Multilayer Perceptron Feed-forward Neural Network Research Articles

Spatial Air Quality Assessment in Peninsular Malaysia: Insights from Environmetric Analyses and Artificial Neural Networks

The research investigated the spatial distribution of air quality in Peninsular Malaysia to offer crucial insights for mitigating air quality degradation. Utilizing historical data obtained from the Malaysian Department of Environment, eleven years' worth (2011-2021) of daily readings of PM10, O3 , SO2 , NO2 , and CO from thirty-four monitoring stations were subjected to environmetric techniques and Artificial Neural Network analysis. HACA successfully classified seven stations into the High Pollution Cluster (HPC), seven stations into the Moderate Pollution Cluster (MPC), and twenty stations into the Low Pollution Cluster (LPC). The discriminant analysis demonstrated a correct assignment rate of 91.87%, suggesting that all five parameters were able to discriminate with a significance level of p<0.0001. Principal Component Analysis (PCA) revealed two Variance Factors (VFs) across all clusters, with cumulative variances of 69.43% (HPC), 82.32% (MPC), and 62.16% (LPC) respectively. Furthermore, employing a Multi-Layer Perceptron Feed-Forward Artificial Neural Network (MLP-FF-ANN) model to predict API readings yielded a significant and strong correlation, as indicated by R2 =0.7774 and RMSE=9.9048. These findings hold significant potential in informing the adoption of effective preventative and management strategies.

Recurrent neural network for pitch control of variable-speed wind turbine.

Wind is one of the most widely used renewable energy sources due to its cost-effectiveness, power requirements, operation, and performance. There are many challenges in wind turbines, such as wind fluctuation, pitch control, and generator speed control. When the wind speed exceeds its rated value, the pitch angle controller limits the generator output power to its rated value. In this research work, several soft computing techniques have been implemented for pitch control of variable-speed wind turbine. The data is collected for the National Renewable Energy Laboratory offshore 5 MW baseline wind turbine. Wind speed, tip speed ratio, and power coefficient are taken as inputs, and pitch angle as output. Machine learning and artificial intelligence-based techniques such as recurrent neural networks (RNNs), adaptive neuro-fuzzy inference system (ANFIS), multilayer perceptron feed-forward neural network (MLPFFNN), and fuzzy logic controller (FLC) are implemented on MATLAB, and their results are evaluated in terms of mean square error (MSE) and root mean square error (RMSE). The controllers have been implemented in MATLAB/Simulink to schedule the wind turbine blade pitch angle and keep the output power stable at the rated value. The experimental results show that RNN provided the best results for 15 neurons in hidden layers and 1000 epochs with MSE of 3.28e-11 and RMSE of 5.54e-06, followed by MLPFFNN with MSE of 2.17e-10 and RMSE of 1.56e-05, ANFIS with MSE of 8.5e-05 and RMSE of 9.22e-03, and FLC with MSE of 6.25e-04 and RMSE of 0.025. The proposed scheme is more reliable and robust and can be easily implemented on a physical setup by using interfacing cards such as dSPACE, NI cards, and data acquisition cards.

Peristaltic transport of Sutterby nanofluid flow in an inclined tapered channel with an artificial neural network model and biomedical engineering application

