# Research on Mathematics Classroom Teaching Optimization Model Based on GA Neural Network

Authors: Yuhui Zheng
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The teaching characteristic of colleges and universities is determined by the teaching quality of teachers, but it is difficult to calculate with a linear mathematical explanation how to judge the teaching quality of teachers. In most colleges and universities, expert evaluations, supervision groups, peers listening to lectures in the classroom, and students' after-class evaluations are still used to determine the teaching ability of professors. It is undeniable that these judgment methods have certain practicality. Especially for new teachers, experts and peers can find problems in time and help new teachers quickly correct them, and they can also know how to better practice the “student-centered” teaching concept from the feedback of students after class. However, these judgment standards also have their limitations. For example, the classroom quality judgment standards for experts and peers are mostly set by some administrative departments according to social requirements, leadership requirements, and subjective cognition. Various institutions should have different weights for the same criterion, and if they all employ the same criteria, it will easily lead to imprecise conclusions. In addition, the expert group and students are also subjective and incomplete in the stage of teacher evaluation. Based on different nonquantitative factors, the evaluation standards for teachers in colleges and universities also need the scientific theoretical basis. Therefore, many scientists are considering whether to use a more intelligent and reasonable way to judge the quality of teaching. Nowadays, with the popularization of artificial intelligence (AI), the use of neural networks (NNs) is becoming more and more comprehensive. According to the characteristics of NNs, this paper uses the GA NNs algorithm to signify that this algorithm can be effectively used in the evaluation of teachers' teaching quality. In this paper, a large number of experimental results show that the use of GA NNs can be used to evaluate the quality of teaching, and the evaluation results can be obtained quantitatively in this way. For the assessment of teaching quality, quantitative results are also more powerful in teaching evaluation.


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## Body

## 1. Introduction

The core of quality education is innovation education, and basic education is the cradle of cultivating students' innovation. Teachers should firmly grasp the characteristics of mathematics, according to the actual age and psychological characteristics of students, with flexible teaching wisdom, optimize teaching strategies, and construct wonderful mathematics. Classroom teaching promotes the formation of open mathematics classrooms, and lays a solid foundation for students' lifelong learning and sustainable development [1–3]. In teaching, students should be awakened to arouse their emotions and resonate with students; situations should be carefully created to ignite spiritual sparks; Life resources should be offered, and students should be encouraged to investigate the secrets of mathematics in order to foster a cooperative environment, spell out wisdom and inspiration; to inspire unconventional, add color to the classroom so that the mathematics classroom teaching is more vibrant and full of youthful vigor [2–5].Education is an indispensable part of life. With the expansion of colleges and universities, the society and schools are more and more concerned about the quality of students' learning. For colleges and universities, how to improve the teaching quality of teachers is a problem that needs to be considered [6–8]. In teaching evaluation, it is difficult to be objective and fair because of the diversity of teaching, the factors of students themselves, and the supervisory factors of the educational affairs department. Back propagation (BP) neural network is an adaptive feed forward learning network (FFLN), which plays an important role in the field of AI. Here, according to the characteristics of BPNN, the factors of teaching quality evaluation are analyzed, and a BPNN model for teaching quality evaluation is constructed. The test proves that GANN can evaluate teaching quality well [9–11].Starting from the basic iterative formula of the algorithm, this paper analyzes the convergence process of the algorithm, demonstrates the defect of “origin preference” in the late convergence stage of the algorithm, and proposes an improvement plan. Aiming at the “premature” convergence phenomenon of the algorithm, the method of learning by subject and learning threshold is used to improve the diversity of students before and miditeration. Therefore, an improved teaching optimization algorithm (modified TLBO, MTLBO) is proposed, and a test function is used to verify the effectiveness of the improved algorithm. Finally, the M’I’LY () algorithm is used to optimize the parameters of the YPNN, and an algorithm-based YPNN prediction model (MTLB + BP) is established. The comparative analysis results show that the improved prediction model proposed in this paper has better prediction effect [12–16].The structure of the NN model is very important for the model, so it is of great significance to obtain the structure of the NN model and analyze it. However, when a black-box model is obtained, its model structure cannot be known, and constructing an equivalent model can simulate an equivalent model to help analyze the black-box model. Therefore, equivalent model construction has practical significance. GA is a computational model that simulates the natural selection and genetic mechanism of Darwin's theory of biological evolution. It is a method to search for the optimal solution by simulating the natural evolution process [17–19]. The algorithm does not need to accurately describe all the characteristics of the problem, and has strong versatility and robustness, and can quickly adapt to changes in the problem and environment. Good optimization results. The essence of constructing an equivalent model of a neural network is a relatively complex optimization combination problem, and the theoretical research on the interpretability of NNs is still in the process of improvement, especially for deep NNs, it is difficult to find suitable mathematical tools for it. Expression and training capabilities are modeled. In view of the above problems, this paper proposes a method of constructing an equivalent model of neural network based on genetic algorithm [20–23]. On the basis of the input and output data of the original model and the structure of the classical neural network model, the structural parameters of the model are encoded, and the genetic algorithm is fully used to search the ability of the optimal solution to construct an equivalent model of the original model [24].In this paper, the Hermite orthonormal basis function is used as the excitation function of the hidden layer of the NN, and a multi-input Hermite orthonormal basis neural network is designed using the phase space reconstruction theory, the properties of Hermite orthonormal basis functions, the best square approximation theory, and neural network theory. The improved teaching-learning-based optimization (ITLBO) algorithm is used to optimize the parameters of the network prediction model. Finally, comparison experiments with various prediction models are used to verify the effectiveness and usefulness of the proposed prediction model [25, 26].The arrangements of the paper as follows:Section2 discuss the Genetic Algorithm (GA) NN and define the different subsections of GANN. To examine the GA-Opitimaltion TLBO is optimization algorithms based on the class teaching process and then discusses the various experiments techniques and analyze the different strategies performance of GA. Section 3 concludes the article.


