Reduced-order modeling: a personal journey

Reduced-order models (ROM) have captured the interest and effort of many investigators over the years. As is well known the cost of computation can easily outpace the available computational resources, especially for multidisciplinary mathematical/computational models. In the present paper a personal account of one investigator's journey is provided as enabled by substantial contributions from colleagues in several organizations over the years. This is not a review of the literature or a history of the subject; it is intended to be an account of key ideas as seen from a single perspective. By a reduced-order model is meant a model that provides a substantial reduction in the size and cost of the original computational model without any essential loss in accuracy. And the motivation for creating such a ROM is not only to reduce computational cost. By extracting the essential elements of a more elaborate model, a much wider range of parameters in the model may be studied and the interpretation of the results may be made easier, thereby advancing our understanding of the model and the physical phenomena it is intended to describe.

Automated summary

This paper provides a personal account of the importance and significance of reduced-order models (ROM) in computational modeling. ROMs reduce the size and cost of the original model without losing accuracy. The motivation for creating a ROM is not only to reduce computational cost, but also to study a wider range of parameters and facilitate the interpretation of results, advancing our understanding of the model and the physical phenomena it describes.