Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …

Abstract Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the
Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they …

The purpose of this paper is to survey some recent advances in variational integrators for
both finite dimensional mechanical systems as well as continuum mechanics. These …

We investigate some basic properties of the proper orthogonal decomposition (POD)
method as it is applied to data compression and model reduction of finite dimensional …

The past few decades have seen a significant spurt in develo** lower-order, parsimonious
models of large-scale dynamical systems used for design and control. These surrogate …

In this paper, we introduce a new method of model reduction for nonlinear control systems.
Our approach is to construct an approximately balanced realization. The method requires …

Model reduction methods are usually based on preliminary computations to build the shape
function of the reduced order model (ROM) before the computation of the reduced state …

Scientific Machine Learning (SciML) and Artificial Intelligence (AI) will have broad use and
transformative effects across the Department of Energy. Accordingly, the January 2018 Basic …

The model reduction problem for (single-input, single-output) linear and nonlinear systems
is addressed using the notion of moment. A re-visitation of the linear theory allows to obtain …

Optimization is an appealing way to compute the motion of an animated character because it
allows the user to specify the desired motion in a sparse, intuitive way. The difficulty of …