is defined. For a two-dimensional grid cell, two adjacent grids are defined as two grid cells having a common edge; for a three-dimensional grid cell, two adjacent grid cells are defined as two grid cells having a common plane. Then, adjacent grid cells are determined according to the definition of the adjacent grid cells. Considering the grid cells corresponding to the hatching in fig. 2 (a), since the grid cells are two-dimensional, the grid cells having a common side therewith are shown as three grid cells in fig. 2 (b). Finally, from the graph data, adjacent grid cells are connected by line segments, constituting a set of edges in the graph data, as shown in (c) and (d) in fig. 2.
Searching for a common edge and a common face according to the relationship between the vertex and the grid unit in the grid dataAs shown in FIG. 5, in whichNumbering vertices. First, the grid cell numbers corresponding to each vertex are sorted according to the total vertex numbers of each grid cell in the finite element grid data. For example, in FIG. 5, the vertex set +.>Is a grid cell->Vertex of (1)Is a grid cell set->Is defined by the common vertex of the pair. Since the simulation data includes the vertex numbers corresponding to the mesh units, the mesh unit sets corresponding to the vertices need to be sorted according to the vertex sets corresponding to the mesh units. Then, a common edge and a common plane are determined from the collective vertex set of the grid cells. For a two-dimensional grid, two vertexes are arbitrarily taken out, the intersection of grid cell number lists corresponding to the two vertexes is taken, if the intersection is not empty and the number of elements is greater than or equal to 2, the edge connected by the two vertexes is a common edge, and the elements in the intersection are the numbers of adjacent grid cells, wherein any two cells are->And->Two sides can be added>And->. For example, the vertex in FIG. 5 +.>The corresponding set of grid cells is +.>Get the collection->And->Is provided withThis illustrates mesh vertex +.>And->The straight line is determined to be->And->Two grid cells, which have a common edge, thus grid +.>And->Adjacent two sides->And->In the collection->Is a kind of medium. For a three-dimensional grid, any three non-collinear vertexes are taken, intersections of grid cells corresponding to the three vertexes are taken, if the intersections are not empty and the number of elements in the intersections is greater than or equal to 3, a common plane is indicated, and then any two grid cells are taken from the intersections>And->Side->。
Step 2: an initial encoding of a graph node is obtained.
And obtaining the position information of the grid cell according to all the vertex coordinates of the grid cell. Grid cellThe position of (a) is the position coordinates of any point inside the grid cell (inside the grid cell, that is, the vertex not including the grid cell and the side and face of the grid cell are described), and can be defined by ∈>Is represented by a weighted sum, wherein the weight of each vertex is greater than 0 and the sum is 1, note ∈ ->Is->The position coordinates of the vertices in space are +.>Then there is
，/>，/>(4)
Here, parametersIs an adjustable superparameter, of which the simplest way can be taken +.>Is used for the averaging of the overall vertex coordinates of (c),
，/>，/>(5)
material property information of the grid cells is obtained from the material properties. The material property parameters affecting the temperature distribution include the density, specific heat and thermal conductivity of the material, wherein the density and specific heat of the material are constants, and the thermal conductivity is a three-dimensional vector, here, the thermal conductivity along three coordinate axes in the straight angle coordinate system. Recording the grid cells according to the corresponding relation between the grid cells and the materialThe material property of (2) is->。
And obtaining the encoding of the grid cell edge condition according to the edge condition. Only the case where the edge condition is constant is considered here, where the edge condition is expressed by a number pairWherein->Representation->Whether or not add->Personal edge condition,/->Express +.>The value of the individual boundary value conditions, if any +.>Personal side value condition, note->The coding of the boundary value condition of +.>。
For temperature field simulation problems that do not change over time, such as steady state thermal problems. Grid cellThe initial encoding of (a) or (b) the initial encoding of the node is to add the position information of the grid cell>Material properties of the grid cell->And the edge condition coding of the grid cells +.>Splicing the above sequences to form a vector +.>The dimension of the initial code at this time is。
For transient thermal simulation problems, temperature fieldsAlso time-dependent, so that the initial encoding of the node needs to be at the position information +.>Material properties of the grid cell->And the edge condition coding of the grid cells +.>On the basis of (3), the coding of the time series and the initial value condition is increased. Taking time sequence according to simulation problem>Here, where. Transient temperature field in three-dimensional space with convection edge condition is considered +.>Simulation problems. The package structure in three-dimensional space is marked +.>Temperature field->The following diffusion equation is satisfied:
，/>(1)
taking convection edge conditions (Robin edge conditions):
，/>(2)
the initial conditions are:
，/>(3)
wherein,is a time variable; />，/>，/>Is a spatial variable; />Is->Is defined by a boundary of (2); />Is an out-of-boundary normal vector; />，/>，/>，/>，/>And->Respectively the density, specific heat and material extension three-dimensional rectangular coordinate system of the material>Shaft (S)>Shaft (S)>The heat conduction coefficients in the three directions of the axis and the heat conduction coefficients in the direction of the normal vector outside the extension boundary; />Is the convection coefficient; />Is ambient temperature; />Is the temperature at the initial time of the package structure.
