  Many engineering systems require accurate simulations of complex physical
systems. Yet, analytical solutions are only available for simple problems,
necessitating numerical approximations such as the Finite Element Method (FEM).
The cost and accuracy of the FEM scale with the resolution of the underlying
computational mesh. To balance computational speed and accuracy meshes with
adaptive resolution are used, allocating more resources to critical parts of
the geometry. Currently, practitioners often resort to hand-crafted meshes,
which require extensive expert knowledge and are thus costly to obtain. Our
approach, Adaptive Meshing By Expert Reconstruction (AMBER), views mesh
generation as an imitation learning problem. AMBER combines a graph neural
network with an online data acquisition scheme to predict the projected sizing
field of an expert mesh on a given intermediate mesh, creating a more accurate
subsequent mesh. This iterative process ensures efficient and accurate
imitation of expert mesh resolutions on arbitrary new geometries during
inference. We experimentally validate AMBER on heuristic 2D meshes and 3D
meshes provided by a human expert, closely matching the provided demonstrations
and outperforming a single-step CNN baseline.
