# Next-Generation Reservoir Computing for Dynamical Inference

arXiv: https://arxiv.org/abs/2509.11338 · HTML: https://mlsanity.com/paper/2509.11338/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 14 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Infinite-dimensional next-generation reservoir computing](https://mlsanity.com/paper/2412.09800/) (2024)
- [Inferring the dynamics of oscillatory systems using recurrent neural networks](https://mlsanity.com/paper/1904.03026/) (2019)
- [Reservoir kernels and Volterra series](https://mlsanity.com/paper/2212.14641/) (2022)
- [How more data can hurt: Instability and regularization in next-generation reservoir computing](https://mlsanity.com/paper/2407.08641/) (2024)
- [Confabulation dynamics in a reservoir computer: Filling in the gaps with untrained attractors](https://mlsanity.com/paper/2505.04792/) (2025)
- [Phase-amplitude descriptions of neural oscillator models](https://mlsanity.com/paper/1302.0476/) (2013)
- [On the emergence of numerical instabilities in Next Generation Reservoir Computing](https://mlsanity.com/paper/2505.00846/) (2025)
- [Inferring the phase response curve from observation of a continuously perturbed oscillator](https://mlsanity.com/paper/1803.00044/) (2018)

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

- [Kolmogorov-Arnold Reservoir Computing](https://mlsanity.com/paper/2606.19984/) (2026)

## Abstract (arXiv)

We present a simple and scalable implementation of next-generation reservoir computing (NGRC) for modeling dynamical systems from time-series data. The method uses a pseudorandom nonlinear projection of time-delay embedded inputs, allowing the feature-space dimension to be chosen independently of the observation size and offering a flexible alternative to polynomial-based NGRC projections. We demonstrate the approach on benchmark tasks, including attractor reconstruction and bifurcation diagram estimation, using partial and noisy measurements. We further show that small amounts of measurement noise during training act as an effective regularizer, improving long-term autonomous stability compared to standard regression alone. Across all tests, the models remain stable over long rollouts and generalize beyond the training data. The framework offers explicit control of system state during prediction, and these properties make NGRC a natural candidate for applications such as surrogate modeling and digital-twin applications.