UC San Diego

Within the context of data assimilation, we describe the use of chaotic synchronization to overcome instabilities in the search space of the associated optimization problem and use numerical examples to demonstrate how the elimination of positive (conditional) Lyapunov exponents allows one to determine both the number and specific state variable choice of dynamical dimensions that must be measured in order to ensure feasibility of synchronization -based optimization techniques. We present a novel objective function based upon the chaotic synchronization- error metric that utilizes a strongly-coupled fiducial trajectory as a full dimensional surrogate of the measured data. This synchronization fiducial serves as the metric origin in the space of model dynamical rajectories, thus making the search over model parameters more informative and eliminating the need for collocation of the dynamical variables. The relationship between this (and other) proposed objective functions and the configuration functions of classical statistical physics are explored, including an additive-noise approximation to errors in the model expressed as a path integral over the joint probability distribution of the dynamics. From these considerations we create two statistical (derivative-free) numerical optimization algorithms on parallel processors that employ Monte Carlo techniques to evaluate the distribution of unknown state variables and model parameters; this is done on chaotic and electrophysiological twin-experiments, where we demonstrate how these methods are used to assist in the design of neuron models and stimulus (current injection) protocols. Finally, we report data-assimilation results, including model error estimates, of a model optimized to a current-clamp recording of a neuron from the High Vocal center (HVc) of the zebra finch birdsong neural pathway