A comparison of reduced-order modeling approaches using artificial neural networks for PDEs with bifurcating solutions

Electronic Transactions on Numerical Analysis

article

Martin W. Hess¹  Annalisa Quaini²  Gianluigi Rozza¹ 

[1] SISSA Mathematics Area, mathLab, International School for Advanced Studies;Department of Mathematics, University of Houston

关键词: Navier–Stokes equations;    reduced-order methods;    reduced basis methods;    parametric geometries;    symmetry breaking bifurcation;   

DOI  :  10.1553/etna_vol56s52

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

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.

【 授权许可】

Unknown