CN117610364A - Super-surface design method, property prediction model training method and device - Google Patents
Super-surface design method, property prediction model training method and device Download PDFInfo
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Abstract
The invention discloses a design method of a super surface, a training method and a training device of a property prediction model, wherein the method comprises the steps of obtaining sample data of a graph model, wherein each group of data in the sample data of the graph model is a sparse matrix obtained by modeling the super surface through a time domain finite difference method; the discrete light source matrix is used as a node, the Maxwell equation set matrix is used as an edge, the numerical solution matrix is used as a label, and the graph neural network is trained. According to the method and the device, on one hand, the sparse matrix generated by the hypersurface through the time domain finite difference method is utilized to be similar to the graph neural network, the graph neural network meeting the property prediction requirement is trained, on the other hand, the hypersurface is utilized to generate the sparsity of the matrix through the time domain finite difference method, so that the hypersurface with the super-large size can be processed through a limited memory, the numerical solution of a light field of the hypersurface can be conveniently solved through the graph neural network, or the required parameters of the hypersurface can be reversely designed based on the target numerical solution and the graph neural network.
Description
Technical Field
The invention relates to the technical field of deep learning and optics, in particular to a training method of a super-surface property prediction model, a super-surface design method and a super-surface design device.
Background
The photoelectric material property simulation technology is a method for predicting and researching the structure, property, function and the like of a photoelectric material by using a computer simulation method, and is a starting point and a foundation of material simulation. Existing photoelectric material property simulation techniques include time domain finite difference method (FDTD), frequency domain finite difference method (FDFD), finite element analysis (FEM), and the like.
In the process of implementing the present invention, the inventor finds that although there are many related existing methods for simulating the properties of the photoelectric material, each of these methods has various problems, such as relatively low operation speed, high requirement of operation on hardware, or inaccurate operation result, etc., especially, the near-field calculation of a smaller system can only be performed, and for the super-surface with elements above tens of millions, the system with large degree of freedom cannot be processed at present, so that the application of the existing property prediction and analysis method on the super-surface is limited, and the development is difficult.
Disclosure of Invention
In order to solve at least one of the above problems, an object of the present invention is to provide a training method, a super-surface design method and a device for a super-surface property prediction model, which can be applied to a super-surface of tens of millions of primitives, can meet the computational power requirement required to be consumed for model training with the processing capability of a current server, and can rapidly perform property prediction after model training, and has at least one of the above effects 。
In order to achieve the above object, an embodiment of the present invention provides a training method for a super surface property prediction model, which is characterized by comprising the following steps:
obtaining graph model sample data, wherein each group of data in the graph model sample data comprises a maxwell's equation set matrix A, a numerical solution matrix E and a discrete light source matrix b, wherein the maxwell's equation set matrix A, the numerical solution matrix E and the discrete light source matrix b are sparse matrixes obtained by modeling the super surface through a time domain finite difference method, and AE=b;
and training a graph neural network by taking the discrete light source matrix b as a node, taking the Maxwell equation set matrix A as an edge, taking the numerical solution matrix E as a label, wherein elements Aij in the Maxwell equation set matrix A are taken as continuous edges of the node bi and the node bj, and the graph neural network is used for predicting the numerical solution of the super surface.
As a further improvement of the present invention, the acquiring the graph model sample data includes:
dividing the super surface into a plurality of sub-blocks;
and obtaining the Maxwell equation set matrix A, the numerical solution matrix E and the discrete light source matrix b corresponding to each sub-block.
As a further improvement of the present invention, the super surface includes a plurality of primitives, and the step of acquiring the graph model sample data includes:
three-dimensional lattice-nodding the super surface;
determining the dielectric constant of each lattice point according to the primitive and non-primitive mediums in the lattice point, wherein the parameters of the Maxwell equation set matrix A comprise the dielectric constant;
the dielectric constant of the lattice is adjusted to be a micro-functional.
As a further improvement of the present invention, the plurality of primitives are arranged as equal-height cylindrical primitives, and the trainable parameter of the super surface is a radius array { r } of the primitives;
the adjusting the dielectric constant of the lattice point to be a micro-functionable includes:
the dielectric constant epsilon (x, y, z, { r }) of each lattice point is adjusted to be a microtechnical of the radius array { r }.
As a further improvement of the present invention, the graph neural network includes a graph information convergence layer, and the definition of the graph information convergence layer is:
wherein k is the k-th iteration round, W1 and W2 are trainable parameters of the model, N (i) is a neighboring node, E is a numerical solution, and f and g represent two nonlinear transformations respectively.
As a further improvement of the present invention, the graph neural network further includes a residual layer, and the data of the graph information convergence layer and the graph model sample data are input into the residual layer, and the residual layer outputs a prediction result.
