
Randomization and reweighted ℓ_1minimization for Aoptimal design of linear inverse problems
We consider optimal design of PDEbased Bayesian linear inverse problems...
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Optimal design of largescale Bayesian linear inverse problems under reducible model uncertainty: good to know what you don't know
We consider optimal design of infinitedimensional Bayesian linear inver...
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A fast and scalable computational framework for largescale and highdimensional Bayesian optimal experimental design
We develop a fast and scalable computational framework to solve largesc...
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Unscented Kalman Inversion: Efficient Gaussian Approximation to the Posterior Distribution
The unscented Kalman inversion (UKI) method presented in [1] is a genera...
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Stochastic Learning Approach to Binary Optimization for Optimal Design of Experiments
We present a novel stochastic approach to binary optimization for optima...
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Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs
Hessian operators arising in inverse problems governed by partial differ...
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Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations
Optimal experimental design (OED) is the general formalism of sensor pla...
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Optimal experimental design under irreducible uncertainty for inverse problems governed by PDEs
We present a method for computing Aoptimal sensor placements for infinitedimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the model that exist in addition to the parameters in the inverse problem, and that cannot be reduced through observations. Specifically, given a statistical distribution for the model uncertainties, we compute the optimal design that minimizes the expected value of the posterior covariance trace. The expected value is discretized using Monte Carlo leading to an objective function consisting of a sum of trace operators and a binaryinducing penalty. Minimization of this objective requires a large number of PDE solves in each step. To make this problem computationally tractable, we construct a composite lowrank basis using a randomized range finder algorithm to eliminate forward and adjoint PDE solves. We also present a novel formulation of the Aoptimal design objective that requires the trace of an operator in the observation rather than the parameter space. The binary structure is enforced using a weighted regularized ℓ_0sparsification approach. We present numerical results for inference of the initial condition in a subsurface flow problem with inherent uncertainty in the flow fields and in the initial times.
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