# Transfer learning for nonlinear dynamics and its application to fluid turbulence

arXiv: https://arxiv.org/abs/2009.01407 · HTML: https://mlsanity.com/paper/2009.01407/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2020.

## Built on by (most cited first, 9 of 9)

- [Explaining the physics of transfer learning a data-driven subgrid-scale closure to a different turbulent flow](https://mlsanity.com/paper/2206.03198/) (2022)
- [Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Data](https://mlsanity.com/paper/2410.04814/) (2024)
- [Global Extreme Heat Forecasting Using Neural Weather Models](https://mlsanity.com/paper/2205.10972/) (2022)
- [Learning Reservoir Dynamics with Temporal Self-Modulation](https://mlsanity.com/paper/2301.09235/) (2023)
- [Reservoir Computing with Generalized Readout based on Generalized Synchronization](https://mlsanity.com/paper/2405.14885/) (2024)
- [Predicting Shallow Water Dynamics using Echo-State Networks with Transfer Learning](https://mlsanity.com/paper/2112.09182/) (2021)
- [Image features of a splashing drop on a solid surface extracted using a feedforward neural network](https://mlsanity.com/paper/2201.09541/) (2022)
- [Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learning](https://mlsanity.com/paper/2505.24099/) (2025)
- [On the Generalisation of Koopman Representations for Chaotic System Control](https://mlsanity.com/paper/2508.18954/) (2025)

## Abstract (arXiv)

We introduce transfer learning for nonlinear dynamics, which enables efficient predictions of chaotic dynamics by utilizing a small amount of data. For the Lorenz chaos, by optimizing the transfer rate, we accomplish more accurate inference than the conventional method by an order of magnitude. Moreover, a surprisingly small amount of learning is enough to infer the energy dissipation rate of the Navier-Stokes turbulence because we can, thanks to the small-scale universality of turbulence, transfer a large amount of the knowledge learned from turbulence data at lower Reynolds number.