  Single-shot wide-angle diffraction imaging is a widely used method to
investigate the structure of non-crystallizing objects such as nanoclusters,
large proteins or even viruses. Its main advantage is that information about
the three-dimensional structure of the object is already contained in a single
image. This makes it useful for the reconstruction of fragile and
non-reproducible particles without the need for tomographic measurements.
However, currently there is no efficient numerical inversion algorithm
available that is capable of determining the object's structure in real time.
Neural networks, on the other hand, excel in image processing tasks suited for
such purpose. Here we show how a physics-informed deep neural network can be
used to reconstruct complete three-dimensional object models of uniform, convex
particles on a voxel grid from single two-dimensional wide-angle scattering
patterns. We demonstrate its universal reconstruction capabilities for silver
nanoclusters, where the network uncovers novel geometric structures that
reproduce the experimental scattering data with very high precision.
