CN111581886A - Electromagnetic field rapid simulation solving method based on convolutional neural network parallel acceleration - Google Patents

Electromagnetic field rapid simulation solving method based on convolutional neural network parallel acceleration Download PDF

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CN111581886A
CN111581886A CN202010397940.4A CN202010397940A CN111581886A CN 111581886 A CN111581886 A CN 111581886A CN 202010397940 A CN202010397940 A CN 202010397940A CN 111581886 A CN111581886 A CN 111581886A
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郭良帅
魏飞鸣
何鸿飞
许勇刚
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Abstract

The invention discloses an electromagnetic field rapid simulation solving method based on convolution neural network parallel acceleration, which is used for carrying out rapid solving aiming at a matrix equation of an electromagnetic field moment method (MoM), converting an electromagnetic field simulation solving problem into a convex optimization problem in a neural network, and then carrying out reverse iteration solving by utilizing a neural network acceleration algorithm, thereby greatly improving the parallel efficiency and saving the simulation solving time. The method has strong adaptability, strong adaptability and novel viewpoint, greatly improves the electromagnetic field simulation solving time, and provides an effective technical means for obtaining target electromagnetic scattering characteristic data and electromagnetic compatibility analysis.

Description

Electromagnetic field rapid simulation solving method based on convolutional neural network parallel acceleration
Technical Field
The invention relates to an electromagnetic field efficient and rapid simulation solving method, in particular to an electromagnetic field rapid simulation solving method based on convolutional neural network parallel acceleration.
Background
The method has important theoretical significance and practical value for rapid simulation modeling of the electromagnetic characteristics of the complex target. As early as 80 s in the last century, some countries apply the electromagnetic simulation modeling technology to airplane stealth design and missile penetration performance analysis, thereby greatly saving development cost and research period. The computer simulation modeling technology can be used for revealing an electromagnetic field propagation mechanism, and has irreplaceable effects on electromagnetic interference and electromagnetic compatibility analysis in a complex electromagnetic environment.
With the continuous increase of the scale of the electromagnetic solving problem, the conventional electromagnetic field numerical solving technology faces the bottlenecks of large consumption of computing resources and slow iterative solving time, and the related application is greatly limited. Wherein the limitation of the solution time becomes a key factor for restricting the relevant design and analysis. In the aspect of electromagnetic field rapid simulation modeling, the multilayer rapid multipole technique (MLFMA), the adaptive cross approximation method (ACA), the finite element area decomposition algorithm (FEM-DG) and the like based on the integral equation greatly improve the related computing capability, but still cannot meet increasingly complex engineering requirements.
The non-patent document "inquiring the application of deep learning for electronic simulation prediction", published in SPIE conference by Stven R.Rice et al in 2018, utilizes deep learning simulation to develop dual-station RCS prediction based on target geometric shape, predicts online learning of a network model, and then utilizes online network prediction to greatly improve target characteristic simulation efficiency. The method is different from the traditional numerical iterative computation method, and the target double-station RCS acquisition is carried out by means of the learning and predicting capability of the neural network architecture, so that the target electromagnetic field double-station scattering speed is greatly improved. However, the method has the problems of uncontrollable error, uncertain prediction precision and the like.
In 2019, a non-patent document ' Study on ambient conditional Neural Network Based FDTD Method ' published in ACES2019 conference by Kuo Liangshuai, Li \25035; ' Kun, and the like discloses an FDTD efficient parallel Method Based on cyclic convolution Neural Network acceleration, thereby greatly improving the parallel efficiency of FDTD and keeping the simulation calculation precision of FDTD. However, the document only considers the function of a single card on a single machine, is limited by the size of a GPU memory, and cannot solve the problem of solving an electromagnetic field with large electrical size.
A Time-harmonic field region Decomposition algorithm of a High-Order basis function is introduced in a non-patent document 'Domain Decomposition Methods for Time-harmonic electronic Waves With High-Order ground Forms' published in IEEE Transactions on magnetic by Nicolas Marsic, Caledonia Waltz and the like in 2016, and the effectiveness of region Decomposition combined With the High-Order basis function for solving an electromagnetic environment effect is verified through electromagnetic field convergence speed simulation analysis of different-Order basis functions. The method greatly improves the electromagnetic field solving capability from an algorithm equation, but the algorithm framework is separated from a computer framework, and the efficiency improvement is limited.
