Data-Driven Discovery of Dynamics from Time-Resolved Coherent Scattering

Coherent X-ray scattering (CXS) techniques, including X-ray photon correlation spectroscopy (XPCS), play a critical role in the investigation of mesoscale phenomena evolving at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex dynamics is often limited by one or more factors – the ability to visualize dynamics in real space, computational cost of high-fidelity simulations, and accuracy of approximate models. Here, we aim to bridge the gap between theory and experiments by extracting mechanistic models of dynamics directly from CXS data. To do so, we develop a data-driven framework which employs neural differential equations to parameterize unknown real-space dynamics and a computational scattering forward model to relate real-space predictions to reciprocal-space observations. This framework is shown to recover dynamics of several computational model systems, including domain synchronization, particle clustering, and source fluctuation, under various simulated conditions of measurement resolution and noise. We further demonstrate the practical application of this approach in the context of two proof-of-concept experiments. Our framework represents a general and versatile platform to discover dynamics from time-resolved CXS measurements without solving the phase reconstruction problem for a complete time series of diffraction patterns.