I research Monte Carlo methods with applications in physics and chemistry.
I work to identify sources of error, prove error bounds, and improve Monte Carlo accuracy.
For my research accomplishments, I was awarded the 2020-2021 Dean’s Dissertation Fellowship, the 2020 Henning Biermann Prize, and the 2020 Moses A. Greenfield Research Prize.
To find out more, check out my curriculum vitae
or take a look at the projects below.
Discovering patterns in time series data
The ``variational approach to conformational dynamics" (VAC)
is a well-established method for discovering patterns in simulated trajectories
from a high-dimensional system.
VAC identifies dynamical patterns
by approximating the leading eigenfunctions of the Markov transition operator.
I proved the convergence of VAC and derived detailed error bounds
Recently, we extended VAC to make it more robust
for applications with limited data.
The new approach, integrated VAC (IVAC), is easy to tune
and works well with neural network approximation spaces
It is challenging to study statistics
of tropical cyclones because
simulations are expensive and intense tropical cyclones are rare.
I developed an efficient new rare event sampling algorithm
and applied the algorithm to study intense tropical cyclones
Resampling schemes are often useful for sampling rare events.
There are a variety of resampling schemes,
yet there is not a good understanding of which schemes work best.
To address this lack of understanding,
I developed new mathematical approaches that identified minimal variance resampling schemes [arXiv][PDF].
The rapid intensification process in tropical cyclones is mysterious.
I helped develop an algorithm that identifies the most likely pathway leading to rapid intensification in a high-resolution weather model
Identifying the ground-state energy for quantum systems
It can be expensive to compute the ground-state energy
for many-electron systems,
particularly systems that are strongly correlated.
I helped design a Monte Carlo scheme for
computing the ground-state energy
that produced efficiency gains of up to a thousand [online publication].
We recently wrote a second paper that further improved the efficiency of the computational approach