title: Observation-based correction of dynamical models using thermostats.
abstract: Models used in simulation may give accurate short-term trajectories but distort long-term (statistical) properties. In this work, we augment a given approximate model with a control law (a 'thermostat') that gently perturbs the dynamical system to target a thermodynamic state consistent with a set of prescribed (possibly evolving) observations. As proof of concept, we provide an example involving a point vortex fluid model on the sphere, for which we show convergence of equilibrium quantities (in the stationary case) and the ability of the thermostat to dynamically track a transient state.
authors.affiliation: Department of Computer Science , KU Leuven , 3001 Leuven, Belgium.
authors.forename: Keith W
authors.identifier: 0000-0001-9718-0404
authors.initials: KW
authors.lastname: Myerscough
authors.affiliation: Mathematical Institute , Utrecht University , PO Box 80010, 3508 TA Utrecht, The Netherlands.
authors.forename: Jason
authors.initials: J
authors.lastname: Frank
authors.affiliation: School of Mathematics , University of Edinburgh , James Clerk Maxwell Building, Kings Buildings, Edinburgh EH9 3JZ, UK.
authors.forename: Benedict
authors.initials: B
authors.lastname: Leimkuhler
keywords: sampling; statistical estimation; statistical fluid dynamics; thermostat