Facility Deployment Decisions through Warp Optimizaton of Regressed Gaussian Processes

University of South Carolina, Department of Mechanical Engineering, Nuclear Engineering Program, Columbia, SC 29201 Send proofs to: Anthony M. Scopatz scopatz@cec.sc.edu 541 Main Street, Columbia, SC 29208 Number of Pages: 35 Number of Tables: 0 Number of Figures: 11 Keywords: nuclear fuel cycle, gaussian process, dynamic time warping Abstract A method for quickly determining deployment schedules that meet a given fuel cycle demand is presented here. This algorithm is fast enough to perform in situ within low-fidelity fuel cycle simulators. It uses Gaussian process regression models to predict the production curve as a function of time and the number of deployed facilities. Each of these predictions is measured against the demand curve using the dynamic time warping distance. The minimum distance deployment schedule is evaluated in a full fuel cycle simulation, whose generated production curve then informs the model on the next optimization iteration. The method converges within five to ten iterations to a distance that is less than one percent of the total deployable production. A representative once-through fuel cycle is used to demonstrate the methodology for reactor deployment. I INTRODUCTION With the recent advent of agent-based nuclear fuel cycle simulators, such as Cyclus [1, 2], there comes the possibility to make in situ, dynamic facility deployment decisions. This would more fully model real-world fuel cycles where institutions (such as utility companies) predict future demand and choose their future deployment schedules appropriately. However, one of the major challenges to making in situ deployment decisions is the speed at which "good enough" decisions can be made. This paper proposes three related deployment-specific optimization algorithms that can be used for any demand curve and facility type. The demands of a fuel cycle scenario can often be simply stated, e.g. Here, the dynamic time warping (DTW) [3] distance is minimized between the demand curve and the regression of a Gaussian Process model (GP) [4] of prior simulations. This minimization produces a guess for a deployment schedule which is subsequently tested using an actual simulator. This process is repeated until an optimal deployment schedule for the given demand is found. Importantly, by using the Gaussian process surrogates, the number of simulation realizations that must be executed as part of the optimization may be reduced to only a handful. Furthermore, it is at least two orders-of-magnitude faster to test the model than it is to run a single low-fidelity fuel cycle simulation. Because of the relative computational cheapness, it is suitable to be used inside of a fuel cycle simulation.