Symbolic regression development of empirical equations for diffusion in Lennard-Jones fluids

Abstract

Symbolic regression (SR) with a multi-gene genetic program has been used to elucidate new empirical equations describing diffusion in Lennard-Jones (LJ) fluids. Examples include equations to predict self-diffusion in pure LJ fluids and equations describing the finite-size correction for self-diffusion in binary LJ fluids. The performance of the SR-obtained equations was compared to that of both the existing empirical equations in the literature and to the results from artificial neural net (ANN) models recently reported. It is found that the SR equations have improved predictive performance in comparison to the existing empirical equations, even though employing a smaller number of adjustable parameters, but show an overall reduced performance in comparison to more extensive ANNs.

Machine Learning Predictions of Simulated Self-Diffusion Coefficients for Bulk and Confined Pure Liquids

“…While our data set contains T and ρ as features, it is likely that D bulk MD is a nonlinear function of these two features. Several nonlinear empirical relationships for LJ diffusion exist, including those generated using symbolic regression. , To test this effect here in real fluid LJ simulations, as well as provide a base model for which to compare our ANN, we developed an ordinary least-squares linear regression model using both sets of descriptors. The descriptors and labels were scaled using the same minmax scaler used during the ANN training.…”

“…Even molecular dynamics (MD) simulation methods are computationally expensive to thoroughly explore the full range of liquid and pore properties and their effect on liquid diffusion. This effort builds on our previous work developing ML models for self-diffusion in bulk and pore fluids, based on experimental or simulated data. − Importantly, we showed that artificial neural networks (ANNs) can accurately predict MD results for pure LJ fluid diffusion in pores of various geometries (planar, cylindrical, hexagonal) over a range of fluid–wall interactions …”

Artificial Intelligence in Physical Sciences: Symbolic Regression Trends and Perspectives

“…Moreover, several applications focus on equation generation from scratch towards the prediction of Lennard–Jones fluid diffusion [ 56 , 145 , 146 ] or the electrical conductivity of ionic liquids [ 101 ]. While others, have equipped SR to investigate lattice thermal conductivity [ 147 ], the critical temperature in superconductors [ 148 ] or the yield strength of polycrystalline metals by key physical quantities [ 149 ].…”

Machine learning predictions of diffusion in bulk and confined ionic liquids using simple descriptors

“…60 The current work builds on our recent efforts applying ML methods to predict the diffusion properties of ideal and real fluids in bulk and confined environments. [56][57][58][61][62][63][64]…”