BoltzmaNN: Predicting effective pair potentials and equations of state using neural networks

Area of Science:

• Computational physics
• Machine learning
• Statistical mechanics

Background:

• Equations of state are crucial for describing thermodynamic properties of matter.
• Predicting these equations from interatomic potentials is a fundamental challenge.
• Neural networks offer a powerful tool for complex data-driven modeling.

Purpose of the Study:

• To apply neural networks for predicting equations of state from isotropic pair potentials.
• To develop neural networks for computing effective pair potentials from radial distribution functions.
• To enhance the accuracy and transferability of machine learning models in physical systems.

Main Methods:

• Training neural networks on molecular dynamics simulation data for monoatomic gases and liquids.
• Utilizing the virial expansion of pressure for equation of state predictions.
• Employing radial pair distribution functions and force data for inverse potential prediction.

Main Results:

• Neural network predictions for equations of state significantly surpass analytic low-density estimates and the Carnahan-Starling model.
• Neural networks effectively compute pair potentials from radial distribution functions.
• Incorporating force information into neural network training substantially improves potential prediction accuracy and transferability.

Conclusions:

• Neural networks provide a highly accurate and efficient method for determining equations of state.
• Machine learning models can successfully perform inverse design of interatomic potentials.
• The inclusion of force data enhances the predictive power and applicability of neural networks in physical modeling.