# Learning noise-induced transitions by multi-scaling reservoir computing

arXiv: https://arxiv.org/abs/2309.05413 · HTML: https://mlsanity.com/paper/2309.05413/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 63 references that are in the map.
- First posted on arXiv 11 Sep 2023.

## Builds on (most cited first, 19 of 19)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Deeptime: a Python library for machine learning dynamical models from time series data](https://mlsanity.com/paper/2110.15013/) (2021)
- [Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data](https://mlsanity.com/paper/2009.08810/) (2020)
- [Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius](https://mlsanity.com/paper/1910.04426/) (2019)
- [Machine-learning inference of fluid variables from data using reservoir computing](https://mlsanity.com/paper/1805.09917/) (2018)
- [Bayesian optimization of hyper-parameters in reservoir computing](https://mlsanity.com/paper/1611.05193/) (2016)
- [Chasing Collective Variables using Autoencoders and biased trajectories](https://mlsanity.com/paper/2104.11061/) (2021)
- [Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamics](https://mlsanity.com/paper/2108.09446/) (2021)
- [Metalearning generalizable dynamics from trajectories](https://mlsanity.com/paper/2301.00957/) (2023)
- [Neural-network solutions to stochastic reaction networks](https://mlsanity.com/paper/2210.01169/) (2022)
- [Learning stochastic dynamics and predicting emergent behavior using transformers](https://mlsanity.com/paper/2202.08708/) (2022)
- [Inferring Global Dynamics Using a Learning Machine](https://mlsanity.com/paper/2009.13032/) (2020)
- [Inferring Attracting Basins of Power System with Machine Learning](https://mlsanity.com/paper/2305.14374/) (2023)
- [Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems](https://mlsanity.com/paper/2305.00669/) (2023)
- [Data-Driven Modeling of Noise Time Series with Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/2207.01110/) (2022)

## Built on by (most cited first, 5 of 5)

- [Signal-noise separation using unsupervised reservoir computing](https://mlsanity.com/paper/2404.04870/) (2024)
- [Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning](https://mlsanity.com/paper/2502.16828/) (2025)
- [Deficiency of equation-finding approach to data-driven modeling of dynamical systems](https://mlsanity.com/paper/2509.03769/) (2025)
- [Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems](https://mlsanity.com/paper/2511.14775/) (2025)
- [Kolmogorov-Arnold Reservoir Computing](https://mlsanity.com/paper/2606.19984/) (2026)

## Abstract (arXiv)

Noise is usually regarded as adversarial to extract the effective dynamics from time series, such that the conventional data-driven approaches usually aim at learning the dynamics by mitigating the noisy effect. However, noise can have a functional role of driving transitions between stable states underlying many natural and engineered stochastic dynamics. To capture such stochastic transitions from data, we find that leveraging a machine learning model, reservoir computing as a type of recurrent neural network, can learn noise-induced transitions. We develop a concise training protocol for tuning hyperparameters, with a focus on a pivotal hyperparameter controlling the time scale of the reservoir dynamics. The trained model generates accurate statistics of transition time and the number of transitions. The approach is applicable to a wide class of systems, including a bistable system under a double-well potential, with either white noise or colored noise. It is also aware of the asymmetry of the double-well potential, the rotational dynamics caused by non-detailed balance, and transitions in multi-stable systems. For the experimental data of protein folding, it learns the transition time between folded states, providing a possibility of predicting transition statistics from a small dataset. The results demonstrate the capability of machine-learning methods in capturing noise-induced phenomena.