École Nationale Supérieure de
Techniques Avancées

Résumé

Learning dynamical systems from data can be done by regressing the vector field with a kernel. In this report, we present kernel flow algorithm as a numerical approach to learn the kernel from data. This algorithm is based on the premise that a kernel is good if there is no significant loss in accuracy in the prediction error if the number of interpolation points is halved. We, then, explore the performance of this algorithm in the context of time series forecasting from the benchmarking dataset TSDL. We also propose a new metric to learn the kernel based on minimizing the error evaluation metrics. We first test this metric on chaotic dynamical systems and synthetic time series. Finally, we apply kernel flows with the proposed metric to TSDL time series. This new metric provides competitive results as it can outperform the original algorithm in terms of prediction accuracy.