Using Machine Learning for Climate Modelling: Application of Neural Networks to a Slow-Fast Chaotic Dynamical System as a Case Study

Abstract

This paper explores the capabilities of two types of recurrent neural networks, unidirectional and bidirectional long short-term memory networks, to build a surrogate model for a coupled fast–slow dynamic system and predicting its nonlinear chaotic behaviour. The dynamical system in question, comprising two versions of the classical Lorenz model with a small time-scale separation factor, is treated as an atmosphere–ocean research simulator. In numerical experiments, the number of hidden layers and the number of nodes in each hidden layer varied from 1 to 5 and from 16 to 256, respectively. The basic configuration of the surrogate model, determined experimentally, has three hidden layers, each comprising between 16 and 128 nodes. The findings revealed the advantages of bidirectional neural networks over unidirectional ones in terms of forecasting accuracy. As the forecast horizon increases, the accuracy of forecasts deteriorates, which was quite expected, primarily due to the chaotic behaviour of the fast subsystem. All other things being equal, increasing the number of neurons in hidden layers facilitates the improvement of forecast accuracy. The obtained results indicate that the quality of short-term forecasts with a lead time of up to 0.75 model time units (MTU) improves most significantly. The predictability limit of the fast subsystem (“atmosphere”) is somewhat greater than the Lyapunov time.