# Reservoir computing model of two-dimensional turbulent convection

arXiv: https://arxiv.org/abs/2001.10280 · HTML: https://mlsanity.com/paper/2001.10280/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2020.

## Built on by (most cited first, 15 of 15)

- [Direct data-driven forecast of local turbulent heat flux in Rayleigh-B'enard convection](https://mlsanity.com/paper/2202.13129/) (2022)
- [Deep learning for surrogate modelling of 2D mantle convection](https://mlsanity.com/paper/2108.10105/) (2021)
- [Predicting Shallow Water Dynamics using Echo-State Networks with Transfer Learning](https://mlsanity.com/paper/2112.09182/) (2021)
- [Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models](https://mlsanity.com/paper/2201.03200/) (2022)
- [RcTorch: a PyTorch Reservoir Computing Package with Automated Hyper-Parameter Optimization](https://mlsanity.com/paper/2207.05870/) (2022)
- [Deterministic Reservoir Computing for Chaotic Time Series Prediction](https://mlsanity.com/paper/2501.15615/) (2025)
- [Physics-aware deep neural networks for surrogate modeling of turbulent natural convection](https://mlsanity.com/paper/2103.03565/) (2021)
- [DeepClouds.ai: Deep learning enabled computationally cheap direct numerical simulations](https://mlsanity.com/paper/2208.08956/) (2022)
- [Solving Partial Differential Equations with Equivariant Extreme Learning Machines](https://mlsanity.com/paper/2404.18530/) (2024)
- [Can neural networks predict dynamics they have never seen?](https://mlsanity.com/paper/2111.06783/) (2021)
- [Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system](https://mlsanity.com/paper/2501.03070/) (2025)
- [Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learning](https://mlsanity.com/paper/2505.24099/) (2025)
- [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)
- [Model Order Reduction of Cerebrovascular Hemodynamics Using POD_Galerkin and Reservoir Computing_based Approach](https://mlsanity.com/paper/2603.18837/) (2026)

## Abstract (arXiv)

Reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics of a two-dimensional turbulent Rayleigh-B'enard convection flow at a Rayleigh number rm Ra=107 and a Prandtl number rm Pr=7 in an extended domain with an aspect ratio of 6. Our data-driven approach which is based on a long-term direct numerical simulation of the convection flow comprises a two-step procedure. (1) Reduction of the original simulation data by a Proper Orthogonal Decomposition (POD) snapshot analysis and subsequent truncation to the first 150 POD modes which are associated with the largest total energy amplitudes. (2) Setup and optimization of a reservoir computing model to describe the dynamical evolution of these 150 degrees of freedom and thus the large-scale evolution of the convection flow. The quality of the prediction of the reservoir computing model is comprehensively tested. At the core of the model is the reservoir, a very large sparse random network charcterized by the spectral radius of the corresponding adjacency matrix and a few further hyperparameters which are varied to investigate the quality of the prediction. Our work demonstrates that the reservoir computing model is capable to model the large-scale structure and low-order statistics of turbulent convection which can open new avenues for modeling mesoscale convection processes in larger circulation models.