This work presents a method to adaptively refine reduced‐order models *a posteriori* without requiring additional full‐order‐model solves. The technique is analogous to mesh‐adaptive $h$‐refinement: it enriches the reduced‐basis space online by …
This work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model …
This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive 'error indicators' to a …
The Gauss–Newton with approximated tensors (GNAT) method is a nonlinear model-reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with residual …
This work proposes a model-reduction methodology that both preserves Lagrangian structure and leads to computationally inexpensive models, even in the presence of high-order nonlinearities. We focus on parameterized simple mechanical systems under …
The goal of this work is to accurately evaluate large-scale, nonlinear, finite-volume-based fluid dynamics models at low computational cost. To accomplish this objective, this work employs the Gauss– Newton with approximated tensors (GNAT) nonlinear …
A novel model reduction technique for static systems is presented. The method is developed using a goal‐oriented framework, and it extends the concept of snapshots for proper orthogonal decomposition (POD) to include (sensitivity) derivatives of the …
A Petrov--Galerkin projection method is proposed for reducing the dimension of a discrete non‐linear static or dynamic computational model in view of enabling its processing in real time. The right reduced‐order basis is chosen to be invariant and is …
A rigorous method for interpolating a set of parameterized linear structural dynamics reduced‐order models (ROMs) is presented. By design, this method does not operate on the underlying set of parameterized full‐order models. Hence, it is amenable to …
We present an adaptive proper orthogonal decomposition (POD)-Krylov reduced-order model (ROM) for structural optimization. At each step of the optimization loop, we compute approximate solutions to the structural state and sensitivity equations using …