Artificial Neural Network Structure Research Articles

FPGA Tabanlı LogSig ve TanSig Transfer Fonksiyonlarının IQ-Math Sayı Standardında Tasarımı ve Gerçeklenmesi

Yapay Sinir Ağları (YSA), günümüzde sinyal işleme, optimizasyon, tahmin, karar verme ve kontrol gibi bir çok mühendislik alanında yoğun şekilde kullanılmaktadır. YSA yapılarının çalışmasını doğrudan etkileyen önemli bölümlerinden birisi de Transfer Fonksiyonlarıdır (TF). Doğrusal olmayan TF tasarımlarının gerçek zamanlı tasarımı üstel fonksiyon içerdiğinden oldukça zor bir şekilde gerçekleştirilmektedir. Bu çalışmanın ilk aşamasında, literatürdeki çalışmalardan farklı olarak doğrusal olmayan Logaritmik Sigmoid (LogSig) ve Tanjant Sigmoid (TanSig) TF, 32-bit (16I-16Q) IQ-Math formatında VHDL dilinde tasarlanmıştır. İkinci aşamada, VHDL dilinde FPGA çiplerinde çalışmak üzere örnek bir üç giriş-üç çıkışlı bir YSA (ileri beslemeli) yapısı 32-bit IQ-Math formatında modellenmiştir. Tasarımın gizli katmanında 8 adet nöron, gizli katmanda LogSig ile TanSig TF ve çıkış katmanında ise PureLin TF kullanılmıştır. Örnek YSA tasarımı iki farklı TF tasarımı için ayrı bir testbench dosyası oluşturulmuş ve bu tasarımlar VHDL ile Xilinx ISE DS programı ile test edilmiştir. Elde edilen simülasyon sonuçlarına göre nümerik tabanlı LogSig ve TanSig TF içeren YSA tasarımları için MSE ve RMSE hata analizleri yapılarak sonuçlar sunulmuştur. Ardından her bir tasarım XC7K70T-3FBG676 FPGA (Kintex-7) için sentezlenerek Place-Route prosesi gerçekleştirilmiştir. Place-Route prosesinden elde edilen FPGA çip kaynak kullanımı istatistikleri sunulmuştur. Tasarımlara ait hata analizi sonuçlarına göre YSA-LS (LogSig-tabanlı YSA) tasarımı 8.86E-06 MSE ve YSA-TS (TanSig-tabanlı YSA) tasarımı 7.92E-02 MSE sonuçları elde edilmiştir. Bu çalışmadan elde edilen sonuçlar ile IQ-Math tabanlı LogSig ve TanSig aktivasyon fonksiyonu tasarımlarının gerçek zamanlı YSA uygulamalarında güvenli bir şekilde kullanılabileceği gösterilmiştir.

Application of Artificial Neural Networks to the Analysis of Friction Behaviour in a Drawbead Profile in Sheet Metal Forming.

