Optimal Recovery from Data of PDEs with Incomplete Information

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• Peter Binev (University of South Carolina)
• Monday 15 July 2024, 10:15-10:55
• Seminar Room 1, Newton Institute.

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DREW01 - Multivariate approximation, discretization, and sampling recovery

We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. Our main example is the Poisson boundary value problem, when the boundary data is unknown and instead one observes finitely many linear measurements of the solution. We view this setting as an optimal recovery problem and develop theory and numerical algorithms for its solution. The main vehicle employed is the derivation and approximation of the Riesz representers of these functionals with respect to relevant Hilbert spaces of harmonic functions.

This is a research collaboration with Andrea Bonito, Albert Cohen, Wolfgang Dahmen, Ronald DeVore, and Guergana Petrova.

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

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