We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing formulation that can be computed on-the-fly, making possible partial corrections using incomplete information, for example measured data or data computed from a different model (or the same model at a different scale). We employ a thermostatting technique to sample the target distribution with the aim of capturing relavant statistical features while introducing mild dynamical perturbation (thermostats). The method is tested for a point vortex fluid model on the sphere, and we demonstrate both convergence of equilibrium quantities and the ability of the formulation to balance stationary and transient-regime errors.

dynamical sampling, least-biased estimation, thermostat, statistical fluid dynamics, point vortex method
Other (theme 6)
Cornell University Library
arXiv.org e-Print archive
Thermostat closures for inviscid fluids
Scientific Computing

Myerscough, K.W, Frank, J.E, & Leimkuhler, B.J. (2014). Least-biased correction of extended dynamical systems using observational data. arXiv.org e-Print archive. Cornell University Library .