# TE-ESN: Time Encoding Echo State Network for Prediction Based on Irregularly Sampled Time Series Data

arXiv: https://arxiv.org/abs/2105.00412 · HTML: https://mlsanity.com/paper/2105.00412/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 2 May 2021.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Interpolation-Prediction Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/1909.07782/) (2019)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [TENER: Adapting Transformer Encoder for Named Entity Recognition](https://mlsanity.com/paper/1911.04474/) (2019)
- [Encoding word order in complex embeddings](https://mlsanity.com/paper/1912.12333/) (2019)
- [Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius](https://mlsanity.com/paper/1910.04426/) (2019)
- [A Review of Deep Learning Methods for Irregularly Sampled Medical Time Series Data](https://mlsanity.com/paper/2010.12493/) (2020)
- [Deep Echo State Network (DeepESN): A Brief Survey](https://mlsanity.com/paper/1712.04323/) (2017)
- [Insights into LSTM Fully Convolutional Networks for Time Series Classification](https://mlsanity.com/paper/1902.10756/) (2019)
- [A Review of Designs and Applications of Echo State Networks](https://mlsanity.com/paper/2012.02974/) (2020)

## Built on by (most cited first, 10 of 10)

- [Universal Time-Series Representation Learning: A Survey](https://mlsanity.com/paper/2401.03717/) (2024)
- [A Systematic Review for Transformer-based Long-term Series Forecasting](https://mlsanity.com/paper/2310.20218/) (2023)
- [Continuous Diagnosis and Prognosis by Controlling the Update Process of Deep Neural Networks](https://mlsanity.com/paper/2210.02719/) (2022)
- [Evolutionary Echo State Network: evolving reservoirs in the Fourier space](https://mlsanity.com/paper/2206.04951/) (2022)
- [MultiWave: Multiresolution Deep Architectures through Wavelet Decomposition for Multivariate Time Series Prediction](https://mlsanity.com/paper/2306.10164/) (2023)
- [Reservoir Computing with a Single Oscillating Gas Bubble: Emphasizing the Chaotic Regime](https://mlsanity.com/paper/2504.07221/) (2025)
- [Curricular and Cyclical Loss for Time Series Learning Strategy](https://mlsanity.com/paper/2312.15853/) (2023)
- [Curriculum Design Helps Spiking Neural Networks to Classify Time Series](https://mlsanity.com/paper/2401.10257/) (2023)
- [Warped Time Series Anomaly Detection](https://mlsanity.com/paper/2404.12134/) (2024)
- [MuSiCNet: A Gradual Coarse-to-Fine Framework for Irregularly Sampled Multivariate Time Series Analysis](https://mlsanity.com/paper/2412.01063/) (2024)

## Abstract (arXiv)

Prediction based on Irregularly Sampled Time Series (ISTS) is of wide concern in the real-world applications. For more accurate prediction, the methods had better grasp more data characteristics. Different from ordinary time series, ISTS is characterised with irregular time intervals of intra-series and different sampling rates of inter-series. However, existing methods have suboptimal predictions due to artificially introducing new dependencies in a time series and biasedly learning relations among time series when modeling these two characteristics. In this work, we propose a novel Time Encoding (TE) mechanism. TE can embed the time information as time vectors in the complex domain. It has the the properties of absolute distance and relative distance under different sampling rates, which helps to represent both two irregularities of ISTS. Meanwhile, we create a new model structure named Time Encoding Echo State Network (TE-ESN). It is the first ESNs-based model that can process ISTS data. Besides, TE-ESN can incorporate long short-term memories and series fusion to grasp horizontal and vertical relations. Experiments on one chaos system and three real-world datasets show that TE-ESN performs better than all baselines and has better reservoir property.