As a further improvement of the invention, the loss function loss of the graph neural network is loss= |e '-e|/E, wherein E' is the prediction result and E is the label.
In order to achieve one of the above objects, an embodiment of the present invention provides a method for designing a super surface, including the steps of:
obtaining a target numerical solution, wherein the target numerical solution is a numerical solution corresponding to a super surface to be designed;
based on the target numerical solution, generating a corresponding target Maxwell equation set matrix and a corresponding target discrete light source matrix through the above-mentioned super-surface property prediction model;
and deducing design parameters of the super surface according to the target Maxwell equation set matrix and the target discrete light source matrix.
As a further improvement of the present invention, the step of inferring design parameters of the super surface from the target maxwell's equations matrix and the target discrete light source matrix includes:
calculating design parameters of the super surface corresponding to the target Maxwell equation set matrix and the target discrete light source matrix through an integral function, wherein in the process of generating a sparse matrix of the super surface through a time domain finite difference method, the dielectric constant of each lattice point of the super surface after three-dimensional lattice is a micro-functional;
or,
training a relation model among the design parameters, the maxwell equation set matrix and the discrete light sources through a neural network, and determining the design parameters of the super surface corresponding to the target maxwell equation set matrix and the target discrete light source matrix based on the relation model.
To achieve one of the above objects, an embodiment of the present invention provides a training device for a super surface property prediction model, including:
the first acquisition module is used for acquiring graph model sample data, wherein each group of data in the graph model sample data is a sparse matrix generated by a hypersurface through a time domain finite difference method, each group of data respectively comprises a maxwell equation set matrix A, a numerical solution matrix E and a discrete light source matrix b, wherein the maxwell equation set matrix A, the numerical solution matrix E and the discrete light source matrix b are sparse matrices obtained by modeling the hypersurface through the time domain finite difference method, and AE=b;
the model training module is used for taking the discrete light source matrix b as a node, taking the Maxwell equation set matrix A as an edge, taking the numerical solution matrix E as a label, and training a graph neural network, wherein elements Aij in the Maxwell equation set matrix A are taken as the continuous edges of the node bi and the node bj, and the graph neural network is used for predicting the numerical solution of the super surface.
In order to achieve one of the above objects, an embodiment of the present invention provides a super surface design apparatus, including the steps of:
the second acquisition module is used for acquiring a target numerical solution, wherein the target numerical solution is a numerical solution corresponding to the super surface to be designed;
the reverse analysis module is used for generating a corresponding target Maxwell equation set matrix and a corresponding target discrete light source matrix through the above-mentioned super-surface property analysis model based on the target numerical solution;
and the deducing module is used for deducing the design parameters of the super surface according to the target Maxwell equation set matrix and the target discrete light source matrix.
To achieve one of the above objects, an embodiment of the present invention provides an electronic device including:
a storage module storing a computer program;
and the processing module can realize the training method of the super-surface property prediction model or the steps in the super-surface design method when executing the computer program.
To achieve one of the above objects, an embodiment of the present invention provides a readable storage medium storing a computer program which, when executed by a processing module, implements the above-mentioned training method of the super-surface property prediction model or the above-mentioned steps in the super-surface design method.
Compared with the prior art, the invention has the following beneficial effects: according to the training method, the super-surface design method and the device of the super-surface property prediction model, on one hand, the graph neural network meeting the property prediction requirement is trained by utilizing the similarity between a sparse matrix generated by the super-surface through a time domain finite difference method and the graph neural network, on the other hand, the super-surface model is enabled to be possible to process super-surfaces with super-large sizes by utilizing the sparsity of the super-surface generated by the super-surface through the time domain finite difference method, the accuracy of the result predicted by the final graph neural network is high and highly consistent with the real result, the numerical solution of a light field of the super-surface can be conveniently solved by utilizing the graph neural network subsequently, and the required parameter of the super-surface can be reversely designed based on the target numerical solution and the graph neural network, so that the requirements of the light field prediction and the design work of the super-surface of a large number of primitives are met.
Drawings
FIG. 1 is a schematic diagram of a Maxwell's equations matrix A according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a neural network model of FIG. 2, in accordance with an embodiment of the present invention;
FIG. 3 is a flow chart of a method of training a subsurface property prediction model according to an embodiment of the invention;
FIG. 4 is a flow chart of a method of subsurface design according to an embodiment of the invention;
FIG. 5 is a comparative schematic diagram of a numerical solution obtained by calculating the light field distribution of the subsurface by a numerical solution method, and a result obtained by predicting the light field distribution of the subsurface by the subsurface property prediction model of the present embodiment;
FIG. 6 is a block diagram of a training apparatus for a subsurface property prediction model according to an embodiment of the present invention;
FIG. 7 is a schematic block diagram of a super surface design apparatus according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to specific embodiments shown in the drawings. These embodiments are not intended to limit the invention and structural, methodological, or functional modifications of these embodiments that may be made by one of ordinary skill in the art are included within the scope of the invention.
