David Kelly

David Kelly, Eric Vanden-Eijnden

How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP) that the standard version of HMM artificially amplifies these fluctuations. A simple modification of HMM, termed parallel HMM, is introduced and is shown to remedy this problem, capturing fluctuations correctly both at the level of the CLT and the LDP. Similar type of arguments can also be used to justify that the tau-leaping method used in the context of Gillespie's stochastic simulation algorithm for Markov jump processes also captures the right CLT and LDP for these processes.

David Kelly

In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and MCMC algorithms. We make no particular probabilistic assumptions on the type of noise appearing in these recursions. Thus, our technique is well suited to recursions where the noise sequence is not a semi-martingale, even though the limiting noise may be. Our main theorem assumes a weak limit theorem on the noise process appearing in the random recursions and lifts it to diffusion approximation for the recursion itself. To achieve this, we approximate the recursion (pathwise) by the solution to a stochastic equation driven by piecewise smooth paths; this can be thought of as a pathwise version of backward error analysis for SDEs. We then identify the limit of this stochastic equation, and hence the original recursion, using tools from rough path theory. We provide several examples of diffusion approximations, both new and old, to illustrate this technique.

Ketan Maheshwari, David Kelly, Scott J. Krieder et al.

Effective use of parallel and distributed computing in science depends upon multiple interdependent entities and activities that form an ecosystem. Active engagement between application users and technology catalysts is a crucial activity that forms an integral part of this ecosystem. Technology catalysts play a crucial role benefiting communities beyond a single user group. An effective user-engagement, use and reuse of tools and techniques has a broad impact on software sustainability. From our experience, we sketch a life-cycle for user-engagement activity in scientific computational environment and posit that application level reusability promotes software sustainability. We describe our experience in engaging two user groups from different scientific domains reusing a common software and configuration on different computational infrastructures.