A deep learning based closure model for the multiscale evolution of Burgers turbulence

We employed a sequence-to-sequence encoding-decoding mechanism with a long short-term memory (LSTM) integration to evolve the Burgers equation using a coarse projective integration multiscale scheme in which the energy spectrum was the coarse variable and the velocity field was the fine variable. This mechanism, commonly referred to as autoencoding, is mostly used in the domain of natural language processing (NLP). Using this autoencoder scheme, we trained our neural network model with a many-to-many type of mapping between the fine and coarse scale of the multiscale problem. This mapping provided a closure model for the lifting operator in the CPI scheme, allowing us to translate the coarse-scale information back to the fine scale accurately and enabled the evolution of the Burgers equation according to the multiscale scheme.