  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 with individual components. Using dataset
aggregation to choose training boundary conditions allows us to learn energy
surrogates which produce accurate macroscopic behavior when composed,
accelerating simulation of parametric meta-materials.
