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Meta-materials are an important emerging class of engineered materials inwhich complex macroscopic behaviour--whether electromagnetic, thermal, ormechanical--arises from modular substructure. Simulation and optimization ofthese materials are computationally challenging, as rich substructuresnecessitate high-fidelity finite element meshes to solve the governing PDEs. Toaddress this, we leverage parametric modular structure to learn component-levelsurrogates, enabling cheaper high-fidelity simulation. We use a neural networkto model the stored potential energy in a component given boundary conditions.This yields a structured prediction task: macroscopic behavior is determined bythe minimizer of the system's total potential energy, which can be approximatedby composing these surrogate models. Composable energy surrogates thus permitsimulation in the reduced basis of component boundaries. Costly ground-truthsimulation of the full structure is avoided, as training data are generated byperforming finite element analysis with individual components. Using datasetaggregation to choose training boundary conditions allows us to learn energysurrogates which produce accurate macroscopic behavior when composed,accelerating simulation of parametric meta-materials.

Learning Composable Energy Surrogates for PDE Order Reduction