DE Seminar: Randy Price (GMU)

Abstract: Abstract: The nudging algorithm for time-dependent differential equations allows the user to control the solution with available data at almost no additional cost.  In the first part of this talk we will cover the basics of the nudging algorithm and give a brief overview of the recent progress. We will show numerical experiments for the 2D Navier-Stokes equations demonstrating the applications in control and data assimilation.  In the second part of this talk we will cover recent work which combines machine learning with the ideas of nudging. Nudging induced neural networks (NINNs) enables the user to solve the data assimilation or control problem with the differential equation replaced by a neural network surrogate. In higher dimensional cases (2D PDEs) however, training the neural network surrogate becomes a time consuming task. The discrete empirical interpolation method (DEIM), a reduced order modeling technique, helps reduce the costs associated with training the high dimensional surrogate. We will conclude with numerical results for the 1D Kuramoto-Sivashinsky and 2D Navier-Stokes equations.