A perspective marking 20 years of using permutationally invariant polynomials for molecular potentials

Area of Science:

• Computational chemistry
• Materials science
• Machine learning

Background:

• Permutationally invariant polynomials (PIPs) were introduced in 2004.
• PIPs are crucial for developing machine learned potentials (MLPs) that respect fundamental symmetries of potential energy surfaces.

Purpose of the Study:

• To provide a comprehensive overview of the progress and applications of PIPs in developing MLPs since 2018.
• To highlight the advantages of PIPs, such as their invariance to atom permutations and use of global descriptors.

Main Methods:

• Review of literature on PIPs and their applications in MLPs.
• Discussion of PIPs' use in linear regression, neural networks, and Gaussian process regression.
• Focus on PIPs' role in modeling chemical reactions, clusters, condensed phases, and materials.

Main Results:

• Over 100 potentials utilizing PIPs have been reported for diverse systems.
• PIPs enable accurate modeling of complex energy landscapes, including chemical reactions with multiple product channels.
• PIPs have been successfully integrated into various machine learning frameworks for high-accuracy predictions.

Conclusions:

• PIPs are a powerful and versatile tool for constructing accurate and efficient machine learned potentials.
• The continued development and application of PIPs are advancing the field of computational chemistry and materials science.
• PIPs offer a robust approach to incorporating fundamental physical symmetries into machine learning models.