State variables (density, X-, Y- and Z-velocity, and pressure) for Dilated Res trained of a timestep Δt=1e-3 on a 1000 step trajectory. Rows correspond to Ground Truth, Dilated ResNet trained with noise (bottom row) and Dilated ResNet trained without noise and spectra comparison.

Training with noise is critical to produce more stable trajectories, which is of particular importance for long model rollouts that with small step sizes like the one shown. This is presumably because the training distribution has broader support and the model is optimized to map deviant inputs back to the training distribution.