Modern energy systems are finding new applications for magnetohydrodynamic rheological bio-inspired pumping systems. The incorporation of the electrically conductive qualities of flowing liquids into the biological geometries, rheological behavior, and propulsion processes of these systems was a significant effort. Additional enhancements to transport properties are possible with the use of nanofluids. Due to their several applications in physiology and industry, including urine dynamics, chyme migration in the gastrointestinal system, and the hemodynamics of tiny blood arteries. Peristaltic processes also move spermatozoa in the human reproductive system and embryos in the uterus. The present research examines heat transport in a two-dimensional deformable channel containing magnetic viscoelastic nanofluids by considering all of these factors concurrently, which is vulnerable to peristaltic waves and hall current under ion slip and other situations. Nanofluid rheology makes use of the Sutterby fluid model, while nanoscale effects are modeled using the Buongiorno model. The current study introduces an innovative numerical computing solver utilizing a Multilayer Perceptron feed-forward back-propagation artificial neural network (ANN) with the Levenberg–Marquardt algorithm. Data were collected for testing, certifying, and training the ANN model. In order to make the dimensional PDEs dimensionless, the non-similar variables are employed and calculated by the Homotopy perturbation technique. The effects of developing parameters such as Sutterby fluid parameter, Froude number, thermophoresis, ion-slip parameter, Brownian motion, radiation, Eckert number, and Hall parameter on velocity, temperature, and concentration are demonstrated. The machine learning model chooses data, builds and trains a network, and subsequently assesses its performance using the mean square error metric. Current results declare that the improving Reynolds number tends to increase the pressure rise. Improving the Hall parameter is shown to result in a decrease in velocity. When raising a fluid's parameter, the temperature profile rises.

Predicting opinion using deep learning: From burning to sustainable management of organic waste in Indian State of Punjab.

In winter season, the burning of crop residues for ease of sowing the next crop, along with industrial emissions and vehicular pollution leads to settling of a thick layer of smog in northern part of India. Therefore, to understand the opinion of farmers regarding sustainable management of organic waste, the present study was conducted in Ludhiana district of Indian state of Punjab. An ex post facto research design was used and a total of 800 dairy farmers having significant crop area were selected randomly for the study, grouped equally as small and large dairy farmers. Results revealed that majority of farmers had a highly favourable opinion regarding organic waste management due to the fact that they were aware of the ill-effects of undesirable practices like crop residue burning. Further, to predict the farmers' opinion and the effect of independent variables on farmers' opinion, a multi-layer perceptron feed-forward deep neural network was developed with mean squared error of 0.036 and 0.137 for validation and training data sets respectively, marking a novel approach of analysing farmers' behaviour. The neural network highlighted that with increase in the magnitude of input variables, namely, education, experience in dairying, information source utilisation, knowledge regarding organic waste management, etc., the farmers' opinion regarding sustainable waste management increases. The study concluded with the impression that cognitive processes like education, information and knowledge play a significant role in forming the opinion of the farmers. Therefore, efforts focusing on enhancing cognition should be made for sustainable management of organic waste.

Artificial neural network model of non-Darcy MHD Sutterby hybrid nanofluid flow over a curved permeable surface: Solar energy applications

The conversion of solar radiation to thermal energy has recently much interest as the requirement for renewable heat and power grows. Due to their enhanced ability to promote heat transmission, nanofluids can significantly improve solar-thermal systems' efficiency. This section aims to study the heat transfer behavior of the Sutterby hybrid nanofluid flow of magnetohydrodynamics in the presence of a non-uniform heat source/sink and linear thermal radiation over a non-Darcy curved permeable surface. A novel implementation of an intelligent numerical computing solver based on multi-layer perceptron (MLP) feed-forward back-propagation artificial neural network (ANN) with the Levenberg-Marquard algorithm is provided in the current study. Data were gathered for the ANN model's testing, certification, and training. Established mathematical equations are nonlinear, which are resolved for velocity, the temperature in addition to the skin friction coefficient, and the rate of heat transfer by using the bvp4c with MATLAB solver. The ANN model selects data, constructs and trains a network, then evaluates its efficacy via mean square error. Graphs illustrate the impact of a wide range of physical factors on variables, including pressure, velocity, and temperature. In the entire study, the thermal energy improved by the SiO2 (silicon dioxide) - Au (gold) hybrid nanofluid than the SiO2-TiO2 (titanium dioxide) hybrid nanofluid. The higher internal heat generation/absorption parameter values increase the temperature.

