  We present a machine learning framework that blends image super-resolution
technologies with passive, scalar transport in the level-set method. Here, we
investigate whether we can compute on-the-fly, data-driven corrections to
minimize numerical viscosity in the coarse-mesh evolution of an interface. The
proposed system's starting point is the semi-Lagrangian formulation. And, to
reduce numerical dissipation, we introduce an error-quantifying multilayer
perceptron. The role of this neural network is to improve the numerically
estimated surface trajectory. To do so, it processes localized level-set,
velocity, and positional data in a single time frame for select vertices near
the moving front. Our main contribution is thus a novel
machine-learning-augmented transport algorithm that operates alongside
selective redistancing and alternates with conventional advection to keep the
adjusted interface trajectory smooth. Consequently, our procedure is more
efficient than full-scan convolutional-based applications because it
concentrates computational effort only around the free boundary. Also, we show
through various tests that our strategy is effective at counteracting both
numerical diffusion and mass loss. In simple advection problems, for example,
our method can achieve the same precision as the baseline scheme at twice the
resolution but at a fraction of the cost. Similarly, our hybrid technique can
produce feasible solidification fronts for crystallization processes. On the
other hand, tangential shear flows and highly deforming simulations can
precipitate bias artifacts and inference deterioration. Likewise, stringent
design velocity constraints can limit our solver's application to problems
involving rapid interface changes. In the latter cases, we have identified
several opportunities to enhance robustness without forgoing our approach's
basic concept.
