Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to ideal approximation of high-level performance goals is a challenging task. In this work, we propose Neural Metamaterial Networks (NMN) -- smooth neural representations that encode the nonlinear mechanics of entire metamaterial families. Given structure parameters as input, NMN return continuously differentiable strain energy density functions, thus guaranteeing conservative forces by construction. Though trained on simulation data, NMN do not inherit the discontinuities resulting from topological changes in finite element meshes. They instead provide a smooth map from parameter to performance space that is fully differentiable and thus well-suited for gradient-based optimization. On this basis, we formulate inverse material design as a nonlinear programming problem that leverages neural networks for both objective functions and constraints. We use this approach to automatically design materials with desired strain-stress curves, prescribed directional stiffness and Poisson ratio profiles. We furthermore conduct ablation studies on network nonlinearities and show the advantages of our approach compared to native-scale optimization.

翻译：具有定制力学特性的非线性超材料在工程、医学、机器人学及其他领域具有广泛应用。然而，对其宏观力学行为进行建模本身极具挑战，而寻找能够理想逼近高层性能目标的结构参数更是一项艰巨任务。本文提出神经超材料网络（NMN）——一种光滑的神经表示方法，可编码整类超材料的非线性力学特性。给定结构参数作为输入，NMN返回连续可微的应变能密度函数，从而通过构造保证保守力。尽管基于仿真数据训练，NMN并未继承有限元网格拓扑变化导致的非连续性，而是提供从参数空间到性能空间的光滑映射，该映射完全可微，因而适用于梯度优化。在此基础上，我们将逆材料设计建模为非线性规划问题，同时利用神经网络处理目标函数与约束条件。采用该方法可自动设计具有期望应力-应变曲线、指定方向刚度及泊松比分布的材料。此外，我们针对网络非线性特性进行了消融研究，并展示了本方法相较于原生尺度优化的优势。