@article{cook_smith_hite_stefanescu_mattingly_2019, title={Application and Evaluation of Surrogate Models for Radiation Source Search}, volume={12}, ISSN={["1999-4893"]}, DOI={10.3390/a12120269}, 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.}, number={12}, journal={ALGORITHMS}, author={Cook, Jared A. and Smith, Ralph C. and Hite, Jason M. and Stefanescu, Razvan and Mattingly, John}, year={2019}, month={Dec} }
 @article{hite_mattingly_2019, title={Bayesian Metropolis methods for source localization in an urban environment}, volume={155}, ISSN={["0969-806X"]}, DOI={10.1016/j.radphyschem.2018.06.024}, abstractNote={We apply Bayesian techniques to determine the location and intensity of a gamma radiation source in an urban environment using count rates taken from a distributed detector network. A simplified model of the radiation transport process is used to construct a statistical model for the detector count rates in the presence of a randomly varying background. Markov Chain Monte Carlo is used to generate samples from the Bayesian posterior density, which can be used to inform search and interdiction efforts. We also present a modification of the traditional Metropolis sampling algorithm that allows us to incorporate fixed parameter uncertainties in building macroscopic cross sections and account for their effects on the posterior distribution. This method is then applied to a test problem based on a real urban geometry with different levels of uncertainty in the building cross sections. The results show that the uncertainty in the estimated source location is modest, even with a large degree of uncertainty in the building cross sections.}, journal={RADIATION PHYSICS AND CHEMISTRY}, author={Hite, Jason and Mattingly, John}, year={2019}, month={Feb}, pages={271–274} }
 @article{hite_mattingly_archer_willis_rowe_bray_carter_ghawaly_2019, title={Localization of a radioactive source in an urban environment using Bayesian Metropolis methods}, volume={915}, ISSN={["1872-9576"]}, DOI={10.1016/j.nima.2018.09.032}, abstractNote={Abstract We present a method for localizing an unknown source of radiation in an urban environment using a distributed detector network. This method employs statistical parameter estimation techniques, relying on an approximation for the response of a detector to the source based on a simplified model of the underlying transport phenomena, combined with a Metropolis-type sampler that is modified to propagate the effect of fixed epistemic uncertainties in the material macroscopic cross sections of objects in the scene. We apply this technique to data collected during a measurement campaign conducted in a realistic analog for an urban scene using a network of six mobile detectors. Our initial results are able to localize the source to within approximately 8 m over a scene of size 300 m × 200 m in two independent trials with 30 min count times, including a characterization of the uncertainty associated with the poorly known macroscopic cross sections of objects in the scene. In these measurements, the nearest detectors were between 20 m to 30 m from the source, and recorded count rates between approximately 3 and 13 times background. A few detectors had line-of-sight to the source, while the majority were obscured by objects present in the scene. After extending our model to account for the orientation of the detectors and correcting for anomalies in the measurement data we were able to further improve the localization accuracy to approximately 2 m in both trials.}, journal={NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT}, author={Hite, Jason and Mattingly, John and Archer, Dan and Willis, Michael and Rowe, Andrew and Bray, Kayleigh and Carter, Jake and Ghawaly, James}, year={2019}, month={Jan}, pages={82–93} }
 @article{schmidt_smith_hite_mattingly_azmy_rajan_goldhahn_2019, title={Sequential optimal positioning of mobile sensors using mutual information}, volume={12}, ISSN={["1932-1872"]}, DOI={10.1002/sam.11431}, abstractNote={Abstract Source localization, such as detecting a nuclear source in an urban area or ascertaining the origin of a chemical plume, is generally regarded as a well‐documented inverse problem; however, optimally placing sensors to collect data for such problems is a more challenging task. In particular, optimal sensor placement—that is, measurement locations resulting in the least uncertainty in the estimated source parameters—depends on the location of the source, which is typically unknown a priori . Mobile sensors are advantageous because they have the flexibility to adapt to any given source position. While most mobile sensor strategies designate a trajectory for sensor movement, we instead employ mutual information, based on Shannon entropy, to choose the next measurement location from a discrete set of design conditions.}, number={6}, journal={STATISTICAL ANALYSIS AND DATA MINING}, author={Schmidt, Kathleen and Smith, Ralph C. and Hite, Jason and Mattingly, John and Azmy, Yousry and Rajan, Deepak and Goldhahn, Ryan}, year={2019}, month={Dec}, pages={465–478} }
