  Coherent X-ray scattering (CXS) techniques are capable of interrogating
dynamics of nano- to mesoscale materials systems 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 effectiveness of approximate or phenomenological
models. In this work, we develop a data-driven framework to uncover mechanistic
models of dynamics directly from time-resolved CXS measurements without solving
the phase reconstruction problem for the entire time series of diffraction
patterns. Our approach uses neural differential equations to parameterize
unknown real-space dynamics and implements a computational scattering forward
model to relate real-space predictions to reciprocal-space observations. This
method is shown to recover the dynamics of several computational model systems
under various simulated conditions of measurement resolution and noise.
Moreover, the trained model enables estimation of long-term dynamics well
beyond the maximum observation time, which can be used to inform and refine
experimental parameters in practice. Finally, we demonstrate an experimental
proof-of-concept by applying our framework to recover the probe trajectory from
a ptychographic scan. Our proposed framework bridges the wide existing gap
between approximate models and complex data.
