Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Goal-oriented optimal design of experiments for large-scale Bayesian linear inverse problems

Journal Article · · Inverse Problems
 [1];  [2];  [2]
  1. Argonne National Lab. (ANL), Argonne, IL (United States); Statistical and Applied Mathematical Science Institute (SAMSI), RTP, NC (United States)
  2. North Carolina State Univ., Raleigh, NC (United States)
+ Show Author Affiliations
We develop a framework for goal-oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs. This framework differs from classical Bayesian optimal design of experiments (ODE) in the following sense: we seek experimental designs that minimize the posterior uncertainty in the experiment end-goal, e.g. a quantity of interest (QoI), rather than the estimated parameter itself. This is suitable for scenarios in which the solution of an inverse problem is an intermediate step and the estimated parameter is then used to compute a QoI. In such problems, a GOODE approach has two benefits: the designs can avoid wastage of experimental resources by a targeted collection of data, and the resulting design criteria are computationally easier to evaluate due to the often low-dimensionality of the QoIs. We present two modified design criteria, A-GOODE and D-GOODE, which are natural analogues of classical Bayesian A- and D-optimal criteria. We analyze the connections to other ODE criteria, and provide interpretations for the GOODE criteria by using tools from information theory. Then, we develop an efficient gradient-based optimization framework for solving the GOODE optimization problems. Additionally, we present comprehensive numerical experiments testing the various aspects of the presented approach. The driving application is the optimal placement of sensors to identify the source of contaminants in a diffusion and transport problem. As a result, we enforce sparsity of the sensor placements using an L1-norm penalty approach, and propose a practical strategy for specifying the associated penalty parameter.
Research Organization:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
1466356
Journal Information:
Inverse Problems, Journal Name: Inverse Problems Journal Issue: 9 Vol. 34; ISSN 0266-5611
Publisher:
IOPscienceCopyright Statement
Country of Publication:
United States
Language:
English

References (66)

