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Title: Learning and Modeling Chaos Using LSTM Recurrent Neural Networks.

Abstract

In nonlinear dynamical systems, long-term prediction is extremely challenging. Small perturbations in an initial state can grow exponentially in time and result in large differences in a later advanced state - a behavior known as chaos. Chaotic systems tend to have sensitive dependence on initial conditions, much like the Butterfly Effect. Recurrent Neural Networks are dynamic and allow for modeling of chaotic behavior. In this paper, we study and investigate the the modeling and prediction abilities of a Long Short-Term Memory (LSTM) recurrent neural network in dynamical systems with chaotic behavior. In particular, we explore the Lorenz System - which comprises of a nonlinear system of differential equations describing two-dimensional flow of a fluid, and describe an architecture that models the systems’ behavior.

Keywords: Chaos, Dynamical Systems, Nonlinear Differential Equations, Long Short-Term Memory RNN, Lorenz System, Recurrent Neural Networks.