  Magnetic skyrmions are topologically protected spin swirling vertices, which
are promising in device applications due to their particle-like nature and
excellent controlability. Magnetic skyrmions have been extensively studied in a
variety of materials and were proposed to exist in the extreme two-dimensional
limit, i.e., in twisted bilayer CrI$_3$ (TBCI). Unfortunately, the magnetic
states of TBCIs with small twist angles are disorderly distributed
ferromagnetic (FM) and antiferromagnetic (AFM) domains in recent experiments,
and thus the method to get rid of disorders in TBCIs is highly desirable. Here
we use intralayer exchange interactions up to the third nearest neighbors
without empirical parameters and very accurate interlayer exchange interactions
to study the magnetic states of TBCIs. We propose the functions of interlayer
exchange interactions obtained using first-principles calculations and stored
in symmetry-adapted artificial neural networks. Based on them, the subsequent
Landau-Lifshitz-Gillbert equation calculations explain the disorderly
distributed FM-AFM domains in TBCIs with small twist angles and predict the
orderly distributed skyrmions in TBCIs with large twist angles. This novel
twisted two-dimensional bilayer magnet can be used to design memory devices,
monochromatic spin wave generators and many kinds of skyrmion lattices.
