Design of cascade artificial neural networks optimized with the memetic computing paradigm for solving the nonlinear Bratu system

Hassan, Aisarul; Ahmad, Siraj-ul-Islam; Kamran, Muhammad; Illahi, Ahsan; Raja, Muhammad Asif Zahoor

doi:10.1140/epjp/i2019-12530-5

Cited by 25 publications

(13 citation statements)

References 62 publications

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“…• We have analyzed a mathematical model which represents the temperature profiles of longitudinal fins with concave parabolic, rectangular, and trapezoidal shapes, see Section 2 and FIGURE 2. Equations (37)(38)(39), and (46)(47)(48). These solutions may be used by researchers to reproduce our results for further studies.…”

Section: Discussionmentioning

confidence: 78%

“…A generalized approximate solution for the problem considered in this research and its nth derivative is given as [39]:…”

Section: A Construction Of Ann Modelmentioning

confidence: 99%

“…Nowadays, mathematical models of real applications are represented as ODEs and different metaheuristics are been designed to solve these problems. Numerical optimization techniques like genetic algorithm [38], [39], different variants of particle swarm optimization (PSO) [40]- [42], interior point algorithm [43], evolutionary programming [44] and others [45], [46] are used to solve mathematical models involving ODEs and PDEs. In [41], a variant of PSO is designed and applied to solve nonlinear ODEs.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Temperature Profiles in Longitudinal Fin Designs by a Novel Neuroevolutionary Approach

et al. 2020

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Real application problems in physics, engineering, economics, and other disciplines are often modeled as differential equations. Classical numerical techniques are computationally expensive when we require solutions to our mathematical problems with no prior information. Hence, researchers are more interested in developing numerical methods that can obtain better solutions with fewer efforts and computational time. Heuristic algorithms are considered suitable candidates for such type of problems. In this research, we have developed a new neuroevolutionary algorithm that combines the power of feed-forward artificial neural networks (ANNs) and a modern metaheuristic, the Symbiotic Organism Search (SOS) algorithm. With our new approach, we have analyzed the simultaneous surface convection and radiation during heat transfer in different models of fins/ heat exchangers. Longitudinal fins are considered with concave parabolic, rectangular and trapezoidal shapes. We have analyzed our problem in two scenarios and six sub-cases. Our solutions are of high quality, with minimum residual errors in all cases. We have established the quality of our results by calculating values of different performance indicators like Root-mean-square error (RMSE), Absolute error (AE), Generational distance (GD), Mean absolute deviation (MAD), Nash-Sutcliffe efficiency (NSE), Error in Nash-Sutcliffe efficiency (ENSE). Statistical and graphical analysis of our results suggests that our approach is suitable for handling real application problems. We have compared our results with state-of-the-art results, and the outcome of our analysis points to the superiority of our approach. INDEX TERMS Approximate solutions, Artificial neural networks, Heat transfer analyses, Longitudinal fins, Metaheuristics, Symbiotic organism search optimizer.

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Section: Discussionmentioning

confidence: 78%

“…A generalized approximate solution for the problem considered in this research and its nth derivative is given as [39]:…”

Section: A Construction Of Ann Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of Temperature Profiles in Longitudinal Fin Designs by a Novel Neuroevolutionary Approach

et al. 2020

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“…In GAs, the population of individual frequently changes/updated, i.e., applicant solutions of optimization assignment, and have the capability to solve various optimization models by unifying its reproduction tools through the operators; crossover, selection, elitism, and mutation. Some recent applications exploited by GAs are optimization of variables in nonlinear Bratu system (Hassan et al 2019), layer thickness optimization for the multilayer piezoelectric transducer (Zameer 2019), integrated load dispatch problems involving both thermal and wind generators (Jamal 2019), estimation of parameters in electromagnetic plane waves (Akbar 2017), and analysis of the dynamics for heartbeat model (Raja et al 2017b). The sluggishness and laziness of GAs through hybridization with the local search algorithms can be upgraded and improved during the process of optimization.…”

Section: Network Optimizationmentioning

confidence: 99%

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

et al. 2020

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In the present study, a novel fractional Meyer neuro-evolution-based intelligent computing solver (FMNEICS) is presented for numerical treatment of doubly singular multi-fractional Lane-Emden system (DSMF-LES) using combined heuristics of Meyer wavelet neural networks (MWNN) optimized with global search efficacy of genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., MWNN-GASQP. The design of novel FMNE-ICS for DSMF-LES is presented after derivation from standard Lane-Emden equation, and the singular points and shape factors along with fractional-order terms are analyzed. The MWNN modeling strength is used to represent the system model DSMF-LES in the meansquared error-based merit function and optimization of the networks is carried out with integrated optimization ability of GASQP. The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures. Moreover, the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver. Keywords Multi-fractional Lane-Emden model • Multi-singular systems • Artificial neural networks • Meyer wavelet neural networks • Sequential quadratic programming • Genetic algorithms Mathematics Subject Classification 34-XX • 34A08 • 34A34 • 82B31

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“…e convolutional and pooling layer's operation permits the DNN network to get more knowledge about spatial. Hence, the CNN architecture shows exceptional results particularly on image applications [21,22].…”

Section: Convolutional Neural Networkmentioning

confidence: 99%

A Review of Deep Learning Security and Privacy Defensive Techniques

Tariq

Memon

Ahmed

et al. 2020

Mobile Information Systems

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In recent past years, Deep Learning presented an excellent performance in different areas like image recognition, pattern matching, and even in cybersecurity. The Deep Learning has numerous advantages including fast solving complex problems, huge automation, maximum application of unstructured data, ability to give high quality of results, reduction of high costs, no need for data labeling, and identification of complex interactions, but it also has limitations like opaqueness, computationally intensive, need for abundant data, and more complex algorithms. In our daily life, we used many applications that use Deep Learning models to make decisions based on predictions, and if Deep Learning models became the cause of misprediction due to internal/external malicious effects, it may create difficulties in our real life. Furthermore, the Deep Learning training models often have sensitive information of the users and those models should not be vulnerable and expose security and privacy. The algorithms of Deep Learning and machine learning are still vulnerable to different types of security threats and risks. Therefore, it is necessary to call the attention of the industry in respect of security threats and related countermeasures techniques for Deep Learning, which motivated the authors to perform a comprehensive survey of Deep Learning security and privacy security challenges and countermeasures in this paper. We also discussed the open challenges and current issues.

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Design of cascade artificial neural networks optimized with the memetic computing paradigm for solving the nonlinear Bratu system

Cited by 25 publications

References 62 publications

Analysis of Temperature Profiles in Longitudinal Fin Designs by a Novel Neuroevolutionary Approach

Analysis of Temperature Profiles in Longitudinal Fin Designs by a Novel Neuroevolutionary Approach

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

A Review of Deep Learning Security and Privacy Defensive Techniques

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