## 1 Introduction  
Since the first discovery of crystal X-ray diffraction by [PERSON] in 1912 [1], diffraction patterns have always been a core analytical tool in materials science, serving as the fingerprint of material structures. The Bragg equation \(n\lambda=2d\sin\theta\), proposed by [PERSON] [2], laid the foundation for diffraction theory, and the invention of the Debye-Scherrer powder diffraction technique [3] made rapid characterization of polycrystalline and amorphous materials possible. With the innovation of synchrotron radiation sources, two-dimensional pixel detectors, and computational methods [4], modern diffraction techniques have evolved from simple lattice constant measurements to multidimensional information probes for analyzing complex structures such as defects, nanodomains, and superlattices. In this development, spectrum analysis and refinement have always been the key bridge connecting experimental data to real structures. Traditional Rietveld refinement methods [5] achieve iterative optimization of structural parameters by minimizing the residual between experimental and theoretical model patterns, but their effectiveness is highly dependent on the accuracy of the initial model, and the computational cost for complex systems (such as mixed phases and low-symmetry materials) grows exponentially. In recent years, the introduction of machine learning techniques [6; 7] has brought a paradigm shift to diffraction analysis: by automatically extracting features such as peak positions, peak widths, and intensity distributions, combined with high-throughput computing, the efficiency of structure analysis has been significantly improved. The bridging role of X-ray diffraction (XRD) technology in this process has become increasingly prominent: experimental XRD patterns are the physical response of real material structures, while simulated XRD patterns of atomic structures provide a gold standard for theoretical verification [8]. Accurate comparison between the two not only verifies the correctness of structural models but also reflects the impact mechanisms of experimental conditions on the data. Traditional XRD phase identification completes the match by comparing the sample diffraction peak positions, relative intensities, and interplanar spacing with the three core parameters of PDF cards [9]. In the unconditional search mode of the well-known Jade software (version 4.6.0), even without specifying the chemical composition, it still relies on the \"three strong peaks\" characteristic data stored in the PDF card database for similarity ranking. For this reason, when a sample contains unknown phases or structures not included in the database, the system cannot generate effective matching results. With the rapid development of new functional materials (such as MOFs and two-dimensional heterojunctions), the growth of existing databases still fails to cover all possible crystal variants [10]. When the diffraction peak positions of unknown structures have a match degree lower than the FOM threshold with existing cards, traditional methods can only classify them as \"unknown phases\" and cannot conduct in-depth analysis. Even advanced methods like Rietveld refinement face convergence difficulties, attributed to the fact that refinement essentially involves adjusting variables such as the unit cell parameters and atomic coordinates of the initial structure, which heavily depends on known crystal structures as the starting point [5]. However, the main difference between search/match analysis and Rietveld analysis is that Rietveld analysis is based on whole-profile fitting, while search/match analysis relies on integrated peak intensities. This discrepancy can be significant for nanocrystalline or anisotropic materials, such as smectites, and can also fail in the common case of preferred orientation or texture.