  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.
