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Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

Journal Article · · Journal of Computational Physics
 [1];  [1];  [2];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
  2. Univ. of Kansas, Lawrence, KS (United States). Dept. of Mathematics
+ Show Author Affiliations
Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. Here, one can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.
Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1524015
Alternate ID(s):
OSTI ID: 22382181
OSTI ID: 1367750
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 282; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (22)

Traveling-Standing Water Waves and Microseisms text January 2013
Implicit particle filters for data assimilation preprint January 2010
Uncertainty quantification and weak approximation of an elliptic inverse problem preprint January 2011
Rare Event Simulation of Small Noise Diffusions journal September 2012
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics journal August 2006
Stochastic spectral methods for efficient Bayesian solution of inverse problems journal June 2007
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems journal April 2009
A random map implementation of implicit filters journal February 2012
Relationship between a Wiener–Hermite expansion and an energy cascade journal April 1970
Gaussian fields and random flow journal March 1974
Inverse problems: A Bayesian perspective journal May 2010
Uncertainty reduction and characterization for complex environmental fate and transport models: An empirical Bayesian framework incorporating the stochastic response surface method: BAYESIAN FRAMEWORK INCORPORATING SRSM journal December 2003
Implicit sampling for particle filters journal September 2009
Solution of inverse problems with limited forward solver evaluations: a Bayesian perspective journal December 2013
Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem journal January 2011
Uncertainty Quantification in MD Simulations. Part II: Bayesian Inference of Force-Field Parameters journal January 2012
Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics journal January 2009
Data Assimilation in the Low Noise Regime with Application to the Kuroshio journal June 2013
Implicit Particle Methods and Their Connection with Variational Data Assimilation journal June 2013
Implicit particle filters for data assimilation journal January 2010
A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems journal January 2009
Fundamental limitations of polynomial chaos for uncertainty quantification in systems with intermittent instabilities journal January 2013

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Magnetometric resistivity tomography using chaos polynomial expansion journal February 2020
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data journal January 2019
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data text January 2019
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data posted_content April 2019

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Bayesian inverse problem
Monte Carlo sampling
Polynomial chaos expansion