A physically-informed Deep-Learning approach for locating sources in a waveguide

A large class of inverse problems in imaging aims at recovering locations of sources of waves from sensor measurements of the wavefield radiated by these sources. Many applications for locating sources exist in the literature, in various fields such as acoustics, geophysics, non-destructive evaluation and more [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. These "inverse source" problems are usually ill-posed. The incomplete data provided only by a few sensors makes the solution very sensitive to that data. In addition, traditional imaging methods such as Kirchhoff migration suffer from the so-called resolution limit, when close-by sources cannot be distinguished from each other in the image due to the nonzero width of the Green's function. Various super-resolution techniques can in principle overcome these limitations, however at the expense of extreme sensitivity to noise in the data and highly nontrivial mathematical theory, which is currently applicable only in a limited number of cases (see Section 2). The use of machine-learning (ML) for solving inverse problems is spreading fast within the scientific community [11, 12, 13, 14]. According to this paradigm, many PDE-based inverse problems of the form A(x) y, including the one in this paper, can be formulated as data-driven problems, i.e. searching for a general neural network model NN