According to formula (3), the initial value condition is. Time of putting the above grid cell->Position coding->Material propertiesSide value condition->And initial condition->Sequentially splicing to form a vector +.>Node of transient thermal problem +.>Is the initial encoding of (1)The dimension of the initial code is +.>。
Step 3: and according to the finite element simulation result and the grid data, sorting target output data. Calculating interpolation according to the position coordinates of the grid unit, the position coordinates of each vertex and the temperature of each vertex in the step 2 to obtain the temperature value of the grid unit。
Step 4: designing a depth map neural network model: firstly, the projection of nodes and edges in a high-dimensional space is obtained by using a neural network, then the characteristics of the nodes and edges are aggregated by using a depth map neural network, and finally, the node data are decoded into temperature field distribution.
An overall flow chart of the depth map neural network model is shown in fig. 3. For nodesFeatures in high-dimensional space, available fully connected networks +.>
(6)
The initial encoding of the node is mapped to a high-dimensional space. Wherein the input data of the fully connected network model is the initial encoding of each grid cell；/>Is a fully connected network->Weight of->Is a fully connected netCollaterals->Bias of->And->Is->Requiring training parameters. Output layer neuron number of fully connected network>The number of hidden layers and the number of neurons in each hidden layer are all adjustable super parameters, and the activation function of the full-connection grid is a nonlinear activation function commonly used, such as ReLU, sigmoid, tanh.
The edge of the graph data is connected with two nodes, and the characteristics of the edge in the high-dimensional space can be extracted according to the characteristics of the two nodes in the high-dimensional space. Extraction edgeThere are two methods of features in high-dimensional space, the first, using bilinear models，/>(7)
Second, a single-layer full-connection network is adopted，(8)
Wherein,is any nonlinear activation function, +.>Representing the node +.>And->Features in high-dimensional space->And->According to->Before->Splicing the following sequences end to form a vector, < >>And->Weights and biases of bilinear models, respectively, +.>And->The weights and biases of the network model are parameters that need to be trained for the weights and biases of the fully connected network.
Feature and graph data for nodes and edges in high-dimensional spaceAs input to the graph neural network, the node and edge encodings are updated. The coding of the node is updated in such a way that the average value of all edges directly connected to the node is taken, +.>Secondary nodeUpdated to
(9)
There are two methods for edge aggregation node feature, the first, bilinear model in the form of residual errorSide->First->The secondary aggregation node is characterized in that:
(10)
second, a fully connected network in the form of a residual errorSide->First->The secondary aggregation node is characterized in that:
(11)
wherein the polymerization timesSatisfy->，/>Here->Is an adjustable super parameter. />、/>、/>And->Is a parameter in the network that needs to be trained.
According to the output of the graph neural network, the node is enabled to re-aggregate the edge characteristics according to the formula (9) to obtain the final code of the nodeThen use the fully connected network +.>Decoding node characteristics into the temperature of the node, i.e. the temperature of the grid cells
(12)
Wherein,the number of hidden layers of the medium network model and the number of neurons contained in each hidden layer are adjustable super parameters.
Step 5: according to the temperature field simulation problem, designing a loss function and training the depth map neural network model in the step 4 by using the input and output data sets which are arranged in the step 2 and the step 3. Considering the physical constant rate that the thermal conduction problem satisfies, the loss function is therefore composed of two parts, the predicted loss of the model and the loss of the equation. Wherein the predictive loss of the model is the network output valueOutput +.>Square of error between
(13)
According to the equation and the boundary value condition, the following loss function is designed by adopting an automatic differentiation mode
(14)
Wherein the second partial derivative is calculated by adopting an automatic differentiation mode. Adding equations (13) and (14) together, the loss function is
(15)
The parameters in the network model are then trained using error back propagation.
