Forecasting the Evolution of Dynamical Systems from Noisy Observations

TL;DR

This paper introduces a nonparametric support vector machine method for forecasting dynamical systems from noisy data, capable of learning near-optimal predictors and adapting to data complexity.

Contribution

It demonstrates that SVM-based forecasting can consistently approximate the optimal predictor for various dynamical systems with noisy observations, addressing limitations of finite memory methods.

Findings

SVM approach learns the optimal predictor under certain conditions.

Method adapts memory length based on data complexity.

Numerical experiments validate the effectiveness of the approach.

Abstract

We consider the problem of designing almost optimal predictors for dynamical systems from a finite sequence of noisy observations and incomplete knowledge of the dynamics and the noise. We first discuss the properties of the optimal (Bayes) predictor and present the limitations of memory-free forecasting methods, and of any finite memory methods in general. We then show that a nonparametric support vector machine approach to forecasting can consistently learn the optimal predictor for all pairs of dynamical systems and bounded observational noise processes that possess summable correlation sequences. Numerical experiments show that this approach adapts the memory length of the forecaster to the complexity of the learning task and the size of the observation sequence.