State Estimation in Reduced Modeling

Add to your list(s) Download to your calendar using vCal

• Peter Binev (University of South Carolina)
• Friday 09 March 2018, 09:00-09:45
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact INI IT.

UNQW03 - Reducing dimensions and cost for UQ in complex systems

Co-authors: Albert Cohen (University Paris 6), Wolfgang Dahmen (University of South Carolina), Ronald DeVore (Texas A&M University), Guergana Petrova (Texas A&M University), Przemyslaw Wojtaszczyk (University of Warsaw)

We consider the problem of optimal recovery of an element u of a Hilbert space H from measurements of the form l_j(u), j = 1, ... , m, where the l_j are known linear functionals on H. Motivated by reduced modeling for solving parametric partial differential equations, we investigate a setting where the additional information about the solution u is in the form of how well u can be approximated by a certain known subspace V_n of H of dimension n, or more generally, in the form of how well u can be approximated by each of a sequence of nested subspaces V_0, V_1, ... , V_n with each V_k of dimension k. The goal is to exploit additional information derived from the whole hierarchy of spaces rather than only from the largest space V_n. It is shown that, in this multispace case, the set of all u that satisfy the given information can be described as the intersection of a family of known ellipsoidal cylinders in H and that a near optimal recovery algorithm in the multi-space pr oblem is provided by identifying any point in this intersection.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.