 @article{stefanescu_hite_cook_smith_mattingly_2019, title={Surrogate-Based Robust Design for a Non-Smooth Radiation Source Detection Problem}, volume={12}, ISSN={["1999-4893"]}, DOI={10.3390/a12060113}, abstractNote={In this paper, we develop and numerically illustrate a robust sensor network design to optimally detect a radiation source in an urban environment. This problem exhibits several challenges: penalty functionals are non-smooth due to the presence of buildings, radiation transport models are often computationally expensive, sensor locations are not limited to a discrete number of points, and source intensity and location responses, based on a fixed number of sensors, are not unique. We consider a radiation source located in a prototypical 250 m × 180 m urban setting. To address the non-smooth properties of the model and computationally expensive simulation codes, we employ a verified surrogate model based on radial basis functions. Using this surrogate, we formulate and solve a robust design problem that is optimal in an average sense for detecting source location and intensity with minimized uncertainty.}, number={6}, journal={ALGORITHMS}, author={Stefanescu, Razvan and Hite, Jason and Cook, Jared and Smith, Ralph C. and Mattingly, John}, year={2019}, month={Jun} }
 @article{ştefănescu_schmidt_hite_smith_mattingly_2017, title={Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem}, volume={111}, ISSN={0029-5981}, url={http://dx.doi.org/10.1002/nme.5491}, DOI={10.1002/nme.5491}, abstractNote={We propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particle swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non-smooth response, and their performances, are shown to significantly decrease the computational time over the global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms. Copyright © 2016 John Wiley & Sons, Ltd.}, number={10}, journal={International Journal for Numerical Methods in Engineering}, publisher={Wiley}, author={Ştefănescu, Răzvan and Schmidt, Kathleen and Hite, Jason and Smith, Ralph C. and Mattingly, John}, year={2017}, month={Feb}, pages={955–982} }
 @inproceedings{hite_mattingly_schmidt_stelanescu_smith_2016, title={Bayesian metropolis methods applied to sensor networks for radiation source localization}, DOI={10.1109/mfi.2016.7849519}, abstractNote={We present an application of statistical techniques to the localization of an unknown gamma source in an urban environment. By formulating the problem as a task of Bayesian parameter estimation, we are able to apply Markov Chain Monte Carlo (MCMC) to generate a full posterior probability density estimating the source location and intensity based on counts reported from a distributed detector network. To facilitate the calibration procedure, we employ a simplified photon transport model with low computational cost and test the proposed methodology in a simulated urban environment, with calibration data generated using the radiation transport code MCNP. The Bayesian methodology is able to identify the source location and intensity along with providing a full posterior density.}, booktitle={2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)}, author={Hite, J. M. and Mattingly, J. K. and Schmidt, K. L. and Stelanescu, R. and Smith, Ralph}, year={2016}, pages={389–393} }
 @article{bang_abdel-khalik_hite_2012, title={Hybrid reduced order modeling applied to nonlinear models}, volume={91}, ISSN={["1097-0207"]}, DOI={10.1002/nme.4298}, abstractNote={SUMMARY Reduced order modeling plays an indispensible role for most real‐world complex models. The objective of this manuscript is to hybridize local and global sensitivity analysis methods to enable the application of reduced order modeling to complex nonlinear models, often encountered in real system design and analysis calculations, for example, nuclear reactors. This is achieved by first employing local variational methods to identify important nonlinear features of the original model that are required to reach a user‐defined accuracy for the reduced model. This information is obtained by sampling local first‐order derivatives of a pseudoresponse utilizing a modified representation of an infinite series expansion around some reference point. The resulting derivative information is aggregated in a subspace of dimension much less than the dimension of the input parameter space. The accuracy of the reduced model can be mathematically quantified using a bounding norm. Next, global sensitivity methods are employed to exhaustively search the reduced subspace for sensitivity information. The theory and implementation details of the proposed method are exposed in this manuscript. Numerical tests based on prototype nonlinear functions and radiation transport models with many input parameters and many responses are conducted as proof of principle. Copyright © 2012 John Wiley & Sons, Ltd.}, number={9}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING}, author={Bang, Youngsuk and Abdel-Khalik, Hany S. and Hite, Jason M.}, year={2012}, month={Aug}, pages={929–949} }