Understanding simple liquids through statistical and deep learning approaches

Statistical and deep learning-based methods are employed to obtain insights into the quasi-universal properties of simple liquids. In the first part, a statistical model is employed to provide a probabilistic explanation for the similarity in the structure of simple liquids interacting with different pair potential forms, collectively known as simple liquids. The methodology works by sampling the radial distribution function and the number of interacting particles within the cutoff distance, and it produces the probability density function of the net force. We show that matching the probability distribution of the net force can be a direct route to parameterize simple liquid pair potentials with a similar structure, as the net force is the main component of the Newtonian equations of motion. The statistical model is assessed and validated against various cases. In the second part, we exploit DeepILST [A. Moradzadeh and N. R. Aluru, J. Phys. Chem. Lett. 10, 1242-1250 (2019)], a data-driven and deep-learning assisted framework to parameterize the standard 12-6 Lennard-Jones (LJ) pair potential, to find structurally equivalent/isomorphic LJ liquids that identify constant order parameter [τ=0ζcfgζ-1ζ2dζ, where gζ and ζ(=rρ13) are the reduced radial distribution function and radial distance, respectively] systems in the space of non-dimensional temperature and density of the LJ liquids. We also investigate the consistency of DeepILST in reproducibility of radial distribution functions of various quasi-universal potentials, e.g., exponential, inverse-power-law, and Yukawa pair potentials, quantified based on the radial distribution functions and Kullback-Leibler errors. Our results provide insights into the quasi-universality of simple liquids using the statistical and deep learning methods.