biological sciences is the prediction of protein functions from protein structures. One function prediction is about protein flexibility, which strongly correlates with biomolecular enzymatic activities, such as allosteric transition, ligand binding and catalysis, as well as protein stiffness and rigidity for structural supporting. For instance, in enzymatic processes, protein flexibility enhances protein-protein interactions, which in turn reduce the activation energy barrier. Additionally, protein flexibility and motion amplify the probability of barrier crossing in enzymatic chemical reactions. Therefore, the investigation of protein flexibility at a variety of energy spectra and time scales is vital to the understanding and prediction of other protein functions. Currently, the most important technique for protein flexibility analysis is X-ray crystallography. Among more than one hundred twenty thousand structures in the protein data bank (PDB), more than eighty percent structures are collected by X-ray crystallography. The Debye-Waller factor, or B-factor, can be directly computed from X-ray diffraction or other diffraction data. In the PDB, biomolecular structures are recorded in terms of (discrete) atomic types, atomic positions, occupation numbers, and B-factors. Although atomic B-factors are directly associated with atomic flexibility, they can be influenced by variations in atomic diffraction cross sections and chemical stability during the diffraction data 