Drawbeads are used when forming drawpieces with complex shapes to equalise the flow resistance of a material around the perimeter of the drawpiece or to change the state of stress in certain regions of the drawpiece. This article presents a special drawbead simulator for determining the value of the coefficient of friction on the drawbead. The aim of this paper is the application of artificial neural networks (ANNs) to understand the effect of the most important parameters of the friction process (sample orientation in relation to the rolling direction of the steel sheets, surface roughness of the counter-samples and lubrication conditions) on the coefficient of friction. The intention was to build a database for training ANNs. The friction coefficient was determined for low-carbon steel sheets with various drawability indices: drawing quality DQ, deep-drawing quality DDQ and extra deep-drawing quality EDDQ. Equivalents of the sheets tested in EN standards are DC01 (DQ), DC03 (DDQ) and DC04 (EDDQ). The tests were carried out under the conditions of dry friction and the sheet surface was lubricated with machine oil LAN46 and hydraulic oil LHL32, commonly used in sheet metal forming. Moreover, various specimen orientations (0° and 90°) in relation to the rolling direction of the steel sheets were investigated. Moreover, a wide range of surface roughness values of the counter-samples (Ra = 0.32 μm, 0.63 μm, 1.25 μm and 2.5 μm) were also considered. In general, the value of the coefficient of friction increased with increasing surface roughness of the counter-samples. In the case of LAN46 machine oil, the effectiveness of lubrication decreased with increasing mean roughness of the counter-samples Ra = 0.32-1.25 μm. With increasing drawing quality of the sheet metal, the effectiveness of lubrication increased, but only in the range of surface roughness of the counter-samples in which Ra = 0.32-1.25 μm. This study investigated different transfer functions and training algorithms to develop the best artificial neural network structure. Backpropagation in an MLP structure was used to build the structure. In addition, the COF was calculated using a parameter-based analytical equation. Garson partitioning weight was used to calculate the relative importance (RI) effect on coefficient of friction. The Bayesian regularization backpropagation (BRB)-Trainbr training algorithm, together with the radial basis normalized-Radbasn transfer function, scored best in predicting the coefficient of friction with R2 values between 0.9318 and 0.9180 for the training and testing datasets, respectively.

Increasing the accuracy of estimating the viscosity of SAE40-based nanofluid containing MWCNT-TiO2 nanoparticles using a creative method in optimizing the structure of the artificial neural network

The viscosity (μnf) is one of the influencing parameters in choosing that nanofluid (NF) that affects its thermal behavior and heat transfer. In this regard, the present study is conducted to investigate the μnfof MWCNT-TiO2 (10:90) /SAE40 NF using an artificial neural network (ANN). ANN design in temperature conditions between 25 and 50°C and in different solid volume fraction (SVF) of nanoparticles (φ =0.0625%−1%). 174 laboratory data were used. Three inputs (temperature(T), φ and shear rate(SR)) and one output (μnf) are determined for ANN. In this study, ANN modeling was done with MLP method and Levenberg-Marquardt (LM) training algorithm. The selected optimal structure, among different ANN structures for MWCNT-TiO2(10:90)/SAE40 NF, has two hidden layers with an optimal structure of 10 and 4 neurons in the first and second layers. The results of R and MSE coefficients prove the accuracy of the proposed model., which in the final stage was set equal to 0.9999507 and 0.004599708, respectively. The margin of deviation (MOD) in the grid data set is in the range − 3% <MOD < + 3%. Based on studies that considered ANN correlation with computational data compared to laboratory data, the results of this comparison show that the ANN is more accurate and reliable for estimating the μnf. The turning point of this article is designing and predicting the viscosity of MWCNT-TiO2/SAE40 NF in the least time and financial costs compared to repetitive and time-consuming experiments through ANN.

An efficient estimation of crop performance in sheep fescue (Festuca ovina L.) using artificial neural network and regression models

Festuca ovina L. (sheep fescue), a perennial grass plant found in mountainous regions, is important from both an ecological and economic viewpoint. However, the variability of biological yield of sheep fescue due to its reliance on different characteristics makes it difficult to accurately prediction using classic modeling techniques. In this study, machine learning methods and multiple regression models (linear and non-linear) are used to investigate the interdependence of various morphological and physiological characteristics on accurate prediction of the biological yield (BY) of sheep fescue. Principal components analysis and stepwise regression were used to select six agronomic parameters i.e. thousand seed weight (TSW), relative water content (RWC), canopy cover (CC), leaf area index, number of florescence, and viability (VA), while the output variable was BY. To optimized the artificial neural network (ANN) structure, different transfer functions and training algorithms, different number of neurons in each layer, different number of hidden layers and training iteration were tested. The accuracy of the models and algorithms is analyzed by root mean square error (RMSE), mean absolute error (MAE), and determination coefficient (R2). According to the findings, ANN models were more accurate than regression models. The ANN model with two hidden layers (i.e. structure of 6–4–8–1) which had RMSE, MAE and R2 scores of 0.087, 0.065 and 0.96, respectively, was discovered as the best model for predicting the BY. In addition, result of the sensitivity analysis showed TSW, RWC and CC, in that order, were the variables most important for high-quality BY estimation in both models regardless of input combination. Finally, the paper concludes that early flowering sheep fescue genotypes with long maturation and great TSW must be regarded as the most suitable model for increasing BY in breeding projects.

