  Architected materials possessing physico-chemical properties adaptable to
disparate environmental conditions embody a disruptive new domain of materials
science. Fueled by advances in digital design and fabrication, materials shaped
into lattice topologies enable a degree of property customization not afforded
to bulk materials. A promising venue for inspiration toward their design is in
the irregular micro-architectures of nature. However, the immense design
variability unlocked by such irregularity is challenging to probe analytically.
Here, we propose a new computational approach using graph-based representation
for regular and irregular lattice materials. Our method uses differentiable
message passing algorithms to calculate mechanical properties, therefore
allowing automatic differentiation with surrogate derivatives to adjust both
geometric structure and local attributes of individual lattice elements to
achieve inversely designed materials with desired properties. We further
introduce a graph neural network surrogate model for structural analysis at
scale. The methodology is generalizable to any system representable as
heterogeneous graphs.
