Numerical treatment for solving one-dimensional Bratu problem using neural networks

2012 ◽  
Vol 24 (3-4) ◽  
pp. 549-561 ◽  
Author(s):  
Muhammad Asif Zahoor Raja ◽  
Siraj-ul-Islam Ahmad
Keyword(s):  
Neural Networks ◽  
Numerical Treatment ◽  
One Dimensional ◽  
Bratu Problem

scholarly journals One Dimensional Convolutional Neural Networks for Seizure Onset Detection Using Long-term Scalp and Intracranial EEG

2021 ◽  
Author(s):  
Xiaoshuang Wang ◽  
Xiulin Wang ◽  
Wenya Liu ◽  
Zheng Chang ◽  
Tommi Karkkainen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Onset Detection ◽  
Seizure Onset ◽  
Intracranial Eeg ◽  
One Dimensional

scholarly journals A Machine Learning Approach as a Surrogate for a Finite Element Analysis: Status of Research and Application to One Dimensional Systems

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1654
Author(s):  
Poojitha Vurtur Badarinath ◽  
Maria Chierichetti ◽  
Fatemeh Davoudi Kakhki
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Artificial Neural Networks ◽  
Stress Distribution ◽  
Maintenance Scheduling ◽  
Element Analysis ◽  
One Dimensional ◽  
Artificial Neural

Current maintenance intervals of mechanical systems are scheduled a priori based on the life of the system, resulting in expensive maintenance scheduling, and often undermining the safety of passengers. Going forward, the actual usage of a vehicle will be used to predict stresses in its structure, and therefore, to define a specific maintenance scheduling. Machine learning (ML) algorithms can be used to map a reduced set of data coming from real-time measurements of a structure into a detailed/high-fidelity finite element analysis (FEA) model of the same system. As a result, the FEA-based ML approach will directly estimate the stress distribution over the entire system during operations, thus improving the ability to define ad-hoc, safe, and efficient maintenance procedures. The paper initially presents a review of the current state-of-the-art of ML methods applied to finite elements. A surrogate finite element approach based on ML algorithms is also proposed to estimate the time-varying response of a one-dimensional beam. Several ML regression models, such as decision trees and artificial neural networks, have been developed, and their performance is compared for direct estimation of the stress distribution over a beam structure. The surrogate finite element models based on ML algorithms are able to estimate the response of the beam accurately, with artificial neural networks providing more accurate results.

CHAOS AND TWO-TORI IN A NEW FAMILY OF 4-CNNS

2007 ◽  
Vol 17 (03) ◽  
pp. 953-963 ◽  
Author(s):  
XIAO-SONG YANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Cellular Neural Networks ◽  
Lyapunov Spectrum ◽  
Regular Array ◽  
Poincaré Maps ◽  
One Dimensional ◽  
Poincare Maps ◽  
New Family

In this paper we demonstrate chaos, two-tori and limit cycles in a new family of Cellular Neural Networks which is a one-dimensional regular array of four cells. The Lyapunov spectrum is calculated in a range of parameters, the bifurcation plots are presented as well. Furthermore, we confirm the nature of limit cycle, chaos and two-tori by studying Poincaré maps.

Numerical treatment of nonlinear singular Flierl–Petviashivili systems using neural networks models

2017 ◽  
Vol 31 (7) ◽  
pp. 2371-2394 ◽  
Author(s):  
Muhammad Asif Zahoor Raja ◽  
Junaid Ali Khan ◽  
Aneela Zameer ◽  
Najeeb Alam Khan ◽  
Muhammad Anwaar Manzar
Keyword(s):  
Neural Networks ◽  
Numerical Treatment

ROBUSTNESS OF COMPLETE STABILITY FOR 1-D CIRCULAR CNNs

2006 ◽  
Vol 16 (08) ◽  
pp. 2177-2190
Author(s):  
MAURO DI MARCO ◽  
CHIARA GHILARDI
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Nearest Neighbor ◽  
Perturbation Parameter ◽  
Relative Magnitude ◽  
Loss Of Stability ◽  
Unique Equilibrium ◽  
Small Perturbations ◽  
Structure Preserving ◽  
One Dimensional

This paper investigates the issue of robustness of complete stability of standard Cellular Neural Networks (CNNs) with respect to small perturbations of the nominally symmetric interconnections. More specifically, a class of circular one-dimensional (1-D) CNNs with nearest-neighbor interconnections only, is considered. The class has sparse interconnections and is subject to perturbations which preserve the interconnecting structure. Conditions assuring that the perturbed CNN has a unique equilibrium point at the origin, which is unstable, are provided in terms of relative magnitude of the perturbations with respect to the nominal interconnection weights. These conditions allow one to characterize regions in the perturbation parameter space where there is loss of stability for the perturbed CNN. In turn, this shows that even for sparse interconnections and structure preserving perturbations, robustness of complete stability is not guaranteed in the general case.

scholarly journals One-dimensional convolutional neural networks for low/high arousal classification from electrodermal activity

2022 ◽  
Vol 71 ◽  
pp. 103203
Author(s):  
Roberto Sánchez-Reolid ◽  
Francisco López de la Rosa ◽  
María T. López ◽  
Antonio Fernández-Caballero
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Electrodermal Activity ◽  
High Arousal ◽  
One Dimensional
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