Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour--whether electromagnetic, thermal, or mechanical--arises from modular substructure. Simulation and optimization of these materials are computationally challenging, as rich substructures necessitate high-fidelity finite element meshes to solve the governing PDEs. To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions. This yields a structured prediction task: macroscopic behavior is determined by the minimizer of the system's total potential energy, which can be approximated by composing these surrogate models. Composable energy surrogates thus permit simulation in the reduced basis of component boundaries. Costly ground-truth simulation of the full structure is avoided, as training data are generated by performing finite element analysis of individual components. Using dataset aggregation to choose training data allows us to learn energy surrogates which produce accurate macroscopic behavior when composed, accelerating simulation of parametric meta-materials.

Weaknesses: The empirical evaluation would benefit from additional exploration. For instance, the outer optimization may be sensitive to the quality of the surrogate model energy predictions and gradients. There is little presentation on the quality of the surrogate model predictions and gradients. Is it understood how sensitive the outer optimization is to the accuracy of the surrogate gradients? Even if the gradients are biased, can the outer optimization still find reasonable solutions?

The paper presents a very nice application of ML techniques to a new problem domain and has the potential to open a new research direction. The authors show how to use neural nets to solve a specific class of PDEs in a novel way. Their technique is elegant and more efficient than traditional finite element analysis. The work is well grounded both in ML and the application domain of computational mechanics. The main issues raised by the reviewers concern clarity and they have been addressed in the authors' rebuttal.

Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour--whether electromagnetic, thermal, or mechanical--arises from modular substructure. Simulation and optimization of these materials are computationally challenging, as rich substructures necessitate high-fidelity finite element meshes to solve the governing PDEs. To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions. This yields a structured prediction task: macroscopic behavior is determined by the minimizer of the system's total potential energy, which can be approximated by composing these surrogate models.