## 2. GA Neural Network (NNs)

Orthogonal basis functions (OBS), Laguerre OBS and Legendre OBS have no limit on the range of independent variables, and the data processing is simple and the amount of calculation is small. Therefore, according to the theoretical basis and combined with the neural network topology, this paper uses the Hermite Orthogonal the basis function is used as the activation function of the hidden layer of the network, and the Hermite Orthogonal Basis Neural Network (HOBNN) prediction model is proposed [27, 28].The research on the dynamic characteristics of chaotic systems is almost always based on the reconstruction of phase space. For chaotic time series, the theorem proves that there is a smooth curvefx such that (1) and satisfied with equation (2)-(6):(1)yi+m−1τ+s=fzm,i,(2)HnX=−1nex2dne−x2dxn,(3)∫−∞+∞e−x2HmxHnxdx,(4)H0x=1,(5)H1x=2x,(6)Hn+1x=2xHnx−2nHn−1x.Since each layer of neurons in the network adopts the identity mapping, and the threshold value of all neurons is 0, the input of the ith neuron in the hidden layer is (7), and the output of the ith neuron in the hidden layer is formula (8), the output layer neuron output is (9) [29, 30].(7)neti=ZmiTWi,(8)Oi=Hi−1neti,(9)yi+m−1τ+s=o1,o2,…,oqτ.A HOBNN with an m-q-1 structure is constructed, and the neurons in each layer adopt the identity mapping, and the threshold value of all neurons in the network is 0. The network is shown in Figure1.Figure 1
Hermite basis neural network.Regarding the training method, considering the training time of the NN model itself, in order to improve the training efficiency, when training the model corresponding to the individual in the population, it is not necessary to wait until the loss function converges to the optimal state, but a fixed value can be set. Number of training steps. Although this measure does not converge the model to the optimum, it speeds up the genetic iteration speed, and the number of training steps is not a factor that causes the difference in model structure. The number of training steps is an irrelevant variable, and the selection of individuals for subsequent selection operators cause an impact. In order to improve the accuracy of the finally constructed equivalent model, the individuals finally selected after the iteration of the genetic algorithm can be retrained until the optimal convergence state, as the constructed equivalent model, which can be shown in Figure2.Figure 2
The GA-based neural network optimitional algorithm diagram.The binary coding method is adopted in this paper, and the crossover operators suitable for binary coding individuals include single-point crossover, two-point crossover, multi-point crossover, uniform crossover and arithmetic crossover, etc. In the crossover process, choosing an appropriate crossover probability is more conducive to the optimization and convergence of the algorithm. If the cadre is too small, new individuals will be generated slowly in the iterative process, which will slow down the optimization process. If the cadre is too large, the optimal individual will be lost, etc. A situation arises that cannot be converged. Under the comprehensive consideration, this paper adopts the two-point crossover method as the crossover operator, randomly sets two crossover points in the binary code string of the individual, and then exchanges the content between the two crossover points. The fully connected layers of the two selected individuals are crossed to obtain two new individuals.The traditional NNs often use the gradient descent method to train the weights of the network, and there are problems such as the selection of the number of nodes in the hidden layer of the network and the selection of training samples. It is not very high, and the network structure is complex and the weight parameters are too many, resulting in slow convergence and precociousness. For efficiency requirements, if the number of nodes increases, the accuracy will not change much or even over-fitting will occur, and the network structure will become more complex due to the increase of parameters, and the modeling time will be delayed at the same time, reducing the timeliness. Therefore, the Hermite orthogonality in this paper is the number of hidden layer nodes of the basic neural network prediction model isq = 3. In addition, the proposed prediction model has no strict requirements on training samples, and the sample size is usually less than the number of traditional neural network samples.The encoding method used in this paper is binary encoding, so the basic bit mutation method can be selected. First calculate the mutation probability. When the result satisfies the mutation conditions; then by calculating the mutation site encoded by the individual, the inversion operation is performed to complete the mutation. Perform mutation operation on the number of units in a fully connected layer to generate new mutant individuals.It can be seen that the HOBNN does not have problems such as difficulty in determining hidden layer nodes and sample selection. The prediction model has a simple structure and few parameters to be optimized. It only needs to find the parameter vector of the model to be optimized with a lower dimension. The ITLBO algorithm is used as a It is a parallel optimization algorithm with strong global search ability, simple operation and fast convergence speed, so it is used to train the model parameter vector to be optimized. Using the ITLBO algorithm to optimize the parameters of the prediction model can not only avoid the cumbersomeness and inefficiency of the traditional gradient descent method to train the neural network, but also take advantage of the advantages of the ITLBO algorithm to prevent premature and local optimization. Efficiency of HOBNNs for the ITLBO Algorithm.When using HOBNN for prediction, the key is the optimization of model parameters, the principle of which is shown as (10) and (11) and the stability of network is defined as follows.(10)ess=minθY−−YTY−−Y.That is, by continuously adjusting the parameters, the sum of squares of the error between the expected output of the system and the actual output is minimized. Therefore, the objective function is taken as(11)Fθ=Y∼−YTY∼−Y.Since the objective function is a multivariate function, there may be multiple local optimal solutions. Traditional gradient descent algorithm, GA, particle swarm optimization (PSO) algorithm and quantum particle Swarm optimization (quantum particle swarm optimization, QPSO) algorithm is very easy to fall into local optimum when training neural network, and the operation is complicated and the convergence speed is slow. The ITLBO algorithm is used as a teaching optimization (teaching-learning-based optimization, TLBO) The improved algorithm of the algorithm makes up for the shortcomings of the traditional algorithm and is an intelligent optimization algorithm with efficient search. Therefore, this paper uses the ITLBO algorithm to optimize the parameters of the prediction model.


