Abstract:
In recent years, X-ray science has seen remarkable advancements, highlighted by breakthroughs like free-electron lasers and the APS+U upgrade. These developments call for enhanced methods for data interpretation, whether through AI and machine learning, or by theoretical framework.
For AI and machine learning, spectra data can serve as either input or output. As input, we can learn from spectra, from simply learning materials’ class using tunneling spectra [1], or learning hidden thermal transport from ultrafast-diffraction and neural ODE approach [2]. As output, a machine learning model for materials has at least two essential ingredients, the representation and the model architecture. For representation, we introduce our latest effort on ensemble representation development for optical spectra prediction [3], while for model architecture we introduce our effort in predicting phonon dispersion prediction for inelastic scattering based on augmentation of a graph neural networks with virtual graph nodes [4]. Given the tight link between materials and spectroscopy, we introduce our latest machine learning model that generates materials structures that are subject to geometrical pattern (e.g. kagome lattice) [5].
For theoretical foundations, we present our recent microscopic quantum theory on XPCS, derived ab initio from electron-photon interaction Hamiltonians, and applicable to general X-ray pulses for both synchrotron and free-electron lasers [6]. We introduce four XPCS configurations, each corresponding to a slightly different fourth-order electron-density correlation function. Given the central role of Siegert relation to XPCS, we examine the validity Siegert relation, with a generalized Siegert relation derived. In fact, the Siegert relation breaks down even in non-interacting Fermi gas due to exchange interactions. Furthermore, we demonstrate that XPCS has the potential to distinguish topological order.
[1] MC, ML, “Machine Learning Detection of Majorana Zero Modes from Zero Bias Peak Measurements,” Matter 7, 2507 (2024).
[2] ZC, ML, "Panoramic mapping of phonon transport from ultrafast electron diffraction and machine learning," Advanced Materials 35, 2206997 (2023).
[3] NT, ML, “Ensemble-Embedding Graph Neural Network for Direct Prediction of Optical Spectra from Crystal Structure,” arXiv:2406.16654. In production, Advanced Materials 2024.
[4] RO, ML, "Virtual Node Graph Neural Network for Full Phonon Prediction," Nature Computational Science 4, 522 (2024).
[5] RO, ML, "Structural Constraint Integration in Generative Model for Discovery of Quantum Material Candidates," arXiv:2407.04557. Submitted.
[6] PS, ML, “Quantum Theory of X-ray Photon Correlation Spectroscopy,” to submit.
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