Optimal Neural Network Architecture Research Articles

Advancing AutoML: A Deep Dive into Neural Architecture Search (NAS) and Its Optimization Techniques

Abstract: Neural Architecture Search (NAS) is a pivotal technique in the field of automated machine learning (AutoML), enabling the automatic design of optimal neural network architectures. As deep learning models grow in complexity, NAS offers a scalable approach to improving model performance by exploring vast search spaces of potential architectures. In our research, we investigate the mathematical foundations and algorithms underpinning NAS, focusing on reinforcement learning-based, evolutionary, and gradient-based approaches. We provide mathematical proofs of convergence and efficiency for each method and analyze real-world applications, such as image classification and natural language processing (NLP). Through a comprehensive exploration of NAS, we aim to highlight its impact on AutoML and its potential to automate neural network design effectively while addressing challenges in computational cost and generalization.

Multi-Objective Evolutionary Neural Architecture Search with Weight-Sharing Supernet

Deep neural networks have played a crucial role in the field of deep learning, achieving significant success in practical applications. The architecture of neural networks is key to their performance. In the past few years, these architectures have been manually designed by experts with rich domain knowledge. Additionally, the optimal neural network architecture can vary depending on specific tasks and data distributions. Neural Architecture Search (NAS) is a class of techniques aimed at automatically searching for and designing neural network architectures according to the given tasks and data. Specifically, evolutionary-computation-based NAS methods are known for their strong global search capability and have aroused widespread interest in recent years. Although evolutionary-computation-based NAS has achieved success in a wide range of research and applications, it still faces bottlenecks in training and evaluating a large number of individuals during optimization. In this study, we first devise a multi-objective evolutionary NAS framework based on a weight-sharing supernet to improve the search efficiency of traditional evolutionary-computation-based NAS. This framework combines the population optimization characteristic of evolutionary algorithms with the weight-sharing ideas in one-shot models. We then design a bi-population MOEA/D algorithm based on the proposed framework to effectively solve the NAS problem. By constructing two sub-populations with different optimization objectives, the algorithm can effectively explore network architectures of various sizes in complex search spaces. An inter-population communication mechanism further enhances the algorithm’s exploratory capability, enabling it to find network architectures with uniform distribution and high diversity. Finally, we conduct performance comparison experiments on image classification datasets of different scales and complexities. Experimental results demonstrate the effectiveness of the proposed multi-objective evolutionary NAS framework and the practicality and transferability of the introduced bi-population MOEA/D-based NAS method compared to existing state-of-the-art NAS methods.

FORECASTING THE SUCCESS OF EDUCATION SEEKERS FROM A SEPARATE EDUCATIONAL COMPONENT BASED ON THE RESULTS OF THE PRELIMINARY MASTERY OF SUBJECT COMPETENCIES

The paper examines the main concepts related to the quality of education in general and the assimilation of educational material by higher education seekers. The task of predicting a seeker's grade in any discipline is formulated with data on his assimilation of program learning outcomes that also correspond to this discipline. The available specialized information system of own development is described which applies a number of methods (multivariate linear regression, artificial neural networks, k-nearest neighbors) and determines which method will be the most effective for the analysis of specific data. It is noted that during the further improvement of the quality system of knowledge assessment, it is important to determine at what level the student of education possesses the acquired competences, i.e. to calculate the success of seekers in terms of general and professional competences and program learning outcomes, determined by the standards of higher education and educational programs developed on their basis. The developed algorithm for calculating the success rate of higher education applicants in terms of program learning outcomes is presented; according to this algorithm, data were prepared on the acquisition of software creation competencies by 78 seekers of the first level of higher education of the educational and professional program Intelligent Decision Support Systems specialty 124, Systems analysis, of the DSEA. To solve the problem of forecasting by the method of artificial neural networks, the programming and data analysis language R is proposed. A script for finding the optimal neural network architecture is created. It was found that the best result (correlation is 0.9599, average absolute reduced error is 0.1132, percentage of correctly predicted points on the Ukrainian scale is 79.2) provides a perceptron with two hidden layers and five neurons in each one. This network was applied to predict the success of the new academic group: correlation is 0.923, the average absolute reduced error is 0.0654, the percentage of correctly predicted points on the Ukrainian scale is 82.4. The obtained results can be used to assess the quality of the structural and logical scheme of the EPP and in the work of the department during the analysis of seekers' success, etc.