Disclosure of Invention
The invention aims to provide an electromagnetic field rapid simulation solving method based on convolution neural network parallel acceleration, which is used for solving the problems of slow simulation time and low parallel efficiency in the prior art and providing technical means and data support for the electromagnetic characteristic simulation modeling of a complex target.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a quick electromagnetic field simulation solving method based on convolutional neural network parallel acceleration is characterized by comprising the following steps:
s1, dispersing the geometric shape of the target by adopting local grid cells, defining local electromagnetic current basis functions on the cells, representing the induced electromagnetic current on the target under external excitation by linear combination of the basis functions on each small cell, wherein the coefficient of each basis function is an unknown induced electromagnetic current coefficient to be solved; establishing an electromagnetic field matrix equation by combining a Maxwell integral equation to form a numerical solution which can be used for describing a complex target electromagnetic field solving problem;
s2, equating an electromagnetic field moment method MoM matrix equation according to a convolutional neural network architecture, carrying out tensor grouping on an original impedance matrix, an unknown current induction coefficient vector and an excitation vector, and converting the original matrix equation solving problem into a neural network optimization problem;
s3, establishing a square root relative error as a neural network loss function, developing optimization solution by combining a backward gradient descent algorithm, developing optimization calculation by adopting an exponential descent update step strategy, and realizing rapid solution of an electromagnetic field matrix equation under a network architecture;
and S4, carrying out electromagnetic field simulation calculation at any spatial position by using the unknown induced electromagnetic current coefficient obtained by optimization in the step S3.
Preferably, the step S1 further includes:
local basis function fn(r) is RWG basis functions, which are defined on two triangular patches with adjacent edges, and the specific form is as follows:
Figure BDA0002488276910000031
wherein, the RWG basis functions correspond to two triangular patches; r is a position vector inside the triangular patch; rho is a position vector from a vertex corresponding to a side of the triangle to r; l isnIs the side length;
Figure BDA0002488276910000032
is the area of two adjacent triangles,
Figure BDA0002488276910000033
two adjacent triangles.
Preferably, the step S1 further includes:
for any metal target, the integral formula of the frequency domain scattered field is obtained as follows:
Figure BDA0002488276910000034
wherein k is the wave number of incident electromagnetic waves; integral multiple ofsdr' is the integral over current source s;
Figure BDA0002488276910000038
is the angular frequency; j (r) target epi-induced current; j is an imaginary unit; r is the spatial fringe fieldA position vector; r' is a current source position vector on the target;
Figure BDA0002488276910000035
is a field point gradient operator;
Figure BDA0002488276910000036
a source point divergence operator; the subscript t represents the tangential projection; g (r, r') -ejk|r-r'|/(4π|r-r'|)。
Preferably, the step S1 further includes:
the matrix equation for a metal target surface is as follows:
ZN×NIN×1＝BN×1(3)
in the formula, ZN×NIs an impedance matrix; i isN×1Is an unknown coefficient vector; b isN×1Is an excitation vector; n is the number of the basis functions, and the specific form is as follows:
Figure BDA0002488276910000037
I＝[a1,a2,.....,an]T(5)
Figure BDA0002488276910000041
wherein z ismnIs the value at position (m, n) in the impedance matrix; sm,SnRespectively corresponding integration regions of the mth basis function and the nth test function; a is1,a2,.....,anThe expansion coefficient corresponding to each basis function is the unknown induction electromagnetic current coefficient to be solved; f. ofm(r),fn(r') are the corresponding mth basis function and nth test function, respectively; bnThe excitation element corresponding to the nth test function; eiAnd (r) is an excitation electric field.
Preferably, the step S2 further includes:
the convolutional neural network CNN comprises a convolutional layer, a pooling layer full-connection layer and a loss layer;
the convolution layer in the convolution neural network comprises a convolution kernel, the digital image is a two-dimensional discrete signal, the convolution operation is carried out in a mode that the convolution kernel slides on the image, values of pixel points of the image are multiplied by numerical values on the convolution kernel, and then multiplication results are added to obtain pixel values of corresponding positions on an output characteristic image, and the method comprises the following steps:
Figure BDA0002488276910000042
in the formula, ym,nIs the pixel value at (m, n) on the output map; m and N are respectively the length and the width of the output graph; b represents an offset; i and J are respectively the length and the width of a convolution kernel;
Figure BDA0002488276910000043
is the weight;
for matrix equation (3), based on the parallel architecture of convolutional neural network CNN, unknown coefficient vector I is processedN×1Writing into a convolution kernel form, performing tensor quantization, maximally utilizing a matching hardware architecture, simultaneously taking data of each row of the matrix as network training data, enabling the sizes of the large convolution kernel and the small convolution kernel of each matrix block to be consistent, and taking an excitation vector as the output of a convolution neural network.
