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

TL;DR

This paper introduces the ROMES method, which uses Gaussian-process regression to statistically model and correct errors in reduced-order models, providing probabilistic error bounds and significantly improving prediction accuracy.

Contribution

The paper presents a novel Gaussian-process-based approach for error modeling in reduced-order models, enabling probabilistic error bounds and enhanced accuracy over existing methods.

Findings

The method achieves near-optimal effectivity compared to traditional error bounds.

Correcting reduced-order-model outputs with ROMES improves accuracy by an order of magnitude.

The approach provides probabilistic error bounds, ensuring controlled uncertainty in predictions.

Abstract

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.