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Journal article
On optimality and bounds for internal solutions generated from boundary data-driven Gramians
Inverse problems, v 41(10), 105008
06 Oct 2025
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Abstract
We consider the computation of internal solutions for a time domain plasma wave equation with unknown coefficients from the data obtained by sampling its transfer function at the boundary. The computation is performed by transforming known background snapshots using the Cholesky decomposition of the data-driven Gramian. We show that this approximation is asymptotically close to the projection of the true internal solution onto the subspace of background snapshots. This allows us to derive a generally applicable bound for the error in the approximation of internal fields from boundary data for a time domain plasma wave equation with an unknown potential $q$. For general $q\in L^\infty$, we prove convergence of these data generated internal fields in one dimension for two examples of initial waves. The first is for piecewise constant initial data and sampling $\tau$ equal to the pulse width. The second is piecewise linear initial data and sampling at half the pulse width. We show that in both cases the data generated solutions converge in $L^2$ at order $\sqrt{\tau}$. We present numerical experiments validating the result and the sharpness of this convergence rate.
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Details
- Title
- On optimality and bounds for internal solutions generated from boundary data-driven Gramians
- Creators
- Vladimir Druskin - Worcester Polytechnic InstituteShari Moskow (Corresponding Author) - Drexel UniversityMikhail Zaslavskiy - Southern Methodist University
- Publication Details
- Inverse problems, v 41(10), 105008
- Publisher
- Institute of Physics
- Number of pages
- 25
- Grants
- Data driven inversion methods and image reconstruction for nonlinear media, 2308200, National Science Foundation (United States, Arlington) - NSF
- Grant note
The authors would like to thank Tarek Habashy for many helpful discussions. V Druskin was partially supported by AFOSR Grants FA 9550-20-1-0079, FA9550-23-1-0220, and NSF Grant DMS-2110773. M Zaslavsky was partially supported by AFOSR Grant FA9550-23-1-0220. S Moskow was partially supported by NSF Grants DMS-2008441 and DMS-2308200.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001595681500001
- Scopus ID
- 2-s2.0-105019384073
- Other Identifier
- 991022123333204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical