A Y-network encoder-decoder model for predicting vorticity fields from kinetic energy spectra in 2D decaying turbulence

We present an encoder-decoder Y-network model as a lifting operator for reconstructing 2D isotropic decaying turbulent vorticity fields from their instantaneous energy spectra. Two initial specialized models were trained separately to capture different features of the turbulence, focusing on either small-scale or large-scale structures. The encoders from these models were then leveraged in a transfer learning framework that combined their outputs through a new decoder in a Y-network architecture. This innovative combination led to a significant improvement in accuracy, with the overall mean squared error (MSE) and mean absolute error (MAE) reduced by 65% and 40%, respectively, for a suite of reconstructed vorticity fields. Previously, we implemented an encoder-decoder model using stacked LSTM layers to serve as a energy spectrum-to-velocity field lifting operator for a 1D Burgers' turbulence model. We integrated that model into a coarse projective integration multiscale simulation scheme that treated the energy spectrum as the coarse (slow) variable and the velocity field as the fine (fast) variable and found that it accelerated the evolution of the flow to statistical stationarity by a factor of 443 (Dhingra et al., Phys. Fluids, 2024). Preliminary tests show that the current model can be integrated into similar multiscale simulation schemes to enable accelerated simulations of 2D turbulent vorticity fields.