  While deep learning has shown tremendous success in a wide range of domains,
it remains a grand challenge to incorporate physical principles in a systematic
manner to the design, training, and inference of such models. In this paper, we
aim to predict turbulent flow by learning its highly nonlinear dynamics from
spatiotemporal velocity fields of large-scale fluid flow simulations of
relevance to turbulence modeling and climate modeling. We adopt a hybrid
approach by marrying two well-established turbulent flow simulation techniques
with deep learning. Specifically, we introduce trainable spectral filters in a
coupled model of Reynolds-averaged Navier-Stokes (RANS) and Large Eddy
Simulation (LES), followed by a specialized U-net for prediction. Our approach,
which we call turbulent-Flow Net (TF-Net), is grounded in a principled physics
model, yet offers the flexibility of learned representations. We compare our
model, TF-Net, with state-of-the-art baselines and observe significant
reductions in error for predictions 60 frames ahead. Most importantly, our
method predicts physical fields that obey desirable physical characteristics,
such as conservation of mass, whilst faithfully emulating the turbulent kinetic
energy field and spectrum, which are critical for accurate prediction of
turbulent flows.
