Paper Info
Title
Online Interpolation Point Refinement for Reduced-Order Models using a Genetic Algorithm.
Abstract
A genetic algorithm procedure is demonstrated that refines the selection of interpolation points of the discrete empirical interpolation method when used for constructing reduced-order models for time-dependent and/or parametrized nonlinear PDEs with proper orthogonal decomposition. The method achieves refinement of the interpolation points with only a few generations of the search, making it potentially useful for online improvement of the sparse sampling used to construct a projection of the nonlinear terms. With the genetic algorithm, the optimization procedure selects points that jointly minimize reconstruction error and enable dynamic regime classification. The efficiency of the method is demonstrated on two canonical nonlinear PDEs: the cubic-quintic Ginzburg Landau equation and the incompressible Navier Stokes equation for flow around a cylinder. Using the former model, the procedure can be compared to the ground-truth optimal interpolation points, showing that the genetic algorithm quickly achieves nearly optimal performance and reduced the reconstruction error by nearly an order of magnitude.
Year
DOI
Venue
2018
10.1137/16M1086352
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
reduced-order modeling,dimensionality reduction,proper orthogonal decomposition,sparse sampling,genetic algorithm,discrete empirical interpolation method
Nearest-neighbor interpolation,Mathematical optimization,Spline interpolation,Multivariate interpolation,Mathematical analysis,Interpolation,Stairstep interpolation,Trilinear interpolation,Genetic algorithm,Mathematics,Inverse quadratic interpolation
Journal
Volume
Issue
ISSN
40
1
1064-8275
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Syuzanna Sargsyan100.34
S. L. Brunton214123.92
J. Nathan Kutz322547.13