  This study introduces a two-scale Graph Neural Operator (GNO), namely,
LatticeGraphNet (LGN), designed as a surrogate model for costly nonlinear
finite-element simulations of three-dimensional latticed parts and structures.
LGN has two networks: LGN-i, learning the reduced dynamics of lattices, and
LGN-ii, learning the mapping from the reduced representation onto the
tetrahedral mesh. LGN can predict deformation for arbitrary lattices, therefore
the name operator. Our approach significantly reduces inference time while
maintaining high accuracy for unseen simulations, establishing the use of GNOs
as efficient surrogate models for evaluating mechanical responses of lattices
and structures.
