CN110826289B - Deep learning-based nano structure design method - Google Patents
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Abstract
The invention provides a nano-structure design method based on deep learning, which comprises the following steps: establishing a training data set containing any one kind of nano-structure information; preprocessing the training data set to transpose and normalize the data in the training data set; constructing a Spectrum Prediction Network (SPN) and a geometric shape prediction network (GPN); integrating the spectrum prediction network SPN and the geometric shape prediction network GPN into a neural network model, wherein the output of the spectrum prediction network SPN is connected with the input of the geometric shape prediction network GPN; training the integrated neural network model by using the preprocessed training data set, and finishing the training of the neural network model when the loss function reaches a preset value; inputting the frequency spectrums and the material properties of the X and Y polarization directions corresponding to the nano structure to be established into the trained neural network model, so as to obtain 8 nano structure characterization points of the nano structure and further obtain the geometric shape of the nano structure.
Description
Technical Field
The invention belongs to the technical field of nanophotonics and deep learning, and particularly relates to a nanostructure design method based on deep learning.
Background
In recent years, the field of nanophotonics has revolutionized the field of optics by manipulating photon-to-substance interactions on sub-wavelength structures. However, nanostructured materials require extensive manual manufacturing, and therefore the spectra and structure of the envisaged cell surface must be accurately predicted in advance. This is limited by complex iterative processes, loop modeling, nanofabrication and nanotechnology. The underlying reason for this is that the complex physical mechanisms that describe these light-substance interactions on the nanoscale cannot be solved with generalized theory, so predicting the optical properties and approximate structure of a material relies on advanced iterative calculations achieved by Finite Element Modeling (FEM) or Finite Difference Time Domain (FDTD) methods.
On the other hand, more obvious reverse design problems exist, namely, corresponding nano structures are designed according to the required spectral response; this class of problems has a high degree of non-linearity, which is almost impossible to accomplish even the most advanced numerical calculation methods; at the same time, computer science has been leveraged to address challenging tasks such as design and characterization in nanophotonic imaging. The main method comprises the following steps: 1. and (4) enhancing the target. 2. Imaging and characterization outside the diffraction limit range (super resolution techniques, such as PALM and STORM techniques). The deep learning method is a characterization learning technology formed by combining nonlinear models, and converts the characterization of the upper level into a higher and more abstract level in a layering mode. Further optimization such as shallow neural networks, evolutionary algorithms, and linear regression, among others, has met with some success in solving the inverse problem task.
Combining deep learning methods with the field of nanophotonics is an emerging technology for nanostructure design in recent years. With the progress of the related technologies, such as characterization technologies, the construction of nano material databases, big data, computational power, mathematical algorithms and other technologies; related researchers have published research results in the super-surface field in the directions of nano-rods (nanorod), nano-microspheres (nanosphere), nano-prisms (nanoprism), nano-films (thin film), and the like.
Zhaoche Liu et al published a "generic Model for the applicant Design of metassurfaces" in the NANO LETTERS journal, published a reverse Design problem of solving a metassurface (metassurface) direction using a generation countermeasure network, and Itzik Malkie et al published a reverse Design problem of solving a nanostructure using a fully connected neural network; dianjing Liu et al published a "Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures" to solve the problem of Neural Networks being difficult to converge in the reverse Design of nanostructures. The artificial intelligence technology is used for designing and searching the nano material, and gradually transits from traditional machine learning algorithms such as decision trees, support vector machines, linear regression, random forests, Bayesian linear regression and the like to the artificial neural network technology in deep learning; in the existing research, the network model relates to a fully-connected neural network, a convolutional neural network, a generation countermeasure network and other structures.
The key point of applying deep learning to the design of the nano structure lies in how to establish a deep neural network model to process the bidirectional design problem of the nano structure. Deep learning requires a large number of data sets to enable the network to learn the functional relationship existing in the study object, and the data sets largely determine the final capability of the network, so that how to design the data sets of the neural network is also important. In addition, the experiment mainly researches the design of a metasurface (metasurface) nano structure, the spectrum response of metal nano particles with different shapes in the subject is very different, and the research on selecting the type and the property of the metal nano particles has great influence on the experiment.
