Michael Small, The University of Western Australia, Australia
Abstract: Machine learning is widely applied to model dynamical systems and make predictions. Instead of doing this, I will introduce the concept of Reservoir Time Series Analysis – using a particular flavour of machine learning (reservoir computing) to represent the state of a dynamical system and characterise the dynamical evolution of that state. How much can we infer about the changing behaviour of a system from the internal representation of these states within a reservoir machine learning model? A second strategy within machine learning for time series analysis is to use the machine learning model as a proxy for the original dynamics – but how well do such models capture chaotic dynamics? I will show via some short examples that persistent homology can be used as an effective tool to quantify that structure. These methods will be illustrated with applications to machine vibration and pump cavitation in industrial processes.