### 2.1. GA Opitimaltion Algorithm

The GA-Opitimaltion TLBO is an optimization algorithm based on the class teaching process, including the teaching stage and the learning stage, but its convergence is slow and the accuracy is not high. On the basis of the TLBO algorithm, this paper proposes the ITLBO algorithm. Join the feedback stage to increase the opportunities for poor students to communicate with teachers, so as to maintain the diversity of students' learning and accelerate the process of poor students moving closer to good students and improve the global search ability and search speed of the algorithm.The specific algorithm steps of the improved teaching optimization algorithm are as follows:(1)
Set the number of students, the learning dimension, the range of students' qualities and learning experience, and initialize the students based on the unique optimization problem(2)
Calculate the fitness of each student, and select the student with the best fitness for teachers(3)
Randomly select a student as the benchmark for the “teaching” stage(4)
In the “teaching” stage, teachers teach according to formulas (7) and (8), improve the average level of students in the class, and update students by means of basic teaching optimization algorithms(5)
Calculate the learning threshold by multiplying the number of iterations by the number of iterations(6)
“Learning” stage, as shown in Equation (9), students learn from each other, or learn from their own experience(7)
Update the trainee's position and learning experience according to Equation (10) if the trainee improves his fitness(8)
Repeat steps (2) to (7) until the termination condition is satisfiedThe algorithm flow chart is shown in Figure3.Figure 3
MTLBO algorithm diagram.Four test functions with many local optima are selected to verify the effectiveness of the algorithm proposed in this paper. In order to verify the “origin preference” feature of the basic algorithm, this paper improves the standard test function. The parameterN is introduced into the standard test function, the variable x in the function is changed to x−N, and the range of variables is adjusted accordingly, as shown in Table 1.Table 1
Adjusting of parameters.
IndexR1R2R3R4R5R6WTestR110.7521.331.331.330.23Dd = 0.0362, <0.1, MEET THE CONDITIONR20.7510.671110.15R30.50.6710.670.670.670.13R40.7511.50.670.750.50.15R50.7511.51.330.670.670.26R60.7511.511.51.330.49The fitness function is used as the main evaluation index to describe the individual performance, and the individual is distinguished from the pros and cons according to the size of the function value. Therefore, the construction of the fitness function is very important, which has a direct impact on the iteration speed of the genetic algorithm and the global optimal solution. In this paper, by establishing a mapping relationship between the loss function during training of the neural network model and the fitness function of the population individuals, the optimization of the optimization function in the process of population evolution.


