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

arXiv: https://arxiv.org/abs/2211.05992 · HTML: https://mlsanity.com/paper/2211.05992/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 21 references that are in the map.
- First posted on arXiv 11 Nov 2022.

## Builds on (most cited first, 2 of 2)

- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Harnessing disordered quantum dynamics for machine learning](https://mlsanity.com/paper/1602.08159/) (2016)

## Built on by (most cited first, 3 of 3)

- [Sequential Learning from Noisy Data: Data-Assimilation Meets Echo-State Network](https://mlsanity.com/paper/2304.00198/) (2023)
- [Feature-Based Echo-State Networks: A Step Towards Interpretability and Minimalism in Reservoir Computer](https://mlsanity.com/paper/2403.19806/) (2024)
- [Forecasting the Forced van der Pol Equation with Frequent Phase Shifts Using Reservoir Computing](https://mlsanity.com/paper/2404.14651/) (2024)

## Abstract (arXiv)

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.