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.