I am a postdoctoral scholar studying theoretical and computational chemistry. This means that, theoretically, I can both use computers and do chemistry. I received my PhD working with Profs. Aaron Dinner and Jonathan Weare working on enhanced sampling algorithms.
Currently, I am appointed at the University of Chicago and a long-term visiting scholar at the Flatiron Institute. I am working with Prof. Risi Kondor on developing new machine learning architectures for molecular systems. This work is in close collaboration with Prof. Frank Noé at Freie Universität Berlin.
New architectures for Neural WavefunctionsLearning the electronic structure of molecules requires explicitly treating many-electron correlations in the electronic wavefunction. At the same time, the wavefunctions must obey global antisymmetry: exchanging any two electrons causes the wavefunction to change sign. I am working to develop neural architectures that explicitly account for these correlations while maintaining global antisymmetry using the mathematics of the permutation group. This work also touches on broader questions regarding inference on sets.
Neural Architectures for CryoEMCryoEM allows one to capture millions of images of a biomolecule, each of which is a two-dimensional projection of the molecular structure. These images must then be combined to form a three-dimensional molecular structure; a task complicated by the high noise levels in the image. A key step in the recombination is learning the relative angles between the projection axis in each image. Hannah Lawrence and I are developing neural techniques for learning these relative rotations.
Improvements in Spectral Analysis of Markov ProcessesSchemes such as Markov state modelling (MSMs) and time-lagged independent component analysis (TICA) are common dimensionality reduction techniques for molecular simulations. These are both examples of a general scheme, the linear Variational Approach to Conformational Dynamics (VAC). However, the accuracy of VAC can be highly sensitive to the choice of basis and statistical error. Moreover, the sensitivity to these error sources can depend strongly on a parameter known as the lag time.
In the last year of my PhD, my collaborators Rob Webber, Douglas Dow, and I began work on error analysis of VAC. This work has resulted in the first convergence proofs for the VAC eigenfunctions, as well as new heuristics in choosing the lag time. In addition, it has motivated a new scheme that combines information from multiple lag times. We are currently preparing this work for publication.
Error Estimates for MBARThe Multistate Bennett Acceptance Ratio is a popular framework for estimating free energies from multiple biased simulations. In the EMUS paper, we introduced the iterative eigenvector method for umbrella sampling (iEMUS) algorithm that allows for extremely rapid (1-2 iterations) convergence of the MBAR equations. Since then, we have found that iEMUS also allows for accurate error estimates for MBAR that account for autocorrelation times and give state-wise contributions to the error. I am mentoring Sherry Li in exploring and extending these expressions.
- Galerkin approximation of dynamical quantities using trajectory data
- Stratification as a general variance reduction method for Markov chain Monte Carlo
- Eigenvector method for umbrella sampling enables error analysis