This study presents a novel physics-enhanced machine learning (ML) and optimization framework tailored to address the challenges of designing intricate spinodal metamaterials with customized mechanical properties in scenarios where computational modeling is restricted, and experimental data is sparse. By utilizing sparse experimental data directly, our approach facilitates the inverse design of spinodal structures with precise finite-strain mechanical responses. Leveraging physics-based inductive biases to compensate for limited data availability, the framework sheds light on instability-induced pattern formation in periodic metamaterials, attributing it to nonconvex energetic potentials. Inspired by phase transformation modeling, the method integrates multiple partial input convex neural networks to create nonconvex potentials, effectively capturing complex nonlinear stress-strain behavior, even under extreme deformations.

翻译：本研究提出了一种新型物理增强机器学习与优化框架，旨在解决计算建模受限且实验数据稀疏条件下，定制化力学性能的复杂旋节线超材料设计难题。通过直接利用稀疏的实验数据，本方法实现了具有精确有限应变力学响应的旋节线结构逆向设计。该框架利用基于物理的归纳偏差弥补数据不足的局限，揭示了周期性超材料中失稳诱导的图案形成机制，并将其归因于非凸能量势。受相变建模启发，该方法集成多个部分输入凸神经网络构建非凸势能函数，有效捕捉了即使在极端变形条件下仍表现出的复杂非线性应力-应变行为。