Mathematics faculty and graduate students are invited to attend the MS defense of Mats Johnson.

Date: Friday, April 1, 2022
Time: 2:00 p.m.
Location: Weber 015

You may also attend by Zoom:

Join Zoom Meeting: https://zoom.us/j/92533923388?pwd=OEhBY2lBUVh1WlBUcWh5YlF5eWgydz09
Meeting ID: 925 3392 3388
Passcode: 691259

Advisor: Dr. David Aristoff

Committee: Dr. Olivier Pinaud, Dr. Margaret Cheney, Dr. Diego Krapf

Title: Weighted Ensemble: Practical Variance Reduction Techniques

Abstract: For a Markov process, the mean-first-passage time (MFPT) describes the average time to transition between two sets. The MFPT is useful in a number of applications including protein folding or enzyme reaction rate estimation. In these complicated systems, these transitions characterize rare-events and direct computation can be computationally infeasible. We analyzed a splitting and killing algorithm called weighted ensemble to address these problems in the context of computing the mean-first-passage time (MFPT). Weighted ensemble works by partitioning the state space into bins and replicating trajectories in an advantageous and unbiased manner to obtain estimates of the MFPT. After presenting a martingale decomposition of the variance of the weighted ensemble estimator, we introduced practical methods to minimize the variance. These methods’ effectiveness are demonstrated on a toy problem where a significant variance reduction over direct simulation and naive weighted ensemble practices is observed.