<p>Most forecasting schemes in the geosciences, and in particular for predicting weather and<br>climate indices such as the El Ni&#241;o Southern Oscillation (ENSO), rely on process-based<br>numerical models [1]. Although statistical modelling[2] and prediction approaches also have<br>a long history, more recently, different machine learning techniques have been used to predict<br>climatic time series. One of the supervised machine learning algorithm which is suited for<br>temporal and sequential data processing and prediction is given by recurrent neural networks<br>(RNNs)[3]. In this study we develop a RNN-based method that (1) can learn the dynamics<br>of a stochastic time series without requiring access to a huge amount of data for training, and<br>(2) has comparatively simple structure and efficient training procedure. Since this algorithm<br>is suitable for investigating complex nonlinear time series such as climate time series, we<br>apply it to different ENSO indices. We demonstrate that our model can capture key features<br>of the complex system dynamics underlying ENSO variability, and that it can accurately<br>forecast ENSO for longer lead times in comparison to other recent studies[4].</p><p>&#160;</p><p>Reference:</p><p>[1] P. Bauer, A. Thorpe, and G. Brunet, &#8220;The quiet revolution of numerical weather prediction,&#8221;<br>Nature, vol. 525, no. 7567, pp. 47&#8211;55, 2015.</p><p>[2] D. Kondrashov, S. Kravtsov, A. W. Robertson, and M. Ghil, &#8220;A hierarchy of data-based enso<br>models,&#8221; Journal of climate, vol. 18, no. 21, pp. 4425&#8211;4444, 2005.</p><p>[3] L. R. Medsker and L. Jain, &#8220;Recurrent neural networks,&#8221; Design and Applications, vol. 5, 2001.</p><p>[4] Y.-G. Ham, J.-H. Kim, and J.-J. Luo, &#8220;Deep learning for multi-year enso forecasts,&#8221; Nature,<br>vol. 573, no. 7775, pp. 568&#8211;572, 2019.</p>