Dynamic Reconstruction from Noise Contaminated Data with Sparse Bayesian Recurrent Neural Networks

Dynamic reconstruction is fundamental to building models of nonlinear processes with unknown governing equations. Dynamic reconstruction attempts to reconstruct the underlying dynamics of the system under consideration from a series of scalar measurements over time. Reconstruction of system dynamics from measurements can be interpreted as an ill posed inverse problem of which Tikhnov regularization has been found to provide stable estimate solutions. In this paper, a Bayesian regularized recurrent neural network is used to perform dynamic reconstruction of a noisy chaotic processes. The Bayesian regularized recurrent network is able to reconstruct attractors from noise contaminated data that are qualitatively similar to and have similar correlation dimension as attractors reconstructed from noise free data