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

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

A decomposition-based approach to uncertainty analysis of feed-forward multicomponent systems

To support effective decision making, engineers should comprehend and manage various uncertainties throughout the design process. Unfortunately, in today's modern systems, uncertainty analysis can become cumbersome and computationally intractable for one individual or group to manage. This is particularly true for systems comprised of a large number of components. In many cases, these components may be developed by different groups and even run on different computational platforms. This paper proposes an approach for decomposing the uncertainty analysis task among the various components comprising a feed-forward system and synthesizing the local uncertainty analyses into a system uncertainty analysis. Our proposed decomposition-based multicomponent uncertainty analysis approach is shown to be provably convergent in distribution under certain conditions. The proposed method is illustrated on quantification of uncertainty for a multidisciplinary gas turbine system and is compared to a traditional system-level Monte Carlo uncertainty analysis approach.SUTD-MIT International Design CentreUnited States. Defense Advanced Research Projects Agency. META Program (United States. Air Force Research Laboratory Contract FA8650-10-C-7083)Vanderbilt University (Contract VU-DSR#21807-S7)United States. Federal Aviation Administration. Office of Environment and Energy (FAA Award 09-C-NE-MIT, Amendments 028, 033, and 038

Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape

In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.Singapore-MIT Alliance (SMA

Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7]

Solution of statistical inverse problems via the frequentist or Bayesian approaches described in earlier chapters can be a computationally intensive endeavor, particularly when faced with large-scale forward models characteristic of many engineering and science applications. High computational cost arises in several ways. First, thousands or millions of forward simulations may be required to evaluate estimators of interest or to characterize a posterior distribution. In the large-scale setting, performing so many forward simulations is often computationally intractable. Second, sampling may be complicated by the large dimensionality of the input space--as when the inputs are fields represented with spatial discretizations of high dimension--and by nonlinear forward dynamics that lead to multimodal, skewed, and/or strongly correlated posteriors. In this chapter, we present an overview of surrogate and reduced order modeling methods that address these computational challenges. For illustration, we consider a Bayesian formulation of the inverse problem. Though some of the methods we review exploit prior information, they largely focus on simplifying or accelerating evaluations of a stochastic model for the data, and thus are also applicable in a frequentist context.Sandia National Laboratories (Laboratory Directed Research and Development (LDRD) program)United States. Dept. of Energy (Contract DE-AC04-94AL85000)Singapore-MIT Alliance Computational Engineering ProgrammeUnited States. Dept. of Energy (Award Number DE-FG02-08ER25858 )United States. Dept. of Energy (Award Number DESC00025217

Antibiotic prescription patterns for acute diarrhea in a hospital in Shanghai in 2016: a cross-sectional study

Background: Unnecessary antibiotic use increases the risk for antibiotic resistance. The rates of antibiotic use for upper respiratory infections are high in hospitals in China. Although most guidelines advise against the use of antibiotics for acute diarrhea, little is known about antibiotic use practices for acute diarrhea in China. Methods: A retrospective prescription review from a Shanghai hospital outpatient electronic health records system was conducted from 1 January 2016 to 30 December 2016. Records were included for adult patients. The microbial resistance seasonal data in 2016 were extracted. Chi-squared and multivariable logistic regression and adjusted odd ratio (aOR) were used to assess the relationships between demographic characteristics and antibiotic prescribing. Results: In total, there were 16,565 prescriptions, 16,060 prescriptions were included in the final analysis after excluding the follow up visits. There were 12,131 (76%) prescriptions with antibiotics prescribed. 5505 (45%) of the antibiotics prescribed were injectable. Of the antibiotics prescribed, levofloxacin was the most frequent (85%), followed by various cephalosporins (14%). Of the cephalosporin prescriptions, 3rd generation products were the most common (97%). Treatment with oral rehydration salts (ORS) was prescribed 34 (0.2%) times, probiotics were prescribed 3414 (21%) times and smectite was prescribed 2209 (14%) times. Multivariable regression analysis showed that those more likely to receive antibiotics were age 31-50 aOR 1.3 (1.1-1.4), p<0.001, evaluated in the late evening (11pm to 7am) aOR 2.6 (2.2-2.9) p<0.001, in the early evening (6pm-11pm) aOR 2.0 (1.8-2.2) p<0.001, in the summer (June-August) aOR 1.7 (1.5-1.9) p<0.001. At the same time, the Gram positive and Gram negative resistance rates to levofloxacin exceeded 40%, including 50% of E. coliisolates. Conclusion: High rates of antibiotic use were observed for acute diarrhea in this hospital. Given the inappropriateness of antibiotics for acute diarrhea and the nonsensical high rates of of intravenous levofloxacin use and the concurrent high rates of the levofloxacin resistance, a more effective antibiotic stewardship program is needed to improve patient outcomes, reduce costs, reinforce policy and address the underlying causes of antibiotic abuse.published_or_final_versio