Artificial Neural Network-Based Real-Time Power Management for a Hybrid Renewable Source Applied for a Water Desalination System

Water desalination systems integrated with stand-alone hybrid energy sources offer a remarkable solution to the water–energy challenge. Given the complexity of these systems, selecting an appropriate energy management system is crucial. In this regard, employing artificial intelligence techniques to develop and validate an energy management system can be an effective approach for handling such intricate systems. Therefore, this paper presents an ANN-based energy management system (ANNEMS) for a pumping and desalination system connected to an isolated hybrid renewable energy source. Thus, a parametric sensitivity algorithm was developed to identify the optimal neural network architecture. The water–energy management-based supervised multi-layer perceptron neural network demonstrated effective power sharing within a short time frame, achieving accuracy criteria of RMSE, R, and R² between the actual and estimated electrical power of the three motor pumps. The ANNEMS is defined to facilitate real-time power sharing distribution among the various system motor pumps on the test bench, considering the generated power profile and water tank levels. The proposed strategy employs power field oriented control to maintain DC bus voltage stability. Experimental results from the implementation of the proposed ANNEMS are provided. Therein, the power levels of the three motor pumps demonstrated consistent adherence to their reference values. In summary, this study highlights the significance of selecting appropriate energy management for real-time experimental validation.

Remote Sensing Image Classification Based on Neural Networks Designed Using an Efficient Neural Architecture Search Methodology

Successful applications of machine learning for the analysis of remote sensing images remain limited by the difficulty of designing neural networks manually. However, while the development of neural architecture search offers the unique potential for discovering new and more effective network architectures, existing neural architecture search algorithms are computationally intensive methods requiring a large amount of data and computational resources and are therefore challenging to apply for developing optimal neural network architectures for remote sensing image classification. Our proposed method uses a differentiable neural architecture search approach for remote sensing image classification. We utilize a binary gate strategy for partial channel connections to reduce the sizes of the network parameters, creating a sparse connection pattern that lowers memory consumption and NAS computational costs. Experimental results indicate that our method achieves a 15.1% increase in validation accuracy during the search phase compared to DDSAS, although slightly lower (by 4.5%) than DARTS. However, we reduced the search time by 88% and network parameter size by 84% compared to DARTS. In the architecture evaluation phase, our method demonstrates a 2.79% improvement in validation accuracy over a manually configured CNN network.

An Open-Circuit Fault Diagnosis System Based on Neural Networks in the Inverter of Three-Phase Permanent Magnet Synchronous Motor (PMSM)

Three-phase motors find extensive applications in various industries. Open-circuit faults are a common occurrence in inverters, and the open-circuit fault diagnosis system plays a crucial role in identifying and addressing these faults to enhance the safety of motor operations. Nevertheless, the current open-circuit fault diagnosis system faces challenges in precisely detecting specific faulty switches. The proposed work presents a neural network-based open-circuit fault diagnosis system for identifying faulty power switches in inverter-driven motor systems. The system leverages trained phase-to-phase voltage data from the motor to recognize the type and location of faults in each phase with high accuracy. Employing separate neural networks for each of the three phases in a three-phase permanent magnet synchronous motor, the system achieves an outstanding overall fault detection accuracy of approximately 99.8%, with CNN and CNN-LSTM architectures demonstrating superior performance. This work makes two key contributions: (1) implementing neural networks to significantly improve the accuracy of locating faulty switches in open-circuit fault scenarios, and (2) identifying the optimal neural network architecture for effective fault diagnosis within the proposed system.

Neural architecture search for radio map reconstruction with partially labeled data

In this paper, we tackle the challenging task of reconstructing Received Signal Strength (RSS) maps by harnessing location-dependent radio measurements and augmenting them with supplementary data related to the local environment. This side information includes city plans, terrain elevations, and the locations of gateways. The quantity of available supplementary data varies, necessitating the utilization of Neural Architecture Search (NAS) to tailor the neural network architecture to the specific characteristics of each setting. Our approach takes advantage of NAS’s adaptability, allowing it to automatically explore and pinpoint the optimal neural network architecture for each unique scenario. This adaptability ensures that the model is finely tuned to extract the most relevant features from the input data, thereby maximizing its ability to accurately reconstruct RSS maps. We demonstrate the effectiveness of our approach using three distinct datasets, each corresponding to a major city. Notably, we observe significant enhancements in areas near the gateways, where fluctuations in the mean received signal power are typically more pronounced. This underscores the importance of NAS-driven architectures in capturing subtle spatial variations. We also illustrate how NAS efficiently identifies the architecture of a Neural Network using both labeled and unlabeled data for Radio Map reconstruction. Our findings emphasize the potential of NAS as a potent tool for improving the precision and applicability of RSS map reconstruction techniques in urban environments.