Fault Location of Doukan-Erbil 132kv Double Transmission Lines Using Artificial Neural Network ANN

Transmission lines are generally subjected to faults, so it is advantageous to determine these faults as quickly as possible. This study uses an Artificial Neural Network technique to locate a fault as soon as it happens on the Doukan-Erbil of 132kv double Transmission lines network. CYME 7.1-Programming/Simulink utilized simulation to model the suggested network. A multilayer perceptron feed-forward artificial neural network with a back propagation learning algorithm is used for the intelligence locator's training, testing, assessment, and validation. Voltages and currents were applied as inputs during the neural network's training. The pre-fault and post-fault values determined the scaled values. The neural network's performance was evaluated, and tests were run. Line-to-ground faults were examined. The study demonstrates how effective, rapid, and precise this method is at locating faults. The neural network's performance was examined, and tests were run on it. The overall performance of the mean square error in the trained network execution was 0.11792 at 35 epochs. The correlation coefficient at the entire target was 0.99987 percent of an error on the Doukan-Erbil double transmission lines.

Experimental Study for Thermophysical Properties of ZrO2/Ethylene Glycol Nanofluid: Developing an ANFIS Modeling and Proposing New Correlations

Nanofluids are potential coolants for heat transfer applications because of their excellent thermal characteristics. Experimentally the thermophysical properties of ZrO2/ethylene glycol nanofluids are determined at 0.2%, 0.4%, 0.6%, 0.8%, and 1.0% vol. concentrations. A two-step method is used to prepare the stable nanofluids. The ZrO2/EG nanofluids properties were estimated over temperature ranging from 20 °C to 60 °C. From the experimental data, a multi-layer perceptron feed-forward back propagation artificial neural network was developed. Additionally, new correlations were proposed for all the thermophysical properties. The experimental analysis showed that thermal conductivity is enhanced by 19.6% at 60 °C and viscosity is enhanced by 86.62% at 20 °C at 1.0% vol. of nanofluid, density is enhanced by 4.9%, and specific heat is decreased by 4.2% at 1.0% vol. of nanofluid and at 60 °C, over base fluid data. The proposed ANN model succeeded in predicting the target property with minimum RMSE. The results of the developed artificial neural network and its correlation analysis perfectly agree with the experimental data.

Indoor 2D Positioning Method for Mobile Robots Based on the Fusion of RSSI and Magnetometer Fingerprints.

Received signal strength indicator (RSSI)-based fingerprinting is a widely used technique for indoor localization, but these methods suffer from high error rates due to various reflections, interferences, and noises. The use of disturbances in the magnetic field in indoor localization methods has gained increasing attention in recent years, since this technology provides stable measurements with low random fluctuations. In this paper, a novel fingerprinting-based indoor 2D positioning method, which utilizes the fusion of RSSI and magnetometer measurements, is proposed for mobile robots. The method applies multilayer perceptron (MLP) feedforward neural networks to determine the 2D position, based on both the magnetometer data and the RSSI values measured between the mobile unit and anchor nodes. The magnetic field strength is measured on the mobile node, and it provides information about the disturbance levels in the given position. The proposed method is validated using data collected in two realistic indoor scenarios with multiple static objects. The magnetic field measurements are examined in three different combinations, i.e., the measurements of the three sensor axes are tested together, the magnetic field magnitude is used alone, and the Z-axis-based measurements are used together with the magnitude in the X-Y plane. The obtained results show that significant improvement can be achieved by fusing the two data types in scenarios where the magnetic field has high variance. The achieved results show that the improvement can be above 35% compared to results obtained by utilizing only RSSI or magnetic sensor data.