Step 6: the temperature of each grid cell is predicted using a trained depth map neural network. The purpose of the deep neural network designed according to steps 1 to 4 is to fit the temperature of each grid cell. When the model is used for temperature field prediction, only the packaging structure and grid division thereof are needed to be provided. First, grid-partitioned map data is constructed according to step 1, then initial encoding of grid cells (i.e., initial encoding of nodes) is obtained according to step 2, and finally, initial encoding of grid cells is input into a network model, and temperature prediction of each grid cell can be obtained.
Step 7: the temperature of each vertex is obtained by an interpolation algorithm according to the coordinates of the vertices in the finite element mesh and the temperature of the mesh unit. Since the final objective is to obtain the temperature value of each vertex, the temperature value of each vertex is obtained by interpolation algorithm only according to the temperature prediction of the grid unit obtained in the step 6
Corresponding to the embodiment of the graph neural network temperature field prediction method for the core particle integrated design, the invention also provides an embodiment of the graph neural network temperature field prediction device for the core particle integrated design.
Referring to fig. 6, a temperature field prediction device for a neural network for a core integration design provided in an embodiment of the present invention includes one or more processors configured to implement a temperature field prediction method for a neural network for a core integration design in the foregoing embodiment.
The embodiment of the temperature field prediction device of the graph neural network for the core particle integrated design can be applied to any device with data processing capability, and the device with data processing capability can be a device or a device such as a computer. The apparatus embodiments may be implemented by software, or may be implemented by hardware or a combination of hardware and software. Taking software implementation as an example, the device in a logic sense is formed by reading corresponding computer program instructions in a nonvolatile memory into a memory by a processor of any device with data processing capability. In terms of hardware, as shown in fig. 6, a hardware structure diagram of an apparatus with data processing capability, where the temperature field prediction device of the neural network for core integration design of the present invention is located, is shown in fig. 6, and in addition to a processor, a memory, a network interface, and a nonvolatile memory shown in fig. 6, any apparatus with data processing capability in the embodiment is generally according to an actual function of the apparatus with data processing capability, and may further include other hardware, which will not be described herein.
The implementation process of the functions and roles of each unit in the above device is specifically shown in the implementation process of the corresponding steps in the above method, and will not be described herein again.
For the device embodiments, reference is made to the description of the method embodiments for the relevant points, since they essentially correspond to the method embodiments. The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purposes of the present invention. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
The embodiment of the invention also provides a computer readable storage medium, and a program is stored on the computer readable storage medium, and when the program is executed by a processor, the method for predicting the temperature field of the graph neural network for the core particle integrated design in the embodiment is realized.
The computer readable storage medium may be an internal storage unit, such as a hard disk or a memory, of any of the data processing enabled devices described in any of the previous embodiments. The computer readable storage medium may be any device having data processing capability, for example, a plug-in hard disk, a Smart Media Card (SMC), an SD Card, a Flash memory Card (Flash Card), or the like, which are provided on the device. Further, the computer readable storage medium may include both internal storage units and external storage devices of any data processing device. The computer readable storage medium is used for storing the computer program and other programs and data required by the arbitrary data processing apparatus, and may also be used for temporarily storing data that has been output or is to be output.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather to enable any modification, equivalent replacement, improvement or the like to be made within the spirit and principles of the invention.

Claims (10)

1. The method for predicting the temperature field of the graph neural network for the core particle integrated design is characterized by comprising the following steps of:
(1) According to finite element meshing, mesh data are arranged into graph data, and the graph data are recorded as a graphThe method comprises the steps of carrying out a first treatment on the surface of the Wherein each grid cell is represented by a node,all nodes form a node set of the graph data; adjacent two grid units are connected by edges, and all edges form a collection of edges of the graph data;
(2) Acquiring an initial code of a node;
(3) Obtaining the temperature of each vertex in each grid unit according to the finite element simulation result; obtaining the temperature of the grid unit by an interpolation method according to the position coordinates of the grid unit, the position coordinates and the temperature of each vertex of the grid unit;
(4) Designing a depth map neural network model: the method comprises the steps of obtaining projection of nodes and edges in a high-dimensional space by using a neural network, aggregating characteristics of the nodes and the edges by using a graph neural network, and finally decoding the characteristics of the nodes into temperature field distribution;
(5) According to the temperature field simulation problem, designing a loss function and taking the initial codes of the nodes and the temperatures of the grid units obtained in the step (2) and the step (3) as a depth map neural network model in the data set training step (4);
(6) Predicting the temperature of each grid cell by using a trained graph neural network;
(7) The temperature of each vertex is obtained by an interpolation algorithm according to the coordinates of the vertices in the finite element mesh and the temperature of the mesh unit.