An embodiment of the present invention provides a training method, a super-surface design method, and a device for a super-surface property prediction model, which can be applied to a super-surface of tens of millions of primitives, and can meet the computational power requirement required to be consumed by model training with the processing capability of a current server, and the model can rapidly perform property prediction after model training, and has at least one of the above effects.
The property simulation technology of the super surface is a starting point and a foundation of material simulation, and can provide powerful support and help for material science research. In photoelectric simulation calculation, particularly in the fields of spectrum simulation and the like, the high-efficiency and accurate simulation of the properties of the super surface is significant. The nature simulation of the super surface, namely the simulation of the super surface, predicts and researches the structure, the nature, the function and the like of the super surface by using a computer simulation method, and the algorithm is essentially to solve maxwell equation sets of various materials and structures under different light sources and different boundary conditions, so as to simulate the propagation and interaction behaviors of electromagnetic waves in a medium space.
As described in the background, the prior art has problems such as relatively slow operation speed, high requirement of hardware for operation, or applicability only to the like. The embodiment can be used for the property simulation of the super-surface, the simulation degree of the expression is accurate, and the reverse super-surface design can be further carried out.
The super-surface comprises a substrate and primitives, the size and the shape of each primitive can be designed independently, and the shape and the period of the primitives as well as the size parameters and the rotation angle parameters corresponding to the shapes can be designed according to different tasks. The shape of the primitive can be linear, cylindrical, cuboid, elliptic cylinder, hollowed elliptic main body, hollowed cuboid and the like, different shapes can correspond to partially identical and partially different size parameters and rotation angle parameters, such as the radius of the cylinder, the length and width of the cuboid, the length diameter, the short diameter and the like of the elliptic cylinder, and in addition, different primitives can have different rotation angle parameters. For simplicity of explanation, the following description will take the case of cylinders whose elements are all equal in height.
The following description is divided into three parts, namely: a training method of a super-surface property prediction model, a super-surface design method, a training device of the super-surface property prediction model and a super-surface design device.
Example 1
The present embodiment mainly describes a training method of the super surface property prediction model.
The model for predicting the nature of the hypersurface in this embodiment is a model for predicting the nature of the hypersurface by using a graph neural network, and is therefore essentially a graph neural network model. The graph neural network model can be used for predicting and analyzing the properties of the known super-surface on one hand, and can be used for carrying out reverse design according to the requirements of a design task on the other hand, namely, the design parameters of the super-surface of the target are determined according to the light field of the target, and the content of the graph neural network model is particularly developed in a super-surface design method. The description of three parts of the representation of the input data of the sub-graph neural network, the structure of the graph neural network model and the training of the model follows.
Representation of input data for a neural network
The representation of the input data of the graph neural network mainly comprises two parts, namely node characteristic representation and edge characteristic representation, and the representation is reflected before the super-surface property prediction model is trained, and corresponding training data, namely graph model sample data, is required to be acquired. The graph model sample data of the embodiment is a sparse matrix obtained by modeling the hypersurface by a time domain finite difference method, and each set of data comprises a maxwell equation set matrix a, a numerical solution matrix E and a discrete light source matrix b, wherein ae=b.
The maxwell equation set matrix a is n×n dimensions, the numerical solution matrix E and the discrete light source matrix b are both n×1 dimensions, and the corresponding number of nodes of the formable graph neural network is N, where the value of N depends on the size of the resolution of the grid point division, for example, taking a super surface of 1000 wavelengths (x direction) by 1000 wavelengths (y direction) by 1 wavelength (z direction) as an example, the resolution is divided into 10 grids for each wavelength, that is, 10 hundred million grid points can be formed.
The maxwell equation set matrix a is extremely sparse, taking a grid of 3 x 3 as an example, and the generated maxwell equation set matrix a is a matrix of 27 rows and 27 columns as shown in fig. 1, and because the maxwell equation set matrix a is a sparse matrix, only has non-zero values on diagonal lines and secondary diagonal lines, so the memory amount occupied by calculation is greatly reduced.
In the graph neural network model of the embodiment, a weighted undirected graph is designed based on an n×n-dimensional maxwell equations matrix a and an n×1-dimensional discrete light source matrix b, wherein b is used as a node, and a forms an edge weight.
