title: Synthesis of recurrent neural networks for dynamical system simulation.
abstract: We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that guarantees the quality of the network approximation. We show that a feedforward neural network can be trained on the vector-field representation of a given dynamical system using backpropagation, then recast it as a recurrent network that replicates the original system's dynamics. After detailing this algorithm and its relation to earlier approaches, we present numerical examples that demonstrate its capabilities. One of the distinguishing features of our approach is that both the original dynamical systems and the recurrent networks that simulate them operate in continuous time.
authors.affiliation: Maluuba Research, 2000 Peel Street, Montreal, Canada. Electronic address: adam.trischler@maluuba.com.
authors.forename: Adam P
authors.initials: AP
authors.lastname: Trischler
authors.affiliation: University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, Canada. Electronic address: gabriele.deleuterio@utoronto.ca.
authors.forename: Gabriele M T
authors.initials: GM
authors.lastname: D'Eleuterio
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016571:Neural Networks, Computer
keywords: Approximation; Attractor; Chaos; Dynamical system; Nonautonomous system; Recurrent neural network