Data-Consistent Inversion for Stochastic Input-to-Output Maps

Butler, Troy; Wildey, Timothy; Yen, Tian Yu

doi:10.1088/1361-6420/ab8f83

Data-Consistent Inversion for Stochastic Input-to-Output Maps

Journal Article · Thu Aug 20 00:00:00 EDT 2020 · Inverse Problems

DOI:https://doi.org/10.1088/1361-6420/ab8f83· OSTI ID:1619228

^[1]; Wildey, Timothy ^[2]; Yen, Tian Yu ^[1]

Univ. of Colorado, Denver, CO (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Data-consistent inversion is a recently developed measure-theoretic framework for solving a stochastic inverse problem involving models of physical systems. The goal is to construct a probability measure on model inputs (i.e., parameters of interest) whose associated push-forward measure matches (i.e., is consistent with) a probability measure on the observable outputs of the model (i.e., quantities of interest). Previous implementations required the map from parameters of interest to quantities of interest to be deterministic. This work generalizes this framework for maps that are stochastic, i.e., contain uncertainties and variation not explainable by variations in uncertain parameters of interest. Generalizations of previous theorems of existence, uniqueness, and stability of the data-consistent solution are provided while new theoretical results address the stability of marginals on parameters of interest. A notable aspect of the algorithmic generalization is the ability to query the solution to generate independent identically distributed samples of the parameters of interest without requiring knowledge of the so-called stochastic parameters. This work therefore extends the applicability of the data-consistent inversion framework to a much wider class of problems. This includes those based on purely experimental and field data where only a subset of conditions are either controllable or can be documented between experiments while the underlying physics, measurement errors, and any additional covariates are either uncertain or not accounted for by the researcher. Finally, numerical examples demonstrate application of this approach to systems with stochastic sources of uncertainties embedded within the modeling of a system and a numerical diagnostic is summarized that is useful for determining if a key assumption is verified among competing choices of stochastic maps.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1619228

Report Number(s):: SAND--2020-3138J; 684755

Journal Information:: Inverse Problems, Journal Name: Inverse Problems Journal Issue: 8 Vol. 36; ISSN 0266-5611

Publisher:: IOPscienceCopyright Statement

Country of Publication:: United States

Language:: English

References (25)

