Neurocomputing 63 (2005) 447–463 Neural network time series forecasting of finite-element mesh adaptation Larry Manevitz a,Ã , Akram Bitar a , Dan Givoli b a Department of Computer Science, University of Haifa, Haifa, Israel b Faculty of Aerospace Engineering, Technion, Israel Institute of Technology, Haifa, Israel Accepted 10 June 2004 Communicated by T. Heskes Available online 9 December 2004 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. r 2004 Elsevier B.V. All rights reserved. Keywords: Neural networks; Mesh adaptation; Time series prediction; Finite-element method; Time- dependent PDEs 1. Introduction The finite-element method (FEM) [1,11] is the most effective numerical techniques for solving various problems arising from mathematical physics and engineering. Actually, it is the most widely used numerical techniques for solving problems which are described by partial differential equations (PDEs). ARTICLE IN PRESS www.elsevier.com/locate/neucom 0925-2312/$-see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2004.06.009 Ã Corresponding author. E-mail addresses: manevitz@cs.haifa.ac.il (L. Manevitz), akram@il.ibm.com (A. Bitar), givolid@aerodyne.technion.ac.il (D. Givoli).