Transfer learning for nonlinear dynamics and its application to fluid turbulence

TL;DR

This paper introduces transfer learning techniques for nonlinear dynamics, significantly improving prediction accuracy in chaotic systems like Lorenz chaos and turbulence with minimal data, leveraging universality in turbulence.

Contribution

It presents a novel transfer learning approach for nonlinear dynamics, demonstrating enhanced predictions in chaotic systems and turbulence with limited data.

Findings

Transfer learning improves Lorenz chaos prediction accuracy by an order of magnitude.

Small data suffices to infer turbulence energy dissipation rates.

Knowledge transfer from lower to higher Reynolds number turbulence is effective.

Abstract

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.