We propose a data-driven, closure model for Reynolds-averaged Navier-Stokes (RANS)
simulations that incorporates aleatoric, model uncertainty. The proposed closure consists of …

A central challenge in the computational modeling and simulation of a multitude of science
applications is to achieve robust and accurate closures for their coarse-grained …

Constructing sparse, effective reduced-order models (ROMs) for high-dimensional
dynamical data is an active area of research in applied sciences. In this work, we study an …

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in
computational physics and engineering. However, finding solutions for these PDEs can be …

In this work, we introduce a Reduced Basis model for turbulence at statistical equilibrium.
This is based upon an a-posteriori error estimation procedure that measures the distance …

Large time-stepping is important for efficient long-time simulations of deterministic and
stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators …

A framework for deriving probabilistic data-driven closure models is proposed for coarse-
grained numerical simulations of turbulence in statistically stationary state. The approach …

Abstract Model reduction by projection-based approaches is often associated with losing
some of the important features that contribute towards the dynamics of the retained scales …

In this thesis, I examine filtering based stabilization methods to design new regularized
reduced order models (ROMs) for under-resolved simulations of unsteady, nonlinear …

We present a novel reduced-order pressure stabilization strategy based on continuous data
assimilation (CDA) for two-dimensional incompressible Navier-Stokes equations. A …