Twenty-year weathering remeasurements at St Paul's Cathedral, London Trudgill, S. T.; Viles, H. A.; Inkpen, R. Earth Surface Processes and Landforms, Vol. 26, Issue 10 https://doi.org/10.1002/esp.260	journal	January 2001
Limestone weathering in Eastern Australia. Part 1: Erosion rates Smith, D. I.; Greenaway, M. A.; Moses, C. Earth Surface Processes and Landforms, Vol. 20, Issue 5 https://doi.org/10.1002/esp.3290200506	journal	August 1995
Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes Huang, S. P.; Quek, S. T.; Phoon, K. K. International Journal for Numerical Methods in Engineering, Vol. 52, Issue 9 https://doi.org/10.1002/nme.255	journal	November 2001
Stochastic Finite Elements: A Spectral Approach Ghanem, Roger G.; Spanos, Pol D. Springer New York, NY https://doi.org/10.1007/978-1-4612-3094-6	book	January 1991
A review of research in mechanical engineering design. Part I: Descriptive, prescriptive, and computer-based models of design processes Finger, Susan; Dixon, John R. Research in Engineering Design, Vol. 1, Issue 1 https://doi.org/10.1007/bf01580003	journal	March 1989
An overview of robust Bayesian analysis Berger, James O.; Moreno, Elías; Pericchi, Luis Raul Test, Vol. 3, Issue 1 https://doi.org/10.1007/bf02562676	journal	June 1994
Efficient real-time reservoir management using adjoint-based optimal control and model updating Sarma, Pallav; Durlofsky, Louis J.; Aziz, Khalid Computational Geosciences, Vol. 10, Issue 1 https://doi.org/10.1007/s10596-005-9009-z	journal	March 2006
Key computational modeling issues in Integrated Computational Materials Engineering Panchal, Jitesh H.; Kalidindi, Surya R.; McDowell, David L. Computer-Aided Design, Vol. 45, Issue 1 https://doi.org/10.1016/j.cad.2012.06.006	journal	January 2013
Measuring erosion with the micro-erosion meter—Contributions to understanding landform evolution Stephenson, W. J.; Finlayson, B. L. Earth-Science Reviews, Vol. 95, Issue 1-2 https://doi.org/10.1016/j.earscirev.2009.03.006	journal	June 2009
Stochastic spectral methods for efficient Bayesian solution of inverse problems Marzouk, Youssef M.; Najm, Habib N.; Rahn, Larry A. Journal of Computational Physics, Vol. 224, Issue 2 https://doi.org/10.1016/j.jcp.2006.10.010	journal	June 2007
Asymptotic Statistics van der Vaart, A. W. Cambridge University Press https://doi.org/10.1017/CBO9780511802256	book	January 2012
Inverse problems: A Bayesian perspective Stuart, A. M. Acta Numerica, Vol. 19 https://doi.org/10.1017/s0962492910000061	journal	May 2010
Hierarchical Bayesian space-time models Wikle, Christopher K.; Berliner, L. Mark; Cressie, Noel Environmental and Ecological Statistics, Vol. 5, Issue 2, p. 117-154 https://doi.org/10.1023/a:1009662704779	journal	June 1998
A comprehensive approach to monitoring volcano deformation as a window on the eruption cycle Dzurisin, Daniel Reviews of Geophysics, Vol. 41, Issue 1 https://doi.org/10.1029/2001rg000107	journal	January 2003
Numerical prediction of thermal and airflow conditions of a naturally ventilated atrium and validation of CFD models Moosavi, Leila; Mahyuddin, Norhayati; Ghafar, Norafida Journal of Renewable and Sustainable Energy, Vol. 10, Issue 6 https://doi.org/10.1063/1.5037386	journal	November 2018
A new method for predicting binding affinity in computer-aided drug design Åqvist, Johan; Medina, Carmen; Samuelsson, Jan-Erik "Protein Engineering, Design and Selection", Vol. 7, Issue 3 https://doi.org/10.1093/protein/7.3.385	journal	January 1994
Computational modelling for decision-making: where, why, what, who and how Calder, Muffy; Craig, Claire; Culley, Dave Royal Society Open Science, Vol. 5, Issue 6 https://doi.org/10.1098/rsos.172096	journal	June 2018
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
Monitoring Volcanoes Sparks, R. S. J.; Biggs, J.; Neuberg, J. W. Science, Vol. 335, Issue 6074 https://doi.org/10.1126/science.1219485	journal	March 2012
Approximation of Bayesian Inverse Problems for PDEs Cotter, S. L.; Dashti, M.; Stuart, A. M. SIAM Journal on Numerical Analysis, Vol. 48, Issue 1 https://doi.org/10.1137/090770734	journal	January 2010
Representing Model Inadequacy: A Stochastic Operator Approach Morrison, Rebecca E.; Oliver, Todd A.; Moser, Robert D. SIAM/ASA Journal on Uncertainty Quantification, Vol. 6, Issue 2 https://doi.org/10.1137/16m1106419	journal	January 2018
Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification Butler, T.; Jakeman, J.; Wildey, T. SIAM Journal on Scientific Computing, Vol. 40, Issue 5 https://doi.org/10.1137/18m1181675	journal	January 2018
A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi. Part I: Model Development and Validation Bunya, S.; Dietrich, J. C.; Westerink, J. J. Monthly Weather Review, Vol. 138, Issue 2 https://doi.org/10.1175/2009mwr2906.1	journal	February 2010
Bayesian Data Analysis Gelman, Andrew; Carlin, John B.; Stern, Hal S. https://doi.org/10.1201/b16018	book	November 2013
Probabilistic programming in Python using PyMC3 Salvatier, John; Wiecki, Thomas V.; Fonnesbeck, Christopher PeerJ Computer Science, Vol. 2 https://doi.org/10.7717/peerj-cs.55	journal	January 2016

Similar Records

Parameter estimation with maximal updated densities

Journal Article · Thu Feb 02 23:00:00 EST 2023 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:2311636

Stability and Convergence of Solutions to Stochastic Inverse Problems Using Approximate Probability Densities

Journal Article · Wed Oct 16 00:00:00 EDT 2024 · International Journal for Uncertainty Quantification · OSTI ID:2565158

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

Journal Article · Thu May 14 00:00:00 EDT 2020 · Journal of Computational Physics · OSTI ID:1630281

Related Subjects

97 MATHEMATICS AND COMPUTING
data consistent
inverse problem
pullback measure
push-forward measure
uncertainty quantification

Data-Consistent Inversion for Stochastic Input-to-Output Maps

Citation Formats

References (25)

Similar Records

Related Subjects