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A new ensemble forecast algorithm, named as the physics-informed data-drivenalgorithm with conditional Gaussian statistics (PIDD-CG), is developed topredict the time evolution of the probability density functions (PDFs) ofcomplex turbulent systems with partial observations. The PIDD-CG algorithmintegrates a unique multiscale statistical closure model with an extremelyefficient nonlinear data assimilation scheme to represent the PDF as a mixtureof conditional statistics, which overcomes the curse of dimensionality forhigh-dimensional systems. The multiscale features in the time evolution of eachconditional statistics ensemble member effectively captured by an appropriatecombination of physics-informed analytic formulae and recurrent neuralnetworks. An information metric is adopted as the loss function for the latterto more accurately calibrate the key turbulent signals with strongfluctuations. The proposed algorithm succeeds in forecasting both the transientand statistical equilibrium non-Gaussian PDFs of strongly turbulent systemswith intermittency, regime switching and extreme events.

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