Specifically, N nodes can be defined by taking the n×1-dimensional discrete light source matrix b as the node, where the characteristic attribute of the i-th node is the i-th value of the discrete light source matrix b. Since ae=b, a certain element Aij of the maxwell's equation set matrix a connects the ith and jth values of the discrete light source matrix b, so the maxwell's equation set matrix a is used as a side, the element Aij in the maxwell's equation set matrix a is used as a connecting side of the node bi and the node bj, and the numerical solution matrix E is used as a label of the graph neural network model.
The acquisition of the graph model sample data can simulate a large number of super surfaces, a Maxwell equation set matrix A and a discrete light source matrix b based on a given super surface can be directly generated, then the calculation of a numerical solution E is carried out through FDTD, namely the light field distribution of the given super surface is calculated, then the Maxwell equation set matrix A and the discrete light source matrix b are used as composition data, and the numerical solution E is used as a label for model training.
Based on the similarity of the sparse matrix of the super-surface generation matrix and the graph neural network by a time domain finite difference method, the graph structure of the graph neural network is very suitable for describing the situation, and the relation between the nodes and the edges can be flexibly represented, so that the sparsity of the problem is better captured. In addition, the sparsity of the matrix is generated by a time domain finite difference method based on the hypersurface instead of a dense matrix, so that the finite memory can process the oversized hypersurface, and the solving of the sparse matrix can be processed through the processing capacity of the existing processor.
Further, in order to further reduce the amount of computation, the following steps may be further performed in the process of generating the graph model sample data:
dividing the super surface into a plurality of sub-blocks;
and obtaining the Maxwell equation set matrix A, the numerical solution matrix E and the discrete light source matrix b corresponding to each sub-block.
Taking the above 10 hundred million lattice points as an example, the method can be divided into 100 sub-blocks, so that the size of each sub-block is 100 wavelengths (x direction) ×100 wavelengths (y direction) ×1 wavelengths, and the number of lattice points in each sub-block is in the order of tens of millions, and the calculated amount is in a square growing relationship when considering the relationship between the calculation nodes, so that the calculation amount of the dividing sub-block is further reduced.
In addition, the generation process of the graph model sample data is directly divided in space, and numerical approximation processing is not needed, so that the graph neural network model obtained based on the data training is higher in precision and meets the requirements of design tasks.
And if the subsurface property prediction model is used only for property prediction and analysis, the dielectric constants ε (x, y, z) in the meshing can be solved in the following way:
for a primitive, after being rasterized by three dimensions of x, y and z, the dielectric constant of the voxel located inside the primitive is the dielectric constant of the primitive material (such as monocrystalline silicon) itself, the dielectric constant located outside the primitive is the dielectric constant of air, and the dielectric constants of the voxels containing the inside and outside the primitive can be calculated by using weighted average.
If the subsurface property prediction model is to be used for both property prediction and analysis and to meet the requirements of the subsurface design method below, two embodiments may be included, where embodiment a continues to employ the above calculation of dielectric constants ε (x, y, z) and then calculates in conjunction with the following way of training a relational model through a neural network. The steps of another embodiment b are:
three-dimensional lattice-nodding the super surface;
determining the dielectric constant of each lattice point according to the primitive and non-primitive mediums in each lattice point, wherein the parameters of the Maxwell equation set matrix A comprise the dielectric constant;
the dielectric constant of the lattice is adjusted to be a micro-functional.
The dielectric constant established by this embodiment b is a micro-functional and, in turn, by virtue of its micro-functional nature, two examples below can design a subsurface based on the inverse of the integral operation performed by this embodiment b.
Specifically, the non-primitive medium may be air, or may be another medium filled between adjacent primitives, and if air, the dielectric constant of the non-primitive medium is the dielectric constant of air, and if another medium, the dielectric constant corresponding to the other medium. Thus, if the cells are all cells, the dielectric constant of the cells is the dielectric constant of the cells, if the cells are all non-cell media, the dielectric constant of the cells is the dielectric constant of the non-cell media, and if the cells include both the cells and the non-cell media, the dielectric constant of the cells is determined according to specific amounts of the cells and the non-cell media in the cells, for example, the calculation method of the dielectric constant of each cell may be calculated by weighting and averaging.
Taking the cylindrical element with the plurality of elements set to be equal height as an example, the step of adjusting the dielectric constant of the lattice point to be a micro-functional is described. In the calculation of the dielectric constant of the contour cylindrical element, the element size is determined by r only because of the high uniformity, so the operation can be greatly simplified and the operation speed is high. Thus, the trainable parameter of the super surface is the radius array { r } of the primitive, and the dielectric constant epsilon (x, y, z, { r } of each lattice point is adjusted to be a micro-function of the radius array { r }, where for example, by superpositionFunction and sigmoidThe function implementation can be replaced by other functions with continuous smooth properties like sigmoid functions.
