The optimization and control of systems governed by partial differential equations (PDEs)
usually requires numerous evaluations of the forward problem or the optimality system …

Optimal control problems for partial differential equations (PDEs) are often hard to tackle
numerically because their discretization leads to very large scale optimization problems …

This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on
a linear control variate framework. The approach allows for rigorous multifidelity extensions …

We develop a variational multiscale proper orthogonal decomposition (POD) reduced‐order
model (ROM) for turbulent incompressible Navier‐Stokes equations. Under two assumptions …

Galerkin reduced order models (ROMs), eg, based on proper orthogonal decomposition
(POD) or reduced basis methods, have achieved significant success in the numerical …

This paper presents a Streamline-Upwind Petrov–Galerkin (SUPG) reduced order model
(ROM) based on proper orthogonal decomposition (POD). This ROM is investigated …

For incompressible flow models, the pressure term serves as a Lagrange multiplier to
ensure that the incompressibility constraint is satisfied. In engineering applications, the …

We propose a novel artificial compression, reduced order model (AC-ROM) for the
numerical simulation of viscous incompressible fluid flows. The new AC-ROM provides …

Abstract Galerkin and Petrov–Galerkin projection-based reduced-order models (ROMs) of
transient partial differential equations are typically obtained by performing a dimension …

We propose, analyze, and test a novel continuous data assimilation reduced order model
(DA-ROM) for simulating incompressible flows. While ROMs have a long history of success …