Robert J. Webber

I am Ph.D. student advised by Jonathan Weare at the Courant Institute of Mathematical Sciences. You can reach me at rw2515 [AT] nyu [DOT] edu.

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. 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 popular approach for analyzing Monte Carlo simulation data. VAC identifies a set of slowly decorrelating functions of the data that approximate eigenfunctions of the Markov transition operator. I established the convergence of VAC estimates and derived asymptotic 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]
• Collaborators: Douglas Dow, Chatipat Lorpaiboon, Erik Thiede, Aaron Dinner, and Jonathan Weare.

Rare event sampling

• 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].
• Many rare event sampling schemes use resampling. Resampling can lead to high or low error levels, and there is not a good understanding of why this occurs. In response to this problem, I developed new mathematics to identify 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].
• Collaborators: David Plotkin, Morgan O'Neill, Jonathan Weare, and Dorian Abbot.

Identifying the ground-state quantum system

• 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 [arXiv] [PDF].
• Collaborators: Samuel Greene, Jonathan Weare, and Timothy Berkelbach.