ANN-based performance prediction of electrical discharge machining of Ti-13Nb-13Zr alloys

PurposeThe purpose of this paper is to predict the machining performance of electrical discharge machining of Ti-13Nb-13Zr (TNZ) alloy, a promising biomedical alloy, using artificial neural networks (ANN) models.Design/methodology/approachIn the research, three major performance characteristics, i.e. the material removal rate (MRR), tool wear rate (TWR) and surface roughness (SR), were chosen for the study. The input parameters for machining were the voltage, current, pulse-on time and pulse-off time. For the ANN model, a two-layer feedforward network with sigmoid hidden neurons and linear output neurons were chosen. Levenberg–Marquardt backpropagation algorithm was used to train the neural networks.FindingsThe optimal ANN structure comprises four neurons in input layer, ten neurons in hidden layer and one neuron in the output layer (4–10-1). In predicting MRR, the 60–20-20 data split provides the lowest MSE (0.0021179) and highest R-value for training (0.99976). On the contrary, the 70–15-15 data split results in the best performance in predicting both TWR and SR. The model achieves the lowest MSE and highest R-value for training in predicting TWR as 1.17E-06 and 0.84488, respectively. Increasing the number of hidden neurons of the network further deteriorates the performance. In predicting SR, the authors find the best MSE and R-value as 0.86748 and 0.94024, respectively.Originality/valueThis is a novel approach in performance prediction of electrical discharge machining in terms of new workpiece material (TNZ alloys).

Prediction of Friction Coefficient for Ductile Cast Iron Using Artificial Neural Network Methodology Based on Experimental Investigation

The key objective of the present study is to analyze the friction coefficient and wear rate for ductile cast iron. Three different microstructures were chosen upon which to perform the experimental tests under different sliding time, load, and sliding speed conditions. These specimens were perlite + ferrite, ferrite, and bainitic. Moreover, an artificial neural network (ANN) model was developed in order to predict the friction coefficient using a set of data collected during the experiments. The ANN model structure was made up of four input parameters (namely time, load, number, and nodule diameter) and one output parameter (friction coefficient). The Levenberg–Marquardt back-propagation algorithm was applied in the ANN model to train the data using feed-forward back propagation (FFBP). The results of the experiments revealed that the coefficient of friction reduced as the sliding speed increased under a constant load. Additionally, it exhibits the same pattern of action when the test is run with a heavy load and constant sliding speed. Additionally, when the sliding speed increased, the wear rate dropped. The results also show that the bainite structure is harder and wears less quickly than the ferrite structure. Additionally, the results pertaining to the ANN structure showed that a single hidden layer model is more accurate than a double hidden layer model. The highest performance in the validation stage, however, was observed at epochs 8 and 20, respectively, for a double hidden layer and at 0.012346 for a single layer at epoch 20.

Modelling of n-Hexadecane bioremediation from soil by slurry bioreactors using artificial neural network method

Diesel oil is known to be one of the major petroleum products that can pollute water and soil. Soil pollution caused by petroleum hydrocarbons has substantially impacted the environment, especially in the Middle East. In this study, modeling and optimization of hexadecane removal from soil was performed using two pure cultures of Acinetobacter and Acromobacter and consortium culture of both bacterial species using artificial neural network (ANN) method. Then the best ANN structure was proposed based on mean square error (MSE) as well as correlation coefficient (R) for pure cultures of Acinetobacter and Acromobacter as well as their consortium. The results showed that the correlations between the actual data and the data predicted by ANN (R2) in Acromobacter, Acinetobacter and consortium of both cultures were 0.50, 0.47 and 0.63, respectively. Despite the low correlation between the experimental data and the data predicted by the ANN, the correlation coefficient and the precision of ANN for the consortium was higher. As a result, ANN had desirable precision to predict hexadecan removal by the cobsertium culture of Ochromobater and Acintobacter.