In addition, if the primitive is a non-equal-height cylindrical primitive or primitives with other shapes, such as a cuboid, an elliptic cylinder, a hollowed cylinder and the like, the corresponding geometric parameters can be determined according to the characteristics of each shape, and then the dielectric constant of each lattice point is determined as a micro-function based on the corresponding geometric parameters by referring to the method.
Structure of graph neural network model
Fig. 2 is a schematic diagram of a graph neural network model of the present embodiment, which includes a graph normalization layer, a graph information convergence layer, an activation layer, and a residual layer. The graph normalization layer is used for normalizing node characteristics, so that the characteristics of nodes and edges of the graph have similar scales and distribution, and training stability and generalization performance of the model are improved; the activation layer is used for introducing nonlinear transformation, allowing the model to learn more complex functional relations, and in addition, based on the graph neural network, sparse graph data are aimed at, namely each node is only connected with a small part of other nodes, and the activation layer can generate meaningful non-zero output under the condition, so that the network is helped to effectively process sparse data.
The graph information convergence layer is used for converging neighbor information, and the information of the neighbor nodes is summarized and combined with the information of the target nodes, so that the context of the nodes in the whole graph structure is captured. The definition of the graph information convergence layer is as follows:where k is the kth iteration, W1 and W2 are trainable parameters of the model, and initial values of W1 and W2 are obtained by random initialization. E is a numerical solution, and f and g represent two nonlinear transformations, respectively. N (i) is a neighboring node, comprising a first-order neighbor, a second-order neighbor and the like, and the balance of depth and breadth information is realized according to a sampling strategy which is designed independently.
Meanwhile, the data of the graph information convergence layer and the graph model sample data are input into the residual layer, the residual layer outputs a prediction result, the residual layer is used for relieving the gradient vanishing problem, and due to the existence of jump connection, even if the graph neural network is very deep, the excessive fitting of training data can be effectively avoided, and the training speed is increased, so that the method is more suitable for the property prediction and analysis of the super surface.
In addition, the graph neural network can adopt the structure of a graph rolling neural network (GCN), the scaled augmented node characteristics are mapped to the approximate direction of the solution, and the node characteristics are processed and improved through the learning process of the graph rolling neural network so as to better represent the relevance and contribution of the nodes in the solution space, so that the model can be used for more accurately predicting or approximately solving the problem. The architecture of the graph convolutional neural network follows an encoding-process-decoding model, and sequentially sets a node encoder, m residual blocks and a decoder, wherein the node encoder is a linear Layer, the decoder is activated by a 2-Layer Multi-Layer Perceptron (MLP) and a LeakyRelu, the decoder outputs a value for each node, and solution vectors formed by all the values have permutation and the like.
The loss function loss of the graph neural network is loss= |E '-E|/E, wherein E' is the prediction result, and E is the label. Through verification, the method corresponding to the embodiment finally has high matching degree on the numerical solution E' calculated by the super surface and the label E, and the precision meets the use requirement.
The learning rate of the graph neural network adopts an adaptive decay learning rate, and the learning rate is reduced by one time after every 10 epochs. Experiments prove that the learning rate can enable training of the graph neural network model to be converged rapidly.
Based on the construction of the graph neural network model, the training method of the super surface property prediction model in the embodiment is shown in fig. 3, and includes the following steps S10-S20:
step S10: and acquiring the graph model sample data.
Step S20: training a graph neural network for predicting a numerical solution to a hypersurface.
The process sends the graph model sample data into the constructed super surface property prediction model for training, and optimizes the graph model sample data through an optimizer until a termination condition is reached, for example, the loss function is smaller than a certain value.
After model training, the light field distribution corresponding to the hypersurface can be solved based on the hypersurface property prediction model, so that subsequent other calculation is facilitated. The calculation force of the model is concentrated in a training stage, the inference process can be almost instantaneously completed, and the property prediction and analysis can be directly and quickly completed on a common single server.
In the prior art, when the FDTD method is used for solving the light field distribution, independent calculation based on the hypersurface to be calculated is needed each time, and each calculation needs longer time consumption, but the method of the embodiment can be quickly completed when the property prediction and analysis are performed on any hypersurface, so that the speed of solving the electric field is improved by 10-5-10-7 levels compared with the traditional method as described in the background art. And as shown in fig. 5, the left side of fig. 5 is a numerical solution obtained by calculating the light field distribution of the super surface by a numerical solution method, here, the result of FDTD calculation, and the right side of fig. 5 is a result obtained by predicting the light field distribution of the super surface by the super surface property prediction model of the present embodiment, and comparing two images, it can be seen that the accuracy of the super surface property prediction model obtained by the present embodiment is quite high with the fitness of the numerical solution, and the application requirements of the super surface field are satisfied.
Example two
The present embodiment mainly describes a super surface design method.
