Data assimilation as an optimization problem and as a path integral evaluation
William G. Whartenby and Mark Kostuk
UCSD (Physics)
Abstract:
We examine the problem of data assimilation in two different ways:
(1) as a special case of optimization where one attempts to
minimize the parameters and state variables of a model set of
equations to a time series of observations. To put this problem
in context, we look at an example from neuroscience where we
optimize spiking neuron models to noisy experimental data.
2) In a path integral formulation using an example from partial
differential equations (the barotropic vorticity equations used
as a model) as a method for obtaining means and distributions
from high level integrals. This approach does not rely on
optimization,but on the evaluation of a high dimensional
integral
Both approaches lend themselves to parallel implementation on
GPUs using NVIDIA's CUDA C language. These algorithms vary in
complexity, with some taking advantage of phenomena from
nonlinear dynamics to improve their behavior. We discuss some
practical limitations to parallelization due to the hardware
architecture and concerns surrounding memory management.