Uncorrected Gaussian residual penalties in full-space sampling converge after marginalization to the graph-lifted reduced posterior multiplied by the inverse absolute determinant of the state Jacobian, requiring explicit determinant corrections for equivalence.
A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion
6 Pith papers cite this work. Polarity classification is still indexing.
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A two-level low-rank approximation enables scalable A-optimal sensor design for passive imaging without repeated PDE solves in the online phase.
Derives error bounds on the root prior-preconditioned Hessian, posterior covariance, and mean for a Petrov-Galerkin reduced-order model, with exact posterior recovery at the intrinsic dimension.
A finite-element variational inference method delivers full-covariance Bayesian field reconstruction at dimensions exceeding 400,000 for 3D porous media flow using sparse precision parameterization from SPDE priors.
New dimension and model reduction techniques for linear Bayesian inverse problems with rank-deficient priors, with approximation guarantees and efficiency demonstrations for high-dimensional inference.
Introduces local information operators that separate pointwise visibility from spatial identifiability via linearized Fisher information and sensitivity Gramians in distributed-parameter inverse problems.
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Scalable High-Dimensional Bayesian Field Reconstruction with Finite Elements: Application to 3D Porous Media Flow
A finite-element variational inference method delivers full-covariance Bayesian field reconstruction at dimensions exceeding 400,000 for 3D porous media flow using sparse precision parameterization from SPDE priors.
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Local Information Operators for Spatial Identifiability in Distributed-Parameter Inverse Problems in Computational Mechanics
Introduces local information operators that separate pointwise visibility from spatial identifiability via linearized Fisher information and sensitivity Gramians in distributed-parameter inverse problems.