Past Applied Dynamical Systems and Inverse Problems Seminar

We propose a powerful prediction algorithm built upon Gaussian
processes (GPs). They are particularly useful for their flexibility,
facilitating accurate prediction even in the absence of strong physical models. GPs further allow us to work within a completely Bayesian framework. As such, we show how the hyperparameters of our system can be marginalised by use of Bayesian Monte Carlo, a principled method of approximate integration. We employ the error bars of the GP's prediction as a means to select only the most informative observations to store. This allows us to introduce an iterative formulation of the GP to give a dynamic, on-line algorithm. We also show how our error bars can be used to perform active data selection, allowing the GP to select where and when it should next take a measurement.

We demonstrate how our methods can be applied to multi-sensor prediction problems where data may be missing, delayed and/or correlated. In particular, we present a real network of weather sensors as a testbed for our algorithm.

Recurrences have been central to the study of dynamical

systems ever since the inception of the subject. Periodic solutions

make the notion of recurrences exact. The Lorenz attractor is the best

known example of a strange attractor and we will describe a method to

find periodic solutions that lie on it. Additionally, we will consider

a turbulent channel flow and describe the computation of time periodic

solutions using nearly $300,000$ degrees of freedom to represent the

velocity field.