  We test the possibility of using a convolutional neural network to infer the
inclination angle of a black hole directly from the incomplete image of the
black hole's shadow in the $uv$-plane. To this end, we develop a
proof-of-concept network and use it to explicitly find how the error depends on
the degree of coverage, type of input and coverage pattern. We arrive at a
typical error of $10^\circ$ at a level of absolute coverage $1\%$ (for a
pattern covering a central part of the $uv$-plane), $0.3\%$ (pattern covering
the central part and the periphery, the $0.3\%$ referring to the central part
only), and $14\%$ (uniform pattern). These numbers refer to a network that
takes both amplitude and phase of the visibility function as inputs. We find
that this type of network works best in terms of the error itself and its
distribution for different angles. In addition, the same type of network
demonstrates similarly good performance on highly blurred images mimicking
sources nearing being unresolved. In terms of coverage, the magnitude of the
error does not change much as one goes from the central pattern to the uniform
one. We argue that this may be due to the presence of a typical scale which can
be mostly learned by the network from the central part alone.
