Large-Scale PDE-Constrained Optimization
TimeSunday, November 11th2:58pm - 3pm
DescriptionOptimization of time-dependent PDE-constrained optimization problems is extremely challenging from a computational perspective. Presume one forward simulation of a differential equation with N degrees of freedom, advancing in time for M timesteps requires a time to solution T. In this case optimizing for a certain parameter constrained by the PDE takes at least 2kT, where k is the number of iterations up to the convergence of the optimization scheme. We hereby explore strategies for achieving maximum speedup under controlled incurred errors. It is noteworthy that high errors in the computation of the gradient increase the number of iterations required to achieve convergence of the optimization algorithm, which is, in essence, more damaging than any gains made in the computation of the PDE.