Parameter Estimation of Large-Scale Chaotic Systems

Abstract

Parameter estimation plays a crucial role in modelling various kinds of phenomena. However, it can be challenging to properly calibrate a model to satisfy the observed quantities and provide reliable forecasts. In the case of large chaotic systems the usual estimation techniques, such as the least squares based optimizations or filtering based methods are, in general, unavailable. Chaoticity makes long-term predictions unreliable, as even slight perturbations in initial values or in the computational scheme would overweight the impact of the parameters. Besides, high dimensionality prevents traditional implementations of filtering methods due to prohibitive computational and memory requirements. Here, we focus on “on-line” parameter estimation, emphasizing that the process takes place sequentially without repetitive reuse of previously observed data and, ideally, with minimal simulations of the heavy models. We are inspired by the Ensemble Prediction System (EPS), which is the framework for uncertainty quantification (UQ) for the weather forecast employed in the European Centre of Medium-Range Weather Forecasts (ECMWF). This framework consists of a number of simulations launched from slightly perturbed initial values, done in order to get estimates of the model forecast skill. Since high CPU computations are carried out there anyway, this framework is promising for testing the impact of different parameters as well. The idea is employed in the Ensemble Prediction and Parameter Estimation System (EPPES), where certain hierarchical statistical modelling is utilized within the EPS in order to conduct parameter estimation. Despite successful results in many application, the original formulation of EPPES has certain deficiencies, such as slow convergence, lack of proper multi-objective optimization implementations and inability to track seasonally varying parameters. In this dissertation we explore possible alternatives in the same area, keeping in mind the benefits for the ensemble/ population based methods provided by the EPS framework. Such an alternative, employed in the dissertation, is Differential Evolution (DE), a population-based method from the broader family of evolutionary algorithms (EA). The use of DE as a stochastic optimizer will be developed, and extensive of comparisons with the original EPPES will be conducted.