Physically Consistent Self-Diffusion Coefficient Calculation with Molecular Dynamics and Symbolic Regression.

Area of Science:

• Computational physics and chemistry
• Materials science
• Chemical engineering

Background:

• Calculating self-diffusion coefficients is crucial for understanding fluid behavior in bulk and confined systems.
• Traditional methods, like mean squared displacement, are computationally intensive and complex.
• Developing efficient predictive models for fluid dynamics is an ongoing challenge.

Purpose of the Study:

• To develop a universal, computationally efficient approach for calculating self-diffusion coefficients in molecular fluids.
• To derive analytical expressions correlating self-diffusion coefficients with macroscopic fluid properties.
• To bypass traditional atomistic-level simulation methods.

Main Methods:

• Utilizing machine learning, specifically symbolic regression, trained on molecular dynamics simulation data.
• Correlating self-diffusion coefficients with macroscopic parameters: density, temperature, and confinement width.
• Employing genetic programming to select simple, interpretable symbolic expressions.

Main Results:

• Derived new analytical expressions for self-diffusion coefficients in nine molecular fluids.
• Extracted a universal equation applicable to all tested fluids, capturing molecular behavior.
• Demonstrated accurate prediction of self-diffusion coefficients, bypassing computationally demanding methods.

Conclusions:

• Machine learning provides a powerful, efficient tool for predicting self-diffusion coefficients.
• The derived universal equation offers a physically consistent and interpretable model for fluid behavior.
• This approach advances fundamental understanding and aids in designing nanoscale confinement devices.