Although deep learning techniques are expected to revolutionize nanomaterial science, many technical challenges remain to be faced with fruitful results. First, there still exists the difficulty of putting the training results into practical use. Since most databases are specialized to handle specific cases, new cases require a database to be rebuilt due to the problem of target mismatch. In addition, the quality of the training data is difficult to control, because the nanomaterial data come from different research institutions and organizations, and the interpretability of selecting bias and noise models is a widely discussed problem in the field of deep learning, and the method is also very critical in the design of nanomaterials. Although deep learning has outperformed humans at some specific tasks, it is still difficult to understand how models learn these knowledge. In most cases, we have little knowledge of how the model handles the inputs to the outputs or what specific knowledge each layer of the network learns. This prevents researchers from migrating specific knowledge to other related tasks, although there is great similarity between these tasks in the nanomaterial domain. Therefore, there is still a need for further experiments and researches in the aspects of data set establishment, model construction, model universality, model interpretability and the like in the application of deep learning to the plasma nano-materials.
Conventional methods of design, fabrication and characterization of nanostructures rely on a number of iterations through Finite Element Modeling (FEM) or Finite Difference Time Domain (FDTD) methods, and the designer can only design the nanostructure empirically and solve the maxwell's system of equations for the structure to obtain its spectral response. Furthermore, reasoning about the corresponding nanostructure on the inverse design problem, i.e. according to the set electromagnetic response, is a very challenging and time consuming task. The design of the nano structure based on deep learning is completely different from the traditional numerical solving method, once effective parameters are learned through a network, the design of the nano structure is disposable and a designer is not required to search a required structure through a large number of experiments according to subjective experience; it will greatly reduce the time cost, material cost of the design.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a nanostructure design method based on deep learning to solve the technical defects, aiming at the technical problem that the conventional methods for designing, manufacturing and characterizing nanostructures consume time and materials.
A deep learning-based nanostructure design method comprises the following steps:
establishing a training data set, wherein the training data set comprises any kind of nano-structure information, the nano-structure information comprises the geometric shape of a nano material and the frequency spectrums of the corresponding X and Y polarization directions and the material properties, and the geometric shape is represented by 8 nano-structure representation points;
preprocessing the training data set to transpose and normalize the data in the training data set;
constructing a Spectrum Prediction Network (SPN) and a geometric shape prediction network (GPN); the input of the spectrum prediction network SPN is the geometric shape of the nano material, and the output is the spectrums of the corresponding X and Y polarization directions; the input of the geometric shape prediction network GPN is the frequency spectrum and the material property of X and Y polarization directions, and the output is the geometric shape of the corresponding nano material;
integrating the spectrum prediction network SPN and the geometric shape prediction network GPN into a neural network model, wherein the output of the spectrum prediction network SPN is connected with the input of the geometric shape prediction network GPN, and the material property is a fixed parameter of each plasma and is directly given;
step five, training the integrated neural network model by using the preprocessed training data set, and finishing the training of the neural network model when the loss function reaches a preset value;
step six: inputting the frequency spectrums and the material properties of X and Y polarization directions corresponding to the nano structure to be established into a trained neural network model to obtain 8 nano structure characterization points of the nano structure so as to obtain the geometric shape of the nano structure; the plasma to be established is of the same kind as the plasma in the training data set.
Further, in step one, the geometry of a plasma corresponds to a set of spectra of both X and Y polarization directions, and the material property of each plasma is a fixed parameter.
Further, the 8 nanostructure characterization points specifically include: l is0、L1Respectively representing the width of the nano particle and the partial length of one side on a two-dimensional plane; leg 1, Leg 2,. Leg 5 respectively represent five sides of the nanoparticle, 1 represents the presence of the side, and 0 represents the absence of the side; phi denotes the rotation angle of the side Leg 1.
Further, in the second step, the training data set is read by using the torch library function and stored in the tensor array, and the data in the training data set is transposed and normalized.
