Data-driven discovery of dynamics from time-resolved coherent X-ray scattering

Coherent X-ray scattering techniques are often used to interrogate materials' structural and dynamical properties at mesoscopic time and length scales. In particular, X-ray photon correlation spectroscopy (XPCS) exploits correlations between scattered intensity fluctuations over time to derive insights about microscopic sample dynamics, from particle diffusion in colloidal suspensions to fluctuations of magnetic domains. However, the interpretation of complex XPCS signatures is often challenging or only in terms of approximate phenomenological models. In this work, we develop a machine learning framework to uncover mechanistic models from time-resolved coherent scattering measurements directly from data. Combining the method of neural differential equations with a computational forward model of the scattering method, we recover the time evolution of several model dynamical systems without access to real-space dynamics. We evaluate our approach against experimental considerations such as sampling and noise and discuss the interpretability of the learned models. Finally, we demonstrate a simple proof of concept for applying our framework to experimental data.