Neural network time series forecasting of finite-element mesh adaptation

Authors:
Larry Manevitz;Akram Bitar;Dan Givoli
Affiliations:
Department of Computer Science, University of Haifa, Haifa, Israel;Department of Computer Science, University of Haifa, Haifa, Israel;Faculty of Aerospace Engineering, Technion, Israel Institute of Technology, Haifa, Israel
Venue:
Neurocomputing
Year:
2005

Citing 13
Cited 8

Adaptive signal processing

Adaptive signal processing
Multilayer feedforward networks are universal approximators

Neural Networks
Original Contribution: On learning the derivatives of an unknown mapping with multilayer feedforward networks

Neural Networks
Original Contribution: Multilayer feedforward networks with a nonpolynomial activation function can approximate any function

Neural Networks
Fundamentals of neural networks: architectures, algorithms, and applications

Fundamentals of neural networks: architectures, algorithms, and applications
Approximating functions by neural networks: a constructive solution in the uniform norm

Neural Networks
Finite element solution of boundary value problems: theory and computation

Finite element solution of boundary value problems: theory and computation
Second-Order Methods for Neural Networks

Second-Order Methods for Neural Networks
Neural Networks for Pattern Recognition

Neural Networks for Pattern Recognition
Pattern Recognition and Neural Networks

Pattern Recognition and Neural Networks
Computational Differential Equations

Computational Differential Equations
Neural Networks for Modelling and Control of Dynamic Systems: A Practitioner's Handbook

Neural Networks for Modelling and Control of Dynamic Systems: A Practitioner's Handbook
Neural Network Time Series Forecasting of Financial Markets

Neural Network Time Series Forecasting of Financial Markets

Time series prediction with single multiplicative neuron model

Applied Soft Computing
A holistic approach for selecting a third-party reverse logistics provider in the presence of vagueness

Computers and Industrial Engineering
PSO-based single multiplicative neuron model for time series prediction

Expert Systems with Applications: An International Journal
A decision support system for demand forecasting with artificial neural networks and neuro-fuzzy models: A comparative analysis

Expert Systems with Applications: An International Journal
Definition of fuzzy logic rules representing finite element method experts' reasoning

Fuzzy Sets and Systems
Unsupervised adaptive neural-fuzzy inference system for solving differential equations

Applied Soft Computing
Unsupervised kernel least mean square algorithm for solving ordinary differential equations

Neurocomputing
A novel self-organizing complex neuro-fuzzy approach to the problem of time series forecasting

Neurocomputing

Quantified Score

Hi-index	0.02

Visualization

Abstract

Basic learning algorithms and the neural network model are applied to the problem of mesh adaptation for the finite-element method for solving time-dependent partial differential equations. Time series prediction via the neural network methodology is used to predict the areas of ''interest'' in order to obtain an effective mesh refinement at the appropriate times. This allows for increased numerical accuracy with the same computational resources as compared with more ''traditional'' methods.