Statistical study of squeezing for soft rocks based on factor and regression analyses of effective parameters

The time-dependent deformation of rocks due to stress released by excavation is referred to as squeezing. Accurate evaluation of the squeezing at the design stage can dramatically reduce technical problems and the financial costs of underground structures. Although various methods are presented to predict tunnel squeezing at the preliminary stage, being site-specific and incorporating incomplete databases are deficiencies of the available procedures. In this study, based on a comprehensive literature review, we prepared a database of tunnel squeezing for soft rocks, including possible effective parameters. Statistical processing methods such as univariate, reduction, and cleaning were employed to improve the statistical quality of the database. The statistically-processed datasets were also validated based on various scales such as accuracy, convergence, and usefulness. Significant predictors of squeezing are recognized as the ratio of strength to stress and the rock mass classification system. New squeezing criteria were developed using binary and multi-class regression methods to predict the squeezing occurrence and intensity of soft rocks. The results are confirmed by a Multilayer Perceptron Feed-Forward Neural Network and are compared to well-known empirical equations. The developed equations are more accurate comparing the empirical equations used to predict the squeezing of soft rocks. This methodology can be utilized at the design stage for another database to predict squeezing rocks for topographic-stress and tectonic-stress-based cases.

Ensemble Machine Learning for Predicting Viscosity of Nanoparticle-Surfactant-Stabilized CO2 Foam

Summary This paper investigates the computational behaviors of simple-to-use, relatively fast, and versatile machine learning (ML) methods to predict apparent viscosity, a key rheological property of nanoparticle-surfactant-stabilized CO2 foam in unconventional reservoir fracturing. The first novelty of our study is the investigation of the predictive performance of ML approaches as viable alternatives for predicting the apparent viscosity of NP-Surf-CO2 foams. The predictive and computational performance of five nonlinear ML algorithms were first compared. Support vector regression (SVR), K-nearest neighbors (KNN), classification and regression trees (CART), feed-forward multilayer perceptron neural network (MLPNN), and multivariate polynomial regression (MPR) algorithms were used to create models. Temperature, foam quality, pressure, salinity, shear rate, nanoparticle size, nanoparticle concentration, and surfactant concentration were identified as relevant input parameters using principal component analysis (PCA). A data set containing 329 experimental data records was used in the study. In building the models, 80% of the data set was used for training and 20% of the data set for testing. Another unique aspect of this research is the examination of diverse ensemble learning techniques for improving computational performance. We developed meta-models of the generated models by implementing various ensemble learning algorithms (bagging, boosting, and stacking). This was done to explore and compare the computational and predictive performance enhancements of the base models (if any). To determine the relative significance of the input parameters on prediction accuracy, we used permutation feature importance (PFI). We also investigated how the SVR model made its predictions by utilizing the SHapely Additive exPlanations (SHAP) technique to quantify the influence of each input parameter on prediction. This work’s application of the SHAP approach in the interpretation of ML findings in predicting apparent viscosity is also novel. On the test data, the SVR model in this work had the best predictive performance of the single models, with an R2 of 0.979, root mean squared error (RMSE) of 0.885 cp, and mean absolute error (MAE) of 0.320 cp. Blending, a variant of the stacking ensemble technique, significantly improved this performance. With an R2 of 1.0, RMSE of 0.094 cp, and MAE of 0.087 cp, an SVR-based meta-model ensembled with blending outperformed all single and ensemble models in predicting apparent viscosity. However, in terms of computational time, the blended SVR-based meta-model did not outperform any of its constituent models. PCA and PFI ranked temperature as the most important factor in predicting the apparent viscosity of NP-Surf-CO2 foams. The ML approach used in this study provides a comprehensive understanding of the nonlinear relationship between the investigated factors and apparent viscosity. The workflow can be used to evaluate the apparent viscosity of NP-Surf-CO2 foam fracturing fluid efficiently and effectively.

