2020/10/14 by Martin W. Hess, Annalisa Quaini, Hess, Martin W. +3 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Refrigeration and Air Conditioning Technologies #Turbomachinery Performance and Optimization #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2010.07370
openalex publication_date 2020/10/14 · arxiv created 2021/12/30 · arxiv updated 2022/01/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
This paper focuses on reduced-order models (ROMs) built for the efficient treatment of PDEs having solutions that bifurcate as the values of multiple input parameters change. First, we consider a method called local ROM that uses k-means algorithm to cluster snapshots and construct local POD bases, one for each cluster. We investigate one key ingredient of this approach: the local basis selection criterion. Several criteria are compared and it is found that a criterion based on a regression artificial neural network (ANN) provides the most accurate results for a channel flow problem exhibiting a supercritical pitchfork bifurcation. The same benchmark test is then used to compare the local ROM approach with the regression ANN selection criterion to an established global projection-based ROM and a recently proposed ANN based method called POD-NN. We show that our local ROM approach gains more than an order of magnitude in accuracy over the global projection-based ROM. However, the POD-NN provides consistently more accurate approximations than the local projection-based ROM.