University of Cambridge > > Isaac Newton Institute Seminar Series > State Estimation in Reduced Modeling

State Estimation in Reduced Modeling

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

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 diff erential 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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2023, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity