  We study the excitation transfer across a fully connected quantum network
whose sites energies can be artificially designed. Starting from a simplified
model of a broadly-studied physical system, we systematically optimize its
local energies to achieve high excitation transfer for various environmental
conditions, using an adaptive Gradient Descent technique and Automatic
Differentiation. We show that almost perfect transfer can be achieved with and
without local dephasing, provided that the dephasing rates are not too large.
We investigate our solutions in terms of resilience against variations in
either the network connection strengths, or size, as well as coherence losses.
We highlight the different features of a dephasing-free and dephasing-driven
transfer. Our work gives further insight into the interplay between coherence
and dephasing effects in excitation-transfer phenomena across fully connected
quantum networks. In turn, this will help designing optimal transfer in
artificial open networks through the simple manipulation of local energies.
