# dual-weighted residual

## Online adaptive basis refinement and compression for reduced-order models via vector-space sieving

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these approximate …

## Statistical closure modeling for reduced-order models of stationary systems by the ROMES method

This work proposes a technique for constructing a statistical closure model for reduced-order models (ROMs) applied to stationary systems modeled as parameterized systems of algebraic equations. The proposed technique extends the reduced-order-model …

## Adaptive $h$-refinement for reduced-order models

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 …

## The ROMES method for statistical modeling of reduced-order-model error

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 …