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

Area of Science:

• Computational Physics and Chemistry
• Statistical Mechanics
• Materials Science

Background:

• Accurate modeling of diffusion is crucial for understanding fluid behavior.
• Existing empirical equations for Lennard-Jones (LJ) fluids have limitations.
• Artificial Neural Networks (ANNs) show promise but can be data-intensive.

Purpose of the Study:

• To derive novel empirical equations for diffusion in LJ fluids using symbolic regression (SR).
• To evaluate the predictive performance of SR-derived equations against existing models and ANNs.
• To explore the efficiency of SR in discovering parsimonious yet predictive diffusion models.

Main Methods:

• Employed multi-gene genetic programming within a symbolic regression framework.
• Developed equations for self-diffusion in pure LJ fluids.
• Formulated equations for finite-size corrections in binary LJ fluid self-diffusion.
• Compared SR results against literature empirical equations and recent ANN models.

Main Results:

• SR successfully generated new empirical equations for LJ fluid diffusion.
• SR equations demonstrated superior predictive performance compared to existing empirical models.
• SR models achieved this improvement with fewer adjustable parameters than traditional methods.
• ANN models exhibited higher overall performance than SR equations, especially for complex scenarios.

Conclusions:

• Symbolic regression is an effective tool for discovering new, accurate empirical models for fluid diffusion.
• SR offers a valuable alternative for developing predictive equations, particularly when parameter parsimony is desired.
• Further research can explore hybrid approaches combining SR and ANNs for enhanced predictive capabilities.