### 2.2. Simulation Experiment and Performance Analysis

The continuous multiple input and multiple output (MIMO) Lorenz system and Liu system are compared respectively. To predict the difference between models, four performance evaluation indicators are introduced: mean modeling time (MMT), mean absolute error (MAE), determination coefficient (DC) and root mean square error (root mean square error, RMSE). Among them,(12)MMT=1NaTf,MAE=1n∑i=1nyi−−yi,DC=∑i=1nyi∼−yi2∑i=1nyi−yi,RMSE=1n−1∑i=1nyi∼−yi2,First, the phase space reconstruction is performed on the sequencex, and the value is 0.01. The acquisition of its two important parameters is shown in Figure 4. Combined with the autocorrelation method, it can be seen from Figure 4 that the optimal delay time is 5; combined with the Cao method, it can be seen from Figure 4 that the minimum embedding dimension m is 20. Therefore, the reconstruction delay time vector can be determined. Fitness with different generations is shown in Figure 5.Figure 4
Phase space reconstruction.Figure 5
Fitness with different generations.Secondly, when using the reconstructed delay time vector and the HOBNN based on the ITLBO algorithm to build the prediction model, the HOBNN is adopted. M-q-1 structure, wherem=2,q=3; the initialization parameters of the ITLBO algorithm are set as: the optimization parameter vector dimension D=5 the number of class members N=40, and the number of teaching times G=30 Statistically significant results, the ITLBO algorithm runs 20 times independently, and establishes a prediction model and performs prediction analysis according to the average value of the optimal solution obtained each time. The algorithm's HOBNN is abbreviated as ITLBO-HOB as Figures 5 and 6.Figure 6
(color online) Simulation curve of ITLBO-HOB.After the iteration, the equivalent model constructed with the optimal parameters is used for retraining until the optimal state. From the analysis of the final area under the curve (AUc) and average precision (AP) results and the comparison results of the original model, it can be seen that the constructed equivalent model is equal to the original model. Although the valence model differs from the original model in terms of structural parameters, it is basically consistent with the original model in terms of prediction accuracy, which proves the effectiveness of the equivalence model construction method proposed in this paper.In addition, compared with other prediction models, the HOBNN has few hidden layer nodes, simple structure, and low dimension of the parameter vector to be optimized, few unknown parameters, simple process and easy optimization operation. At the same time, ITLBO as an efficient intelligent optimization algorithm, the algorithm avoids the shortcomings of other traditional optimization algorithms, and has simple operation, strong optimization ability and fast convergence speed. Therefore, combining the advantages of the two, the ITLBO algorithm is used to optimize the HOBNN. The network parameters greatly improve the operation efficiency: (1) The proposed prediction model has a simple structure and few parameters to be optimized, which makes the operation simple, easy to implement, and shortens the modeling time; (2) Combined with the advantages of the ITLBO algorithm, the operation is simple and the search ability is strong, the convergence speed is fast, which can not only improve the search accuracy, thereby improving the prediction accuracy, but also improve the search speed, thereby reducing the modeling time.It can be seen from Figure7 that the TLBO algorithm has the defects of search stagnation in the early stage of iteration and low solution accuracy of the algorithm. The FETLBO and C-TLBO algorithms have been improved, and the global search ability of the algorithm has been enhanced, but around the 600th iteration of the algorithm, the algorithm falls into a local optimum. The MTLBO algorithm eliminates the “origin preference” characteristic, and the algorithm has the ability to seek optimization during the iteration, and is significantly better than the other three algorithms in terms of convergence speed and solution accuracy. Aiming at the problems of slow convergence speed of traditional BP neural network, easy to fall into local optimum and premature convergence of GA optimized BP NN (GA-BP) algorithm, a genetic simulated annealing algorithm optimized bp neural network (GSA-BP) algorithm was proposed. The simulated annealing algorithm (SA) is added to the population update of GA to preserve the diversity of the population. The GSA-BP algorithm is used to fit the elevation anomaly in a certain area, and the results are compared with the BP algorithm and the GA-BP algorithm. The results show that the accuracy of the GSA-BP algorithm can be increased by about 51% and 25%, and the speed by about 77% and 39%, and can basically meet the requirements of the fourth-class leveling accuracy. The method is feasible in GPS elevation fitting.Figure 7
Extrapolation factor.Through the above analysis, the HOBNN prediction model based on the ITLBO algorithm has simple structure, high prediction accuracy and short modeling time, which well illustrates the effectiveness and practicability of the prediction model, and can be further promoted and applied.


