Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach

TLDR

Extreme events in chaotic turbulent flows are abrupt transitions from turbulent to quasi‑laminar states that are deterministic yet traditionally unpredictable due to chaos. The study proposes a physics‑constrained reservoir computing method to time‑accurately predict extreme events and long‑term velocity statistics in a chaotic flow model. The method combines empirical reservoir computing that learns chaotic dynamics from data with physical modelling based on conservation laws, enabling physical predictions even when training data are unavailable. The combined approach accurately reproduces velocity statistics, predicts the occurrence and amplitude of extreme events, is robust to noise, and opens possibilities for synergistically enhancing data‑driven methods with physical knowledge for time‑accurate prediction of chaotic flows.

Abstract

We propose a physics-constrained machine learning method-based on reservoir computing-to time-accurately predict extreme events and long-term velocity statistics in a model of chaotic flow. The method leverages the strengths of two different approaches: empirical modelling based on reservoir computing, which learns the chaotic dynamics from data only, and physical modelling based on conservation laws. This enables the reservoir computing framework to output physical predictions when training data are unavailable. We show that the combination of the two approaches is able to accurately reproduce the velocity statistics, and to predict the occurrence and amplitude of extreme events in a model of self-sustaining process in turbulence. In this flow, the extreme events are abrupt transitions from turbulent to quasi-laminar states, which are deterministic phenomena that cannot be traditionally predicted because of chaos. Furthermore, the physics-constrained machine learning method is shown to be robust with respect to noise. This work opens up new possibilities for synergistically enhancing data-driven methods with physical knowledge for the time-accurate prediction of chaotic flows.