Delay Embedded Echo-State Network: A Predictor for Partially Observed Systems

TL;DR

This paper introduces a delay embedded echo-state network that predicts partially observed systems by combining echo-state networks with time delay embedding, supported by Takens' theorem, and demonstrates its effectiveness on synthetic and real data.

Contribution

It develops a novel predictor for partially observed systems using delay embedding and echo-state networks, grounded in Takens' theorem and strong observability.

Findings

Effective prediction on chaotic systems and traffic data

Theoretically justified with Takens' embedding theorem

Outperforms traditional methods in partial observation scenarios

Abstract

This paper considers the problem of data-driven prediction of partially observed systems using a recurrent neural network. While neural network based dynamic predictors perform well with full-state training data, prediction with partial observation during training phase poses a significant challenge. Here a predictor for partial observations is developed using an echo-state network (ESN) and time delay embedding of the partially observed state. The proposed method is theoretically justified with Taken's embedding theorem and strong observability of a nonlinear system. The efficacy of the proposed method is demonstrated on three systems: two synthetic datasets from chaotic dynamical systems and a set of real-time traffic data.