Dissipative Particle Dynamics

Dissipative particle dynamics (DPD) is a particle simulation method for fluids and fluidic structures at the mesoscale, i.e., the bridge between the atomic and continuum scales. Due to its parallelizability and coarse-grained approach, DPD is capable of simulating structures orders of magnitude larger than are possible with "ground truth" methods, such as molecular dynamics (MD), while retaining nonequilibrium phenomena in the fluid which may be lost in equilibrium approaches, such as Brownian dynamics (BD). It thus has a number of applications in nano- and microscopic biology and physics, where structures such as polymers and membranes derive many of their mechanical properties from fluid interactions. I use DPD to model experiments of interdisciplinary interest, providing insight into dynamics which may be difficult or impossible to observe directly. A joint work with experimental physicists Daniel Kim and Derek Stein which used a DPD model (right video) was featured in the Physical Review Letters.


Bayesian Uncertainty Quantification

As the name would suggest, uncertainty quantification (UQ) is a broad field which involves the mathematical treatment of uncertainty in physical and model systems. Such uncertainties are ubiquitous - whether studying inherently stochastic phenomena such as branching processes or deterministic systems corrupted by observational, systemic, or sampling noise, uncertainty quantification almost surely has applications to the questions of interest. A common subset of UQ is parameter estimation, which concerns the inverse problem, i.e., trying to map the outputs of a system back to the inputs which generated them. In the presence of uncertainty, many sets of parameters could feasibly yield identical data; the Bayesian approach to this problem (Bayesian uncertainty quantification) places a rigorous probabilistic framework on this problem in order to derive the target distributions. I work with collaborators from the CSElab at ETH Zürich on an approach to Bayesian UQ which uses Markov chain Monte Carlo methods; this high-performance framework, known as Pi4U, can be adapted to a variety of expensive mathematical models (including particle simulations) to produce some very nice visualizations of high-dimensional samples from the posterior, such as those seen below for a network epidemic model (collaboration with Zhizhong Chen, Karen Larson, Panagiotis Hadjidoukas, Costas Papadimitriou, Petros Koumoutsakos, and Anastasios Matzavinos).