A Dimension-Reduced Artificial Neural Network Model for the Cell Voltage Consistency Prediction of a Proton Exchange Membrane Fuel Cell Stack

The voltage consistency of hundreds of cells in a proton exchange membrane fuel cell stack significantly influences the stack’s performance and lifetime. Using the physics-based model to estimate the cell voltage consistency is highly challenging due to the massive calculation efforts and the complicated fuel cell designs. In this research, an artificial neural network (ANN) model is developed to efficiently predict the cell voltage distribution and the consistency of a commercial-size fuel cell stack. To balance the computation efficiency and accuracy, a dimension-reduced method is proposed with different output-grouping strategies to optimize the ANN structure based on the experiment test of a 100-cell stack. The model’s training time falls nonlinearly from 16 min to 6 s with the output neuron number decreasing from 100 to 5, while the model can still predict the cell voltage distribution trends. With the proposed model, the stack’s cell voltage distributions could be reproduced with significantly lowered computation time, which is beneficial to evaluate the fuel cell status and optimize the control strategies.

Increasing the accuracy of estimating the dynamic viscosity of hybrid nano-lubricants containing MWCNT-MgO by optimizing using an artificial neural network

Artificial neural network (ANN) is utilized as efficient models to forecast the nanofluids (NFs) viscosity (μnf). In this examination, ANN is used to forecast the μnf of the MWCNT-MgO (25 % −75 %) / SAE40 nano-lubricant (NL) experimental data set. Experimental evaluation of NLs is taken in volume fraction of nanoparticles (NPs) φ= 0.0625 % −1% and temperature range of T = 25 to 50 °C. To predict the μnf of the data using ANN, a multilayer perceptron (MLP) ANN with the algorithm of Levenberg-Marquardt (LM) is utilized. For ANN modeling, temperature, φ and shear rate (γ̇) are determined as inputs and μnf is determined as output. From 400 various ANN samples for NL, the optimal sample (OS) is selected, comprising two hidden layers (HLs) with the OS of 8 and 5 neurons in the primary and second layer, respectively. Eventually, for the OS, the amount of the regression coefficient (RC) and the mean square error (MSE) are set equal to 0.9999882 and 0.001453292, respectively. The margin of deviation (MOD) for all ANN information is in the range of less than −1% <MOD <+1%. It's good because the ANN pattern is more precise and has a great ability to forecast μnf. The main goal of this research is to model and estimate the μnf of MWCNT-MgO (25:75)/SAE40 NL through ANN and also to select the optimal structure from the set of predicted ANN structures and manage time and cost.

Integration of an artificial neural network and a simulated annealing algorithm for the optimization of the river water pollution index

The Shatt Al-Arab River is the primary source of the water supply in the Al-Basrah province. Therefore, this study aimed to assess the water pollution index (WPI) of the Shatt Al-Arab River at 15 water treatment plants (WTPs) from 2011 to 2020 (except for WTP No. 11, which was sampled from 2012 to 2020). The WPI included 12 physicochemical parameters: turbidity (Tur), pH, electrical conductivity (EC), total dissolved solids (TDS), total hardness (TH), potassium (K+), sodium (Na+), magnesium (Mg+2), calcium (Ca+2), alkalinity (Alk), chloride (Cl−), and sulfate (SO4−2). Two modeling methods, multiple linear regression (MLR) and an artificial neural network (ANN), were utilized to forecast the minimum value of the WPI. The simulated annealing (SA) technique and an integrated ANN-SA technique were used to estimate the best independent variable values that minimized the value of the WPI. A multilayer feed-forward neural network with a backpropagation algorithm was chosen for this study. A regression technique was employed to generate the WPI predicted equation which was also chosen as an objective function of the SA and combined ANN-SA. For the MLR method, the correlation coefficient (R) and mean squared error (MSE) values for the WPI were 4.746 × 10−7 and 1, respectively. The best ANN structure (10-17-1) predicted a WPI with MSE and R values of 8.851 × 10−11 and 1, respectively, for the training, 1.220 × 10−7 and 1 for the validation, and 1.354 × 10−9 and 1 for the testing. In contrast to the results obtained from the measured data, MLR analysis, and ANN technique, the combined ANN-SA method demonstrated the lowest WPI value at optimal parameters. The minimum WPI value for the integrated ANN-SA was 0.373.

