Inverse design of heterodeformations for strain soliton networks in bilayer 2D materials

Strain soliton networks strongly influence the structural and electronic properties of heterodeformed bilayer systems, yet their design remains challenging due to the high dimensionality of heterodeformation space and the absence of a direct map between deformation and network geometry. In this work, we introduce a geometric framework that establishes a one-to-one mapping between heterodeformations and the geometry of the strain soliton network expressed as line vector-Burgers vector pairs. The admissible networks are constrained by topology dictated by the generalized stacking fault energy landscape. We show that the moiré Bravais lattice, corresponding to a uniform heterodeformation, alone is insufficient to characterize the interface: distinct heterodeformations can share identical moiré Bravais lattices while producing different soliton networks, reflecting an inherent many-to-one mapping when only translational symmetry is considered. In contrast, the soliton network encodes the full multilattice geometry of the interface, including topology and connectivity, which are not captured by the moiré Bravais lattice alone. The proposed framework enables the direct construction of heterodeformations from target networks, providing a systematic route for inverse design of moiré interfaces beyond conventional twist-based approaches.