Date
Tue, 29 Oct 2013
Time
14:30 - 15:00
Location
L5
Speaker
Patrick Farrell
Organisation
University of Oxford

Hessians of functionals of PDE solutions have important applications in PDE-constrained optimisation (Newton methods) and uncertainty quantification (for accelerating high-dimensional Bayesian inference).  With current techniques, a typical cost for one Hessian-vector product is 4-11 times the cost of the forward PDE solve: such high costs generally make their use in large-scale computations infeasible, as a Hessian solve or eigendecomposition would have costs of hundreds of PDE solves.

In this talk, we demonstrate that it is possible to exploit the common structure of the adjoint, tangent linear and second-order adjoint equations to greatly accelerate the computation of Hessian-vector products, by trading a large amount of computation for a large amount of storage. In some cases of practical interest, the cost of a Hessian-
vector product is reduced to a small fraction of the forward solve, making it feasible to employ sophisticated algorithms which depend on them.

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