Periodic Complex Stochastic Processes for Retrieving Atomic Structures of Unknown Matters

Retrieving unknown atomic structures from observable analytical spectra or images remains a long-standing challenge in natural sciences. Although cross-modal retrieval methods achieved some notable successes in identifying atomic structures from the corresponding analytical data, their accuracy remains suboptimal because they have overlooked the underlying nature of analytical data: most analytical observations essentially reflect aggregations of multiple structural phases induced by periodic quantum mechanical perturbations. This paper proposes a periodic complex stochastic process (PCSP) that models such periodic perturbations and establishes theoretical backgrounds of PCSP, including its sample diversity, process length, and periodicity. Finally, for accurate atomic structure identifications on analytical data, we develop a complex-valued cross-modal retrieval (CVCR) by integrating PCSP with cross-modal retrieval frameworks. CVCR achieves state-of-the-art accuracy in cross-modal retrieval tasks of real-world analytical chemistry.