From data-to dynamics: predicting chaotic time series by hierarchical Bayesian neural nets

A hierarchical Bayesian algorithm was used to make predictions of chaotic time series data generated by the Rossler system which is a continuous dynamical system. The scheme infers a nonlinear dynamical system model using feedforward neural nets. The most difficult task, estimation of the embedding dimension, was naturally achieved by computing marginal likelihood. The results presented take into account only the system noise. Observation noise is significantly more difficult to deal with than the system noise due to the sensitive dependence of chaotic dynamics on initial conditions.