Besides being used for property prediction, the super-surface property prediction model can also be used for reversely solving the corresponding parameter condition of the super-surface according to the property. Since the super surface property prediction model has no directivity, the operation from the target numerical solution to the maxwell's equations matrix and the target discrete light source matrix is reversible and can be directly obtained. That is, based on the non-directionality of the trained subsurface property prediction model, if the input data of the subsurface property prediction model is a maxwell's equations matrix and a discrete light source matrix, the output data is a numerical solution, and if the input data is a numerical solution, the output data is a maxwell's equations matrix and a discrete light source matrix.
Specifically, the method for designing a super surface provided in this embodiment, as shown in fig. 4, includes the following steps:
step S30: obtaining a target numerical solution, wherein the target numerical solution is a numerical solution corresponding to a super surface to be designed;
step S40: based on the target numerical solution, generating a corresponding target Maxwell equation set matrix and a corresponding target discrete light source matrix through the above-mentioned super-surface property prediction model;
step S50: and deducing design parameters of the super surface according to the target Maxwell equation set matrix and the target discrete light source matrix.
Step S50 includes the following two embodiments.
Embodiment 1
Training a relation model among the design parameters, the maxwell equation set matrix and the discrete light sources through a neural network, and determining the design parameters of the super surface corresponding to the target maxwell equation set matrix and the target discrete light source matrix based on the relation model.
Embodiment 1 corresponds to embodiment a above, in which the discretized dielectric constants epsilon (x, y, z) are used in the process of meshing, then the relationship between the maxwell's equations matrix and the discrete light source matrix and the design parameters of the super-surface is learned by a relational model of the neural network, and then the design parameters of the super-surface are obtained based on the relational model.
Embodiment 2
Calculating design parameters of the super surface corresponding to the target Maxwell equation set matrix and the target discrete light source matrix through an integral function, wherein in the process of generating a sparse matrix of the super surface through a time domain finite difference method, the dielectric constant of each lattice point of the super surface after three-dimensional lattice is a micro-functional;
embodiment 2 corresponds to embodiment b above, in which a continuous, differentiable dielectric constant, e.g., dielectric constant epsilon (x, y, z, { r }), is used in the meshing process, so that the continuity thereof ensures the reversibility of the operation, and the design parameters of the corresponding hypersurface can be obtained by integral calculation.
Therefore, the super-surface property prediction model can be used for predicting properties and designing super-surfaces.
Compared with the prior art, the embodiment has the following beneficial effects:
according to the training method, the super-surface design method and the device of the super-surface property prediction model, on one hand, the graph neural network meeting the property prediction and analysis requirements is trained by utilizing the similarity between a sparse matrix generated by the super-surface through a time domain finite difference method and the graph neural network, on the other hand, the super-surface model is enabled to be possible to be processed by a limited memory through the sparsity of the matrix generated by the super-surface through the time domain finite difference method, the accuracy of a result predicted by the final graph neural network is high and is highly consistent with a real result, the follow-up utilization of the graph neural network to solve the numerical solution of a light field of the super-surface is facilitated, and the required parameter of the super-surface can be reversely designed based on the target numerical solution and the graph neural network, so that the requirements of the light field prediction and design work of the super-surface of a large number of primitives are met.
Example III
The present embodiment mainly describes a training device for a subsurface property analysis model.
In one embodiment, a training apparatus for a subsurface property prediction model is provided, as shown in FIG. 6. The training device of the super-surface property prediction model comprises modules and specific functions of each module are as follows:
the first acquisition module is used for acquiring graph model sample data, wherein each group of data in the graph model sample data is a sparse matrix generated by a hypersurface through a time domain finite difference method, each group of data respectively comprises a maxwell equation set matrix A, a numerical solution matrix E and a discrete light source matrix b, wherein the maxwell equation set matrix A, the numerical solution matrix E and the discrete light source matrix b are sparse matrices obtained by modeling the hypersurface through the time domain finite difference method, and AE=b;
the model training module is configured to train a graph neural network by using the discrete light source matrix b as a node, the maxwell equation set matrix a as an edge, the numerical solution matrix E as a label, wherein an element Aij in the maxwell equation set matrix a is used as a connecting edge of the node bi and the node bj, and the graph neural network is used for predicting the numerical solution to the hypersurface.
Example IV
This embodiment mainly describes a super surface design apparatus.
In one embodiment, a super surface design apparatus is provided, as shown in FIG. 7. The super surface design device comprises modules and specific functions of the modules as follows:
the second acquisition module is used for acquiring a target numerical solution, wherein the target numerical solution is a numerical solution corresponding to the super surface to be designed;
the reverse analysis module is used for generating a corresponding target Maxwell equation set matrix and a corresponding target discrete light source matrix through the above-mentioned super-surface property prediction model based on the target numerical solution;
and the deducing module is used for deducing the design parameters of the super surface according to the target Maxwell equation set matrix and the target discrete light source matrix.
