Rapid inverse design of double-curved beams for multi-stable metamaterials based on prescribed deformation histories through artificial neural network

To address the lack of robust inverse‑design methods for multi‑stable mechanical metamaterials, we propose an artificial neural network (ANN) framework for rapid inverse design of double‑curved beam units that meet prescribed force–deflection specifications. A von Mises truss model generates an interpretable dataset spanning bistable, self-recovering, and monostable regimes; a hybrid network, including a Forward Prediction Neural Network (FPNN) for forward mapping and a serially constrained Inverse Prediction Neural Network (IPNN) for inverse design, learns bidirectional mappings between geometry parameters and force–deflection curves. PLA–TPU bimaterial units are fabricated with symmetric supports to enforce boundary conditions, and compression tests and finite element (FE) simulations corroborate targeted stability. The proposed framework achieves forward predictions in 1.9 ms and inverse designs in 2.3 ms—over two and seven orders of magnitude faster than analytical models and FE simulations, while remaining robust in handling parameter ranges where FE often fails to converge. This framework enables scalable, reproducible inverse design of multi-stable metamaterials from prescribed mechanical responses.