2. The method for predicting the temperature field of the graphic neural network for the integrated design of the core particles according to claim 1, wherein in the step (1), the grid data comprises the number of the grid cells, the material number corresponding to the grid cells, the number of the whole vertexes of the grid cells, the position coordinates of the vertexes, the number list of the vertexes of each grid cell and the boundary condition; and according to the vertex number list of each grid, sorting the number list of the grid unit to which each vertex belongs.
3. The method for predicting the temperature field of the graph neural network for the core particle integrated design according to claim 1, wherein in the step (1), the nodes are any point inside the grid cells, and the nodes of two adjacent grid cells are connected to form an edge.
4. The method for predicting the temperature field of the graph neural network for the core particle integrated design according to claim 1, wherein in the step (2), initial codes of nodes are obtained according to coordinates and material properties of all vertexes of the grid unit and boundary conditions in the temperature field simulation problem; the initial coding of the node is formed by splicing the position of the node, the material property of the grid unit and the boundary value condition;
for the transient thermal simulation problem, the initial coding of the nodes needs to code time variable and initial value conditions besides the positions of the nodes, the material properties of the grid cells and the edge value conditions;
the positions of the nodes are obtained through the weighted summation of coordinates of all vertexes of the grid unit.
5. The method for predicting the temperature field of the graph neural network for the core particle integrated design according to claim 1, wherein in the step (4), the projection of the nodes and the edges in the high-dimensional space is obtained by using a neural network, specifically: for nodesFeatures in high-dimensional space, available fully connected networks +.>
Wherein,representing the real number field, ++>Representing the dimension of the initial encoding of a node, +.>For the dimension of the high-dimensional space +.>Representing nodesFeatures in high-dimensional space, +.>Is a fully connected network->Weight of->Is a fully connected network->Is offset from (a);
the edge is connected with two nodes, and the characteristics of the edge in the high-dimensional space are extracted according to the characteristics of the two nodes in the high-dimensional space.
6. The method for predicting the temperature field of the graph neural network for the core particle integrated design of claim 5, wherein features of edges in a high-dimensional space are extracted by adopting a bilinear model or a single-layer full-connection network;
using bilinear models
Using single-layer fully-connected networks
Wherein,representing edge->Features in high-dimensional space, +.>Is any nonlinear activation function, +.>Representing the node +.>And->Features in high-dimensional space->And->According to->Before->The following sequences are spliced end to form a vector, the superscript T representing the transpose,/->And->Weights and biases of bilinear models, respectively, +.>And->Weights and biases for fully connected networks.
7. The method for predicting the temperature field of the graph neural network for the core particle integrated design according to claim 1, wherein in the step (4), the characteristics of nodes and edges are aggregated by the graph neural network, and finally the node codes are decoded into the temperature field distribution; the method comprises the following steps: features and graphs of nodes and edges in high-dimensional spaceUpdating the codes of the nodes and the edges as input of the graph neural network; the updating mode of the node code is that the average value of all edges directly connected with the node is taken, the node is +.>The secondary polymeric edge is characterized by:
the method for aggregating the characteristics of the nodes by the edges is two methods, namely, a bilinear model in the form of residual errorsSide->First->The secondary aggregation node is characterized in that:
second, a fully connected network in the form of a residual errorSide->First->The secondary aggregation node is characterized in that:
wherein the polymerization timesSatisfy->，/>；
After the aggregation for s times, the node is enabled to aggregate the edge characteristics again to obtain the final code of the nodeThen use the fully connected network +.>Decoding node characteristics into the temperature of the node, i.e. the temperature of the grid cells。
8. The method for predicting the temperature field of a graph neural network for a core particle integrated design according to claim 1, wherein in the step (5), the loss function consists of two parts, namely a predicted loss and an equation loss of a model;
the predicted loss of the model is；
The loss of the equation is:；
loss function。
9. A temperature field prediction device for a graph neural network for a core particle integrated design, comprising one or more processors configured to implement the temperature field prediction method for a graph neural network for a core particle integrated design of any one of claims 1-8.
10. A computer readable storage medium having stored thereon a program which, when executed by a processor, is adapted to carry out the method of temperature field prediction for a graph neural network for a core integration design according to any one of claims 1-8.
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