Preferably, the step S3 further includes:
the loss function set for solving the problem of the MoM matrix equation is:
Figure BDA0002488276910000051
wherein | · | purple sweet2Is the 2 norm of the vector with the corresponding gradient:
Figure BDA0002488276910000052
carrying out optimization solution on the equation (8) according to a gradient descent method, wherein the selected optimization iteration method is an adaptive moment estimation Adam method, and the method comprises the following specific steps:
Figure BDA0002488276910000053
wherein, β1,β2The number is a hyper-parameter, n is an iteration number, and η is a parameter updating step length;
Figure BDA0002488276910000054
second moment of the gradient of the loss function; v. ofnRepresenting a correction factor based on a gradient correction; snRepresenting a second moment based correction factor.
Preferably, the step S3 further includes:
step size ηnThe updating method comprises the following steps:
ηn＝a·pn/l(11)
in the formula, a is the initial update length; p is an attenuation factor; l is an exponential decay constant;
substituting equation (11) into equation (10) results in an MoM-Adam optimization solution algorithm that decays with the number of update steps.
Compared with the prior art, the invention has the beneficial effects that: the electromagnetic field rapid simulation solving method based on the convolutional neural network parallel acceleration can solve the problems of slow simulation time and low parallel efficiency in the prior art, and provides technical means and data support for the electromagnetic characteristic simulation modeling of the complex target.
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FIG. 1 is a flow chart of the fast electromagnetic field solving method based on the convolutional neural network of the present invention;
FIG. 2 is a diagram of RWG basis functions defined on adjacent edges of the invention;
FIG. 3 is a schematic diagram of a matrix equation of the MoM (moment of electromagnetic field method) of the present invention;
FIG. 4 is a schematic diagram of a multi-layer convolutional neural network of the present invention;
FIG. 5 is a CNN-MoM neural network architecture of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in FIG. 1, the invention provides a method for solving electromagnetic field rapid simulation based on convolutional neural network parallel acceleration, which comprises the following steps:
s1, according to the solving problem, the geometric shape of the target adopts the discrete local grid cells, local electromagnetic current basis functions are defined on the cells, and the induced electromagnetic current on the target under external excitation is characterized through the linear combination of the basis functions on each small cell (the coefficient of each basis function is the unknown induced electromagnetic current coefficient to be solved); and establishing an electromagnetic field matrix equation by combining a Maxwell integral equation to form a numerical solution which can be used for describing a complex target electromagnetic field solving problem. Wherein, discrete units of FDTD (finite difference time domain) are triangular grids, and RWG basis functions are defined on the sides of adjacent units.
In step S1, the local basis functions defined on each small cell are RWG basis functions, as shown in fig. 2, the RWG basis functions are defined on two triangles with adjacent sides, and since the derivative of the RWG basis function is 0 and the normal component of the RWG basis function is 1, the continuity of the current is ensured and no charge is accumulated, and the specific form is:
Figure BDA0002488276910000061
wherein r is a position vector inside the triangular patch; rho is a position vector from a vertex corresponding to a side of the triangle to r; l isnIs the side length;
Figure BDA0002488276910000062
is the area of two adjacent triangles,
Figure BDA0002488276910000063
two adjacent triangles.
