Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions

Abstract

Atomic fingerprints are commonly used for the characterization of local environments of atoms in machine learning and other contexts. In this work, we study the behavior of two widely used fingerprints, namely the smooth overlap of atomic positions (SOAP) and the atom-centered symmetry functions (ACSF), under finite changes of atomic positions and demonstrate the existence of manifolds of quasi-constant fingerprints. These manifolds are found numerically by following eigenvectors of the sensitivity matrix with quasi-zero eigenvalues. The existence of such manifolds in ACSF and SOAP causes a failure to machine learn four-body interactions such as torsional energies that are part of standard force fields. No such manifolds can be found for the Overlap Matrix (OM) fingerprint due to its intrinsic many-body character.

8 pages, 5 figures

References in corpus (6)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• A Spectral Analysis Method for Automated Generation of Quantum-Accurate Interatomic Potentials
• Comment on "Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning"
• A Novel Approach to Describe Chemical Environments in High Dimensional Neural Network Potentials
• An assessment of the structural resolution of various fingerprints commonly used in machine learning
• BenchML: an extensible pipelining framework for benchmarking representations of materials and molecules at scale

Cited by in corpus (10)

• GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations
• Neural Network Potentials for Chemistry: Concepts, Applications and Prospects
• Spin-Dependent Graph Neural Network Potential for Magnetic Materials
• Roadmap on machine learning glassy dynamics
• Completeness of Atomic Structure Representations
• Describe, Transform, Machine Learning: Feature Engineering for Grain Boundaries and Other Variable-Sized Atom Clusters
• A smooth basis for atomistic machine learning
• Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four body interactions"
• EOSnet: Embedded Overlap Structures for Graph Neural Networks in Predicting Material Properties
• Spectral Operator Representations