A common strategy for the dimensionality reduction of nonlinear partial differential equations
(PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced …

This paper proposes a supervised machine learning framework for the non-intrusive model
order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state …

We study the performance of long short-term memory networks (LSTMs) and neural ordinary
differential equations (NODEs) in learning latent-space representations of dynamical …

We propose a data-driven filtered reduced order model (DDF-ROM) framework for the
numerical simulation of fluid flows. The novel DDF-ROM framework consists of two steps:(i) …

Many reduced-order models are neither robust with respect to parameter changes nor cost-
effective enough for handling the nonlinear dependence of complex dynamical systems. In …

We have recently proposed a data‐driven correction reduced‐order model (DDC‐ROM)
framework for the numerical simulation of fluid flows, which can be formally written as …

For over a century, reduced order models (ROMs) have been a fundamental discipline of
theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr …

Abstract We develop a Reduced Order Model (ROM) for the Navier-Stokes equations with
nonlinear filtering stabilization. Our approach, that can be interpreted as a Large Eddy …

Abstract We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced
Order Model (ROM) for an implementation of the Leray model that combines a two-step …

We put forth a data-driven closure modeling approach for stabilizing projection based
reduced order models for the Bousinessq equations. The effect of discarded modes is taken …