Identification of the Optimal Neural Network Architecture for Prediction of Bitcoin Return

Neural networks (NNs) are well established and widely used in time series forecasting due to their frequent dominance over other linear and nonlinear models. Thus, this paper does not question their appropriateness in forecasting cryptocurrency prices; rather, it compares the most commonly used NNs, i.e. feedforward neural networks (FFNNs), long short-term memory (LSTM) and convolutional neural networks (CNNs). This paper contributes to the existing literature by defining the appropriate NN structure comparable across different NN architectures, which yields the optimal NN model for Bitcoin return forecasting. Moreover, by incorporating turbulent events such as COVID and war, this paper emerges as a stress test for NNs. Finally, inputs are carefully selected, mostly covering macroeconomic and market variables, as well as different attractiveness measures, the importance of which in cryptocurrency forecasting is tested. The main results indicate that all NNs perform the best in an environment of bullish market, where CNNs stand out as the optimal models for continuous dataset, and LSTMs emerge as optimal in direction forecasting. In the downturn periods, CNNs stand out as the best models. Additionally, Tweets, as an attractiveness measure, enabled the models to attain superior performance.

Neural Network Predictive Models for Alkali-Activated Concrete Carbon Emission Using Metaheuristic Optimization Algorithms

Due to environmental impacts and the need for energy efficiency, the cement industry aims to make more durable and sustainable materials with less energy requirements without compromising mechanical properties based on UN Sustainable Development Goals 9 and 11. Carbon dioxide (CO2) emission into the atmosphere is mostly the result of human-induced activities and causes dangerous environmental impacts by increasing the average temperature of the earth. Since the production of ordinary Portland cement (PC) is a major contributor to CO2 emissions, this study proposes alkali-activated binders as an alternative to reduce the environmental impact of ordinary Portland cement production. The dataset required for the training processes of these algorithms was created using Mendeley as a data-gathering instrument. Some of the most efficient state-of-the-art meta-heuristic optimization algorithms were applied to obtain the optimal neural network architecture with the highest performance. These neural network models were applied in the prediction of carbon emissions. The accuracy of these models was measured using statistical measures such as the mean squared error (MSE) and coefficient of determination (R2). The results show that carbon emissions associated with the production of alkali-activated concrete can be predicted with high accuracy using state-of-the-art machine learning techniques. In this study, in which the binders produced by the alkali activation method were evaluated for their usability as a binder material to replace Portland cement, it is concluded that the most successful hyperparameter optimization algorithm for this study is the genetic algorithm (GA) with accurate mean squared error (MSE = 161.17) and coefficient of determination (R2 = 0.90) values in the datasets.

Evolutionary Architecture Optimization for Retinal Vessel Segmentation.

Retinal vessel segmentation (RVS) is crucial in medical image analysis as it helps identify and monitor retinal diseases. Deep learning approaches have shown promising results for RVS, but designing optimal neural network architecture is challenging and time-consuming. Neural architecture search (NAS) is a recent technique that automates the design of neural network architectures within a predefined search space. This study proposes a new NAS method for U-shaped networks, MedUNAS, that discovers deep neural networks with high segmentation performance and lower inference time for RVS problem. We perform opposition-based differential evolution (ODE) and genetic algorithm (GA) to search for the best network structure and compare discrete and continuous encoding strategies on the proposed search space. To the best of our knowledge, this is the first NAS study that performs ODE for RVS problems. The results show that the MedUNAS ODE and GA yield the best and second-best results regarding segmentation performance with less than 50% of the parameters of U-shaped state-of-the-art methods on most of the compared datasets. In addition, the proposed methods outperform the baseline U-Net on four datasets with networks with up to 15 times fewer parameters. Furthermore, ablation studies are performed to evaluate the generalizability of the generated networks to medical image segmentation problems that differ from the trained domain, revealing that such networks can be effectively adapted to new tasks with fine-tuning. The MedUNAS can be a valuable tool for automated and efficient RVS in clinical practice.