Further, in step four, a fully connected residual network is used in the SPN, and the functional relationship of one residual unit is as follows:
yl＝h(xl)+F(xl,wl)(wl＝{wl,k|1≤k≤K})
xl+1＝f(yl)
yldenotes the output of the l-th cell, and xlIs the first oneInputting; when we order h (x)l)＝xl,xl+1＝ylFinally, can calculate
That is, the input of any residual node in the middle layer is the input of a certain shallow unit plus all the mapping values in the middle.
Further, in step five, the training process specifically includes:
s51, forward propagation: in a geometric shape prediction network GPN, input data consists of three tensors (tensors), the input data is input into a parallel network, then is connected to a layer, then is connected to a hidden layer with the same number of nodes, and finally 8 nano-structure representation points are output;
in the spectrum prediction network SPN network model, the input of the network is 8 nanostructure representation points output by GPN and 25 data points representing the material property; adding two data points for the input of the SPN, wherein the two points are used for controlling the output of the network, when the two data points are 01, the predicted result of the network is a transmission spectrum in the horizontal polarization direction, and when the two data points are 10, the predicted result of the network corresponds to the transmission spectrum in the vertical polarization direction, so that the weight parameter required to be stored by the neural network is reduced;
s52, calculating loss: and comparing the predicted output of the network with an expected value to calculate a loss value, and adopting a mean square error as a loss function:
Loss＝GPN_MSE(predictedGeometry，groundTruthGeometry)
creating a double-sized batch for the SPN throughout the batch, then performing a forward on the SPN by providing data to the GPN output, finally moving both networks backwards, calculating the loss for each network, adding the losses and sending them to the optimizer along with the gradients of the two networks, the loss function for the networks being as follows:
Loss＝GPN_MSE(predictedGeometry，groundTruthGeometry+
SPNx_MSE(predictedSpetrumX，groundTruthSpectrumX)+
SPNy_MSE(predictedSpetrumY，groundTruthSpectrumY)；
s53, backward propagation: updating the weight and the deviation in forward propagation according to a gradient descent algorithm when training by using a training data set; updating the weight w to w-V, wherein V is an update quantity, and V is dw lambda + V momentum and is an update quantity after gradient is introduced, so that the parameters of each layer are updated by using a back propagation method;
s54, updating parameters: firstly, trying to update the weight parameters of the SPN and the GPN at the same time, and then adopting an unequal learning mode: GPN and SPN are transmitted forward and backward for one time; then in the subsequent training, for the GPN, forward propagation is executed in each epoch, and backward propagation is executed at regular intervals; for SPN, each epoch performs forward and backward propagation.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a deep learning-based nanostructure design method of the present invention;
FIG. 2 is a schematic diagram of nanoparticle shapes and their structures in an embodiment of the invention;
FIG. 3 is a schematic diagram of a geometric prediction network in an embodiment of the present invention;
fig. 4 is a schematic diagram of a spectrum prediction network in an embodiment of the present invention;
FIG. 5 is a basic block diagram of a residual network in an embodiment of the present invention;
FIG. 6 is a diagram of a fully connected residual network architecture in an embodiment of the present invention;
fig. 7 is a diagram of a bidirectional network architecture in an embodiment of the present invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
A method for designing a nanostructure based on deep learning, as shown in fig. 1, includes:
establishing a training data set, wherein the training data set comprises any kind of nano-structure information, the nano-structure information comprises the geometric shape of a nano material and the frequency spectrums of the corresponding X and Y polarization directions and the material properties, and the geometric shape is represented by 8 nano-structure representation points;
preprocessing the training data set to transpose and normalize the data in the training data set;
constructing a Spectrum Prediction Network (SPN) and a geometric shape prediction network (GPN); the input of the spectrum prediction network SPN is the geometric shape of the nano material, and the output is the spectrums of the corresponding X and Y polarization directions; the input of the geometric shape prediction network GPN is the frequency spectrum and the material property of X and Y polarization directions, and the output is the geometric shape of the corresponding nano material;
integrating the spectrum prediction network SPN and the geometric shape prediction network GPN into a neural network model, wherein the output of the spectrum prediction network SPN is connected with the input of the geometric shape prediction network GPN, and the material property is a fixed parameter of each plasma and is directly given;
step five, training the integrated neural network model by using the preprocessed training data set, and finishing the training of the neural network model when the loss function reaches a preset value;
step six: inputting the frequency spectrums and the material properties of X and Y polarization directions corresponding to the nano structure to be established into a trained neural network model to obtain 8 nano structure characterization points of the nano structure so as to obtain the geometric shape of the nano structure; the plasma to be established is of the same kind as the plasma in the training data set.
