Simplified Newton Method for POD Computation in Optimal Control

Paul Manns, Argonne National Laboratory
Future of supercomputing

Proper orthogonal decomposition (POD) provides surrogate models of potentially expensive PDE discretizations. Executing optimization iterations on them may lead to frequent updates or recomputations because POD models usually provide good approximation quality only locally. We take the view of a simplified Newton method for solving semilinear evolution equations to derive an algorithm that produces POD models of higher approximation quality. Approaches that build the POD model with impulse response snapshots can be regarded as the first Newton step in this context. POD models that are based on impulse response snapshots are extended by adding a second simplified Newton step. This procedure improves the approximation quality of the POD model significantly by introducing a moderate amount of extra computational costs during optimization. The cost of computing the POD model increases substantially, however.

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