Data-driven methods for discovery of observables and Koopman embeddings in dynamical systems J. Nathan Kutz University of Washington Applied Mathematics We demonstrate that we can use emerging, large-scale time-series data from modern sensors to directly construct, in an adaptive manner, governing equations, even nonlinear dynamics, that best model the system measured using sparsity-promoting techniques. The methods also help determine appropriate variables, or Koopman embeddings, that best exemplify the dynamics. Recent innovations also allow for handling multi-scale physics phenomenon and control protocols in an adaptive and robust way. The overall architecture is equation-free in that the dynamics and control protocols are discovered directly from data acquired from sensors. The theory developed is demonstrated on a number of example problems.