For any metal target, a frequency domain scattering field integral formula can be obtained according to a Maxwell equation set and metal boundary conditions as follows:
Figure BDA0002488276910000071
wherein k is the wave number of incident electromagnetic waves; integral multiple ofsdr' is the integral over current source s;
Figure BDA0002488276910000076
is the angular frequency; j (r) target epi-induced current; j is an imaginary unit; r is a spatial scattering field position vector; r' is a current source position vector on the target;
Figure BDA0002488276910000072
is a field point gradient operator;
Figure BDA0002488276910000073
a source point divergence operator; the subscript t represents the tangential projection; g (r, r') -ejk|r-r'|/(4π|r-r'|)。
By matching the target dispersion with the test function, a matrix equation of the metal surface can be obtained, as shown in fig. 3:
ZN×NIN×1＝BN×1(3)
in the formula, ZN×NIs an impedance matrix; i isN×1Is an unknown coefficient vector; b isN×1Is an excitation vector; n is the number of the basis functions, and the specific form is as follows:
Figure BDA0002488276910000074
I＝[a1,a2,.....,an]T(5)
Figure BDA0002488276910000075
wherein z ismnIs the value at position (m, n) in the impedance matrix; sm,SnRespectively corresponding integration regions of the mth basis function and the nth test function; a is1,a2,.....,anThe expansion coefficient corresponding to each basis function is the unknown induction electromagnetic current coefficient to be solved; f. ofm(r),fn(r') is the test function corresponding to the mth basis function and the nth, respectively, in the specific form of RWG basis function; bnThe excitation element corresponding to the nth test function; eiAnd (r) is an excitation electric field.
S2, carrying out equivalence on the matrix equation (3) strictly according to a Convolutional Neural Network (CNN) architecture, and carrying out equivalence on an original impedance matrix, an unknown current induction coefficient vector I and an excitation vector BN×1And performing tensor grouping, and converting a starting matrix equation solving problem into a neural network optimization problem.
In step S2, the Convolutional Neural Network (CNN) is most often used for analyzing visual images, and local connections and weight sharing are used to reduce the complexity of the model, greatly reduce training parameters, improve training speed, and improve generalization ability to a certain extent. A typical convolutional neural network structure mainly includes convolutional layers, pooling layers, full-link layers, and lossy layers, etc., as shown in fig. 4. The present invention is not limited to the convolutional neural network structure shown in fig. 4.
The main component in the convolution layer in the convolution neural network is convolution kernel, the digital image is two-dimensional discrete signal, the convolution operation is carried out on the digital image in such a way that the convolution kernel slides on the image, the values of the pixel points of the image are multiplied by the numerical values on the convolution kernel, and then the multiplication results are added to obtain the pixel values of the corresponding positions on the output characteristic diagram.
Figure BDA0002488276910000081
In the formula, ym,nIs the pixel value at (m, n) on the output map; m and N are respectively the length and the width of the output graph; b represents an offset; i and J are respectively the length and the width of a convolution kernel;
Figure BDA0002488276910000082
is a weight value.
For the matrix equation (3), the most time-consuming operation in the conventional solution method is the complex multiplication operation of the matrix and the vector, and the solution efficiency of the MoM simulation is greatly reduced. The parallel architecture based on CNN is to use unknown coefficient vector IN×1Writing into a convolution kernel form, performing tensor quantization, and maximally utilizing a matching hardware architecture. And simultaneously, taking the data of each row of the impedance matrix as network training data. The sizes of the convolution kernels of the sizes of each matrix block are consistent, and the excitation vector is regarded as the output of the network. The structure of the established two-layer neural network is shown in fig. 5, the first layer is convolution operation, and the second layer finishes data collection.
In the invention, the input of the equivalent network is a tensor form of an impedance matrix, the original complex impedance matrix is represented by two real number tensors, and the induced electromagnetic current coefficient vector to be solved of the original complex number is represented by two real number tensors. To adapt to neural network training under tensor architecture.
S3, establishing a square root relative error as a neural network loss function, developing optimization solution by combining a backward gradient descent algorithm, developing optimization calculation by adopting an exponential descent update step strategy, and realizing rapid solution of an electromagnetic field matrix equation under a network architecture.
Illustratively, the set loss function for solving the problem for the MoM matrix equation is:
Figure BDA0002488276910000091
wherein | · | purple sweet2Is the 2 norm of the vector with the corresponding gradient:
Figure BDA0002488276910000092
carrying out optimization solution on the equation (8) according to a gradient descent method, wherein the selected optimization iteration method is an adaptive moment estimation (Adam) method, and the method comprises the following specific steps:
Figure BDA0002488276910000093
wherein, β1,β2Typically β for superparametric1＝0.9,β2＝0.99,＝1.0e-10N is the number of iteration times, η is the parameter updating step length;
Figure BDA0002488276910000094
second moment of the gradient of the loss function; v. ofnRepresenting correction factors, s, based on gradient correctionnRepresenting a second moment based correction factor.
