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-dimensional 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 a many-to-one mapping considering translational symmetry only. In contrast, the soliton network encodes the interfacial multilattice geometry, including topology and connectivity, not captured by the moiré Bravais lattice alone. The 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. Finally, we show that the framework enables the design of symmetry-broken soliton networks in bilayer graphene that exhibit anisotropic (tensorial) interfacial friction, demonstrating its potential for engineering superlubric interfaces.