Fig. 3: Implementation of initialization methods, constraints and resolution conversions.
From: Shaping freeform nanophotonic devices with geometric neural parameterization

a Controlled initialization showing the transformation from initial shapes to distance mapping and the training process through randomly sampled batches. b Implementation of periodicity and symmetry constraints using triangle wave functions and coordinate mapping. c Feature size and curvature penalty calculation demonstrating gradient-based measurement of local geometric properties. d Connectivity penalty implementation using PDE-based approach with specified boundary conditions. e Resolution conversion process illustrating the relationship between high-resolution reference structures and differentiable sub-pixel averaged structures at different resolution for simulation.