bachelor thesis

Great progress for the prediction of time series has been made in the past by using Echo State Networks (ESNs), which are part of reservoir computing. In this thesis they will be used to predict the spatio-temporal (chaotic) dynamics of a two dimensional system. Thereby, the possible application for medical studies of the heart shall be considered. Therefore, at first ESNs are applied on to the Barkley and the Michell-Schaeffer model, which both can be used to describe the heart’s dynamics, and are compared to existing methods. Later, the Bueno-Orovio-Cherry-Fenton model is investigated and the ESN applied another time using the previously obtained insights. These models describe an excitable medium with multiple variables.

Three questions will be studied: In the beginning a cross-prediction between the different variables of the systems will be performed. Next, the real dynamics will be predicted by knowing artificially blurred measurements of those. Finally, the excitations of unmeasured regions of the system will be predicted by measuring the boundary values of those. These questions are analyzed using ESNs; the classical methods of the nearest neighbour prediction and the radial basis functions are used to compare the performance. While the ESN can solve the first two tasks, it fails the last one. But in all three questions it gains a higher accuracy than the two classical approaches.

You can find the paper itself and the source code at GitHub