  Deep learning has revolutionized the field of computer vision by introducing
large scale neural networks with millions of parameters. Training these
networks requires massive datasets and leads to intransparent models that can
fail to generalize. At the other extreme, models designed from partial
differential equations (PDEs) embed specialized domain knowledge into
mathematical equations and usually rely on few manually chosen hyperparameters.
This makes them transparent by construction and if designed and calibrated
carefully, they can generalize well to unseen scenarios. In this paper, we show
how to bring model- and data-driven approaches together by combining the
explicit PDE-based approaches with convolutional neural networks to obtain the
best of both worlds. We illustrate a joint architecture for the task of
inpainting optical flow fields and show that the combination of model- and
data-driven modeling leads to an effective architecture. Our model outperforms
both fully explicit and fully data-driven baselines in terms of reconstruction
quality, robustness and amount of required training data. Averaging the
endpoint error across different mask densities, our method outperforms the
explicit baselines by 11-27%, the GAN baseline by 47% and the Probabilisitic
Diffusion baseline by 42%. With that, our method sets a new state of the art
for inpainting of optical flow fields from random masks.