In step one, a plasma geometry corresponds to a set of spectra of both X and Y polarization directions, and the material properties of each plasma are a fixed parameter.
The 8 nanostructure characterization points specifically include: l is0、L1Respectively representing the width of the nano particle and the partial length of one side on a two-dimensional plane; leg 1, Leg 2,. Leg 5 respectively represent five sides of the nanoparticle, 1 represents the presence of the side, and 0 represents the absence of the side; phi denotes the rotation angle of the side Leg 1.
In the second step, a torch library function is used for reading the training data set and storing the training data set in a tensor array, and data in the training data set is transposed and normalized, wherein the training data set is a matrix data set, and the transposition is convenient for subsequent data processing.
In step four, using a fully connected residual network in the SPN, the functional relationship of one residual unit is as follows:
yl＝h(xl)+F(xl,wl)(wl＝{wl,k|1≤k≤K})
xl+1＝f(yl)
yldenotes the output of the l-th cell, and xlIs the first input; when we order h (x)l)＝xl,xl+1＝ylFinally, can calculate
That is, the input of any residual node in the middle layer is the input of a certain shallow unit plus all the mapping values in the middle.
In the fifth step, the training process specifically includes:
s51, forward propagation: in a geometric shape prediction network GPN, input data consists of three tensors (tensors), the input data is input into a parallel network, then is connected to a layer, then is connected to a hidden layer with the same number of nodes, and finally 8 nano-structure representation points are output;
in the spectrum prediction network SPN network model, the input of the network is 8 nanostructure representation points output by GPN and 25 data points representing the material property; adding two data points for the input of the SPN, wherein the two points are used for controlling the output of the network, when the two data points are 01, the predicted result of the network is a transmission spectrum in the horizontal polarization direction, and when the two data points are 10, the predicted result of the network corresponds to the transmission spectrum in the vertical polarization direction, so that the weight parameter required to be stored by the neural network is reduced;
s52, calculating loss: and comparing the predicted output of the network with an expected value to calculate a loss value, and adopting a mean square error as a loss function:
Loss＝GPN_MSE(predictedGeometry，groundTruthGeometry)
creating a double-sized batch for the SPN throughout the batch, then performing a forward on the SPN by providing data to the GPN output, finally moving both networks backwards, calculating the loss for each network, adding the losses and sending them to the optimizer along with the gradients of the two networks, the loss function for the networks being as follows:
Loss＝GPN_MSE(predictedGeometry，groundTruthGeometry+
SPNx_MSE(predictedSpetrumX，groundTruthSpectrumX)+
SPNy_MSE(predictedSpetrumY，groundTruthSpectrumY)；
s53, backward propagation: updating the weight and the deviation in forward propagation according to a gradient descent algorithm when training by using a training data set; updating the weight w to w-V, wherein V is an update quantity, and V is dw lambda + V momentum and is an update quantity after gradient is introduced, so that the parameters of each layer are updated by using a back propagation method;
s54, updating parameters: firstly, trying to update the weight parameters of the SPN and the GPN at the same time, and then adopting an unequal learning mode: GPN and SPN are transmitted forward and backward for one time; then in the subsequent training, for the GPN, forward propagation is executed in each epoch, and backward propagation is executed at regular intervals; for SPN, each epoch performs forward and backward propagation.
In the embodiment of the invention, firstly, FDTD simulation software is used for obtaining frequency spectrum response synthesis for the gold nanoparticles of the 'H' cluster in two polarization directions of X and Y respectively in an input field, as shown in figure 2, 8 discrete data points are adopted in data set to represent the nanoparticles. L is0、L1Let 1, let 2,. Leg 5 respectively represent five sides of the nanoparticle, 1 represents the presence of the side, and 0 represents the absence of the side. Phi denotes the rotation angle of the edge 1.
