Long-time turbulence prediction at fine time steps using multi-stride neural operators

Abstract

Long-time turbulence prediction at fine time steps is costly and prone to error accumulation, while accurate short-term fields do not ensure accurate long-time statistics. We propose a multi-stride neural operator for three-dimensional turbulence, combining implicit factorized Transformer (IFF) predictors with a factorized-attention cross-stride fusion (FA-CSF) module. All predictors take the same current velocity field as input. FA-CSF reuses their outputs and latent features to generate intermediate velocity fields through interpolation and learned correction. The corrected largest-stride field drives the next autoregressive step, decoupling the autoregressive step from the output time step. Stride-conditioned IFF (SC-IFF) predictors are first trained at power-of-two strides using three conditioning strategies, then frozen while FA-CSF is trained on long rollouts with field-data and statistical losses. Tests on turbulent channel flow and forced homogeneous isotropic turbulence (HIT) show improved long-time predictions and statistics. At a sampling interval of 10 direct numerical simulation (DNS) time steps, fixed-stride IFF yields relative L2 errors above 100% in channel-flow root-mean-square (RMS) velocity fluctuation profiles and the Reynolds shear stress profile, and in the temporal evolution of velocity and vorticity RMS values and the time-averaged energy spectrum in HIT. SC-IFF with independent stride-specific predictors and FA-CSF keeps statistics close to filtered DNS data over the tested prediction times. Relative to fixed-stride IFF, it reduces errors in the channel-flow profiles by more than 98% and in the HIT spectrum by more than 99%. Multi-stride prediction with FA-CSF generates trajectories at fine time steps 3.69 times faster than fixed-stride IFF autoregression and 2.41 times faster than hierarchical multi-stride prediction.

arXiv comment43 pages, 20 figures