Reconstruction of nanoscale particles from single-shot wide-angle free-electron-laser diffraction patterns with physics-informed neural networks.

Single-shot wide-angle diffraction imaging is a widely used method to investigate the structure of noncrystallizing 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 nonreproducible 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.