4 papers
An Introduction to Solving the Least-Squares Problem in Variational Data Assimilation
I. Daužickaitė, M. A. Freitag, S. Gürol +4
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weath…
Efficient Dynamic Image Reconstruction with motion estimation
Toluwani Okunola, Mirjeta Pasha, Misha Kilmer +1
Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale natu…
Chebyshev HOPGD with sparse grid sampling for parameterized linear systems
Siobhán Correnty, Melina A. Freitag, Kirk M. Soodhalter
We consider approximating solutions to parameterized linear systems of the form . Here the matrix is nonsingular…
POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations
Saddam Hijazi, Melina Freitag, Niels Landwehr
We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier--Stokes equations…