It should be noted that, for details not disclosed in the training device and the super-surface design device of the super-surface property prediction model in the embodiments of the present invention, please refer to details disclosed in the training method and the super-surface design method of the super-surface property prediction model in the embodiments of the present invention.
The training device and the subsurface design device of the subsurface property prediction model may further include a computing device such as a computer, a notebook, a palm computer, and a cloud server, and include, but are not limited to, a processing module, a storage module, and a computer program stored in the storage module and executable on the processing module, for example, the above-mentioned training method and subsurface design method program of the subsurface property prediction model. The processing module, when executing the computer program, implements the steps in the embodiments of the training method and the subsurface design method of each subsurface property prediction model described above, such as the steps shown in fig. 3 and 4.
In addition, the invention also provides electronic equipment, which comprises a storage module and a processing module, wherein the processing module can realize the steps in the training method and the super-surface design method of the super-surface property analysis model when executing the computer program, namely, realize the steps in any technical scheme in the training method and the super-surface design method of the super-surface property prediction model.
The electronic device may be part of a training device and a super-surface design device integrated in the super-surface property prediction model, or may be a local terminal device, or may be part of a cloud server.
The processing module may be a central processing unit (Central Processing Unit, CPU), but may also be other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), off-the-shelf programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. The general purpose processor may be a microprocessor, but in the alternative, it may be any conventional processor. The processing module is a control center of the training device and the super-surface design device of the super-surface property prediction model, and various interfaces and lines are utilized to connect various parts of the training device and the super-surface design device of the whole super-surface property prediction model.
The memory module may be used to store the computer program and/or module, and the processing module may implement various functions of the training device and the subsurface design device of the subsurface property prediction model by running or executing the computer program and/or module stored in the memory module and invoking data stored in the memory module. The memory module may mainly include a memory program area and a memory data area, wherein the memory program area may store an operating system, application programs required for at least one function, and the like. In addition, the memory module may include high-speed random access memory, and may also include non-volatile memory, such as a hard disk, memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash Card (Flash Card), at least one disk storage device, a Flash memory device, or other volatile solid-state storage device.
The computer program may be divided into one or more modules/units, which are stored in a storage module and executed by a processing module to accomplish the present invention, for example. The one or more modules/units may be a series of computer program instruction segments capable of performing specific functions for describing the execution of the computer program in a training apparatus and a subsurface design apparatus of a subsurface property prediction model.
Further, an embodiment of the present invention provides a readable storage medium storing a computer program, where the computer program can implement the steps in the above-described method for training a super-surface property prediction model and method for designing a super-surface, that is, implement the steps in any one of the above-described method for training a super-surface property prediction model and method for designing a super-surface when executed by a processing module.
The modules of the training method and the super-surface design method of the super-surface property prediction model, if implemented in the form of software functional units and sold or used as independent products, may be stored in a computer-readable storage medium. Based on such understanding, the present invention may implement all or part of the flow of the method of the above embodiment, or may be implemented by a computer program to instruct related hardware, where the computer program may be stored in a computer readable storage medium, and the computer program may implement the steps of each of the method embodiments described above when executed by the processing module.
Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. The computer readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a U-disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random-access Memory (RAM, random Access Memory), an electrical carrier signal, a telecommunication signal, a software distribution medium, and so forth. It should be noted that the computer readable medium contains content that can be appropriately scaled according to the requirements of jurisdictions in which such content is subject to legislation and patent practice, such as in certain jurisdictions in which such content is subject to legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunication signals.
It should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is for clarity only, and that the skilled artisan should recognize that the embodiments may be combined as appropriate to form other embodiments that will be understood by those skilled in the art.
The above list of detailed descriptions is only specific to practical embodiments of the present invention, and they are not intended to limit the scope of the present invention, and all equivalent embodiments or modifications that do not depart from the spirit of the present invention should be included in the scope of the present invention.
Claims (13)
1. The training method of the super-surface property prediction model is characterized by comprising the following steps of:
obtaining graph model sample data, wherein each group of data in the graph model sample data comprises a maxwell's equation set matrix A, a numerical solution matrix E and a discrete light source matrix b, wherein the maxwell's equation set matrix A, the numerical solution matrix E and the discrete light source matrix b are sparse matrixes obtained by modeling the super surface through a time domain finite difference method, and AE=b;
and training a graph neural network by taking the discrete light source matrix b as a node, taking the Maxwell equation set matrix A as an edge, taking the numerical solution matrix E as a label, wherein elements Aij in the Maxwell equation set matrix A are taken as continuous edges of the node bi and the node bj, and the graph neural network is used for predicting the numerical solution of the super surface.
