# Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing

arXiv: https://arxiv.org/abs/2203.13294 · HTML: https://mlsanity.com/paper/2203.13294/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 24 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [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)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Lattice gauge equivariant convolutional neural networks](https://mlsanity.com/paper/2012.12901/) (2020)
- [Machine-learning hidden symmetries](https://mlsanity.com/paper/2109.09721/) (2021)
- [A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/2201.08910/) (2022)
- [Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systems](https://mlsanity.com/paper/2002.05514/) (2020)
- [Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components](https://mlsanity.com/paper/2102.07819/) (2021)
- [Data-driven super-parameterization using deep learning: Experimentation with multi-scale Lorenz 96 systems and transfer-learning](https://mlsanity.com/paper/2002.11167/) (2020)
- [Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformers](https://mlsanity.com/paper/2103.09360/) (2021)
- [Machine Learning, Deepest Learning: Statistical Data Assimilation Problems](https://mlsanity.com/paper/1707.01415/) (2017)
- [Symmetry-Aware Reservoir Computing](https://mlsanity.com/paper/2102.00310/) (2021)

## Built on by (most cited first, 20 of 20)

- [Learning unseen coexisting attractors](https://mlsanity.com/paper/2207.14133/) (2022)
- [Controlling Chaos Using Edge Computing Hardware](https://mlsanity.com/paper/2406.12876/) (2024)
- [Extrapolating tipping points and simulating non-stationary dynamics of complex systems using efficient machine learning](https://mlsanity.com/paper/2312.06283/) (2023)
- [Infinite-dimensional next-generation reservoir computing](https://mlsanity.com/paper/2412.09800/) (2024)
- [Controlling Chaotic Maps using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2307.03813/) (2023)
- [Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamics](https://mlsanity.com/paper/2308.14239/) (2023)
- [Physical Reservoir Computing Enabled by Solitary Waves and Biologically-Inspired Nonlinear Transformation of Input Data](https://mlsanity.com/paper/2402.03319/) (2024)
- [How more data can hurt: Instability and regularization in next-generation reservoir computing](https://mlsanity.com/paper/2407.08641/) (2024)
- [Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence](https://mlsanity.com/paper/2305.00100/) (2023)
- [Controlling dynamical systems to complex target states using machine learning: next-generation vs. classical reservoir computing](https://mlsanity.com/paper/2307.07195/) (2023)
- [Artificial Intelligence for the Electron Ion Collider (AI4EIC)](https://mlsanity.com/paper/2307.08593/) (2023)
- [On the emergence of numerical instabilities in Next Generation Reservoir Computing](https://mlsanity.com/paper/2505.00846/) (2025)
- [Versatile Reservoir Computing for Heterogeneous Complex Networks](https://mlsanity.com/paper/2505.15219/) (2025)
- [Controlling Dynamical Systems into Unseen Target States Using Machine Learning](https://mlsanity.com/paper/2412.10251/) (2024)
- [Tailored minimal reservoir computing: on the bidirectional connection between nonlinearities in the reservoir and in data](https://mlsanity.com/paper/2504.17503/) (2025)
- [Using Echo-State Networks to Reproduce Rare Events in Chaotic Systems](https://mlsanity.com/paper/2505.16208/) (2025)
- [A tensor network approach for chaotic time series prediction](https://mlsanity.com/paper/2505.17740/) (2025)
- [Next-generation reservoir computing validated by classification task](https://mlsanity.com/paper/2512.12903/) (2025)
- [Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error](https://mlsanity.com/paper/2605.31438/) (2026)
- [Causal Local States: Scalable Simultaneous Causal Network Inference and Forecasting for Dynamical Systems](https://mlsanity.com/paper/2608.17452/) (2026)

## Abstract (arXiv)

Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture that, when combined with a next-generation reservoir computer, displays state-of-the-art performance with a computational time 103-104 times faster for training process and training data set ~ 102 times smaller than other machine learning algorithms. We also take advantage of the translational symmetry of the model to further reduce the computational cost and training data, each by a factor of ~10.