  Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving
transport equations with many advantages and have been widely deployed in the
fields of computational fluid dynamics, plasma physics modeling, numerical
weather prediction, among others. In this work, we develop a novel machine
learning-assisted approach to accelerate the conventional SL finite volume (FV)
schemes. The proposed scheme avoids the expensive tracking of upstream cells
but attempts to learn the SL discretization from the data by incorporating
specific inductive biases in the neural network, significantly simplifying the
algorithm implementation and leading to improved efficiency. In addition, the
method delivers sharp shock transitions and a level of accuracy that would
typically require a much finer grid with traditional transport solvers.
Numerical tests demonstrate the effectiveness and efficiency of the proposed
method.
