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

N A K Doan,W Polifke,L Magri

doi:10.1098/rspa.2021.0135

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.

Highlights

Many fluid dynamics systems exhibit extreme events, which are violent and sudden changes of a flow from the average evolution [1]
We will start from a reservoir computing framework based on the echo state network (ESN) and show that, by embedding physical knowledge during the training, the proposed physics-informed machine learning framework can achieve short- and long-term time-accurate predictions
To learn the reduced-order dynamics of shear turbulence, we constrain the physical knowledge of the governing equations into a reservoir computing data-driven method based on the ESN [16,17]: the physics-informed echo state network (PI-ESN) [20]

Summary

Introduction

Many fluid dynamics systems exhibit extreme events, which are violent and sudden changes of a flow from the average evolution [1]. The objective of this paper is to propose a machine learning method that (i) produces physical solutions to time-accurately predict extreme events in a qualitative model of shear turbulence and (ii) reproduces the long-term statistics. To achieve this objective, we will start from a reservoir computing framework based on the ESN and show that, by embedding physical knowledge during the training, the proposed physics-informed machine learning framework can achieve short- and long-term time-accurate predictions.

Extreme events in a model of chaotic flow

Physics-constrained reservoir computing

Results

Final discussion and future directions