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.

相干 X 射线散射 (CXS) 技术能够在跨越几个数量级的时间尺度上研究纳米到介观尺度材料系统的动力学。然而，获得复杂动力学的准确理论描述通常受到一个或多个因素的限制——在真实空间中可视化动力学的能力、高保真模拟的计算成本以及近似或唯象模型的有效性。在这项工作中，我们开发了一个数据驱动的框架，直接从时间分辨的 CXS 测量中揭示动力学的机械模型，而无需解决衍射图案的整个时间序列的相位重建问题。我们的方法使用神经微分方程来参数化未知的真实空间动力学，并实现计算散射前向模型以将真实空间预测与倒易空间观测联系起来。该方法可以在测量分辨率和噪声的各种模拟条件下恢复多个计算模型系统的动态。此外，经过训练的模型能够估计远远超出最大观察时间的长期动态，这可用于在实践中告知和完善实验参数。最后，我们通过应用我们的框架从叠层扫描中恢复探针轨迹来演示实验概念验证。我们提出的框架弥合了近似模型和复杂数据之间现有的巨大差距。