ETNAS: An energy consumption task-driven neural architecture search

Neural Architecture Search (NAS) is crucial in the field of sustainable computing as it facilitates the development of highly efficient and effective neural networks. However, it cannot automate the deployment of neural networks to accommodate specific hardware resources and task requirements. This paper introduces ETNAS, which is a hardware-aware multi-objective optimal neural network architecture search algorithm based on the differentiable neural network architecture search method (DARTS). The algorithm searches for a lower-power neural network architecture with guaranteed inference accuracy by modifying the loss function of the differentiable neural network architecture search. We modify the dense network in DARTS to simultaneously search for networks with a lower memory footprint, enabling them to run on memory-constrained edge-end devices. We collected data on the power consumption and time consumption of numerous common operators on FPGA and Domain-Specific Architectures (DSA). The experimental results demonstrate that ETNAS achieves comparable accuracy performance and time efficiency while consuming less power compared to state-of-the-art algorithms, thereby validating its effectiveness in practical applications and contributing to the reduction of carbon emissions in intelligent cyber–physical systems (ICPS) edge computing inference.

FORMATION OF ENSEMBLES OF SIGNALS WITH TIME DIVISION USING A NEURAL NETWORK

In telecommunications, time-division signals play an extremely important role in the process of information transmission and processing. These signals, which are presented as electromagnetic waves, serve as the main means of transport for the transmission of data from one communication device to another, effectively constituting the circulatory system of modern communication networks. The defining feature that distinguishes these signals is their temporal nature, or more precisely, the changes they undergo over time as they travel over the network. These signals contain a rich spectrum of parameters, covering not only the attributes of amplitude, frequency and phase, but also many other parameters. This article provides a scientific rationale for the feasibility and relevance of researching the process of forming signal ensembles with temporal separation using neural networks. It has been established that one of the key tasks in creating ensembles of complex signals with temporal separation through the application of neural networks is the selection of an optimal neural network architecture. This entails determining the type of neural network that best aligns with a specific research objective. An algorithm for forming signal ensembles with temporal separation using a recurrent neural network (RNN) has been developed. Special attention is devoted to methods for assessing the overall error of signal ensembles with temporal separation using PNN. These analytical methods encompass the utilization of pertinent metrics, the evaluation of which depends on the specific nature of the task, whether it involves regression or classification. The findings of this research will contribute to the further advancement of methods for forming signal ensembles with temporal separation through the utilization of neural networks and enhance their application in contemporary telecommunications systems.

Deep learning based solution of nonlinear partial differential equations arising in the process of arterial blood flow

The present work introduces a deep learning approach to describe the perturbations of the pressure and radius in arterial blood flow. A mathematical model for the simulation of viscoelastic arterial flow is developed based on the assumption of long wavelength and large Reynolds number. Then, the reductive perturbation method is used to derive nonlinear evolutionary equations describing the resistance of the medium, the elastic properties, and the viscous properties of the wall. Using automatic differentiation, the solutions of nonlinear evolutionary equations at different time scales are represented using state-of-the-art physics-informed deep neural networks that are trained on a limited number of data points. The optimal neural network architecture for solving the nonlinear partial differential equations is found by employing Bayesian Hyperparameter Optimization. The proposed technique provides an alternate approach to avoid time-consuming numerical discretization methods such as finite difference or finite element for solving higher order nonlinear partial differential equations. Additionally, the capability of the trained model is demonstrated through graphs, and the solutions are also validated numerically. The graphical illustrations of pulse wave propagation can provide the correct interpretation of cardiovascular parameters, leading to an accurate diagnosis and successful treatment. Thus, the findings of this study could pave the way for the rapid development of emerging medical machine learning applications.

Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems

In recent years, physics-informed neural networks (PINNs) have emerged as an alternative to conventional numerical techniques to solve forward and inverse problems involving partial differential equations (PDEs). Despite its success in problems with smooth solutions, implementing PINNs for problems with discontinuous boundary conditions (BCs) or discontinuous PDE coefficients is a challenge. The accuracy of the predicted solution is contingent upon the selection of appropriate hyperparameters. In this work, we performed hyperparameter optimization of PINNs to find the optimal neural network architecture, number of hidden layers, learning rate, and activation function for heat conduction problems with a discontinuous solution. Our aim was to obtain all the settings that achieve a relative L2 error of 10% or less across all the test cases. Results from five different heat conduction problems show that the optimized hyperparameters produce a mean relative L2 error of 5.60%.