## 2.1. GA Opitimaltion Algorithm

The GA-Opitimaltion TLBO is an optimization algorithm based on the class teaching process, including the teaching stage and the learning stage, but its convergence is slow and the accuracy is not high. On the basis of the TLBO algorithm, this paper proposes the ITLBO algorithm. Join the feedback stage to increase the opportunities for poor students to communicate with teachers, so as to maintain the diversity of students' learning and accelerate the process of poor students moving closer to good students and improve the global search ability and search speed of the algorithm.The specific algorithm steps of the improved teaching optimization algorithm are as follows:(1)
Set the number of students, the learning dimension, the range of students' qualities and learning experience, and initialize the students based on the unique optimization problem(2)
Calculate the fitness of each student, and select the student with the best fitness for teachers(3)
Randomly select a student as the benchmark for the “teaching” stage(4)
In the “teaching” stage, teachers teach according to formulas (7) and (8), improve the average level of students in the class, and update students by means of basic teaching optimization algorithms(5)
Calculate the learning threshold by multiplying the number of iterations by the number of iterations(6)
“Learning” stage, as shown in Equation (9), students learn from each other, or learn from their own experience(7)
Update the trainee's position and learning experience according to Equation (10) if the trainee improves his fitness(8)
Repeat steps (2) to (7) until the termination condition is satisfiedThe algorithm flow chart is shown in Figure3.Figure 3
MTLBO algorithm diagram.Four test functions with many local optima are selected to verify the effectiveness of the algorithm proposed in this paper. In order to verify the “origin preference” feature of the basic algorithm, this paper improves the standard test function. The parameterN is introduced into the standard test function, the variable x in the function is changed to x−N, and the range of variables is adjusted accordingly, as shown in Table 1.Table 1
Adjusting of parameters.
IndexR1R2R3R4R5R6WTestR110.7521.331.331.330.23Dd = 0.0362, <0.1, MEET THE CONDITIONR20.7510.671110.15R30.50.6710.670.670.670.13R40.7511.50.670.750.50.15R50.7511.51.330.670.670.26R60.7511.511.51.330.49The fitness function is used as the main evaluation index to describe the individual performance, and the individual is distinguished from the pros and cons according to the size of the function value. Therefore, the construction of the fitness function is very important, which has a direct impact on the iteration speed of the genetic algorithm and the global optimal solution. In this paper, by establishing a mapping relationship between the loss function during training of the neural network model and the fitness function of the population individuals, the optimization of the optimization function in the process of population evolution.


