7 research outputs found
Basin structure of optimization based state and parameter estimation
Most data based state and parameter estimation methods require suitable
initial values or guesses to achieve convergence to the desired solution, which
typically is a global minimum of some cost function. Unfortunately, however,
other stable solutions (e.g., local minima) may exist and provide suboptimal or
even wrong estimates. Here we demonstrate for a 9-dimensional Lorenz-96 model
how to characterize the basin size of the global minimum when applying some
particular optimization based estimation algorithm. We compare three different
strategies for generating suitable initial guesses and we investigate the
dependence of the solution on the given trajectory segment (underlying the
measured time series). To address the question of how many state variables have
to be measured for optimal performance, different types of multivariate time
series are considered consisting of 1, 2, or 3 variables. Based on these time
series the local observability of state variables and parameters of the
Lorenz-96 model is investigated and confirmed using delay coordinates. This
result is in good agreement with the observation that correct state and
parameter estimation results are obtained if the optimization algorithm is
initialized with initial guesses close to the true solution. In contrast,
initialization with other exact solutions of the model equations (different
from the true solution used to generate the time series) typically fails, i.e.
the optimization procedure ends up in local minima different from the true
solution. Initialization using random values in a box around the attractor
exhibits success rates depending on the number of observables and the available
time series (trajectory segment).Comment: 15 pages, 2 figure