Using artificial intelligence-based algorithms to identify critical fouling factors and predict fouling behavior in anaerobic membrane bioreactors

Membrane fouling is one of the major obstacles that hinder the widespread applications of anerobic membrane bioreactors (AnMBRs) for wastewater treatment. Due to the intrinsic complexity of membrane fouling, identifying critical fouling factors and predicting fouling behavior are of great significance in membrane fouling control. Herein, artificial intelligence (AI) algorithms and their modeling framework were developed to predict membrane fouling behaviors in AnMBRs. Operating parameters, biomass properties, and membrane characteristics were considered as input variables for membrane fouling prediction. The results of hyper-parameter optimization showed that the optimal architecture of artificial neural network (ANN) model for membrane fouling prediction was “14-9-6-1” while the best hyper-parameters of random forest (RF) model were n_trees = 1200 and n_features = 14. After hyper-parameter adjusting, RF had more robustness of predictive capabilities (R2=0.906, mean squared error (MSE) = 0.061) for membrane fouling than the ANN model (R2=0.800, MSE = 0.118). More importantly, the feature importance and Shapley additive explanations analysis indicated SMPp/SMPc (0.281) > EPSp/EPSc (0.110) > organic loading rate (0.106), which were the most critical factors affecting membrane fouling. Partial dependence plot analysis further verified the marginal and interaction effects of various input features on membrane fouling. The revealed partial dependence relationships of critical variables can provide theoretical reference for optimization of practical operation. Overall, this study established a novel AI-based approach for predicting membrane fouling and comprehensively understanding the complicated effects of various influencing factors on membrane fouling while overcoming the “black-box” nature of conventional models.

An artificial neural network (ANN) approach for early cost estimation of concrete bridge systems in developing countries: the case of Sri Lanka

PurposeThe Government’s investment in infrastructure projects is considerably high, especially in bridge construction projects. Government authorities must establish an initial forecasted budget to have transparency in transactions. Early cost estimating is challenging for Quantity Surveyors due to incomplete project details at the initial stage and the unavailability of standard cost estimating techniques for bridge projects. To mitigate the difficulties in the traditional preliminary cost estimating methods, there is a requirement to develop a new initial cost estimating model which is accurate, user friendly and straightforward. The research was carried out in Sri Lanka, and this paper aims to develop the artificial neural network (ANN) model for an early cost estimate of concrete bridge systems.Design/methodology/approachThe construction cost data of 30 concrete bridge projects which are in Sri Lanka constructed within the past ten years were trained and tested to develop an ANN cost model. Backpropagation technique was used to identify the number of hidden layers, iteration and momentum for optimum neural network architectures.FindingsAn ANN cost model was developed, furnishing the best result since it succeeded with around 90% validation accuracy. It created a cost estimation model for the public sector as an accurate, heuristic, flexible and efficient technique.Originality/valueThe research contributes to the current body of knowledge by providing the most accurate early-stage cost estimate for the concrete bridge systems in Sri Lanka. In addition, the research findings would be helpful for stakeholders and policymakers to propose policy recommendations that positively influence the prediction of the most accurate cost estimate for concrete bridge construction projects in Sri Lanka and other developing countries.

Jaringan Syaraf Tiruan Mendeteksi Penyakit Pneumonia Infeksi Saluran Pernafasan Akut Dengan Algoritma Backpropagation

Acute Respiratory Infections (ARI) are a health problem that often affects children and adults. For adults, acute respiratory infections are mild or common, but in children under five, this disease is a threat that can cause death. One of the causes of death due to acute respiratory infections is incorrect diagnosis. This study aims to determine the level of accuracy and optimal neural network architecture in detecting ARI using the backpropagation method. This research was implemented using MATLAB software with several forms of network architecture. Symptoms of ARI that were used as input for detection of the disease consisted of 13 variables targeting non-pneumonia and pneumonia ARDs. Based on the research results, the architecture with the best configuration consists of 13 input layer neurons, 20 hidden layer neurons, and two output layer neurons with a binary sigmoid activation function (logs), a learning rate value of 0.5, an error tolerance value of 0.001, a maximum of the epoch of 216 and MSE 0.000997. Artificial neural networks with the backpropagation method used for weight adjustment can respond to training data and testing data well, marked by the resulting network accuracy of 100% in accordance with the desired target.