2. The method of claim 1, wherein the obtaining graph model sample data comprises:
dividing the super surface into a plurality of sub-blocks;
and obtaining the Maxwell equation set matrix A, the numerical solution matrix E and the discrete light source matrix b corresponding to each sub-block.
3. The method of training a model of a subsurface property prediction according to claim 1 or 2, wherein the subsurface comprises a plurality of primitives, and the step of obtaining graph model sample data comprises:
three-dimensional lattice-nodding the super surface;
determining the dielectric constant of each lattice point according to the primitive and non-primitive mediums in the lattice point, wherein the parameters of the Maxwell equation set matrix A comprise the dielectric constant;
the dielectric constant of the lattice is adjusted to be a micro-functional.
4. A method of training a model of a subsurface property prediction according to claim 3, wherein the plurality of primitives are arranged as equal-height cylindrical primitives, and the trainable parameter of the subsurface is the radius array { r } of the primitives;
the adjusting the dielectric constant of the lattice point to be a micro-functionable includes:
the dielectric constant epsilon (x, y, z, { r }) of each lattice point is adjusted to be a microtechnical of the radius array { r }.
5. The method of claim 1, wherein the graph neural network comprises a graph information convergence layer defined as:
wherein k is the k-th iteration round, W1 and W2 are trainable parameters of the model, N (i) is a neighboring node, E is a numerical solution, and f and g represent two nonlinear transformations respectively.
6. The method according to claim 5, wherein the graph neural network further comprises a residual layer, and the data of the graph information convergence layer and the graph model sample data are input to the residual layer, and the residual layer outputs a prediction result.
7. The method of claim 6, wherein the loss function loss of the graph neural network is loss= |e '-e|/E, where E' is the prediction result and E is the label.
8. A method of subsurface design, comprising the steps of:
obtaining a target numerical solution, wherein the target numerical solution is a numerical solution corresponding to a super surface to be designed;
generating a corresponding target maxwell's equations matrix and a target discrete light source matrix by the super surface property prediction model of any one of claims 1-7 based on the target numerical solution;
and deducing design parameters of the super surface according to the target Maxwell equation set matrix and the target discrete light source matrix.
9. The method of claim 8, wherein the step of inferring design parameters for the subsurface from the target maxwell's equations matrix and target discrete light source matrix comprises:
calculating design parameters of the super surface corresponding to the target Maxwell equation set matrix and the target discrete light source matrix through an integral function, wherein in the process of generating a sparse matrix of the super surface through a time domain finite difference method, the dielectric constant of each lattice point of the super surface after three-dimensional lattice is a micro-functional;
or,
training a relation model among the design parameters, the maxwell equation set matrix and the discrete light sources through a neural network, and determining the design parameters of the super surface corresponding to the target maxwell equation set matrix and the target discrete light source matrix based on the relation model.
10. A training device for a super-surface property prediction model, comprising:
the first acquisition module is used for acquiring graph model sample data, wherein each group of data in the graph model sample data is a sparse matrix generated by a hypersurface through a time domain finite difference method, each group of data respectively comprises a maxwell equation set matrix A, a numerical solution matrix E and a discrete light source matrix b, wherein the maxwell equation set matrix A, the numerical solution matrix E and the discrete light source matrix b are sparse matrices obtained by modeling the hypersurface through the time domain finite difference method, and AE=b;
the model training module is used for taking the discrete light source matrix b as a node, taking the Maxwell equation set matrix A as an edge, taking the numerical solution matrix E as a label, and training a graph neural network, wherein elements Aij in the Maxwell equation set matrix A are taken as the continuous edges of the node bi and the node bj, and the graph neural network is used for predicting the numerical solution of the super surface.
11. A super surface design apparatus, comprising the steps of:
the second acquisition module is used for acquiring a target numerical solution, wherein the target numerical solution is a numerical solution corresponding to the super surface to be designed;
a reverse analysis module, configured to generate a corresponding target maxwell's equations matrix and a target discrete light source matrix by the super surface property prediction model according to any one of claims 1 to 7 based on the target numerical solution;
and the deducing module is used for deducing the design parameters of the super surface according to the target Maxwell equation set matrix and the target discrete light source matrix.
12. An electronic device, comprising:
a storage module storing a computer program;
processing module for implementing the training method of the model for predicting the properties of a subsurface according to any one of claims 1 to 7 or the steps of the method for designing a subsurface according to any one of claims 8 to 9 when executing the computer program.
13. A readable storage medium storing a computer program, wherein the computer program, when executed by a processing module, implements the method of training the model of subsurface property prediction of any one of claims 1 to 7 or the steps of the method of subsurface design of any one of claims 8 to 9.
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