Machine learning and sequential subdomain optimization for ultrafast inverse design of 4D-printed active composite structures

Shape transformations of active composites (ACs) depend on the spatial distribution and active response of constituent materials. Voxel-level complex material distributions offer a vast possibility for attainable shape changes of 4D-printed ACs, while also posing a significant challenge in efficiently designing material distributions to achieve target shape changes. Here, we present an integrated machine learning (ML) and sequential subdomain optimization (SSO) approach for ultrafast inverse designs of 4D-printed AC structures. By leveraging the inherent sequential dependency, a recurrent neural network ML model and SSO are seamlessly integrated. For multiple target shapes of various complexities, ML-SSO demonstrates superior performance in optimization accuracy and speed, delivering results within second(s). When integrated with computer vision, ML-SSO also enables an ultrafast, streamlined design-fabrication paradigm based on hand-drawn targets. Furthermore, ML-SSO empowered with a splicing strategy is capable of designing diverse lengthwise voxel configurations, thus showing exceptional adaptability to intricate target shapes with different lengths without compromising high speed and accuracy. As a comparison, for the benchmark three-period shape, the finite element and evolutionary algorithm (EA) method was estimated to need 219 days for the inverse design; the ML-EA achieved the design in 54min; the new ML-SSO with splicing strategy requires only 1.97s. By further leveraging appropriate symmetries, the highly efficient ML-SSO is employed to design active shape changes of 4D-printed lattice structures. The new ML-SSO approach thus provides a highly efficient tool for the design of various 4D-printed, shape-morphing AC structures.