Artificial Neural Networks for Microwave Computer-Aided Design: The State of the Art

This article presents an overview of artificial neural network (ANN) techniques for a microwave computer-aided design (CAD). ANN-based techniques are becoming useful for performing forward/inverse modeling for active/passive components to enhance a circuit design. With measured or simulated data of microwave devices, ANNs can be trained to learn relevant microwave relationships, which are, otherwise, computationally expensive or for which efficient analytical formulas are not available. Fundamental concepts of the ANN structure and training, such as feedforward neural networks (FFNNs), recurrent neural networks (RNNs)/dynamic neural networks (DNNs)/time-delay neural networks (TDNNs), deep neural networks, and neural network training and extrapolation, are described. Knowledge-based neural networks (KBNNs) are described for improving the accuracy and reliability of modeling and design optimization. Various advanced ANN techniques, such as neuro-transfer function (neuro-TF) modeling, neural network inverse modeling, and deep neural network modeling, are discussed. The existing and emerging applications of ANN in microwave CAD are identified, such as electromagnetic (EM)/multiphysics modeling, modeling of nonlinear circuits and transistors, filter design, very large-scale integration (VLSI) interconnects, oscillator, transmitter and receiver modeling, and CAD applications in such as gallium nitride (GaN) high electron-mobility transistor (HEMT), wireless power transfer (WPT), microelectromechanical system (MEMS), and substrate-integrated waveguide (SIW).

A Robust Learning Algorithm Based on Particle Swarm Optimization for Pi-Sigma Artificial Neural Networks.

Artificial neural networks (ANNs) have been frequently used in forecasting problems in recent years. One of the most popular types of ANNs in these days is Pi-Sigma artificial neural networks (PS-ANNs). PS-ANNs have a high order ANN structure and they use both multiplicative and additive neuron models in their architecture. PS-ANNs produce superior forecasting performance because of their high order structure. PS-ANNs are affected negatively by an outlier or outliers in a data set because of having a multiplicative neuron model in their architecture. In this study, a new robust learning algorithm based on particle swarm optimization and Huber's loss function for PS-ANNs is proposed. To evaluate the performance of the proposed method, Dow Jones stock exchange and Australian beer consumption data sets are analyzed and the obtained results are compared with many ANNs types proposed in the literature. Besides, the performance of the proposed method in outlier cases is also investigated by injecting outliers into these data sets. It is seen that the proposed learning algorithm has a satisfying performance both the data have an outlier or outliers' case and original case.

Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network

This study suggests a novel method for estimation of uncertain stock model parameters driven by Liu process. The proposed method decomposes the parameter estimation problem into two sub-problems: the first sub-problem implements an optimized artificial neural network based on the observed data, and the next sub-problem estimates the uncertain model parameters according to the optimized artificial neural network. We apply Nelder–Mead algorithm to optimize the artificial neural network and parameter estimation problem. The main supremacy of the presented method is that the estimation problem is independent of time intervals among observations and can be used to model future data. Providing a comparative method shows that the proposed approach can be effective for non-linear problems in which the artificial neural network structures perform well.

