A Physics-Informed Data-Driven Algorithm for Ensemble Forecast of Complex Turbulent Systems

TL;DR

This paper introduces a novel physics-informed, data-driven ensemble forecasting algorithm that effectively predicts the probability density functions of complex turbulent systems, capturing non-Gaussian features and extreme events.

Contribution

The paper presents the PIDD-CG algorithm, combining multiscale statistical closure, neural networks, and physics-informed formulas to improve turbulence PDF forecasting.

Findings

Successfully predicts transient and equilibrium PDFs of turbulent systems

Captures non-Gaussian features, intermittency, and extreme events

Overcomes high-dimensional challenges in turbulence modeling

Abstract

A new ensemble forecast algorithm, named as the physics-informed data-driven algorithm with conditional Gaussian statistics (PIDD-CG), is developed to predict the time evolution of the probability density functions (PDFs) of complex turbulent systems with partial observations. The PIDD-CG algorithm integrates a unique multiscale statistical closure model with an extremely efficient nonlinear data assimilation scheme to represent the PDF as a mixture of conditional statistics, which overcomes the curse of dimensionality for high-dimensional systems. The multiscale features in the time evolution of each conditional statistics ensemble member effectively captured by an appropriate combination of physics-informed analytic formulae and recurrent neural networks. An information metric is adopted as the loss function for the latter to more accurately calibrate the key turbulent signals with strong fluctuations. The proposed algorithm succeeds in forecasting both the transient and statistical equilibrium non-Gaussian PDFs of strongly turbulent systems with intermittency, regime switching and extreme events.