Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons

Abstract

We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, derived from quantum mechanical calculations. The resulting model does not have a fixed functional form and hence is capable of modeling complex potential energy landscapes. It is systematically improvable with more data. We apply the method to bulk carbon, silicon and germanium and test it by calculating properties of the crystals at high temperatures. Using the interatomic potential to generate the long molecular dynamics trajectories required for such calculations saves orders of magnitude in computational cost.

v3-4: added new material and references

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• Constructing and evaluating machine-learned interatomic potentials for Li-based disordered rocksalts
• Modeling Extensive Defects in Metals through Classical Potential-Guided Sampling and Automated Configuration Reconstruction
• Anomalous phase separation dynamics in a correlated electron system: machine-learning enabled large-scale kinetic Monte Carlo simulations
• Modeling of many-body interactions between elastic spheres through symmetry functions
• Stress and heat flux via automatic differentiation
• Reducing the cost of neural network potential generation for reactive molecular systems
• Intramolecular and water mediated tautomerism of solvated glycine
• Gaussian Process States: A data-driven representation of quantum many-body physics
• Computational study of crystal defects formation in Mo by machine learned molecular dynamics simulations
• Machine learning reconstruction of depth-dependent thermal conductivity profile from pump-probe thermoreflectance signals
• The fundamentals of quantum machine learning
• Sampling algorithms for validation of supervised learning models for Ising-like systems
• DeePKS+ABACUS as a Bridge between Expensive Quantum Mechanical Models and Machine Learning Potentials
• Understanding the flat thermal conductivity of La2Zr2O7 at ultrahigh temperatures
• Predicting ionic conductivity in solids from the machine-learned potential energy landscape
• Transferable and Robust Machine Learning Model for Predicting Stability of Si Anodes for Multivalent Cation Batteries
• Neural Networks Potential from the Bispectrum Component: A Case Study on Crystalline Silicon
• Data-Driven Dynamical Mean-Field Theory: an error-correction approach to solve the quantum many-body problem using machine learning
• FeNNol: an Efficient and Flexible Library for Building Force-field-enhanced Neural Network Potentials
• Optimized Multifidelity Machine Learning for Quantum Chemistry
• Self-learning hybrid Monte Carlo method for isothermal-isobaric ensemble: Application to liquid silica
• Infrared spectra of neutral polycyclic aromatic hydrocarbons by machine learning
• Machine learning for phase ordering dynamics of charge density waves
• GPU-Accelerated Approximate Kernel Method for Quantum Machine Learning
• Machine-Learned Atomic Cluster Expansion Potentials for Fast and Quantum-Accurate Thermal Simulations of Wurtzite AlN
• A machine learning potential for simulating infrared spectra of nanosilicate clusters
• Thermal conductivity of Li${}_3$PS${}_4$ solid electrolytes with ab initio accuracy
• Phase Transition Pathway Sampling via Swarm Intelligence and Graph Theory
• Machine learning predictions for local electronic properties of disordered correlated electron systems
• Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties
• A collinear-spin machine learned interatomic potential for Fe${}_7$Cr${}_2$Ni alloy
• Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields
• Analytical Gradients for Molecular-Orbital-Based Machine Learning
• Dynamical theory of angle-resolved electron energy loss and gain spectroscopies of phonons and magnons in transmission electron microscopy including multiple scattering effects
• Hydrogen-induced degradation dynamics in silicon heterojunction solar cells via machine learning
• Exploring the design space of machine-learning models for quantum chemistry with a fully differentiable framework
• Machine-learning of atomic-scale properties based on physical principles
• Fully analytic valence force field model for the elastic and inner elastic properties of diamond and zincblende crystals
• Transferable Interatomic Potentials for Aluminum from Ambient Conditions to Warm Dense Matter
• Modelling complex proton transport phenomena -- Exploring the limits of fine-tuning and transferability of foundational machine-learned force fields
• Mean-Field Density Matrix Decompositions
• Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning
• Exploring Li-ion Transport Properties of Li${}_3$TiCl${}_6$: A Machine Learning Molecular Dynamics Study
• Understanding High-Temperature Chemical Reactions on Metal Surfaces
• Defects induce phase transition from dynamic to static rippling in graphene
• Ab initio Canonical Sampling based on Variational Inference
• Phase transitions of LaMnO${}_3$ and SrRuO${}_3$ from DFT + U based machine learning force fields simulations
• Quantum Gaussian process model of potential energy surface for a polyatomic molecule
• Deep Density: circumventing the Kohn-Sham equations via symmetry preserving neural networks
• Proper Orthogonal Descriptors for Efficient and Accurate Interatomic Potentials
• Complex Strengthening Mechanisms in the NbMoTaW Multi-Principal Element Alloy
• How Graph Neural Network Interatomic Potentials Extrapolate: Role of the Message-Passing Algorithm
• