Rare event simulation is the process of finding unlikely probabilities through computational simulation of dynamic systems by sampling from rare event spaces as frequently as possible while keeping sample sizes and confidence intervals low. An efficient rare event simulation method is multilevel splitting: an algorithm which systematically clones simulations to incentivize trends toward desired rare events. Inefficiencies occur when insufficient cloning conditions are chosen. The goal of this project is to determine how effectively properties of the Ornstein-Uhlenbeck operator may estimate or inform researchers of dynamic systems’ importance functions: the functions that determine cloning conditions for a given system but are typically hard and computationally expensive to solve directly.

I applied to SuperUROP with the goal of conducting more formalized research with tangible outcomes than through my traditional UROP experience. As I start thinking about graduate school, I hope to learn more about computational engineering and the research process through this program. I’ m most excited about having a paper at the end of all this that I know will have been made possible through my own research and blood, sweat, and tears!