# A Novel Reservoir Computing Framework for Chaotic Time Series Prediction Using Time Delay Embedding and Random Fourier Features

arXiv: https://arxiv.org/abs/2511.02877 · HTML: https://mlsanity.com/paper/2511.02877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 4 Nov 2025.

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

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guarantees](https://mlsanity.com/paper/1804.09893/) (2018)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learning](https://mlsanity.com/paper/2307.15092/) (2023)
- [Machine-learning inference of fluid variables from data using reservoir computing](https://mlsanity.com/paper/1805.09917/) (2018)
- [Reservoir computing model of two-dimensional turbulent convection](https://mlsanity.com/paper/2001.10280/) (2020)
- [Unveiling the role of plasticity rules in reservoir computing](https://mlsanity.com/paper/2101.05848/) (2021)

## Abstract (arXiv)

Forecasting chaotic time series requires models that can capture the intrinsic geometry of the underlying attractor while remaining computationally efficient. We introduce a novel reservoir computing (RC) framework that integrates time-delay embedding with Random Fourier Feature (RFF) mappings to construct a dynamical reservoir without the need for traditional recurrent architectures. Unlike standard RC, which relies on high-dimensional recurrent connectivity, the proposed RFF-RC explicitly approximates nonlinear kernel transformations that uncover latent dynamical relations in the reconstructed phase space. This hybrid formulation offers two key advantages: (i) it provides a principled way to approximate complex nonlinear interactions among delayed coordinates, thereby enriching the effective dynamical representation of the reservoir, and (ii) it reduces reliance on manual reservoir hyperparameters such as spectral radius and leaking rate. We evaluate the framework on canonical chaotic systems-the Mackey-Glass equation, the Lorenz system, and the Kuramoto-Sivashinsky equation. This novel formulation demonstrates that RFF-RC not only achieves superior prediction accuracy but also yields robust attractor reconstructions and long-horizon forecasts. These results show that the combination of delay embedding and RFF-based reservoirs reveals new dynamical structure by embedding the system in an enriched feature space, providing a computationally efficient and interpretable approach to modeling chaotic dynamics.