Deep Inverse Design of Patchy Particles for Mesoscale Assembly of Superlattices

The rational design of mesoscale superlattices with prescribed architectures remains a fundamental challenge in materials science. While self-assembly of patchy colloidal particles offers a powerful route to such structures, the combinatorial complexity linking patch number, placement, and interaction properties to emergent assembly architecture has hindered systematic inverse design. Here, we present a discrete neural-adjoint framework that enables direct optimization of building-block design for target superlattice formation. Leveraging a Gumbel–Softmax relaxation, our approach renders discrete patch configurations differentiable, allowing efficient gradient-based exploration of an otherwise intractable design space. Applied to a model system of self-assembling two-dimensional tiles, our method discovers patch designs that robustly assemble into complex superlattices, including multiple Archimedean tilings as well as previously unrealized Pythagorean and gyrated truncated hexagonal tilings. These results establish differentiable inverse design as a powerful approach for programming self-assembly, opening new avenues for the discovery of architected materials with tailored structure and function.