Nonlinear dynamics is the field of studying the evolutionary dynamics of nonlinear systems. While initially the "analysis" was dominated by "Analysis" in the mathematical sense, in modern times numerical integration methods are often a useful tool for scientists to explore their behavior. They allow for visualization, and more importantly, for finding long-term behaviors, attractors and time-scales. Numerical methods require a description using an evolution equation but can succeed where analytical tools fail. Recently, machine learning methods are increasingly used throughout the scientific disciplines. They allow for the description of a target system with nothing but data, so that not even a closed model is needed anymore. In this talk, we will review the state of machine learning methods from the perspective of nonlinear dynamics, in particular with respect to finding and reconstructing attractors. We show how "unseen attractors" can be extracted from time-series data that never visited their part of phase space and never crossed into attractor basin of the unseen attractors. We use a 4-dimensional extension of the well-known Lorenz chaotic system, but the method itself requires in principle no knowledge about the evolution equation.

These new machine learning methods are driven from a "user" perspective, and important questions about stability, convergence or fundamental limits are so far not addressed in the literature. We will try to highlight these open questions as an inspiration for the audience, as future work is needed.