Reduced-order non-Markovian closure models for statistical prediction of turbulent systems

This repository implements the Machine Learning non-Markovian closure modeling framework described in [1] and the improved statistical-stochastic surrogate model in [2] for accurate predictions of inhomogeneous statistical responses of turbulent dynamical systems subjected to external forcings. The closure frameworks employ a Long-Short-Term-Memory architecture to represent the higher-order unresolved statistical feedbacks with careful consideration to account for the intrinsic instability yet producing stable long-time predictions.

Three models are provides to run the experiment under different truncation scenarios:

train_pert_var_closure.py: the full mean-covariance closure model;

train_pert_mvar_closure.py: the reduced-order mean-covariance closure model;

train_pert_mean_closure.py: the mean closure model.

train_statstoc_inhomo.py: the statistical-stochastic surrogate model;

To train the neural network model without using a pretrained checkpoint, run the following command:

python train_*.py --exp_dir=<EXP_DIR> --pretrained FALSE --eval FALSE

To test the trained model with the path to the latest checkpoint, run the following command:

python train_*.py --exp_dir=<EXP_DIR> --pretrained TRUE --eval TRUE

Datasets for training and prediction in the neural network model are generated from direct Monte-Carlo simulations of the L-96 system:

• training datasets 'l96_nt1_fpert_F8amp1' and 'l96_nt1_upert_F8amp1': model statistics with constant forcing or initial state perturbations in short time length;
• prediction datasets 'l96_nt1_ramp1_F8df1', 'l96_nt1_ramp2_F8df1', 'l96_nt1_peri_F8df1', 'l96_nt1_peri_F8df2': model statistics with different time-dependent external forcings in long time series.

A wider variety of problems in different perturbation scenarios can be also tested by adding new corresponding dataset into the data/ folder.

• PyTorch >= 1.2.0

[1] D. Qi and J. Harlim (2021), “Machine Learning-Based Statistical Closure Models for Turbulent Dynamical Systems”, arXiv:2108.13220.

[2] D. Qi and J. Harlim (2022), “A Data-Driven Statistical-Stochastic Surrogate Modeling Strategy for Complex Nonlinear Non-stationary Dynamics”, arXiv:2208.10612.