Tim Sullivan

Junior Professor in Applied Mathematics:
Risk and Uncertainty Quantification

Optimal uncertainty quantification for legacy data observations of Lipschitz functions

UQ for Legacy Data from Lipschitz Functions in M2AN

Mathematical Modelling and Numerical Analysis has just published a paper by Mike McKerns, Dominic Meyer, Florian Theil, Houman Owhadi and Michael Ortiz and myself on optimal UQ for legacy data observations of Lipschitz functions.

In this paper, we address both mathematically and numerically the challenge of giving optimal bounds on quantities of interest of the form \(\mathbb{P}_{X \sim \mu}[f(X) \geq t]\), where the probability distribution \(\mu\) of \(X\) is only partially known through some of its moments, and the forward model \(f\) is partially known through some pointwise observations and smoothness information.

T. J. Sullivan, M. McKerns, D. Meyer, F. Theil, H. Owhadi & M. Ortiz. “Optimal uncertainty quantification for legacy data observations of Lipschitz functions.” ESAIM. Mathematical Modelling and Numerical Analysis 47(6):1657–1689, 2013. doi:10.1051/m2an/2013083

Published on Friday 30 August 2013 at 18:00 UTC #publication

Optimal Uncertainty Quantification

Optimal Uncertainty Quantification in SIAM Review

The 2013 Q2 issue of SIAM Review will carry an article by Houman Owhadi, Clint Scovel, Mike McKerns, Michael Ortiz and myself on the optimization approaches to uncertainty quantification in the presence of infinite-dimensional epistemic uncertainties about the probability measures and response functions of interest.

We present both a mathematical framework for the reduction of such infinite-dimensional problems to finite-dimensional effective feasible sets, and apply the methods to practical examples arising in hypervelocity impact and seismic safety certification.

H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns & M. Ortiz. “Optimal Uncertainty Quantification.” SIAM Review 55(2):271–345, 2013. doi:10.1137/10080782X

Published on Monday 10 June 2013 at 20:00 UTC #publication

Optimal Uncertainty Quantification

Graphene Plasmonics in Phys. Rev. B

Physical Review B has published an article by Lauren Rast, Vinod Tewary and myself on stratified graphene/noble metal systems for low-loss plasmonics applications. This paper constitutes an initial study of the effect of geometric parameters such as layer thicknesses on the electron energy loss spectra of laminar metamaterials, consisting of a graphene surface, an intermediate noble metal layer, and a substrate.

L. Rast, T. J. Sullivan & V. K. Tewary. “Stratified graphene/noble metal systems for low-loss plasmonics applications.” Physical Review B 87(4):045428, 2013. doi:10.1103/PhysRevB.87.045428

Published on Thursday 31 January 2013 at 12:00 UTC #publication

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