  Synthetic dimensions (SDs) opened the door for exploring previously
inaccessible phenomena in high-dimensional synthetic space. However,
construction of synthetic lattices with desired coupling properties is a
challenging and unintuitive task, largely limiting the exploration and current
application of SD dynamics. Here, we overcome this challenge by using deep
learning artificial neural networks (ANNs) to validly design the dynamics in
SDs. We use ANNs to construct a lattice in real space that has a predesigned
spectrum of mode eigenvalues. By employing judiciously chosen perturbations
(wiggling of waveguides), we show experimentally and theoretically resonant
mode coupling and tailored dynamics in SDs, which leads to effective transport
or confinement of a complex beam profile. As an enlightening example, we
demonstrate morphing of light into a topologically protected edge mode in
ANN-designed Su-Schrieffer-Heeger photonic lattices. Such ANN-assisted
construction of SDs advances towards utopian networks, opening new avenues in
fundamental research beyond geometric limitations. Our findings may offer a
flexible and efficient solution for mode lasing, optical switching, and
communication technologies.