Automatic diagnosis of newly emerged heart failure from serial electrocardiography by repeated structuring & learning procedure

Heart failure (HF) diagnosis, typically visually performed by serial electrocardiography, may be supported by machine-learning approaches. Repeated structuring & learning procedure (RS&LP) is a constructive algorithm able to automatically create artificial neural networks (ANN); it relies on three parameters, namely maximal number of hidden layers (MNL), initializations (MNI) and confirmations (MNC), arbitrarily set by the user. The aim of this study is to evaluate RS&LP robustness to varying values of parameters and to identify an optimized combination of parameter values for HF diagnosis. To this aim, the Leiden University Medical Center HF database was used. The database is constituted by 129 serial ECG pairs acquired in patients who experienced myocardial infarction; 48 patients developed HF at follow-up (cases), while 81 remained clinically stable (controls). Overall, 15 ANNs were created by considering 13 serial ECG features as inputs (extracted from each serial ECG pair), 2 classes as outputs (cases/controls), and varying values of MNL (1, 2, 3, 4 and 10), MNI (50, 250, 500, 1000 and 1500) and MNC (2, 5, 10, 20 and 50). The area under the curve (AUC) of the receiver operating characteristic did not significantly vary with varying parameter values (P ≥ 0.09). The optimized combination of parameter values, identified as the one showing the highest AUC, was obtained for MNL = 3, MNI = 500 and MNC = 50 (AUC = 86 %; ANN structure: 3 hidden layers of 14, 14 and 13 neurons, respectively). Thus, RS&LP is robust, and the optimized ANN represents a potentially useful clinical tool for a reliable automatic HF diagnosis.

Https://dsr.mutah.edu.jo/index.php/jje/article/view/3

This paper presents a new islanding detection technique based on an artificial neural network (ANN) for a doubly fed induction wind turbine (DFIG). This technique takes advantage of ANN as pattern classifiers. Five different ANN systems are presented in this paper based on various inputs: three phase power, phase voltage, phase current, neutral voltage, and neutral current. An ANN structure is trained for each input, and the comparison between the different structures is presented. Feedforward ANN structures are used for the five systems. Three different learning algorithms are used: backpropagation and two artificial optimization techniques: Genetic Algorithm (GA) and Cuckoo optimization algorithm. For each method in each training technique, the results and the cost function are presented. The comparison of different inputs different algorithms is conducted. MATLAB 2020a is used to simulate the ANN structure and code the training algorithms. A detailed discussion of the input sample rate has also been manipulated to make the computational burden a factor in assessing the performance.

Machine-Learning-Based Compact Modeling for Sub-3-nm-Node Emerging Transistors

In this paper, we present an artificial neural network (ANN)-based compact model to evaluate the characteristics of a nanosheet field-effect transistor (NSFET), which has been highlighted as a next-generation nano-device. To extract data reflecting the accurate physical characteristics of NSFETs, the Sentaurus TCAD (technology computer-aided design) simulator was used. The proposed ANN model accurately and efficiently predicts currents and capacitances of devices using the five proposed key geometric parameters and two voltage biases. A variety of experiments were carried out in order to create a powerful ANN-based compact model using a large amount of data up to the sub-3-nm node. In addition, the activation function, physics-augmented loss function, ANN structure, and preprocessing methods were used for effective and efficient ANN learning. The proposed model was implemented in Verilog-A. Both a global device model and a single-device model were developed, and their accuracy and speed were compared to those of the existing compact model. The proposed ANN-based compact model simulates device characteristics and circuit performances with high accuracy and speed. This is the first time that a machine learning (ML)-based compact model has been demonstrated to be several times faster than the existing compact model.

