2,003 research outputs found
Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems
One of the major challenges in the Bayesian solution of inverse problems
governed by partial differential equations (PDEs) is the computational cost of
repeatedly evaluating numerical PDE models, as required by Markov chain Monte
Carlo (MCMC) methods for posterior sampling. This paper proposes a data-driven
projection-based model reduction technique to reduce this computational cost.
The proposed technique has two distinctive features. First, the model reduction
strategy is tailored to inverse problems: the snapshots used to construct the
reduced-order model are computed adaptively from the posterior distribution.
Posterior exploration and model reduction are thus pursued simultaneously.
Second, to avoid repeated evaluations of the full-scale numerical model as in a
standard MCMC method, we couple the full-scale model and the reduced-order
model together in the MCMC algorithm. This maintains accurate inference while
reducing its overall computational cost. In numerical experiments considering
steady-state flow in a porous medium, the data-driven reduced-order model
achieves better accuracy than a reduced-order model constructed using the
classical approach. It also improves posterior sampling efficiency by several
orders of magnitude compared to a standard MCMC method
A comparative analysis of the cephalic microbiome: The ocular, aural, nasal/nasopharyngeal, oral and facial dermal niches
The human face/head supports a highly diverse population of microorganisms across a diverse range of microhabitats. This biogeographical diversity has given rise to selection pressure resulting in the formation of distinct bacterial communities between sites. This review investigates the similarity and differences of microbiomes across the different biogeographies of the human face and discusses a potential pathway for microbial circulation within individuals and within a population to maintain microbiome niches and diversity
Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction
Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a h eterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.United States. Department of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0009297
Multi-output multilevel best linear unbiased estimators via semidefinite programming
Multifidelity forward uncertainty quantification (UQ) problems often involve
multiple quantities of interest and heterogeneous models (e.g., different
grids, equations, dimensions, physics, surrogate and reduced-order models).
While computational efficiency is key in this context, multi-output strategies
in multilevel/multifidelity methods are either sub-optimal or non-existent. In
this paper we extend multilevel best linear unbiased estimators (MLBLUE) to
multi-output forward UQ problems and we present new semidefinite programming
formulations for their optimal setup. Not only do these formulations yield the
optimal number of samples required, but also the optimal selection of
low-fidelity models to use. While existing MLBLUE approaches are single-output
only and require a non-trivial nonlinear optimization procedure, the new
multi-output formulations can be solved reliably and efficiently. We
demonstrate the efficacy of the new methods and formulations in practical UQ
problems with model heterogeneity.Comment: 22 pages, 5 figures, 3 table
Candida auris: an emerging antimicrobial-resistant organism with the highest level of concern
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