The method adopts an adaptive moment estimation (Adam) method to carry out backward gradient optimization, and utilizes a step length updating strategy of exponential descent; the Adam algorithm considers the effect of the exponential average of the gradient and the exponential average of the gradient square on the step length at the same time, so that the method has excellent convergence performance.
In the formula (10), the target updating step length is updated only by the gradient information at the previous moment, which is still insufficient, and the rapid optimization of a complex target electromagnetic field matrix equation (with a poor condition number and slow convergence) under most conditions cannot be met, so that the method adopts an exponential descent method to artificially correct the optimization process, and simultaneously combines the matrix gradient information and artificial prior to design, thereby greatly improving the Adam convergence speed.
Step size ηnThe updating method comprises the following steps:
ηn＝a·pn/l(11)
where a is the initial update length, and is generally selected to be 1.0e in the solution of the MoM matrix equation-5(ii) a p is an attenuation factor, and is generally selected to be 0.8-0.9; l is an exponential decay constant, and is generally selected to be 50-70.
And (3) substituting the equation (11) into the equation (10) to obtain the MoM-Adam optimization solution algorithm which attenuates along with the updating step number.
And S4, substituting the unknown coefficients of the induced electromagnetic currents obtained through optimization in the step S3 into a formula (2) to carry out electromagnetic field simulation calculation at any spatial position (such as an internal field or an external radiation field), specifically, expanding induced currents J (r) into linear combination of local basis functions, and then carrying out integral operation to provide data basis for correlation analysis.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (7)

1. A quick electromagnetic field simulation solving method based on convolutional neural network parallel acceleration is characterized by comprising the following steps:
s1, dispersing the geometric shape of the target by adopting local grid cells, defining local electromagnetic current basis functions on the cells, representing the induced electromagnetic current on the target under external excitation by linear combination of the basis functions on each small cell, wherein the coefficient of each basis function is an unknown induced electromagnetic current coefficient to be solved; establishing an electromagnetic field matrix equation by combining a Maxwell integral equation to form a numerical solution which can be used for describing a complex target electromagnetic field solving problem;
s2, equating an electromagnetic field moment method MoM matrix equation according to a convolutional neural network architecture, carrying out tensor grouping on an original impedance matrix, an unknown current induction coefficient vector and an excitation vector, and converting the original matrix equation solving problem into a neural network optimization problem;
s3, establishing a square root relative error as a neural network loss function, developing optimization solution by combining a backward gradient descent algorithm, developing optimization calculation by adopting an exponential descent update step strategy, and realizing rapid solution of an electromagnetic field matrix equation under a network architecture;
and S4, carrying out electromagnetic field simulation calculation at any spatial position by using the unknown induced electromagnetic current coefficient obtained by optimization in the step S3.
2. The electromagnetic field rapid simulation solving method of claim 1,
the step S1 further includes:
local basis function fn(r) is RWG basis functions, which are defined on two triangular patches with adjacent edges, and the specific form is as follows:
Figure FDA0002488276900000011
wherein, the RWG basis functions correspond to two triangular patches; r is a position vector inside the triangular patch; rho is a position vector from a vertex corresponding to a side of the triangle to r; l isnIs the side length;
Figure FDA0002488276900000012
is the area of two adjacent triangles,
Figure FDA0002488276900000013
two adjacent triangles.
3. The electromagnetic field rapid simulation solving method of claim 2,
the step S1 further includes:
for any metal target, the integral formula of the frequency domain scattered field is obtained as follows:
Figure FDA0002488276900000021
wherein k is the wave number of incident electromagnetic waves; integral multiple ofsdr' is the integral over current source s;
Figure FDA0002488276900000026
is the angular frequency; j (r) target epi-induced current; j is an imaginary unit; r is a spatial scattering field position vector; r' is a current source position vector on the target;
Figure FDA0002488276900000022
is a field point gradient operator;
Figure FDA0002488276900000023
a source point divergence operator; the subscript t represents the tangential projection; g (r, r') -ejk|r-r'|/(4π|r-r'|)。
4. The electromagnetic field rapid simulation solving method of claim 3,
the step S1 further includes:
the matrix equation for a metal target surface is as follows:
ZN×NIN×1＝BN×1(3)
in the formula, ZN×NIs an impedance matrix; i isN×1Is an unknown coefficient vector; b isN×1Is an excitation vector; n is the number of the basis functions, and the specific form is as follows:
Figure FDA0002488276900000024
I＝[a1,a2,.....,an]T(5)
Figure FDA0002488276900000025
wherein z ismnIs the value at position (m, n) in the impedance matrix; sm,SnRespectively corresponding integration regions of the mth basis function and the nth test function; a is1,a2,.....,anThe expansion coefficient corresponding to each basis function is the unknown induction electromagnetic current coefficient to be solved; f. ofm(r),fn(r') are the corresponding mth basis function and nth test function, respectively; bnThe excitation element corresponding to the nth test function; eiAnd (r) is an excitation electric field.
