This paper presents a review of proper orthogonal decomposition (POD) methods for order
reduction in a variety of research areas. The historical development and basic mathematical …

Uncertainty quantification serves a central role for simulation-based analysis of physical,
engineering, and biological applications using mechanistic models. From a broad …

Error estimates for Galerkin proper orthogonal decomposition (POD) methods for nonlinear
parabolic systems arising in fluid dynamics are proved. For the time integration the …

In this work error estimates for Galerkin proper orthogonal decomposition (POD) methods for
linear and certain non-linear parabolic systems are proved. The resulting error bounds …

This paper presents a literature review on methods for enabling real-time analysis in digital
twins, which are virtual models of physical systems. The advantages of digital twins are …

The proper orthogonal decomposition (POD) technique (or the Karhunan Loève procedure)
has been used to obtain low-dimensional dynamical models of many applications in …

Proper orthogonal decomposition (POD) is a method to derive reduced-order models for
dynamical systems. In this paper, POD is utilized to solve open-loop and closed-loop optimal …

In this paper, we present a discussion of the proper orthogonal decomposition (POD) as
applied to simulation and feedback control of the one-dimensional heat equation. We …

Four‐dimensional variational data assimilation (4DVAR) is a powerful tool for data
assimilation in meteorology and oceanography. However, a major hurdle in use of 4DVAR …

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the
potential applications of POD reduced-order numerical methods in increasing computational …