When the neural network is trained, as the difference between transmission spectrum data of materials with different shapes and properties is large, the data is sparse, and an adapelta optimization method is selected. The network adopts a full-connection network structure, because the input data are three tensors (tensors), the three tensors are firstly input into the parallel network blocks, then the three network blocks are fully connected to one layer, then hidden layers with the same number of nodes are connected, and finally 8 data points are output, and the schematic diagram of the network structure is shown in fig. 3.
A spectral-predicting-network (Spectrum-predicting-network) for predicting spectral properties of nanomaterials, the input to the network being 8 data points representing geometry and 25 data points representing material properties. In this embodiment, transmission spectra in two polarization directions of an input field are considered, so the output of the spectrum prediction network should also be two corresponding transmission spectra, and if the output is directly output, the network should correspond to 84 data points; in order to reduce the parameter quantity of the network, two data points are added at the input of the network and are used for controlling the output of the network, for example, when the two points at the input are 01, the result of the network prediction is a transmission spectrum in a horizontal polarization direction; when the two points are 10, the prediction result of the network corresponds to the transmission spectrum in the vertical polarization direction. Thus the neural network requires a certain reduction of the stored weight parameters. A model schematic of a spectral prediction network is shown in fig. 4.
In the design of a frequency spectrum prediction network, after the number of network layers exceeds 10, the performance of a model is seriously reduced, and the network is not converged; thus, a residual network is introduced, which (ResNet) corresponds to changing the learning objective, as shown in fig. 5, and does not learn a complete output h (x) any more, but only the difference h (x) -x between the output and the input, i.e. the residual.
As shown in fig. 6, the SPN uses a fully-connected residual network, and the input of any residual node in the middle is the sum of the input of a shallow cell and all the mapped values in the middle. Assuming the loss function of the residual network as epsilon, the back propagation can be calculated as:
as can be seen from the above formula, the gradients of the layers are no longer multiplied in cascade, and the problem of gradient disappearance caused by the multiplication in cascade is no longer existed.
Although both networks may be designed and trained separately, such training may lead to instability of the network; given a pair of desired spectra, the GPN will provide the geometry and the SPN provides its spectrum. For two separate networks, there is no guarantee that the two spectra of the SPN prediction applied to the prediction geometry will closely match the original spectra. Therefore, a method of integrating two networks together for learning training is adopted: a network comprising SPNs and GPNs is trained to optimize them together so that the networks can adapt to each other.
The bidirectional network structure is shown in fig. 7, where during training, one forward pass is performed on the GPN, and then the output is cloned, creating two queries for each experiment, one for each polarization. The two queries are different in the polarization marker, indicating the corresponding input field polarization direction. Since the present embodiment uses small batch learning, it is performed throughout the batch and creates a double sized batch for the SPN. The progression is then performed on the SPN by providing data to the GPN output. Finally, moving the two networks backwards, calculating the loss of each network, adding the losses and sending the sum and the gradient of the two networks to the optimizer. The loss function of the network is as follows:
Loss＝GPN_MSE(predictedGeometry,groundTruthGeometry+
SPNx_MSE(predictedSpetrumX,groundTruthSpectrumX)+
SPNy_MSE(predictedSpetrumY,groundTruthSpectrumY)。
while the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (5)
1. A deep learning-based nanostructure design method is characterized by comprising the following steps:
establishing a training data set, wherein the training data set comprises any kind of nano-structure information, the nano-structure information comprises the geometric shape of a nano material and the frequency spectrums of the corresponding X and Y polarization directions and the material properties, and the geometric shape is represented by 8 nano-structure representation points;
preprocessing the training data set to transpose and normalize the data in the training data set;
constructing a Spectrum Prediction Network (SPN) and a geometric shape prediction network (GPN); the input of the spectrum prediction network SPN is the geometric shape of the nano material, and the output is the spectrums of the corresponding X and Y polarization directions; the input of the geometric shape prediction network GPN is the frequency spectrum and the material property of X and Y polarization directions, and the output is the geometric shape of the corresponding nano material;
