Approximation of Anisotropic Pair Potentials Using Multivariate Interpolation.

Area of Science:

• Computational physics
• Materials science
• Mathematical modeling

Background:

• Modeling anisotropic particle interactions requires complex potential energy functions.
• Data-driven methods offer flexibility but demand large datasets, which are often costly to acquire.
• Existing methods face challenges in efficiently approximating anisotropic pair potentials.

Purpose of the Study:

• To investigate the use of multivariate polynomial interpolation for approximating anisotropic pair potentials.
• To develop a method that requires a limited set of training data.
• To address the computational cost associated with data collection for training.

Main Methods:

• Utilizing standard Chebyshev polynomial interpolation.
• Employing mixed-basis polynomial interpolation with trigonometric polynomials for periodic potentials.
• Refining interpolation domains and designing interpolants using mathematical and physical insights.
• Testing the approach on 2D and 3D model anisotropic nanoparticles.

Main Results:

• Demonstrated successful approximation of anisotropic pair potentials using limited data.
• Validated the effectiveness of both Chebyshev and mixed-basis interpolation methods.
• Showcased the applicability of the method across different dimensions (2D and 3D).

Conclusions:

• Multivariate polynomial interpolation provides an effective solution for approximating anisotropic pair potentials.
• The proposed method significantly reduces the dependency on large, computationally expensive training datasets.
• This technique offers a feasible and efficient approach for modeling complex particle interactions.