Detection of Cardiovascular Abnormalities Using Artificial Intelligence and Heart Sounds

Auscultation of the heart is one of the most crucial techniques physicians use to learn about a patient’s heart. Therefore, a lot of effort has been devoted to developing more sophisticated stethoscopes to assist physicians for better diagnosis. Most of this work has been to design stethoscopes to provide clearer signals. This work is an initial effort to include an Artificial Intelligence (AI) system in the stethoscope to perform a preliminary diagnosis of multiple heart conditions. To train the neural network, heart sounds representing 42 different issues are used. Due to the limited number of training data, noise is added to the available heart sounds. This serves the dual purpose of increasing the training data and to partially account for the variation in the heart sounds collected from different patients. These heart sounds are used to extract features such as mean, median, standard deviation, signal entropy, kurtosis, skewness, etc. for neural network training. An optimal neural network architecture is developed to classify these 42 heart conditions with 98% accuracy.

A hybrid data-driven and metaheuristic optimization approach for the compressive strength prediction of high-performance concrete

Compressive strength determination of high-performance concrete (HPC) is necessary for its practical usage. However, experimental testing for this purpose is resource intensive and time-consuming. Recently, machine learning has emerged in this field, especially data-driven modeling. In this study, a novel hybrid model for the compressive strength prediction of HPC is developed using the cascade forward neural network (CFNN) and artificial bee colony (ABC) optimization. The hybrid model used the ABC optimization method to select the optimal architecture of the neural network. A comprehensive database of 2171 data points containing information about cement, blast furnace slag, fly ash, water, coarse aggregate, sand, and age as input variables, and compressive strength as output variable is used to develop the model. Results indicated that the optimal neural network architecture selected by the ABC method consists of 2 layers and the developed model (CFNN-ABC) could accurately predict the compressive strength of HPC with correlation (R) and determination coefficients (R2) of 0.976 and 0.953, respectively. The feature importance of the model revealed that the cement and sand were more influential features as compared to the other features. The partial dependence analysis demonstrated the effect of variation in input parameters on the attained compressive strength. Furthermore, the model validation with previously developed models using performance indices showed that the proposed hybrid model outperformed other models in all performance indices including root mean square error (RMSE ∼ 4.04) and mean absolute error (MAE ∼ 3.10). Therefore, the present work provides a novel and efficient option to predict the compressive strength of HPC which can aid in the design of sustainable infrastructures without going through costly and time-intensive experimentation.

Rapid construction of Rayleigh wave dispersion curve based on deep learning

Introduction:The dispersion curve of the Rayleigh-wave phase velocity (VR) is widely utilized to determine site shear-wave velocity (Vs) structures from a distance of a few metres to hundreds of metres, even on a ten-kilometre crustal scale. However, the traditional theoretical-analytical methods for calculating VRs of a wide frequency range are time-consuming because numerous extensive matrix multiplications, transfer matrix iterations and the root searching of the secular dispersion equation are involved. It is very difficult to model site structures with many layers and apply them to a population-based inversion algorithm for which many populations of multilayers forward modelling and many generations of iterations are essential.Method:In this study, we propose a deep learning method for constructing the VR dispersion curve in a horizontally layered site with great efficiency. A deep neural network (DNN) based on the fully connected dense neural network is designed and trained to directly learn the relationships between Vs structures and dispersion curves. First, the training and validation sets are generated randomly according to a truncated Gaussian distribution, in which the mean and variance of the Vs models are statistically analysed from different regions’ empirical relationships between soil Vs and its depth. To be the supervised dataset, the corresponding VRs are calculated by the generalized reflection-transmission (R/T) coefficient method. Then, the Bayesian optimization (BO) is designed and trained to seek the optimal architecture of the deep neural network, such as the number of neurons and hidden layers and their combinations. Once the network is trained, the dispersion curve of VR can be constructed instantaneously without building and solving the secular equation.Results and Discussion:The results show that the DNN-BO achieves a coefficient of determination (R2) and MAE for the training and validation sets of 0.98 and 8.30 and 0.97 and 8.94, respectively, which suggests that the rapid method has satisfactory generalizability and stability. The DNN-BO method accelerates the dispersion curve calculation by at least 400 times, and there is almost no increase in computation expense with an increase in soil layers.