integrating the spectrum prediction network SPN and the geometric shape prediction network GPN into a neural network model, wherein the output of the spectrum prediction network SPN is connected with the input of the geometric shape prediction network GPN, and the material property is a fixed parameter of each plasma and is directly given;
step five, training the integrated neural network model by using the preprocessed training data set, and finishing the training of the neural network model when the loss function reaches a preset value;
the training process specifically comprises:
s51, forward propagation: in a geometric shape prediction network GPN, input data consists of three tensors, the input data is input into a parallel network, then is connected to a layer, is connected with hidden layers with the same number of nodes, and finally outputs 8 nanostructure representation points;
in the spectrum prediction network SPN network model, the input of the network is 8 nanostructure representation points output by GPN and 25 data points representing the material property; adding two data points for the input of the SPN, wherein the two points are used for controlling the output of the network, when the two data points are 01, the predicted result of the network is a transmission spectrum in the horizontal polarization direction, and when the two data points are 10, the predicted result of the network corresponds to the transmission spectrum in the vertical polarization direction, so that the weight parameter required to be stored by the neural network is reduced;
s52, calculating loss: and comparing the predicted output of the network with an expected value to calculate a loss value, and adopting a mean square error as a loss function:
Loss＝GPN_MSE(predictedGeometry，groundTruthGeometry)
creating a double-sized batch for the SPN throughout the batch, then performing a forward on the SPN by providing data to the GPN output, finally moving both networks backwards, calculating the loss for each network, adding the losses and sending them to the optimizer along with the gradients of the two networks, the loss function for the networks being as follows:
Loss＝GPN_MSE(predictedGeometry，groundTruthGeometry)+
SPNx_MSE(predictedSpetrumX，groundTruthSpectrumX)+
SPNy_MSE(predictedSpetrumY，groundTruthSpectrumY)；
s53, backward propagation: updating the weight and the deviation in forward propagation according to a gradient descent algorithm when training by using a training data set; updating the weight w to w-V, wherein V is an update quantity, and V is dw lambda + V momentum and is an update quantity after gradient is introduced, so that the parameters of each layer are updated by using a back propagation method;
s54, updating parameters: firstly, trying to update the weight parameters of the SPN and the GPN at the same time, and then adopting an unequal learning mode: GPN and SPN are transmitted forward and backward for one time; then in the subsequent training, for the GPN, forward propagation is executed in each epoch, and backward propagation is executed at regular intervals; for the SPN, each epoch performs forward propagation and backward propagation;
step six: inputting the frequency spectrums and the material properties of X and Y polarization directions corresponding to the nano structure to be established into a trained neural network model to obtain 8 nano structure characterization points of the nano structure so as to obtain the geometric shape of the nano structure; the plasma to be established is of the same kind as the plasma in the training data set.
2. The method as claimed in claim 1, wherein in step one, the geometry of a plasma corresponds to a set of spectra of X and Y polarization directions, and the material property of each plasma is a fixed parameter.
3. The deep learning-based nanostructure design method of claim 1, wherein the 8 nanostructure characterization points specifically comprise: l is0、L1Respectively representing the width of the nano particle and the partial length of one side on a two-dimensional plane; leg 1, Leg 2,. Leg 5 respectively represent five sides of the nanoparticle, 1 represents the presence of the side, and 0 represents the absence of the side; phi denotes the rotation angle of the side Leg 1.
4. The method as claimed in claim 1, wherein in step two, the training data set is read and stored in the tensor array by using the function of the torch library, and the data in the training data set is transposed and normalized.
5. The deep learning based nanostructure design method of claim 1, wherein in step four, a fully connected residual network is used in the SPN, and the functional relationship of one residual unit is as follows:
yl＝h(xl)+F(xl,wl)(wl＝{wl,k|1≤k≤K})
xl+1＝f(yl)
yldenotes the output of the l-th cell, and xlIs the first input; when we order h (x)l)＝xl,xl+1＝ylFinally, can calculate
I.e. the input of any residual node in the middle layerIn is the sum of the shallow cell input and the intermediate full map value.
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