# Machine-learning inference of fluid variables from data using reservoir computing

arXiv: https://arxiv.org/abs/1805.09917 · HTML: https://mlsanity.com/paper/1805.09917/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 16 of 16)

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- [Anticipating synchronization with machine learning](https://mlsanity.com/paper/2103.13358/) (2021)
- [Adaptable Hamiltonian neural networks](https://mlsanity.com/paper/2102.13235/) (2021)
- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [Learning noise-induced transitions by multi-scaling reservoir computing](https://mlsanity.com/paper/2309.05413/) (2023)
- [Machine-learning parameter tracking with partial state observation](https://mlsanity.com/paper/2311.09142/) (2023)
- [Predicting extreme events from data using deep machine learning: when and where](https://mlsanity.com/paper/2203.17155/) (2022)
- [Digital twins of nonlinear dynamical systems](https://mlsanity.com/paper/2210.06144/) (2022)
- [Learning to learn ecosystems from limited data -- a meta-learning approach](https://mlsanity.com/paper/2410.07368/) (2024)
- [Reconstructing dynamics from sparse observations with no training on target system](https://mlsanity.com/paper/2410.21222/) (2024)
- [Digital twins of nonlinear dynamical systems: A perspective](https://mlsanity.com/paper/2309.11461/) (2023)
- [Long-term prediction of El Ni~no-Southern Oscillation using reservoir computing with data-driven realtime filter](https://mlsanity.com/paper/2501.17781/) (2025)
- [Reservoir observer enhanced with residual calibration and attention mechanism](https://mlsanity.com/paper/2604.08592/) (2026)
- [Variability of echo state network prediction horizon for partially observed dynamical systems](https://mlsanity.com/paper/2306.10797/) (2023)
- [A Novel Reservoir Computing Framework for Chaotic Time Series Prediction Using Time Delay Embedding and Random Fourier Features](https://mlsanity.com/paper/2511.02877/) (2025)
- [Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems](https://mlsanity.com/paper/2511.14775/) (2025)

## Abstract (arXiv)

We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its behavior is complex but deterministic. We present two ways of inference of the complex behavior; the first called partial-inference requires continued knowledge of partial time-series data during the inference as well as past time-series data, while the second called full-inference requires only past time-series data as training data. For the first case, we are able to infer long-time motion of microscopic fluid variables. For the second case, we show that the reservoir dynamics constructed from only past data of energy functions can infer the future behavior of energy functions and reproduce the energy spectrum. It is also shown that we can infer a time-series data from only one measurement by using the delay coordinates. These implies that the obtained two reservoir systems constructed without the knowledge of microscopic data are equivalent to the dynamical systems describing macroscopic behavior of energy functions.