First, I will introduce nonlinear model reduction methods that employ spatial simulation data and subspace projection to reduce the dimensionality of nonlinear dynamical-system models while preserving critical dynamical-system properties such as discrete-time optimality, global conservation, and Lagrangian structure.
Second, I will describe methods for data-driven error modeling, which apply regression methods from machine learning to construct an accurate, low-variance statistical model of the error incurred by model reduction. This quantifies the (epistemic) uncertainty introduced by reduced-order models and enables them to be rigorously integrated in uncertainty-quantification applications.
Finally, I will present data-driven numerical solvers that use simulation data to improve the performance of linear/nonlinear solvers and time-integration methods. I will present one such approach: an adaptive-discretization method that applies Krylov-subspace iteration or h-adaptivity to enrich an initial solution subspace extracted from spatial simulation data.
Discovery Building, Orchard View Room