5. The electromagnetic field rapid simulation solving method of claim 4,
the step S2 further includes:
the convolutional neural network CNN comprises a convolutional layer, a pooling layer full-connection layer and a loss layer;
the convolution layer in the convolution neural network comprises a convolution kernel, the digital image is a two-dimensional discrete signal, the convolution operation is carried out in a mode that the convolution kernel slides on the image, values of pixel points of the image are multiplied by numerical values on the convolution kernel, and then multiplication results are added to obtain pixel values of corresponding positions on an output characteristic image, and the method comprises the following steps:
Figure FDA0002488276900000031
in the formula, ym,nIs the pixel value at (m, n) on the output map; m and N are respectively the length and the width of the output graph;
b represents an offset; i and J are respectively the length and the width of a convolution kernel;
Figure FDA0002488276900000032
is the weight;
for matrix equation (3), based on the parallel architecture of convolutional neural network CNN, unknown coefficient vector I is processedN×1Writing into a convolution kernel form, performing tensor quantization, maximally utilizing a matching hardware architecture, simultaneously taking data of each row of the matrix as network training data, enabling the sizes of the large convolution kernel and the small convolution kernel of each matrix block to be consistent, and taking an excitation vector as the output of a convolution neural network.
6. The electromagnetic field rapid simulation solving method of claim 5,
the step S3 further includes:
the loss function set for solving the problem of the MoM matrix equation is:
Figure FDA0002488276900000033
wherein | · | purple sweet2Is the 2 norm of the vector with the corresponding gradient:
Figure FDA0002488276900000034
carrying out optimization solution on the equation (8) according to a gradient descent method, wherein the selected optimization iteration method is an adaptive moment estimation Adam method, and the method comprises the following specific steps:
Figure FDA0002488276900000041
wherein, β1,β2The number is a hyper-parameter, n is an iteration number, and η is a parameter updating step length;
Figure FDA0002488276900000042
second moment of the gradient of the loss function; v. ofnRepresenting a correction factor based on a gradient correction; snRepresenting a second moment based correction factor.
7. The electromagnetic field rapid simulation solving method of claim 6,
the step S3 further includes:
step size ηnThe updating method comprises the following steps:
ηn＝a·pn/l(11)
in the formula, a is the initial update length; p is an attenuation factor; l is an exponential decay constant;
substituting equation (11) into equation (10) results in an MoM-Adam optimization solution algorithm that decays with the number of update steps.
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CN112906325A (en) * 2021-04-21 2021-06-04 湖北九同方微电子有限公司 Electromagnetic field quick solver for large scale integrated circuit
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CN112526476A (en) * 2020-12-21 2021-03-19 上海无线电设备研究所 Radar target identification method based on resonance scattering echo signals
CN112906325A (en) * 2021-04-21 2021-06-04 湖北九同方微电子有限公司 Electromagnetic field quick solver for large scale integrated circuit
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CN113821947A (en) * 2021-07-29 2021-12-21 清华大学 Time domain finite difference fast solving method based on cyclic convolution neural network
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CN115935802A (en) * 2022-11-23 2023-04-07 中国人民解放军军事科学院国防科技创新研究院 Electromagnetic scattering boundary element calculation method and device, electronic equipment and storage medium
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CN116451584A (en) * 2023-04-23 2023-07-18 广东云湃科技有限责任公司 Thermal stress prediction method and system based on neural network
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CN117892097A (en) * 2024-03-14 2024-04-16 陕西省杂交油菜研究中心 Rape chemical killing effect evaluation method and system based on big data
CN117892097B (en) * 2024-03-14 2024-05-28 陕西省杂交油菜研究中心 Rape chemical killing effect evaluation method and system based on big data

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