  Fast and stable fluid simulations are an essential prerequisite for
applications ranging from computer-generated imagery to computer-aided design
in research and development. However, solving the partial differential
equations of incompressible fluids is a challenging task and traditional
numerical approximation schemes come at high computational costs. Recent deep
learning based approaches promise vast speed-ups but do not generalize to new
fluid domains, require fluid simulation data for training, or rely on complex
pipelines that outsource major parts of the fluid simulation to traditional
methods.
  In this work, we propose a novel physics-constrained training approach that
generalizes to new fluid domains, requires no fluid simulation data, and allows
convolutional neural networks to map a fluid state from time-point t to a
subsequent state at time t + dt in a single forward pass. This simplifies the
pipeline to train and evaluate neural fluid models. After training, the
framework yields models that are capable of fast fluid simulations and can
handle various fluid phenomena including the Magnus effect and Karman vortex
streets. We present an interactive real-time demo to show the speed and
generalization capabilities of our trained models. Moreover, the trained neural
networks are efficient differentiable fluid solvers as they offer a
differentiable update step to advance the fluid simulation in time. We exploit
this fact in a proof-of-concept optimal control experiment. Our models
significantly outperform a recent differentiable fluid solver in terms of
computational speed and accuracy.
