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ONLINE INTERPOLATION POINT REFINEMENT FOR REDUCED-ORDER MODELS USING A GENETIC ALGORITHM
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DOI：10.1137/16M1086352.png)
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Abstract
En 中文
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.
Keywords:
reduced-order modeling
dimensionality reduction
proper orthogonal decomposition
sparse sampling
genetic algorithm
discrete empirical interpolation method
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