# Application and Evaluation of Surrogate Models for Radiation Source Search
## 7 Conclusions and Future Work  
Our goal is to construct surrogate models that could approximate the non-smooth model solution accurately and inexpensively. We employ surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. Table 6 displays the \(rRMSE\) of the surrogate models, as well as the computational efficiency of the surrogate models. We see that all of the surrogate models yield a dramatic decrease in the time required to evaluate the model at the 500 test points. The evaluation of the ray-tracing model required nearly 14 min, whereas all the surrogate models required merely seconds for the same evaluation. The relative errors in Table 6 are acceptable for many applications, including for this model. Additionally, we show that the choice of training points is important when choosing a surrogate model and can affect the performance of the surrogate model approximation. We show that the surrogate models investigated here provide sufficiently accurate approximations for use in Bayesian inference when solving the source localization problem.  
An area of present and future work is the application of a selection of these surrogate models to approximate high-fidelity 3D radiation transport simulations in a similar urban domain. Whereas these simulations require multiple minutes for a single evaluation with low uncertainty, they incorporate more complex physics and allow for three-dimensional domain construction. However, this computational expense precludes Bayesian inference and motivates the development of surrogate models. An additional area of future work is the use of these surrogate models for optimal detector placement and moving detectors, similar to the work done in Ref. [2; 5]. The surrogate models developed here would require being retrained for every new detector location considered for optimal placement, making these surrogate models in their current framework infeasible for use in that problem. However, the surrogate modeling techniques can be reused to approximate, for instance, mutual information to inform optimal surrogate placement.  
**Author Contributions:** Conceptualization, J.A.C., R.S. and J.M.; methodology, J.A.C.; software, J.A.C. and J.M.H.; validation, J.A.C. and J.M.H.; formal analysis, J.A.C.; investigation, J.A.C.; resources, J.A.C.; data curation, J.A.C. and J.M.H.; writing-original draft preparation, J.A.C. and R.S.; writing-review and editing, R.S. and J.M.; visualization, J.A.C. and J.M.; supervision, R.C.S. and J.M.; project administration, R.C.S.; funding acquisition, R.C.S. and J.M.  
**Funding:** This research was supported by the Department of Energy National Nuclear Security Administration (NNSA) under the Award Number DE-NA0002576 through the Consortium for Nonproliferation Enabling Capabilities (CNEC).  
**Acknowledgments:** Satellite imagery used in this report is (c)2015 Commonwealth of Virginia, DigitalGlobe, District of Columbia (DC GIS), Sanborn, as well as the U.S. Geological Survey and is provided by Google Maps. Building footprints shown in satellite overlays is (c)2015 OpenStreetMaps contributors and is publicly available under the terms of the Open Database License ([[http://www.openstreetmap.org/copyright](http://www.openstreetmap.org/copyright)]([http://www.openstreetmap.org/copyright](http://www.openstreetmap.org/copyright))).  
**Conflicts of Interest:** The authors declare no conflict of interest.