Optimal Experimental Design Using a Consistent Bayesian Approach

Walsh, Scott; Wildey, Timothy Michael; Jakeman, John Davis

doi:10.1115/1.4037457

Optimal Experimental Design Using a Consistent Bayesian Approach

Journal Article · Thu Sep 07 00:00:00 EDT 2017 · ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems. Part B. Mechanical Engineering

DOI:https://doi.org/10.1115/1.4037457· OSTI ID:1478379

Walsh, Scott ^[1]; Wildey, Timothy Michael ^[2]; Jakeman, John Davis ^[2]

Univ. of Colorado, Denver, CO (United States). Dept. of Mathematical and Statistical Sciences
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research

We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent Bayesian approach for solving stochastic inverse problems, which seeks a posterior probability density that is consistent with the model and the data in the sense that the push-forward of the posterior (through the computational model) matches the observed density on the observations almost everywhere. Given a set of potential observations, our optimal experimental design (OED) seeks the observation, or set of observations, that maximizes the expected information gain from the prior probability density on the model parameters. We discuss the characterization of the space of observed densities and a computationally efficient approach for rescaling observed densities to satisfy the fundamental assumptions of the consistent Bayesian approach. Finally, numerical results are presented to compare our approach with existing OED methodologies using the classical/statistical Bayesian approach and to demonstrate our OED on a set of representative partial differential equations (PDE)-based models.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1478379

Report Number(s):: SAND--2017-4749J; 666529

Journal Information:: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems. Part B. Mechanical Engineering, Journal Name: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems. Part B. Mechanical Engineering Journal Issue: 1 Vol. 4; ISSN 2332-9017

Publisher:: American Society of Mechanical EngineersCopyright Statement

Country of Publication:: United States

Language:: English

References (30)

A Laplace method for under-determined Bayesian optimal experimental designs Long, Quan; Scavino, Marco; Tempone, Raúl Computer Methods in Applied Mechanics and Engineering, Vol. 285 https://doi.org/10.1016/j.cma.2014.12.008	journal	March 2015
Rényi Divergence and Kullback-Leibler Divergence van Erven, Tim; Harremoes, Peter IEEE Transactions on Information Theory, Vol. 60, Issue 7 https://doi.org/10.1109/tit.2014.2320500	journal	July 2014
On the Statistical Calibration of Physical Models: STATISTICAL CALIBRATION OF PHYSICAL MODELS Sargsyan, K.; Najm, H. N.; Ghanem, R. International Journal of Chemical Kinetics, Vol. 47, Issue 4 https://doi.org/10.1002/kin.20906	journal	February 2015
Optimal Bayesian Experimental Design for Priors of Compact Support with Application to Shock-Tube Experiments for Combustion Kinetics: Optimal Bayesian Experimental Design for Priors of Compact Support Bisetti, Fabrizio; Kim, Daesang; Knio, Omar International Journal for Numerical Methods in Engineering, Vol. 108, Issue 2 https://doi.org/10.1002/nme.5211	journal	February 2016
Numerical methods for A-optimal designs with a sparsity constraint for ill-posed inverse problems Haber, Eldad; Magnant, Zhuojun; Lucero, Christian Computational Optimization and Applications, Vol. 52, Issue 1 https://doi.org/10.1007/s10589-011-9404-4	journal	April 2011
Numerical methods for optimum experimental design in DAE systems Bauer, Irene; Bock, Hans Georg; Körkel, Stefan Journal of Computational and Applied Mathematics, Vol. 120, Issue 1-2 https://doi.org/10.1016/S0377-0427(00)00300-9	journal	August 2000
Stochastic collocation and mixed finite elements for flow in porous media Ganis, Benjamin; Klie, Hector; Wheeler, Mary F. Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 43-44 https://doi.org/10.1016/j.cma.2008.03.025	journal	August 2008
A multiscale preconditioner for stochastic mortar mixed finite elements Wheeler, Mary F.; Wildey, Tim; Yotov, Ivan Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 9-12 https://doi.org/10.1016/j.cma.2010.10.015	journal	February 2011
Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations Long, Quan; Scavino, Marco; Tempone, Raúl Computer Methods in Applied Mechanics and Engineering, Vol. 259 https://doi.org/10.1016/j.cma.2013.02.017	journal	June 2013
An efficient, high-order perturbation approach for flow in random porous media via Karhunen–Loève and polynomial expansions Zhang, Dongxiao; Lu, Zhiming Journal of Computational Physics, Vol. 194, Issue 2 https://doi.org/10.1016/j.jcp.2003.09.015	journal	March 2004
Simulation-based optimal Bayesian experimental design for nonlinear systems Huan, Xun; Marzouk, Youssef M. Journal of Computational Physics, Vol. 232, Issue 1 https://doi.org/10.1016/j.jcp.2012.08.013	journal	January 2013
Numerical methods for optimum experimental design in DAE systems Bauer, Irene; Bock, Hans Georg; Körkel, Stefan Journal of Computational and Applied Mathematics, Vol. 120, Issue 1-2 https://doi.org/10.1016/s0377-0427(00)00300-9	journal	August 2000
Inverse problems: A Bayesian perspective Stuart, A. M. Acta Numerica, Vol. 19 https://doi.org/10.1017/S0962492910000061	journal	May 2010
Inverse problems: A Bayesian perspective Stuart, A. M. Acta Numerica, Vol. 19 https://doi.org/10.1017/s0962492910000061	journal	May 2010
Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes Körkel *, Stefan; Kostina, Ekaterina; Bock, Hans Georg Optimization Methods and Software, Vol. 19, Issue 3-4 https://doi.org/10.1080/10556780410001683078	journal	June 2004
Numerical methods for experimental design of large-scale linear ill-posed inverse problems Haber, E.; Horesh, L.; Tenorio, L. Inverse Problems, Vol. 24, Issue 5 https://doi.org/10.1088/0266-5611/24/5/055012	journal	September 2008
Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems Haber, E.; Horesh, L.; Tenorio, L. Inverse Problems, Vol. 26, Issue 2 https://doi.org/10.1088/0266-5611/26/2/025002	journal	December 2009
Rényi Divergence and Kullback-Leibler Divergence van Erven, Tim; Harremoes, Peter IEEE Transactions on Information Theory, Vol. 60, Issue 7 https://doi.org/10.1109/TIT.2014.2320500	journal	July 2014
Bayesian calibration of computer models Kennedy, Marc C.; O'Hagan, Anthony Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 63, Issue 3 https://doi.org/10.1111/1467-9868.00294	journal	August 2001
A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis Breidt, J.; Butler, T.; Estep, D. SIAM Journal on Numerical Analysis, Vol. 49, Issue 5 https://doi.org/10.1137/100785946	journal	January 2011
Experimental Design for Biological Systems Chung, Matthias; Haber, Eldad SIAM Journal on Control and Optimization, Vol. 50, Issue 1 https://doi.org/10.1137/100791063	journal	January 2012
A-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with Regularized $\ell_0$-Sparsification Alexanderian, Alen; Petra, Noemi; Stadler, Georg SIAM Journal on Scientific Computing, Vol. 36, Issue 5 https://doi.org/10.1137/130933381	journal	January 2014
A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problems Alexanderian, Alen; Petra, Noemi; Stadler, Georg SIAM Journal on Scientific Computing, Vol. 38, Issue 1 https://doi.org/10.1137/140992564	journal	January 2016
Optimal Bayesian Design by Inhomogeneous Markov Chain Simulation Müller, Peter; Sansó, Bruno; De Iorio, Maria Journal of the American Statistical Association, Vol. 99, Issue 467 https://doi.org/10.1198/016214504000001123	journal	September 2004
Simulation-Based Optimal Design Using a Response Variance Criterion Solonen, Antti; Haario, Heikki; Laine, Marko Journal of Computational and Graphical Statistics, Vol. 21, Issue 1 https://doi.org/10.1198/jcgs.2011.10070	journal	January 2012
On Information and Sufficiency Kullback, S.; Leibler, R. A. The Annals of Mathematical Statistics, Vol. 22, Issue 1 https://doi.org/10.1214/aoms/1177729694	journal	March 1951
Bayesian Experimental Design: A Review Chaloner, Kathryn; Verdinelli, Isabella Statistical Science, Vol. 10, Issue 3 https://doi.org/10.1214/ss/1177009939	journal	August 1995
Gradient-Based Stochastic Optimization Methods in Bayesian Experimental Design Huan, Xun; Marzouk, Youssef International Journal for Uncertainty Quantification, Vol. 4, Issue 6 https://doi.org/10.1615/Int.J.UncertaintyQuantification.2014006730	journal	January 2014
Gradient-Based Stochastic Optimization Methods in Bayesian Experimental Design Huan, Xun; Marzouk, Youssef International Journal for Uncertainty Quantification, Vol. 4, Issue 6 https://doi.org/10.1615/int.j.uncertaintyquantification.2014006730	journal	January 2014
Simulation-based optimal Bayesian experimental design for nonlinear systems Huan, Xun; Marzouk, Youssef M. arXiv https://doi.org/10.48550/arxiv.1108.4146	text	January 2011