Effect of Heat Input and Filling Ratio on Raise in Temperature of the Oscillating Heat Pipe with Different Working Fluids Using ANN Model

In the present article, feed forward multilayer perceptron neural network (FFMLPNN) model has been used to predict the rise in temperature in closed loop oscillating heat pipe filled with three different fluid i.e., Acetone, methanol and ethanol respectively. Experimental test was carried out for the inner diameter of 1.7mm copper tube for all the combinations of filling ratio, heat input and time taken to evaluate the performance of the OHP. Totally 2000 data sets have been used for Acetone and Methanol, 1500 data sets is used for ethanol in the present NN model. ANN model with FFMLPNN using three input parameter (Filling ratio, heat input and time taken) and rise in temperature has output parameter respectively. Levenberg-Marquardt algorithm with a 4-10 neurons has been used for the determination of optimal model. The 3-8-1 combinations predict the rise in temperature for ethanol and acetone whereas for methanol 3-7-1 is the optimal combinations was achieved. For all the combinations RMSE values are 0.3414, 0.1285 and 0.1237 (Training-70%), 0.3526, 0.1375, 0.1234 (testing-15%) and 0.3010, 0.1515, 0.1425 (validation-15%). The values for coefficient of determinations are 0.9941, 0.9975 and 0.9971 for methanol, acetone and ethanol was achieved. The results clearly indicated that the proposed MLPANN model can successfully predict the rise in temperature.

A unique artificial intelligence approach and mathematical model to accurately evaluate viscosity and density of several nanofluids from experimental data

In the present research paper, a unique single feed-forward multilayer perceptron neural network (MLPNN) based on data transformation technique and mathematical models were proposed for forecasting density and dynamic viscosity of Alumina (Al2O3)/distilled water (DW), multiwall carbon nanotube (MWCNT)/DW, and Graphene nanoparticle (GNP)/DW nanofluids. The density and dynamic viscosity of nanofluids (0.1%, 0.25%, 0.5%, 0.75%, and 1%) were experimentally measured in temperature range 30–80 °C. Nanofluids, volume concentration, and temperature were given as input and density and dynamic viscosity as output from the network. The statistical analysis was performed to predict the accuracy of both models. The experiments revealed that density and viscosity increase with an increase in nanofluid concentration, and decrease with an increase in temperature. The maximum increase in dynamic viscosity and density of 41.59% and 5.06% was noticed for Al2O3/DW nanofluid. The outcome shows that the MLPNN model is well trained at 12 perceptrons in the hidden layer using the Levenberg-Marquardt algorithm. The output obtained from MLPNN and the mathematical model were compared with experimental results. The maximum error < 0.2% in density and < 1% in viscosity measurement was noticed for both models.

A machine learning approach based on neural networks for energy diagnosis of telecommunication sites

Multi-layer-perceptron-feedforward neural-networks (MLPFFNNs) are proposed to monitor electricity consumption of generic telecommunication sites, thus addressing well-known energy saving and environmental issues. The proposed prediction tool helps infer telecommunication site efficiency, thus enabling undertaking suitable energy intelligence actions (monitoring, control and diagnosis, supervision) as a function of a large number of data and information. A trial-and-error analysis was performed to find the most accurate neural network for such a prediction task. Physical knowledge and intrinsic behavioral features of telecommunication sites indicated that 2 electricity consumptions- and 4 weather-related variables shall populate the input layer. The number of hidden neurons, along with training and test splitting percentages, were selected as the variables to refine within the networks development task. Statistical assessment of accuracy was conducted via joint evaluation of root mean square error and coefficient of determination. The precision and generalization of the best MLPFFNN were successfully assessed on a relevant sites dataset. Prediction percentage errors set to 5.65% and 5.77% for monthly and weekly assessment, respectively, thus confirming the suitability of the proposed modelling approach to meet regulatory standards (i.e., ISO 50001), requiring reliable and continuous monitoring and diagnosis of large fleets of industrial buildings, such as central offices and datacenters.

