Local- and Cluster Weighted Modeling for Prediction and State Estimation of Nonlinear Dynamical Systems

TL;DR: Cluster Weighted Models will be used for the concept of Active Learning, where one strives to actively choose data points for measurements which yield the most information, and a new method based on nearest neighbors will be introduced, which tries to maximize the overlap between the original and the model's attractor.

Abstract: This thesis deals with black-box modeling techniques, in particular local models based on nearest neighbors, and Cluster Weighted Models, which combine a stochastic clustering of the input space with a deterministic parametric model in each cluster. Given observations obtained from a dynamical system, often corrupted by noise, those models are then used to predict future states, or to reconstruct the current internal state of the system. The performance of both techniques will be evaluated on various examples, from numerical chaotic oscillators to experimental friction data.Using the concept of probabilistic scoring, Cluster Weighted Models will be compared against other modeling techniques which produce a probabilistic output, using data from different numerical as well as experimental systems with various degress of noise. Also, several regularization techniques and their effect on the model's score will be discussed. Cluster Weighted Models will then be used for the concept of Active Learning, where one strives to actively choose data points for measurements which yield the most information. The models will be used to find points with a high information gain, also in terms of detecting interesting features like extremal values.Lastly, tackling the problem of long term prediction, a new method based on nearest neighbors will be introduced, which tries to maximize the overlap between the original and the model's attractor. This method is then used to fit the coefficients of a system of ordinary differential equations, targeting numerical as well as experimental systems.