A smooth basis for atomistic machine learning.

Area of Science:

• Computational materials science
• Machine learning for physics and chemistry

Background:

• Machine learning models for materials science often use discretized atomic density descriptions.
• Choosing an appropriate radial basis for these descriptions remains a challenge.
• Existing methods lack a clear rationale for basis selection.

Purpose of the Study:

• To investigate a novel radial basis derived from the Laplacian eigenvalue problem.
• To evaluate the performance of this basis in atomic density representations and potential energy modeling.
• To establish the importance of basis function smoothness in machine learning for materials.

Main Methods:

• Solving the Laplacian eigenvalue problem within a sphere to generate a radial basis.
• Utilizing tensor products of Laplacian eigenstates for higher-order correlations.
• Assessing basis performance using unsupervised metrics and regression tasks.
• Comparing Laplacian eigenstate basis with existing heuristic and data-driven bases.

Main Results:

• The Laplacian eigenstate basis provides controllable smoothness, analogous to plane waves in periodic systems.
• This basis demonstrates superior performance compared to widely used sets and is competitive with optimized data-driven bases.
• Models using the Laplacian eigenstate basis achieve equal or improved regression performance for potential energy prediction.

Conclusions:

• The smoothness of basis functions is crucial for effective atomic density representations in machine learning.
• The Laplacian eigenstate basis offers a principled and high-performing approach for materials modeling.
• This work provides a new foundation for developing accurate and efficient machine learning potentials.