A neural network approach to estimate non-Newtonian behavior of nanofluid phase change material containing mesoporous silica particles

Neural networks are powerful tools for evaluating the thermophysical characteristics of nanofluids to reduce the cost and time of experiments. Dynamic viscosity is an important property in nanofluids that usually needs to be accurately computed in heat transfer and nanofluid flow problems. In this paper, the rheological properties of nanofluid phase change material containing mesoporous silica nanoparticles are predicted by the artificial neural networks (ANNs) method based on the experimental database reported in literature. Experimental inputs include nanoparticle mass fractions (0-5 wt.%), temperatures (35-55℃), and shear rates (10-200 s-1), and targets include dynamic viscosities and shear stresses. A multilayer perceptron feedforward neural network with Levenberg-Marquardt back-propagation training algorithm is utilized to predict rheological properties. The optimal network architecture consists of 22 neurons in the hidden layer based on the minimum mean square error (MSE). The results showed that the developed ANN has an MSE of 6.67×10-4 and 6.55×10-3 for the training and test dataset, respectively. The predicted dynamic viscosity and shear stress also have the maximum relative error of 6.26% and 0.418%, respectively.

Estimation of unsteady hydromagnetic Williamson fluid flow in a radiative surface through numerical and artificial neural network modeling

In current investigation, a novel implementation of intelligent numerical computing solver based on multi-layer perceptron (MLP) feed-forward back-propagation artificial neural networks (ANN) with the Levenberg–Marquard algorithm is provided to interpret heat generation/absorption and radiation phenomenon in unsteady electrically conducting Williamson liquid flow along porous stretching surface. Heat phenomenon is investigated by taking convective boundary condition along with both velocity and thermal slip phenomena. The original nonlinear coupled PDEs representing the fluidic model are transformed to an analogous nonlinear ODEs system via incorporating appropriate transformations. A data set for proposed MLP-ANN is generated for various scenarios of fluidic model by variation of involved pertinent parameters via Galerkin weighted residual method (GWRM). In order to predict the (MLP) values, a multi-layer perceptron (MLP) artificial neural network (ANN) has been developed. There are 10 neurons in hidden layer of feed forward (FF) back propagation (BP) network model. The predictive performance of ANN model has been analyzed by comparing the results obtained from the ANN model using Levenberg-Marquard algorithm as the training algorithm with the target values. When the obtained Mean Square Error (MSE), Coefficient of Determination (R) and error rate values have been analyzed, it has been concluded that the ANN model can predict SFC and NN values with high accuracy. According to the findings of current analysis, ANN approach is accurate, effective and conveniently applicable for simulating the slip flow of Williamson fluid towards the stretching plate with heat generation/absorption. The obtained results showed that ANNs are an ideal tool that can be used to predict Skin Friction Coefficients and Nusselt Number values.

Energy eigenvalues and neural network analysis for broken bars fault diagnosis in induction machine under variable load: experimental study

In this paper, a technique primarily based on the discrete wavelet transform (DWT) and the slip associated with a neural network (NN) for classification and fault detection of broken rotor bars in an induction machine has been proposed. The calculated energy in each decomposition level obtained by the DWT analysis and the slip of the motor are used as input to the classifier in order to diagnose the healthy and faulty classes. The advantage of this method lays in the use of one single current sensor with the slip factor in order to detect the presence of the fault and identify the number of broken bars under different load conditions. The DWT analysis is proposed to overcome the limitation of the Fourier analysis and it is mainly adapted for the non-stationary signals. Moreover, the slip factor is applied as a second input on the classifier of NN to eliminate the problem of low-load. Feed-forward multi-layer Perceptron neural network is chosen as a technique to classify the fault in an induction machine. This technique is performed and validated by experimental data.

