Predicting Complex Time Series Using Knowledge Based Hybrid Reservoir Computing

Kurzfassung

Tremendous advances in predicting the behavior of complex systems have been made in recent years by applying machine learning. Standard machine learning techniques, like the commonly used Reservoir Computing (RC), are by default purely data-driven which, while generally useful, is suboptimal for cases where some approximate model of the underlying system is known. Adding this additional system knowledge into the data driven techniques gives rise to hybrid approaches, improving their overall prediction quality. Doan et al. introduced such a physics-informed, "output-hybrid", approach for RC, which uses approximations of the systems' true physical equations in order to fine-tune the RC output matrix in a second training phase.\\ Another, "full-hybrid", approach was introduced by Pathak et al. where, in contrast to the simpler output-hybrid approach, the physical knowledge becomes an integral part of the hybrid RC architecture by augmenting the reservoir's input with an "input-hybrid" approach at each step of the calculation. Here, we compare the different hybrid approaches on a variety of commonly known three dimensional chaotic systems. We show that the simpler output-hybrid approach matches the full-hybrid and beats the input-hybrid approach for most reasonable systems with the additional advantages of being more interpretable and resulting in a significantly higher prediction quality for inaccurate models.