Precise mechanism behind the low-height performance crossover

Determine the precise mechanism responsible for the observed performance crossover at low minimum-height constraints h_min between the neural network–based reflector design method (multilayer perceptron parameterization with a height-penalty term optimized by a quasi-Newton method) and the modified Van Cittert deconvolution baseline in the two-dimensional finite-source reflector design problem with a uniform far-field target (Example D), where the deconvolution method slightly outperforms the neural network for small h_min values.

Background

In Example D, the authors compare a neural network–based solver and a deconvolution baseline on a two-dimensional finite-source reflector design problem with a uniform far-field target under varying minimum-height constraints h_min.

They observe that for small h_min the deconvolution method slightly outperforms the neural network, whereas for larger h_min the neural method regains advantage. They hypothesize the difference may stem from the different ways height constraints are enforced (exactly via initialization for deconvolution versus a soft penalty for the neural method), but this is not confirmed.

The authors explicitly note that the exact cause of this crossover remains unresolved, identifying it as an open question.