ARTICLE IN PRESS Review article Neural networks in auroral data assimilation Fabrı ´cio P. Ha ¨ rter a,b,c,Ã , Haroldo F. de Campos Velho a,b,c , Erico L. Rempel a,b,c , Abraham C.-L. Chian a,b,c a University of Waterloo (UofW), Waterloo, ON, Canada 2NL 3G1 b National Institute for Space Research (INPE), Sa ˜o Jose´ dos Campos, SP,12227-010, Brazil c Instituto Tecnolo ´gico de Aerona ´utica, Prac - a Marechal Eduardo Gomes, 50, CEP 12228-900, Sa ˜o Jose´ dos Campos, Brazil article info Article history: Received 14 November 2006 Received in revised form 14 February 2008 Accepted 23 March 2008 Available online 18 April 2008 Keywords: Auroral radio emissions Nonlinear dynamics Chaos Data assimilation Kalman filter Neural networks abstract Data assimilation is an essential step for improving space weather forecasting by means of a weighted combination between observational data and data from a mathematical model. In the present work data assimilation methods based on Kalman filter (KF) and artificial neural networks are applied to a three-wave model of auroral radio emissions. A novel data assimilation method is presented, whereby a multilayer perceptron neural network is trained to emulate a KF for data assimilation by using cross-validation. The results obtained render support for the use of neural networks as an assimilation technique for space weather prediction. & 2008 Elsevier Ltd. All rights reserved. Contents 1. Introduction ......................................................................................... 1243 2. Nonlinear coupled wave equations ....................................................................... 1244 3. Methodology ........................................................................................ 1245 3.1. Kalman filter .................................................................................. 1245 3.2. Artificial neural network ......................................................................... 1246 4. Numerical experiments ................................................................................ 1246 5. Concluding remarks ................................................................................... 1248 Acknowledgments .................................................................................... 1249 References .......................................................................................... 1249 1. Introduction Space weather research is the study of the disturbances in the space environment, usually caused by the solar activity and/or interactions of interstellar medium and galactic cosmic rays with the heliosphere. Due to the potential impact of space weather on technological systems, as well as on human health (Chian, 2003), space weather forecasting is today an essential task. One of the main problems in forecasting is the chaotic nature of the mathematical models. Nonlinear and chaotic phenomena represented by mathematical models have an intrinsic relationship with the initial conditions (ICs). Therefore, Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jastp Journal of Atmospheric and Solar-Terrestrial Physics 1364-6826/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2008.03.018 Ã Corresponding author at: University of Waterloo (UofW), Waterloo, ON, Canada 2NL 3G1. Tel.: +55 6133431779; fax: +55 6133431619. E-mail address: fabricio.harter@inmet.gov.br (F.P. Ha ¨ rter). Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 1243–1250