InverseStatMech.jl: Extract Interactions from Materials' Spectra

This talk introduces InverseStatMech.jl, a Julia package that provides various efficient and robust algorithms to infer geometric structures of ordered and disordered materials from their spectra and other structural descriptors, which is a crucial inverse problem in statistical mechanics, crystallography and soft materials sciences. (Package currently under development.)

The relationship between materials structure, statistical descriptors and intermolecular forces is of paramount importance in statistical mechanics. With its collection of state-of-the-art inverse algorithms, InverseStatMech.jl enables researchers to infer structures and forces from given statistical descriptors for materials in one, two and three dimensions. Input statistical descriptors include pair correlation functions and structure factors for point patterns, as well as two-point correlation functions for multi-phase media. Key algorithms available in the package are -reverse Monte-Carlo based on simulated annealing; see J. Phys.: Condens. Matter 13, R877–R913 (2001). -iterative Boltzmann inversion; see Chem. Phys. 202, 295–306 (1996). -iterative HNC inversion; see Phys. Rev. Lett. 54, 451–454 (1985) and J. Comput. Chem. 39, 1531–1543 (2018). -ensemble-based algorithm; see Phys. Rev. E 101, 032124 (2020). -algorithm based on optimizing parametrized potentials; see Phys. Rev. E 106 (4), 044122 (2022).