Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds
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Publication:5139358
DOI10.1137/19M1295222zbMath1448.65205arXiv1910.10669OpenAlexW3107254801MaRDI QIDQ5139358
Daniel Sanz-Alonso, Ruiyi Yang, John Harlim
Publication date: 8 December 2020
Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1910.10669
Inverse problems in geophysics (86A22) Elliptic equations on manifolds, general theory (58J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)
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HODLR\(d\)D: a new black-box fast algorithm for \(N\)-body problems in \(d\)-dimensions with guaranteed error bounds. Applications to integral equations and support vector machines ⋮ Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement ⋮ Spectral methods for solving elliptic PDEs on unknown manifolds ⋮ Optimization on Manifolds via Graph Gaussian Processes ⋮ Ghost Point Diffusion Maps for Solving Elliptic PDEs on Manifolds with Classical Boundary Conditions ⋮ Diffusion maps for embedded manifolds with boundary with applications to PDEs ⋮ Fractional diffusion maps ⋮ The SPDE approach to Matérn fields: graph representations ⋮ Graph-based prior and forward models for inverse problems on manifolds with boundaries
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