Approximation of forces and torques from anisotropic pairwise interactions using multivariate polynomials.

Area of Science:

• Computational physics
• Materials science
• Nanotechnology

Background:

• Simulating anisotropic particle dynamics is complex due to challenging force and torque representations.
• Existing data-driven methods often require extensive training datasets, which are difficult to obtain.

Purpose of the Study:

• To extend a framework for approximating anisotropic pair potentials to pairwise forces and torques.
• To develop accurate approximations using limited data for particle dynamics.

Main Methods:

• Utilized multivariate polynomials and physics-motivated coordinate transformations.
• Derived expressions relating forces and torques to partial derivatives of approximated potential energy.
• Explored and assessed options for approximating pairwise interactions from force and torque measurements.

Main Results:

• The framework accurately approximates forces and torques using limited data.
• Interpolation of pairwise potential energy yielded the best results when potential energy was known.
• Force and torque matching (regression) proved effective when only force and torque data were available.

Conclusions:

• The developed framework offers an efficient method for simulating anisotropic particle dynamics.
• The approach reduces the need for large datasets in computational simulations.
• Both potential energy interpolation and force/torque matching are viable strategies depending on data availability.