# Deterministic Reservoir Computing for Chaotic Time Series Prediction

arXiv: https://arxiv.org/abs/2501.15615 · HTML: https://mlsanity.com/paper/2501.15615/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 26 Jan 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Reservoir computing model of two-dimensional turbulent convection](https://mlsanity.com/paper/2001.10280/) (2020)
- [Direct data-driven forecast of local turbulent heat flux in Rayleigh-B'enard convection](https://mlsanity.com/paper/2202.13129/) (2022)
- [Hierarchical Architectures in Reservoir Computing Systems](https://mlsanity.com/paper/2105.06923/) (2021)
- [Tuning the activation function to optimize the forecast horizon of a reservoir computer](https://mlsanity.com/paper/2312.13151/) (2023)
- [Temporal Convolution Derived Multi-Layered Reservoir Computing](https://mlsanity.com/paper/2407.06771/) (2024)

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

- [Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamics](https://mlsanity.com/paper/2507.06050/) (2025)
- [Parallel BiLSTM-Transformer networks for forecasting chaotic dynamics](https://mlsanity.com/paper/2510.23685/) (2025)
- [Storage and selection of multiple chaotic attractors in minimal reservoir computers](https://mlsanity.com/paper/2603.15155/) (2026)

## Abstract (arXiv)

Reservoir Computing was shown in recent years to be useful as efficient to learn networks in the field of time series tasks. Their randomized initialization, a computational benefit, results in drawbacks in theoretical analysis of large random graphs, because of which deterministic variations are an still open field of research. Building upon Next-Gen Reservoir Computing and the Temporal Convolution Derived Reservoir Computing, we propose a deterministic alternative to the higher-dimensional mapping therein, TCRC-LM and TCRC-CM, utilizing the parametrized but deterministic Logistic mapping and Chebyshev maps. To further enhance the predictive capabilities in the task of time series forecasting, we propose the novel utilization of the Lobachevsky function as non-linear activation function. As a result, we observe a new, fully deterministic network being able to outperform TCRCs and classical Reservoir Computing in the form of the prominent Echo State Networks by up to 99.99% for the non-chaotic time series and 87.13% for the chaotic ones.