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 54 min; the new ML-SSO with splicing strategy requires only 1.97 s. 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.

中文翻译：

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用于 4D 打印活性复合结构超快逆向设计的机器学习和顺序子域优化

活性复合材料（AC）的形状转变取决于组成材料的空间分布和活性响应。体素级的复杂材料分布为 4D 打印 AC 的形状变化提供了巨大的可能性，同时也对有效设计材料分布以实现目标形状变化提出了重大挑战。在这里，我们提出了一种集成机器学习 (ML) 和顺序子域优化 (SSO) 方法，用于 4D 打印 AC 结构的超快逆向设计。通过利用固有的顺序依赖性，循环神经网络 ML 模型和 SSO 可以无缝集成。对于各种复杂程度的多个目标形状，ML-SSO 在优化精度和速度方面表现出卓越的性能，可在几秒钟内提供结果。当与计算机视觉集成时，ML-SSO 还可以实现基于手绘目标的超快、简化的设计制造范例。此外，具有拼接策略的 ML-SSO 能够设计不同的纵向体素配置，从而在不影响高速和准确性的情况下，对不同长度的复杂目标形状表现出卓越的适应性。作为比较，对于基准三周期形状，有限元和进化算法（EA）方法估计需要219天进行逆设计； ML-EA在54分钟内完成了设计；采用拼接策略的新 ML-SSO 仅需要 1.97 秒。通过进一步利用适当的对称性，高效的 ML-SSO 用于设计 4D 打印晶格结构的主动形状​​变化。因此，新的 ML-SSO 方法为设计各种 4D 打印、形状变形 AC 结构提供了一种高效的工具。