Mathematical Programming: Series A and B
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
On directional Metropolis---Hastings algorithms
Statistics and Computing
Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models
SIAM Journal on Scientific Computing
Statistics and Computing
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Journal of Computational Physics
Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing (Surveys and Tutorials in the Applied Mathematical Sciences)
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Lagrange Multiplier Approach to Variational Problems and Applications
Lagrange Multiplier Approach to Variational Problems and Applications
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space
SIAM Journal on Scientific Computing
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Journal of Computational Physics
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
An Online Method for Interpolating Linear Parametric Reduced-Order Models
SIAM Journal on Scientific Computing
Bayesian inference with optimal maps
Journal of Computational Physics
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A greedy algorithm for the construction of a reduced model with reduction in both parameter and state is developed for an efficient solution of statistical inverse problems governed by partial differential equations with distributed parameters. Large-scale models are too costly to evaluate repeatedly, as is required in the statistical setting. Furthermore, these models often have high-dimensional parametric input spaces, which compounds the difficulty of effectively exploring the uncertainty space. We simultaneously address both challenges by constructing a projection-based reduced model that accepts low-dimensional parameter inputs and whose model evaluations are inexpensive. The associated parameter and state bases are obtained through a greedy procedure that targets the governing equations, model outputs, and prior information. The methodology and results are presented for groundwater inverse problems in one and two dimensions.