## 2.2. Simulation Experiment and Performance Analysis

The continuous multiple input and multiple output (MIMO) Lorenz system and Liu system are compared respectively. To predict the difference between models, four performance evaluation indicators are introduced: mean modeling time (MMT), mean absolute error (MAE), determination coefficient (DC) and root mean square error (root mean square error, RMSE). Among them,(12)MMT=1NaTf,MAE=1n∑i=1nyi−−yi,DC=∑i=1nyi∼−yi2∑i=1nyi−yi,RMSE=1n−1∑i=1nyi∼−yi2,First, the phase space reconstruction is performed on the sequencex, and the value is 0.01. The acquisition of its two important parameters is shown in Figure 4. Combined with the autocorrelation method, it can be seen from Figure 4 that the optimal delay time is 5; combined with the Cao method, it can be seen from Figure 4 that the minimum embedding dimension m is 20. Therefore, the reconstruction delay time vector can be determined. Fitness with different generations is shown in Figure 5.Figure 4
Phase space reconstruction.Figure 5
Fitness with different generations.Secondly, when using the reconstructed delay time vector and the HOBNN based on the ITLBO algorithm to build the prediction model, the HOBNN is adopted. M-q-1 structure, wherem=2,q=3; the initialization parameters of the ITLBO algorithm are set as: the optimization parameter vector dimension D=5 the number of class members N=40, and the number of teaching times G=30 Statistically significant results, the ITLBO algorithm runs 20 times independently, and establishes a prediction model and performs prediction analysis according to the average value of the optimal solution obtained each time. The algorithm's HOBNN is abbreviated as ITLBO-HOB as Figures 5 and 6.Figure 6
(color online) Simulation curve of ITLBO-HOB.After the iteration, the equivalent model constructed with the optimal parameters is used for retraining until the optimal state. From the analysis of the final area under the curve (AUc) and average precision (AP) results and the comparison results of the original model, it can be seen that the constructed equivalent model is equal to the original model. Although the valence model differs from the original model in terms of structural parameters, it is basically consistent with the original model in terms of prediction accuracy, which proves the effectiveness of the equivalence model construction method proposed in this paper.In addition, compared with other prediction models, the HOBNN has few hidden layer nodes, simple structure, and low dimension of the parameter vector to be optimized, few unknown parameters, simple process and easy optimization operation. At the same time, ITLBO as an efficient intelligent optimization algorithm, the algorithm avoids the shortcomings of other traditional optimization algorithms, and has simple operation, strong optimization ability and fast convergence speed. Therefore, combining the advantages of the two, the ITLBO algorithm is used to optimize the HOBNN. The network parameters greatly improve the operation efficiency: (1) The proposed prediction model has a simple structure and few parameters to be optimized, which makes the operation simple, easy to implement, and shortens the modeling time; (2) Combined with the advantages of the ITLBO algorithm, the operation is simple and the search ability is strong, the convergence speed is fast, which can not only improve the search accuracy, thereby improving the prediction accuracy, but also improve the search speed, thereby reducing the modeling time.It can be seen from Figure7 that the TLBO algorithm has the defects of search stagnation in the early stage of iteration and low solution accuracy of the algorithm. The FETLBO and C-TLBO algorithms have been improved, and the global search ability of the algorithm has been enhanced, but around the 