Emulating nonlinear dynamical systems from data using scientific machine learning

In this talk, I will present recent research that builds fast and accurate predictive models for various high-dimensional systems through a combination of data-driven and physics-based modeling. Moreover, through my examples, I will argue that such algorithm development must occur with consideration for data from multiple sources and fidelities, for deployment scenarios that leverage high-performance computing, and with appropriate emphasis on incorporating prior knowledge from physics-based modeling. I will give specific examples that highlight such themes for learning (both canonical and off-nominal) nonlinear dynamical systems from data. Some examples of the former include learning solutions to the advection-dominated viscous Burgers equations, and learning the chaotic nature of the Kuramoto-Sivashinsky equation. For the latter, I will discuss deployments of such learning algorithms for building reduced-order models for geophysical forecasting from numerical simulations as well as ship and satellite observation data.