Application and Evaluation of Surrogate Models for Radiation Source Search
Abstract
Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation algorithms. We consider the problem of inferring the 2D location and intensity of a radiation source in an urban environment using a ray-tracing model based on Boltzmann transport theory. Whereas the code implementing this model is relatively efficient, extension to 3D Monte Carlo transport simulations precludes subsequent Bayesian inference to infer source locations, which typically requires thousands to millions of simulations. Additionally, the resulting likelihood exhibits discontinuous derivatives due to the presence of buildings. To address these issues, we discuss the construction of surrogate models for optimization, Bayesian inference, and uncertainty propagation. Specifically, we consider surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. We detail strategies for computing training points and discuss the merits and deficits of each method.
- Authors:
- Publication Date:
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1579414
- Grant/Contract Number:
- NA0002576
- Resource Type:
- Published Article
- Journal Name:
- Algorithms
- Additional Journal Information:
- Journal Name: Algorithms Journal Volume: 12 Journal Issue: 12; Journal ID: ISSN 1999-4893
- Publisher:
- MDPI AG
- Country of Publication:
- Switzerland
- Language:
- English
Citation Formats
Cook, Jared A., Smith, Ralph C., Hite, Jason M., Stefanescu, Razvan, and Mattingly, John. Application and Evaluation of Surrogate Models for Radiation Source Search. Switzerland: N. p., 2019.
Web. doi:10.3390/a12120269.
Cook, Jared A., Smith, Ralph C., Hite, Jason M., Stefanescu, Razvan, & Mattingly, John. Application and Evaluation of Surrogate Models for Radiation Source Search. Switzerland. doi:10.3390/a12120269.
Cook, Jared A., Smith, Ralph C., Hite, Jason M., Stefanescu, Razvan, and Mattingly, John. Thu .
"Application and Evaluation of Surrogate Models for Radiation Source Search". Switzerland. doi:10.3390/a12120269.
@article{osti_1579414,
title = {Application and Evaluation of Surrogate Models for Radiation Source Search},
author = {Cook, Jared A. and Smith, Ralph C. and Hite, Jason M. and Stefanescu, Razvan and Mattingly, John},
abstractNote = {Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation algorithms. We consider the problem of inferring the 2D location and intensity of a radiation source in an urban environment using a ray-tracing model based on Boltzmann transport theory. Whereas the code implementing this model is relatively efficient, extension to 3D Monte Carlo transport simulations precludes subsequent Bayesian inference to infer source locations, which typically requires thousands to millions of simulations. Additionally, the resulting likelihood exhibits discontinuous derivatives due to the presence of buildings. To address these issues, we discuss the construction of surrogate models for optimization, Bayesian inference, and uncertainty propagation. Specifically, we consider surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. We detail strategies for computing training points and discuss the merits and deficits of each method.},
doi = {10.3390/a12120269},
journal = {Algorithms},
number = 12,
volume = 12,
place = {Switzerland},
year = {2019},
month = {12}
}
DOI: 10.3390/a12120269
Works referenced in this record:
Diagnostics for Gaussian Process Emulators
journal, November 2009
- Bastos, Leonardo S.; O’Hagan, Anthony
- Technometrics, Vol. 51, Issue 4
Is Gauss Quadrature Better than Clenshaw–Curtis?
journal, January 2008
- Trefethen, Lloyd N.
- SIAM Review, Vol. 50, Issue 1
Nonparametric Estimation of Spatial and Space-Time Covariance Function
journal, July 2013
- Choi, InKyung; Li, Bo; Wang, Xiao
- Journal of Agricultural, Biological, and Environmental Statistics, Vol. 18, Issue 4
Multivariate Adaptive Regression Splines
journal, March 1991
- Friedman, Jerome H.
- The Annals of Statistics, Vol. 19, Issue 1
Initial MCNP6 Release Overview
journal, December 2012
- Goorley, T.; James, M.; Booth, T.
- Nuclear Technology, Vol. 180, Issue 3
Surrogate-Based Robust Design for a Non-Smooth Radiation Source Detection Problem
journal, May 2019
- Ştefănescu, Răzvan; Hite, Jason; Cook, Jared
- Algorithms, Vol. 12, Issue 6
Deep learning
journal, May 2015
- LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey
- Nature, Vol. 521, Issue 7553
Radiation detection with distributed sensor networks
journal, August 2004
- Brennan, S. M.; Mielke, A. M.; Torney, D. C.
- Computer, Vol. 37, Issue 8
Monte Carlo Variance of Scrambled Net Quadrature
journal, October 1997
- Owen, Art B.
- SIAM Journal on Numerical Analysis, Vol. 34, Issue 5
A survey of cross-validation procedures for model selection
journal, January 2010
- Arlot, Sylvain; Celisse, Alain
- Statistics Surveys, Vol. 4, Issue 0
Multivariate adaptive regression splines for analysis of geotechnical engineering systems
journal, March 2013
- Zhang, W. G.; Goh, A. T. C.
- Computers and Geotechnics, Vol. 48
Efficient emulators of computer experiments using compactly supported correlation functions, with an application to cosmology
journal, December 2011
- Kaufman, Cari G.; Bingham, Derek; Habib, Salman
- The Annals of Applied Statistics, Vol. 5, Issue 4
Strictly Proper Scoring Rules, Prediction, and Estimation
journal, March 2007
- Gneiting, Tilmann; Raftery, Adrian E.
- Journal of the American Statistical Association, Vol. 102, Issue 477
Recent advances in surrogate-based optimization
journal, January 2009
- Forrester, Alexander I. J.; Keane, Andy J.
- Progress in Aerospace Sciences, Vol. 45, Issue 1-3
Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem: INFERENCE TECHNIQUES FOR A RADIATION DETECTION PROBLEM
journal, February 2017
- Ştefănescu, Răzvan; Schmidt, Kathleen; Hite, Jason
- International Journal for Numerical Methods in Engineering, Vol. 111, Issue 10
Distance-Distributed Design for Gaussian Process Surrogates
journal, October 2019
- Zhang, Boya; Cole, D. Austin; Gramacy, Robert B.
- Technometrics
DRAM: Efficient adaptive MCMC
journal, December 2006
- Haario, Heikki; Laine, Marko; Mira, Antonietta
- Statistics and Computing, Vol. 16, Issue 4
Advances in surrogate based modeling, feasibility analysis, and optimization: A review
journal, January 2018
- Bhosekar, Atharv; Ierapetritou, Marianthi
- Computers & Chemical Engineering, Vol. 108
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
journal, January 1995
- Green, Peter J.
- Biometrika, Vol. 82, Issue 4
Large Sample Properties of Simulations Using Latin Hypercube Sampling
journal, May 1987
- Stein, Michael
- Technometrics, Vol. 29, Issue 2
Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation
journal, December 2005
- Yang, Yuhong
- Biometrika, Vol. 92, Issue 4
An evaluation of adaptive surrogate modeling based optimization with two benchmark problems
journal, October 2014
- Wang, Chen; Duan, Qingyun; Gong, Wei
- Environmental Modelling & Software, Vol. 60
Sequential optimal positioning of mobile sensors using mutual information
journal, July 2019
- Schmidt, Kathleen; Smith, Ralph C.; Hite, Jason
- Statistical Analysis and Data Mining: The ASA Data Science Journal, Vol. 12, Issue 6
Interpolation in the limit of increasingly flat radial basis functions
journal, February 2002
- Driscoll, T. A.; Fornberg, B.
- Computers & Mathematics with Applications, Vol. 43, Issue 3-5