On the Completeness of Atomic Structure Representations

Abstract

Many-body descriptors are widely used to represent atomic environments in the construction of machine learned interatomic potentials and more broadly for fitting, classification and embedding tasks on atomic structures. It was generally believed that 3-body descriptors uniquely specify the environment of an atom, up to a rotation and permutation of like atoms. We produce several counterexamples to this belief, with the consequence that any classifier, regression or embedding model for atom-centred properties that uses 3 (or 4)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centred contributions mitigates, but does not eliminate, the impact of this fundamental deficiency -- explaining the success of current "machine-learning" force fields. We anticipate the issues that will arise as the desired accuracy increases, and suggest potential solutions.

References in corpus (24)

• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• On representing chemical environments
• Moment Tensor Potentials: a class of systematically improvable interatomic potentials
• Quantum-Chemical Insights from Deep Tensor Neural Networks
• Machine Learning of Accurate Energy-Conserving Molecular Force Fields
• A Spectral Analysis Method for Automated Generation of Quantum-Accurate Interatomic Potentials
• Machine Learning Unifies the Modelling of Materials and Molecules
• Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra
• Machine learning a general purpose interatomic potential for silicon
• Alchemical and structural distribution based representation for improved QML
• Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
• Hierarchical modeling of molecular energies using a deep neural network
• Automatic Selection of Atomic Fingerprints and Reference Configurations for Machine-Learning Potentials
• A Transferable Machine-Learning Model of the Electron Density
• Understanding molecular representations in machine learning: The role of uniqueness and target similarity
• Accurate Interatomic Force Fields via Machine Learning with Covariant Kernels
• Incorporating long-range physics in atomic-scale machine learning
• Accurate molecular polarizabilities with coupled-cluster theory and machine learning
• Atom-Density Representations for Machine Learning
• Efficient nonparametric $n$-body force fields from machine learning
• Metrics for measuring distances in configuration spaces
• Feature Optimization for Atomistic Machine Learning Yields A Data-Driven Construction of the Periodic Table of the Elements
• A fingerprint based metric for measuring similarities of crystalline structures
• Bispectrum Inversion with Application to Multireference Alignment

Cited by in corpus (66)

• Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems
• Big-Data Science in Porous Materials: Materials Genomics and Machine Learning
• Physics-inspired structural representations for molecules and materials
• GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations
• Machine learning for electronically excited states of molecules
• Machine-learning interatomic potentials for materials science
• SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects
• Unified Representation of Molecules and Crystals for Machine Learning
• Towards high-throughput superconductor discovery via machine learning
• General-purpose machine-learned potential for 16 elemental metals and their alloys
• A practical guide to machine learning interatomic potentials -- Status and future
• Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning
• Learning the electronic density of states in condensed matter
• Neural Network Potentials for Chemistry: Concepts, Applications and Prospects
• How to validate machine-learned interatomic potentials
• Machine Learning for Predicting Thermal Transport Properties of Solids
• Physically Motivated Recursively Embedded Atom Neural Networks: Incorporating Local Completeness and Nonlocality
• Tutorial: How to Train a Neural Network Potential
• Ephemeral data derived potentials for random structure search
• Complex ${\mathrm{Ga}}_2{\mathrm{O}}_3$ Polymorphs Explored by Accurate and General-Purpose Machine-Learning Interatomic Potentials
• A complete description of thermodynamic stabilities of molecular crystals
• The Evolution of Machine Learning Potentials for Molecules, Reactions and Materials
• MAISE: Construction of neural network interatomic models and evolutionary structure optimization
• Efficient implementation of atom-density representations
• Structural Dynamics Descriptors for Metal Halide Perovskites
• Convolutional neural networks enable high-fidelity prediction of path-dependent diffusion barrier spectra in multi-principal element alloys
• E(n)-Equivariant Cartesian Tensor Passing Potential
• Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions
• Model-free quantification of completeness, uncertainties, and outliers in atomistic machine learning using information theory
• Completeness of Atomic Structure Representations
• Lightweight and Effective Tensor Sensitivity for Atomistic Neural Networks
• UV-Visible Absorption Spectra of Solvated Molecules by Quantum Chemical Machine Learning
• Linear Jacobi-Legendre expansion of the charge density for machine learning-accelerated electronic structure calculations
• Through the eyes of a descriptor: Constructing complete, invertible descriptions of atomic environments
• Optimal radial basis for density-based atomic representations
• Kernel based quantum machine learning at record rate : Many-body distribution functionals as compact representations
• An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storage
• Phase Transition of Two-Dimensional Ferroelectric and Paraelectric Ga2O3 Monolayer: A Density Functional Theory and Machine-Learning Study
• Quantum chemical roots of machine-learning molecular similarity descriptors
• Inorganic synthesis-structure maps in zeolites with machine learning and crystallographic distances
• Ab initio machine learning of phase space averages
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• Geometry-enhanced graph neural network for learning the smoothness of glassy dynamics from static structure
• Decomposing Chemical Space: Applications to the Machine Learning of Atomic Energies
• Mean-Field Density Matrix Decompositions
• Probing the effects of broken symmetries in machine learning
• Symmetry-invariant quantum machine learning force fields
• Tell machine learning potentials what they are needed for: Simulation-oriented training exemplified for glycine
• Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four body interactions"
• Fast proper orthogonal descriptors for many-body interatomic potentials
• A neural network potential with self-trained atomic fingerprints: a test with the mW water potential
• Generic families of finite metric spaces with identical or trivial 1-dimensional persistence
• Inversion of the chemical environment representations
• Complete Neural Networks for Complete Euclidean Graphs
• Ab initio machine learning in chemical compound space
• Spectral Operator Representations
• Revving up 13C NMR shielding predictions across chemical space: Benchmarks for atoms-in-molecules kernel machine learning with new data for 134 kilo molecules
• Learning to Make Chemical Predictions: the Interplay of Feature Representation, Data, and Machine Learning Algorithms
• Resolving the Body-Order Paradox of Machine Learning Interatomic Potentials
• Representing spherical tensors with scalar-based machine-learning models
• Unified theory of atom-centered representations and message-passing machine-learning schemes
• Detect the Interactions that Matter in Matter: Geometric Attention for Many-Body Systems
• Compressing local atomic neighbourhood descriptors
• Machine learning of electronic structure and atomistic properties from the external potential
• REANN: A PyTorch-based End-to-End Multi-functional Deep Neural Network Package for Molecular, Reactive and Periodic Systems
• Smooth Overlap of Spin Orientations: Machine Learning Exchange Fields for Ab-initio Spin Dynamics