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

arXiv: https://arxiv.org/abs/1405.5170 · HTML: https://mlsanity.com/paper/1405.5170/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2014.

## Built on by (most cited first, 3 of 3)

- [Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling](https://mlsanity.com/paper/2205.12419/) (2022)
- [Improving CFD simulations by local machine-learned correction](https://mlsanity.com/paper/2305.00114/) (2023)
- [Conformal risk control for model-form uncertainty in parametric non-intrusive reduced-order models](https://mlsanity.com/paper/2608.03360/) (2026)

## Abstract (arXiv)

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 distribution over the true error. The variance of this distribution can be interpreted as the (epistemic) uncertainty introduced by the reduced-order model. To model normed errors, the method employs existing rigorous error bounds and residual norms as indicators; numerical experiments show that the method leads to a near-optimal expected effectivity in contrast to typical error bounds. To model errors in general outputs, the method uses dual-weighted residuals---which are amenable to uncertainty control---as indicators. Experiments illustrate that correcting the reduced-order-model output with this surrogate can improve prediction accuracy by an order of magnitude; this contrasts with existing `multifidelity correction' approaches, which often fail for reduced-order models and suffer from the curse of dimensionality. The proposed error surrogates also lead to a notion of `probabilistic rigor', i.e., the surrogate bounds the error with specified probability.