Machine learning-energized framework for rapid and precise inverse design of programmable structures with multiple design variables

Programmable structures enable autonomous deformation to achieve target three-dimensional (3D) shapes by triggering stimuli-responsive mismatch strain embedded in precursory configurations. However, the growing complexity of target 3D geometries makes it challenging to efficiently and accurately find optimal precursory design variables in a high-dimensional design space. Here, we propose a machine learning-energized framework for rapid and precise inverse design of programmable 3D structures. Firstly, a finite substructure algorithm is proposed to rapidly generate a large-scale database that accurately maps multiple design variables to programmable deformations. To this end, we decompose the full-scale structure into overlapping substructures and employ machine learning to augment the design variable-substructural deformation data pairs from limited finite element analyses. The deformed substructures are then sequentially stitched to reconstruct global deformation by optimal rotation and translation that minimize the Euclidean distance of overlapping regions. Compared to finite element analysis, the proposed finite substructure algorithm accelerates the forward prediction by four orders of magnitude. Based on the large-scale database, a well-trained neural network is obtained to inversely generate the coarse estimation of target design variables, which equips the gradient-free optimization with prior knowledge to approach the optimal result at an accelerated pace. Also, we establish a 3D printing and vacuum actuation platform to validate the inversely designed pneumatically programmable structures. Finally, we show a bio-inspired robotic arm capable of warping and grasping complex 3D objects to highlight the applicability of the proposed inverse design approach. This work provides a feasible paradigm for the inverse design of programmable structures, paving the way for potential applications in soft robotics and deployable devices.