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
[arXiv][PDF].
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
[arXiv][PDF].
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
[online publication][PDF].
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
[online publication][PDF].
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
[online publication].
