A numerical method for solving a stochastic inverse problem for parameters

Butler, Troy; Estep, Donald

doi:10.1016/j.anucene.2012.05.016

Cited by 8 publications

(17 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[], Butler et al . [], Butler and Estep [], Butler et al . [2014], and T. Butler et al (Solving stochastic inverse problems using sigma‐algebras on contour maps, 1407.3851, 2014).…”

Section: Measure‐theoretic Framework For Uncertainty Quantificationmentioning

confidence: 99%

“…This section summarizes the mathematical methodology and numerical methods for a measure-theoretic framework for stochastic inverse problems for physics-based maps as formulated by Breidt et al [2011], Butler et al [2012], Butler and Estep [2013], Butler et al [2014], and T. Butler et al (Solving stochastic inverse problems using sigma-algebras on contour maps, 1407.3851, 2014). Below, we emphasize the core deterministic forward and inverse maps at the heart of all the computations involving uncertainties modeled with probability measures.…”

Section: Measure-theoretic Framework For Uncertainty Quantificationmentioning

confidence: 99%

“…We present a recently developed measure-theoretic framework for the formulation and solution to a physically meaningful stochastic inverse problem for quantifying uncertainties in a physics-based model [Breidt et al, 2011;Butler et al, 2012;Butler and Estep, 2013;Butler et al, 2014; Solving stochastic inverse problems using sigma-algebras on contour maps, 1407.3851, 2014]. A computational algorithm is described in detail and applied to a mathematical model for groundwater contamination.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parameter estimation and prediction for groundwater contamination based on measure theory

et al. 2015

Self Cite

View full text Add to dashboard Cite

The problem of groundwater contamination in an aquifer is one with many uncertainties. Properly quantifying these uncertainties is essential in order to make reliable probabilistic-based predictions and decisions regarding remediation strategies. In this work, a measure-theoretic framework is employed to quantify uncertainties in a simplified groundwater contamination transport model. Given uncertain data from observation wells, the stochastic inverse problem is solved numerically to obtain a probability measure on the space of unknown model parameters characterizing groundwater flow and contaminant transport in an aquifer, as well as unknown model boundary or source terms such as the contaminant source release into the environment. This probability measure is used to make predictions of future contaminant concentrations and to analyze possible remediation techniques. The ability to identify regions of small but nonzero probability using this method is illustrated.

show abstract

“…[], Butler et al . [], Butler and Estep [], Butler et al . [2014], and T. Butler et al (Solving stochastic inverse problems using sigma‐algebras on contour maps, 1407.3851, 2014).…”

Section: Measure‐theoretic Framework For Uncertainty Quantificationmentioning

confidence: 99%

Section: Measure-theoretic Framework For Uncertainty Quantificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parameter estimation and prediction for groundwater contamination based on measure theory

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…A fundamental categorization classifies schemes as either stochastic (e.g. [9], [10], [11]) or gradient based (e.g. [12], [13], [14], [15]).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear thermal parameter estimation for embedded internal Joule heaters

Tutcuoglu

Majidi

Shan

2016

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

We propose a novel inverse scheme, which allows for estimation of thermal parameters of internal Joule heaters through measurements of surface temperature distributions during a Joule heating process. The inverse scheme is based on the governing nonlinear, inhomogeneous heat conduction and generation equation and solely assumes knowledge of the electric resistivity of the Joule heater. Polynomial forms are assumed for the thermal conductivity κ = κ(T) and c p ρ =: λ = λ(T), while the method can be easily generalized to estimate parameters of any suitable form. Both the sensitivity and the adjoint method are developed and compared. Owing to the ill-conditioning of the inverse scheme, the performance of relaxation methods and regularization schemes are analyzed (to improve numerical conditioning). A verification was conducted using polydimethylsiloxane (PDMS) embedded with a strip of conductive propylene-based elastomer (cPBE). Good agreement was achieved between theoretical predictions by the inverse scheme and experimental measurements regardless of the approximated effective potential difference across the cPBE. While constant parameter estimations sufficed to approximate one reference temperature, the inclusion of multiple instants of time required an increase in the polynomial order. The improved parameter estimation is shown to remain of the same order of magnitude for the temperature range encountered when compared with the constant approximation, i.e. κ=10.

show abstract

“…Second, all of the available data is subject to natural variation as well as experimental/observational error so the solutions of the inverse problem for parameter determination and the forward prediction problem are described in terms of probability measures. Both of these issues can be addressed directly by measure theory, which provides a very natural framework for the formulation, solution, and numerical approximation of the inverse problem for scientific inference [ 23 , 24 , 25 , 26 ].…”

Section: Introductionmentioning

confidence: 99%

Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

Butler

Graham

Estep

et al. 2015

Advances in Water Resources

Self Cite

View full text Add to dashboard Cite

The uncertainty in spatially heterogeneous Manning’s n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of “condition” for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning’s n parameter and the effect on model predictions is analyzed.

show abstract

A numerical method for solving a stochastic inverse problem for parameters

Cited by 8 publications

References 12 publications

Parameter estimation and prediction for groundwater contamination based on measure theory

Parameter estimation and prediction for groundwater contamination based on measure theory

Nonlinear thermal parameter estimation for embedded internal Joule heaters

Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

Contact Info

Product

Resources

About