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A REGISTRATION METHOD FOR MODEL ORDER REDUCTION: DATA COMPRESSION AND GEOMETRY REDUCTION
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DOI：10.1137/19M1271270.png)
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Abstract
En 中文
We propose a general-i.e., independent of the underlying equation-registration method for parameterized model order reduction. Given the spatial domain Omega subset of R-d and the manifold M-u = {u(mu) : mu is an element of P} associated with the parameter domain P subset of R-P and the parametric field mu (sic) u(mu) is an element of L-2(Omega), the algorithm takes as input a set of snapshots {u(k)}(k=1)(ntrain) subset of M-u and returns a parameter-dependent bijective mapping Phi : Omega x P -> R-d: the mapping is designed to make the mapped manifold {u(mu) o Phi(mu) : mu is an element of P} more suited for linear compression methods. We apply the registration procedure, in combination with a linear compression method, to devise low-dimensional representations of solution manifolds with slowly decaying Kolmogorov N-widths; we also consider the application to problems in parameterized geometries. We present a theoretical result to show the mathematical rigor of the registration procedure. We further present numerical results for several two-dimensional problems, to empirically demonstrate the effectivity of our proposal.
Keywords:
parameterized partial differential equations
model order reduction
data compression
geometry registration
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