A proof-of-concept neural network for inferring parameters of a black hole from partial interferometric images of its shadow

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.