Cited By (6)

Goal-oriented optimal design of experiments for large-scale Bayesian linear inverse problems Attia, Ahmed; Alexanderian, Alen; Saibaba, Arvind K. Inverse Problems, Vol. 34, Issue 9 https://doi.org/10.1088/1361-6420/aad210	journal	July 2018
Efficient D-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems Alexanderian, Alen; Saibaba, Arvind K. SIAM Journal on Scientific Computing, Vol. 40, Issue 5 https://doi.org/10.1137/17m115712x	journal	January 2018
Optimal Experimental Design for Constrained Inverse Problems Ruthotto, Lars; Chung, Julianne; Chung, Matthias arXiv https://doi.org/10.48550/arxiv.1708.04740	preprint	January 2017
Optimum Experimental Design for Interface Identification Problems Etling, Tommy; Herzog, Roland; Siebenborn, Martin arXiv https://doi.org/10.48550/arxiv.1808.05776	text	January 2018
Learning Quantities of Interest from Dynamical Systems for Observation-Consistent Inversion Mattis, Steven; Steffen, Kyle Robert; Butler, Troy arXiv https://doi.org/10.48550/arxiv.2009.06918	preprint	January 2020
Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems Attia, Ahmed; Alexanderian, Alen; Saibaba, Arvind K. arXiv https://doi.org/10.48550/arxiv.1802.06517	text	January 2018

Similar Records

Optimal experimental design for prediction based on push-forward probability measures

Journal Article · Wed May 13 20:00:00 EDT 2020 · Journal of Computational Physics · OSTI ID:1630281

Combining Push-Forward Measures and Bayes' Rule to Construct Consistent Solutions to Stochastic Inverse Problems

Journal Article · Mon Apr 02 20:00:00 EDT 2018 · SIAM Journal on Scientific Computing · OSTI ID:1469654

Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients

Journal Article · Tue Oct 15 00:00:00 EDT 2019 · Journal of Computational Physics · OSTI ID:1572471

Related Subjects

42 ENGINEERING

Optimal Experimental Design Using a Consistent Bayesian Approach

Citation Formats

References (30)

Cited By (6)

Similar Records

Related Subjects