Optimal Experimental Design Using a Consistent Bayesian Approach journal September 2017
Optimal Design of Experiments book December 2005
Fast Bayesian Optimal Experimental Design for Seismic Source Inversion preprint January 2015
A-optimal encoding weights for nonlinear inverse problems, with applications to the Helmholtz inverse problem text January 2016
The reduced-order hybrid Monte Carlo sampling smoother: The reduced-order hybrid Monte Carlo sampling smoother journal June 2016
A Hybrid Monte-Carlo sampling smoother for four-dimensional data assimilation: HMC SAMPLING SMOOTHER FOR 4D-DA journal June 2016
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 journal February 2016
An Algorithm for Construction of Constrained D-Optimum Designs book January 2015
Data Assimilation for Numerical Weather Prediction: A Review book January 2009
Automated Solution of Differential Equations by the Finite Element Method book January 2012
Randomized matrix-free trace and log-determinant estimators journal April 2017
Numerical methods for A-optimal designs with a sparsity constraint for ill-posed inverse problems journal April 2011
Numerical methods for optimum experimental design in DAE systems journal August 2000
Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations journal June 2013
A Laplace method for under-determined Bayesian optimal experimental designs journal March 2015
Fast Bayesian optimal experimental design for seismic source inversion journal July 2015
Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain journal June 2018
Simulation-based optimal Bayesian experimental design for nonlinear systems journal January 2013
Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet journal September 2015
A scalable design of experiments framework for optimal sensor placement journal July 2018
Dynamic Sensor Network Configuration in InfoSymbiotic Systems Using Model Singular Vectors journal January 2013
Numerical methods for optimum experimental design in DAE systems journal August 2000
Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes journal June 2004
Numerical methods for experimental design of large-scale linear ill-posed inverse problems journal September 2008
Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems journal December 2009
Guided Bayesian optimal experimental design journal April 2010
A-optimal encoding weights for nonlinear inverse problems, with application to the Helmholtz inverse problem journal June 2017
Dynamic Data-Driven Inversion for Terascale Simulations: Real-Time Identification of Airborne Contaminants conference January 2005
Dynamic Data-Driven Inversion for Terascale Simulations: Real-Time Identification of Airborne Contaminants conference January 2005
Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations journal January 2011
A Limited Memory Algorithm for Bound Constrained Optimization journal September 1995
Inverse Problem Theory and Methods for Model Parameter Estimation book January 2005
Experimental Design for Biological Systems journal January 2012
Goal-Oriented Inference: Approach, Linear Theory, and Application to Advection Diffusion journal January 2012
A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion journal January 2013
A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion journal January 2013
Goal-Oriented Inference: Approach, Linear Theory, and Application to Advection Diffusion journal January 2013
Nonlinear Goal-Oriented Bayesian Inference: Application to Carbon Capture and Storage journal January 2014
A-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with Regularized $\ell_0$-Sparsification journal January 2014
A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problems journal January 2016
Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems journal January 2017
Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems journal January 2017
Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix journal April 2011
Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization” journal November 2011
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization journal December 1997
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind journal January 1962
Experimental design in the context of Tikhonov regularized inverse problems journal October 2013
Experimental design in the context of Tikhonov regularized inverse problems journal October 2013
Bayesian survey design to optimize resolution in waveform inversion journal March 2012
On Bayesian A- and D-Optimal Experimental Designs in Infinite Dimensions journal September 2016
On Bayesian A- and D-Optimal Experimental Designs in Infinite Dimensions journal September 2016
Optimum Designs in Regression Problems journal June 1959
On a Measure of the Information Provided by an Experiment journal December 1956
Optimum Allocation in Linear Regression Theory journal June 1952
On Information and Sufficiency journal March 1951
A note on Bayesian c - and D -optimal designs in nonlinear regression models journal June 1996
Expected Information as Expected Utility journal May 1979
Bayesian Experimental Design: A Review journal August 1995
Gradient-Based Stochastic Optimization Methods in Bayesian Experimental Design journal January 2014
Gradient-Based Stochastic Optimization Methods in Bayesian Experimental Design journal January 2014
Simulation-based optimal Bayesian experimental design for nonlinear systems text January 2011
On Bayesian A- and D-optimal experimental designs in infinite dimensions preprint January 2014
Randomized Matrix-free Trace and Log-Determinant Estimators preprint January 2016
Goal-oriented optimal approximations of Bayesian linear inverse problems preprint January 2016
Optimal Experimental Design Using A Consistent Bayesian Approach text January 2017
Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain text January 2017

Cited By (2)

Sequentially optimized projections in x-ray imaging * journal June 2021
Logical Inference Framework for Experimental Design of Mechanical Characterization Procedures journal September 2018

Figures / Tables (15)

Figure 1(p. 3)figure Figure 1
Figure 2(p. 13)figure Figure 2
Table 1(p. 13)table Table 1
Table 2(p. 14)table Table 2
Figure 3(p. 15)figure Figure 3
Figure 4(p. 15)figure Figure 4
Figure 5(p. 16)figure Figure 5
Figure 6(p. 17)figure Figure 6
Figure 7(p. 17)figure Figure 7
Figure 8(p. 17)figure Figure 8
Figure 10(p. 18)figure Figure 10
Figure 9(p. 18)figure Figure 9
Figure 11(p. 19)figure Figure 11
Figure 12(p. 19)figure Figure 12
Figure 13(p. 19)figure Figure 13

Similar Records

A scalable design of experiments framework for optimal sensor placement
Journal Article · Mon Apr 10 20:00:00 EDT 2017 · Journal of Process Control · OSTI ID:1460969
Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation
Journal Article · Sun Sep 04 20:00:00 EDT 2022 · Journal of Computational Physics · OSTI ID:2421114
Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments
Journal Article · Tue Apr 12 20:00:00 EDT 2022 · SIAM Journal on Scientific Computing · OSTI ID:1909666

Related Subjects

97 MATHEMATICS AND COMPUTING
Data Assimilation
Design of Experiments
Inverse Problems
Sensor placement