Open Positions: UMass Dartmouth undergraduate and graduate students interested in research opportunities should contact Scott.

The research group currently consists of one PhD student, two masters students, and two undergraduate students. I hope to describe some of their interesting projects and developments here soon!

Markov chain Monte Carlo (MCMC) algorithms are a commonly used technique for sampling the posterior probability distribution function. When dealing with high dimensional problems, however, the process of mapping the posterior can become prohibitively expensive. Additionally, the posterior is multimodal and the gravitational wave signal is buried in detector noise, thereby rendering otherwise useful computational tricks ineffective. For example, millions of degrees of freedom characterize a typical advanced detector dataset, and equally long MCMC chains are necessary to compute parameter means and variances. In total, from model evaluations one should expect to generate around one Petabyte per analysis. Such data science challenges constitute a major computational bottleneck of the experiment and are among the most pressing questions in gravitational wave parameter estimation.

To overcome these challenges I have been involved in a long-term research program to develop and apply surrogate and reduced order modeling tools for both the rapid evaluation of gravitational waveforms and rapid parameter estimation using "compressed" likelihoods. These results rely upon identification of a low-dimensional representation for a given waveform family which in turn forms the building blocks for fast, scalable algorithms. For more information about this research please visit these websites on reduced order modeling for gravitational waves, reduced order quadratures for accelerated Bayesian inference and surrogate models.

In the context of extreme mass ratio (binary black hole) inspiral systems the solutions are forced by distributional (i.e. Dirac delta function) source terms. We proposed and implemented a DG scheme to exactly represent such distributional solutions through a modification of the relevant numerical flux terms. Furthermore, it was demonstrated that the method maintains spectral accuracy even at the location of the Dirac delta distribution. Accurate numerical modeling is crucial for the incorporation of important physical effects neglected by linearization such as the gravitational self-force.

Additional details can be found in my dissertation "Applications of Discontinuous Galerkin Methods to Computational General Relativity".

To avoid these issues we proposed a simple smooth “switching on” of the source terms and diagnostics necessary to claim that a physically correct solution has been achieved. When including additional physical effects or performing high-accuracy comparisons between techniques, improved modeling will increasingly require the identification and reduction of all error sources and especially systematic numerical ones of the type listed above.