  We use a constant velocity steered molecular dynamics (SMD) simulation of the
stretching of deca-alanine in vacuum to demonstrate a technique that can be
used to create surrogate stochastic processes using the time series that come
out of SMD simulations. The surrogate processes are constructed by first
estimating a sequence of local parametric models along a SMD trajectory and
then a single global model is constructed by piecing the local models together
through smoothing splines (estimation is made computationally feasible by
likelihood function approximations). The calibrated surrogate models are then
"bootstrapped" in order to simulate the large number of work paths typically
needed to construct a potential of mean force (PMF) by appealing to Jarzynski's
work theorem. When this procedure is repeated for a small number of SMD paths,
it is shown that the global models appear to come from a single family of
closely related diffusion processes. Possible techniques for exploiting this
observation are also briefly discussed. The findings of this paper have
potential relevance to computationally expensive computer simulations and
experimental works involving optical tweezers where it difficult to collect a
large number of samples, but possible to sample accurately and frequently in
time.
