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.Algorithms 2019, 12, 269 2 of 24 responses within this test environment [4]. Whereas this algorithm is based on Boltzmann transport theory, scattering is neglected to significantly improve the efficiency. It is shown in Ref.[5] that, despite these simplifying assumptions, the code can resolve source locations to within meters for the considered geometry and background levels. To solve the source localization problem, we employ Bayesian inference by using a Delayed Rejection Adaptive Metropolis (DRAM) algorithm [6], which requires thousands to millions of model evaluations to infer the 2D position (x, y) and intensity I, which are the design variables used throughout this paper. Whereas the use of DRAM is tractable for this model, two issues motivate the construction of surrogate models: (1) extension to 3D models employing Monte Carlo N-Particle (MCNP) [7] simulations that incorporate more comprehensive physics; and (2) addressing the non-differentiable likelihood due to the presence of buildings in the geometry. We extend the analysis presented in Ref.[2] by exploring the choice of surrogate modeling technique and training point selection in this paper.We performed preliminary research regarding the use of Monte Carlo simulations [7] to generate measurement data for nine point detectors in three dimensions with scattering in an extremely simplified geometry detailed in Ref. [8]. A Monte Carlo simulation was run once to generate synthetic measurements, and calibration was then performed against the calculated detector responses using the ray-tracing model. In this geometry, four rectangular prisms in a 2 × 2 layout were considered in a 100 m × 100 m domain, each adjusted to have wall thicknesses of 0.5 m of concrete. Employing the ray-traci...

Simulations and Experimental Verifications of an Algorithm for Radiation Source Mapping and Navigational Path Generation

“…Existing algorithms for such purposes use Monte Carlo simulations, recursive Bayesian estimation, or image reconstruction techniques (Towler et al 2012; Cook et al 2019; Zhang et al 2018; Liu et al 2015). However, they are often computation-heavy, lack robustness and adaptability, or require the detector to move awkwardly and inefficiently in grids, which may not even be possible depending on the terrain and vehicle type.…”