Study of Neural-Kinematics Architectures for Model-Less Calibration of Industrial Robots

Modeless industrial robot calibration plays an important role in the increasing employment of robots in industry. This approach allows to develop a procedure able to compensate the pose errors without complex parametric model. The paper presents a study aimed at comparing neural-kinematic (N-K) architectures for a modeless non-parametric robotic calibration. A multilayer perceptron feed-forward neural network, trained in a supervised manner with the back-propagation learning technique, is coupled in different modes with the ideal kinematic model of the robot. A comparative performance analysis of different neural-kinematic architectures was executed on a two degrees of freedom SCARA manipulator, for direct and inverse kinematics. Afterward the optimal schemes have been identified and further tested on a three degrees of freedom full SCARA robot and on a Stewart platform. The analysis on simulated data shows that the accuracy of the robot pose can be improved by an order of magnitude after compensation.

A novel comparative analysis between the experimental and numeric methods on viscosity of zirconium oxide nanofluid: Developing optimal artificial neural network and new mathematical model

In this study, the viscosity of five different ZrO2/Water nanofluids of 0.0125%, 0.025%, 0.05%, 0.1% and 0.2% prepared by the two-step method were experimentally investigated. Using the experimental data obtained, a multi-layer perceptron feed-forward back-propagation artificial neural network and a new mathematical correlation have been developed in order to predict the viscosity of ZrO2/Water nanofluid. Experimental results revealed that viscosity decreases with increasing temperature and increases with increasing concentration. The outputs obtained from the developed artificial neural network and the new correlation were compared with the experimental results and analyzed. The results show that the developed artificial neural network can predict the viscosity of ZrO2/Water nanofluid with an average error rate of −0.11%. The new mathematical model developed has been able to calculate the viscosity of ZrO2/Water nanofluid with an error rate of −0.74%.

Solving Riccati-Type Nonlinear Differential Equations with Novel Artificial Neural Networks

In this study we investigate neural network solutions to nonlinear differential equations of Ricatti-type. We employ a feed-forward Multilayer Perceptron Neural Network (MLPNN), but avoid the standard back-propagation algorithm for updating the intrinsic weights. Our objective is to minimize an error, which is a function of the network parameters i.e., the weights and biases. Once the weights of the neural network are obtained by our systematic procedure, we need not adjust all the parameters in the network, as postulated by many researchers before us, in order to achieve convergence. We only need to fine-tune our biases which are fixed to lie in a certain given range, and convergence to a solution with an acceptable minimum error is achieved. This greatly reduces the computational complexity of the given problem. We provide two important ODE examples, the first is a Ricatti type differential equation to which the procedure is applied, and this gave us perfect agreement with the exact solution. The second example however provided us with only an acceptable approximation to the exact solution. Our novel artificial neural networks procedure has demonstrated quite clearly the function approximation capabilities of ANN in the solution of nonlinear differential equations of Ricatti type.

A Novel Method for Solving Ordinary Differential Equations with Artificial Neural Networks

This research work investigates the use of Artificial Neural Network (ANN) based on models for solving first and second order linear constant coefficient ordinary differential equations with initial conditions. In particular, we employ a feed-forward Multilayer Perceptron Neural Network (MLPNN), but bypass the standard back-propagation algorithm for updating the intrinsic weights. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial or boundary conditions and contains no adjustable parameters. The second part involves a feed-forward neural network to be trained to satisfy the differential equation. Numerous works have appeared in recent times regarding the solution of differential equations using ANN, however majority of these employed a single hidden layer perceptron model, incorporating a back-propagation algorithm for weight updation. For the homogeneous case, we assume a solution in exponential form and compute a polynomial approximation using statistical regression. From here we pick the unknown coefficients as the weights from input layer to hidden layer of the associated neural network trial solution. To get the weights from hidden layer to the output layer, we form algebraic equations incorporating the default sign of the differential equations. We then apply the Gaussian Radial Basis function (GRBF) approximation model to achieve our objective. The weights obtained in this manner need not be adjusted. We proceed to develop a Neural Network algorithm using MathCAD software, which enables us to slightly adjust the intrinsic biases. We compare the convergence and the accuracy of our results with analytic solutions, as well as well-known numerical methods and obtain satisfactory results for our example ODE problems.