Low-dimensional Data-driven Models for Forecasting and Control of Chaotic Dynamical Systems

Book excerpt: Modeling high-dimensional and chaotic dynamics remains a challenging problem with a wide range of applications from controlling turbulent flows, to weather forecasting, to predicting cardiac arrhythmias - to name a few. Two major challenge in modeling these systems is that sometimes the equations are unknown and when they are known solving them can be prohibitively expensive. Due to these issues, only recently have experimental databases become mature enough and computational resources fast enough for there to exist large datasets of high-dimensional chaotic dynamical systems. The existence of these large datasets and advances in machine learning techniques opens the possibility for drastic improvements in the modeling and interpretability of chaotic dynamical systems through data-driven low-dimensional models. Here, we generate extremely low-dimensional "exact" models of chaotic dynamics in dissipative systems.