Data-based prediction and causality inference of nonlinear dynamics

TL;DR

This paper reviews recent advances in reconstructing nonlinear dynamical systems from data, focusing on state space methods for prediction and causality inference, especially with short-term time series.

Contribution

It provides a comprehensive overview of state space reconstruction techniques and discusses recent developments in system prediction and causality inference from measured data.

Findings

Advances in state space reconstruction enable better system understanding.

New methods improve prediction accuracy for short-term time series.

Challenges remain in handling complex, noisy data.

Abstract

Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due to the advances of modern technology, big data becomes increasingly accessible and consequently the problem of reconstructing systems from measured data or time series plays a central role in many scientific disciplines. In recent decades, nonlinear methods rooted in state space reconstruction have been developed, and they do not assume any model equations but can recover the dynamics purely from the measured time series data. In this review, the development of state space reconstruction techniques will be introduced and the recent advances in systems prediction and causality inference using state space reconstruction will be presented. Particularly, the cutting-edge method to deal with short-term time series data will be focused. Finally, the advantages as well as the remaining problems in this field are discussed.