Non-Destructive Prediction of Piperine in Javanese Chilli (Piper Retrofractum Vahl) Based on Color and Texture Analysis Using Artificial Neural Network

Measurement of active substances in herbal plants is currently becoming the major focus of the health industry in Indonesia. Previously, measurement of the active substance had been carried out destructively by extraction methods such as maceration and reflux, which was done by damaged the substrate and required a complicated step. The Artificial Neural Network (ANN), which combined with color and textural analysis methods provides a fast, easy process, does not damage the sample, and minimize errors due to human factors. This study aims to determine and build a relation model between image parameters and the piperine content of Javanese chilli using an optimized ANN with feature selection. The best topology in this study was obtained with an 8-30-40-1 structure (8 inputs, 30 hidden layers 1 node, 40 hidden layers 2 nodes, and 1 output) with a learning rate of 0.1 and a momentum of 0.9; traincgf as a learning function and an activation function of tansig-tansig-purelin. The ANN structure produces a training correlation coefficient (R) of 0.0975, an R validation of 0.9457, a training Mean Square Error (MSE) value of 0.01, and a validation MSE value of 0.0215.

Uncertainty Propagation Based MINLP Approach for Artificial Neural Network Structure Reduction

The performance of artificial neural networks (ANNs) is highly influenced by the selection of input variables and the architecture defined by hyper parameters such as the number of neurons in the hidden layer and connections between network variables. Although there are some black-box and trial and error based studies in the literature to deal with these issues, it is fair to state that a rigorous and systematic method providing global and unique solution is still missing. Accordingly, in this study, a mixed integer nonlinear programming (MINLP) formulation is proposed to detect the best features and connections among the neural network elements while propagating parameter and output uncertainties for regression problems. The objective of the formulation is to minimize the covariance of the estimated parameters while by (i) detecting the ideal number of neurons, (ii) synthesizing the connection configuration between those neurons, inputs and outputs, and (iii) selecting optimum input variables in a multi variable data set to design and ensure identifiable ANN architectures. As a result, suggested approach provides a robust and optimal ANN architecture with tighter prediction bounds obtained from propagation of parameter uncertainty, and higher prediction accuracy compared to the traditional fully connected approach and other benchmarks. Furthermore, such a performance is obtained after elimination of approximately 85% and 90% of the connections, for two case studies respectively, compared to traditional ANN in addition to significant reduction in the input subset.

A pretraining domain decomposition method using artificial neural networks to solve elliptic PDE boundary value problems

Developing methods of domain decomposition (DDM) has been widely studied in the field of numerical computation to estimate solutions of partial differential equations (PDEs). Several case studies have also reported that it is feasible to use the domain decomposition approach for the application of artificial neural networks (ANNs) to solve PDEs. In this study, we devised a pretraining scheme called smoothing with a basis reconstruction process on the structure of ANNs and then implemented the classic concept of DDM. The pretraining process that is engaged at the beginning of the training epochs can make the approximation basis become well-posed on the domain so that the quality of the estimated solution is enhanced. We report that such a well-organized pretraining scheme may affect any NN-based PDE solvers as we can speed up the approximation, improve the solution’s smoothness, and so on. Numerical experiments were performed to verify the effectiveness of the proposed DDM method on ANN for estimating solutions of PDEs. Results revealed that this method could be used as a tool for tasks in general machine learning.

A Neural Network Approach to Estimate Transient Aerodynamic Properties of a Flapping Wing System

Understanding the causal impacts among various parameters is essential for designing micro aerial vehicles (MAVs). The simulation of computational fluid dynamics (CFD) provides us with a technique to calculate aerodynamic forces precisely. However, even a single result regularly takes considerable computational time. Machine learning, due to the advance in computer hardware, shows another approach that can speed up the analysis process. In this study, we introduce an artificial neural network (ANN) framework to predict the transient aerodynamic forces and the corresponding energy consumption. Instead of considering the whole transient changes of each parameter as inputs, we utilised the technique of Fourier transform to simplify the ANN structure for minimising the computation cost. Furthermore, two typical activation functions, rectified linear unit (ReLU) and sigmoid, were attempted to build the network. The validity of the method was further examined by comparing it with CFD simulation. The result shows that both functions are able to provide highly accurate estimations that can be implemented for model construction under this framework. Consequently, this novel approach makes it possible to reduce the complexity of analysis, study the flapping wing aerodynamics and enable a more efficient way to optimise parameters.