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Temporal Downsampling Factor Scan
Rollouts for models trained with different temporal downsampling factors.
An advantage of learned simulators is that they can exploit a much larger step size than the numerical solver. The videos below show qualitative examples of Dil-ResNet trained on a large range of exponentially increasing coarse timesteps, which the model can seamlessly adapt to. Larger step sizes can lead to greater stability, as there are fewer opportunities for errors to accumulate.
initial_condition_066_comparison_downsampling_in_time.mp43D Compressible Decaying Turbulence (CompDecay-3D)
3D Compressible Decaying Turbulence (CompDecay-3D)
Rollouts for models trained on CompDecay-3D with different values of Δt from 1e-3 to 256e-13 State variables shown in each row are density, X-, Y-, and Z-velocity, and pressure. The final column shows spectra for each value of Δt.
Note how the model can learn to make predictions for significantly coarse timesteps (>=128), for which subsequent steps are considerably different. Our best model uses Δt=32e-3
comparison_downsampling_in_time.mp42D Incompressible Decaying Turbulence (Incomp-2D)
2D Incompressible Decaying Turbulence (Incomp-2D)
Rollouts for models trained on Incomp-2D with different temporal downsampling factors. State variables shown in each row are X- and Y-velocity and vorticity. The final column shows spectra for each downsampling factor.
Downsampling factor of 1 corresponds to Δt=0.0523. Our best model uses Δt=3.35 (downsampling factor of 64 in this video). Note the ground truth simulator runs at Δt=0.00436, that is 768x smaller timesteps than our model.
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