 |
Center for Nonlinear Studies |
Inferring the current state of an evolving system from measurements is a prerequisite for forecasting the future evolution of the system, for control of the system, or for scientific studies of the system\\\'s dynamics. A common case is where measurements are continually made and where there is some model of the system dynamics. We address the problem of using this information to estimate the system state as the system evolves taking into account that the measured data is noisy and incomplete. [By incomplete we mean that not all the dynamical variables neccessary to specify the full system state are measured at any given measurement time.] There is a well known classical solution to this problem for the case of linear dynamics called the Kalman filter. Furthermore, this solution can be extended to nonlinear systems. However, the classical techniques are completely infeasable for large high dimensional systems because their computational requirements would be many orders of magnitude beyond what is possible. This talk will discuss a new approach to this problem [1]. Although originally motivated by the goal of improving weather forecasts, the technique is generally applicable to large spatiotemporally chaotic systems. Illustrative examples will be presented from weather forecasting and from an application to laboratory experiments on Rayleigh-Benard convection. [1] E. Ott, B.R. Hunt, I. Szunyogh, et al., Tellus A, vol.56, p.415 (2004).
Host: David Roberts - dcr@lanl.gov