# Sequential Learning from Noisy Data: Data-Assimilation Meets Echo-State Network

arXiv: https://arxiv.org/abs/2304.00198 · HTML: https://mlsanity.com/paper/2304.00198/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 23 references that are in the map.
- First posted on arXiv 1 Apr 2023.

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

- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Delay Embedded Echo-State Network: A Predictor for Partially Observed Systems](https://mlsanity.com/paper/2211.05992/) (2022)

## Built on by (most cited first, 1 of 1)

- [Feature-Based Echo-State Networks: A Step Towards Interpretability and Minimalism in Reservoir Computer](https://mlsanity.com/paper/2403.19806/) (2024)

## Abstract (arXiv)

This paper explores the problem of training a recurrent neural network from noisy data. While neural network based dynamic predictors perform well with noise-free training data, prediction with noisy inputs during training phase poses a significant challenge. Here a sequential training algorithm is developed for an echo-state network (ESN) by incorporating noisy observations using an ensemble Kalman filter. The resultant Kalman-trained echo-state network (KalT-ESN) outperforms the traditionally trained ESN with least square algorithm while still being computationally cheap. The proposed method is demonstrated on noisy observations from three systems: two synthetic datasets from chaotic dynamical systems and a set of real-time traffic data.