Abstract
This work incorporates symbolic regression to propose simple and accurate expressions that fit to material datasets. The incorporation of symbolic regression in physical sciences opens the way to replace “black-box” machine learning techniques with representations that carry the physical meaning and can reveal the underlying mechanism in a purely data-driven approach. The application here is the extraction of analytical equations for the self-diffusion coefficient of the Lennard-Jones fluid by exploiting widely incorporating data from the literature. We propose symbolic formulas of low complexity and error that achieve better or comparable results to well-known microscopic and empirical expressions. Results refer to the material state space both as a whole and in distinct gas, liquid, and supercritical regions.
Highlights
IntroductionSymbolic Regression (SR) (very high order and advanced mathematics), the Machine Learning (ML) method used in the present research, tries to unveil hidden phenomena occurring at the nanoscale by incorporating simulation data
Symbolic Regression (SR), the Machine Learning (ML) method used in the present research, tries to unveil hidden phenomena occurring at the nanoscale by incorporating simulation data
II–IV, we describe a SR procedure to acquire an analytical prediction of the LJ fluid diffusion coefficient based entirely on literature data concerning diffusion data obtained at gas, liquid, and supercritical (SC) states
Summary
Symbolic Regression (SR) (very high order and advanced mathematics), the Machine Learning (ML) method used in the present research, tries to unveil hidden phenomena occurring at the nanoscale by incorporating simulation data. After a period of idleness, the concept of SR has been reintroduced at times where the increased computational power and the application of ML algorithms in physical sciences have reached a mature level, allowing the wide applicability of this method.. ML has been exploited to accelerate quantum mechanical (QM), molecular dynamics (MD) and continuum simulations, the construction of coarse-grained models, and the solution of physics-based partial difference equations.. The construction of a ML model is often an ambiguous task, since its inherent “black box” nature would make predictions difficult to rationalize and reveal the physical meaning behind the data Following the vast deployment of material databases in the last decade, with several simulation and experimental data being available to the scientific community, statistical and data science has given a boost in material-related fields by incorporating ML techniques. ML has been exploited to accelerate quantum mechanical (QM), molecular dynamics (MD) and continuum simulations, the construction of coarse-grained models, and the solution of physics-based partial difference equations. ML can capture data behavior and reach predictions at only a fraction of the initial computational cost with comparable accuracy. the construction of a ML model is often an ambiguous task, since its inherent “black box” nature would make predictions difficult to rationalize and reveal the physical meaning behind the data
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