# Predicting Spatio-Temporal Time Series Using Dimension Reduced Local States

## TL;DR

This paper introduces a method for predicting spatio-temporal time series by combining local state reconstruction, PCA dimension reduction, and nearest neighbor modeling, validated on various complex models.

## Contribution

It presents a novel approach integrating PCA and local modeling for accurate spatio-temporal prediction of complex dynamical systems.

## Key findings

- Effective on noisy data from multiple models
- Accurate cross estimation and iterative prediction
- Demonstrates robustness in complex systems

## Abstract

We present a method for both cross estimation and iterated time series prediction of spatio temporal dynamics based on reconstructed local states, PCA dimension reduction, and local modelling using nearest neighbour methods. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio-Cherry-Fenton model, and the Kuramoto-Sivashinsky model.