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

STEP: extraction of underlying physics with robust machine learning

A prevalent class of challenges in modern physics are inverse problems, where physical quantities must be extracted from experimental measurements. End-to-end machine learning approaches to inverse problems typically require constructing sophisticated estimators to achieve the desired accuracy, largely because they need to learn the complex underlying physical model. Here, we discuss an alternative paradigm: by making the physical model auto-differentiable we can construct a neural surrogate to represent the unknown physical quantity sought, while avoiding having to relearn the known physics entirely. We dub this process surrogate training embedded in physics (STEP) and illustrate that it generalizes well and is robust against overfitting and significant noise in the data. We demonstrate how STEP can be applied to perform dynamic kernel deconvolution to analyse resonant inelastic X-ray scattering spectra and show that surprisingly simple estimator architectures suffice to extract the relevant physical information.

Three-dimensional femtosecond snapshots of isolated faceted nanostructures

The structure and dynamics of isolated nanosamples in free flight can be directly visualized via single-shot coherent diffractive imaging using the intense and short pulses of x-ray free-electron lasers. Wide-angle scattering images encode three-dimensional (3D) morphological information of the samples, but its retrieval remains a challenge. Up to now, effective 3D morphology reconstructions from single shots were only achieved via fitting with highly constrained models, requiring a priori knowledge about possible geometries. Here, we present a much more generic imaging approach. Relying on a model that allows for any sample morphology described by a convex polyhedron, we reconstruct wide-angle diffraction patterns from individual silver nanoparticles. In addition to known structural motives with high symmetries, we retrieve imperfect shapes and agglomerates that were not previously accessible. Our results open unexplored routes toward true 3D structure determination of single nanoparticles and, ultimately, 3D movies of ultrafast nanoscale dynamics.