Math @ Duke

Publications [#287358] of James H. Nolen
Papers Published
 Nolen, J; Papanicolaou, G, Fine scale uncertainty in parameter estimation for elliptic equations,
Inverse Problems, vol. 25 no. 11
(2009), ISSN 02665611 [pdf], [doi]
(last updated on 2018/03/21)
Abstract: We study the problem of estimating the coefficients in an elliptic partial differential equation using noisy measurements of a solution to the equation. Although the unknown coefficients may vary on many scales, we aim only at estimating their slowly varying parts, thus reducing the complexity of the inverse problem. However, ignoring the finescale fluctuations altogether introduces uncertainty in the estimates, even in the absence of measurement noise. We propose a strategy for quantifying the uncertainty due to the finescale fluctuations in the coefficients by modeling their effect on the solution of the forward problem using the central limit theorem. When this is possible, the Bayesian estimation of the coefficients reduces to a weighted leastsquares problem with a covariance matrix whose rank is low regardless of the number of measurements and does not depend on the details of the coefficient fluctuations. © 2009 IOP Publishing Ltd.


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