600th iteration of the algorithm, the algorithm falls into a local optimum. The MTLBO algorithm eliminates the “origin preference” characteristic, and the algorithm has the ability to seek optimization during the iteration, and is significantly better than the other three algorithms in terms of convergence speed and solution accuracy. Aiming at the problems of slow convergence speed of traditional BP neural network, easy to fall into local optimum and premature convergence of GA optimized BP NN (GA-BP) algorithm, a genetic simulated annealing algorithm optimized bp neural network (GSA-BP) algorithm was proposed. The simulated annealing algorithm (SA) is added to the population update of GA to preserve the diversity of the population. The GSA-BP algorithm is used to fit the elevation anomaly in a certain area, and the results are compared with the BP algorithm and the GA-BP algorithm. The results show that the accuracy of the GSA-BP algorithm can be increased by about 51% and 25%, and the speed by about 77% and 39%, and can basically meet the requirements of the fourth-class leveling accuracy. The method is feasible in GPS elevation fitting.Figure 7
Extrapolation factor.Through the above analysis, the HOBNN prediction model based on the ITLBO algorithm has simple structure, high prediction accuracy and short modeling time, which well illustrates the effectiveness and practicability of the prediction model, and can be further promoted and applied.


## 3. Conclusion

As an important part of deep learning, the structure of NN model determines the performance of deep learning to a large extent. At present, most of the applications based on deep learning are modified from classic network models. Since the structure of the original NN model cannot be obtained, this paper constructs the prediction model of the original model according to the input and output data of the original model and the structure of the classical NN model. This method mainly constructs the equivalent model of the original model by encoding the structural parameters of the prediction model, and using the GA to perform selection, crossover and mutation operations. For the same input data, the output of the equivalent model and the original model are basically the same. The construction method proposed in this paper has achieved good results in the fields of image classification, signal modulation type classification and network link prediction.The ubiquitous phenomenon of chaos in human society and nature has made people's understanding and research on chaos continue to strengthen, especially the problem of chaotic time series prediction, which has become the focus and hot issue of current research. However, due to the complexity of chaotic systems, the resulting chaotic time series has strong nonlinearity, which brings great trouble to prediction and application. Therefore, combined with the phase space reconstruction theory, the properties of Hermite orthonormal basis functions, the best square approximation theory and NN theory, this paper proposes a HOBNN prediction model based on the ITLBO algorithm. By comparing with the comparative prediction model for single-step and multi-step prediction experiments, the simulation results confirm that the proposed prediction model has high prediction accuracy and convergence. The excellent characteristics of fast speed and simple model structure are convenient for application in production and life, and have certain theoretical significance and practical value, especially in traffic forecasting, stock market analysis, weather forecast, hydrological monitoring, fault diagnosis, secure communication, and synchronous and asynchronous. Control and other fields can play an extremely important role.



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*Source: 5414306-2022-04-13.xml*