Lyapunov Regularized Forecaster

Turbulent flow prediction plays a crucial role in climate change prediction. Especially, the long-term prediction of turbulent flow is a primary and promising goal for its future development and attracts more attention from researchers. However, because the Navier-Stokes equations on which turbulent flow relies are chaotic systems, imperceptible initial differences can lead to large differences in future states, making the long-term prediction extremely difficult, even for the state-of-the-art turbulence prediction model Turbulent-Flow Net (TF-Net) that introduces a trainable bispectral decomposition and combines the temporal properties of turbulence with spatial modeling. Realizing that the error propagation leads to severe instability over time in long-term prediction, we propose a time-based Lyapunov regularizer to the loss function of TF-Net to avoid training error propagation and improve the trained long-term prediction. The comparison experiment shows that our Lyapunov-regularized forecaster does have more stable long-term predictions.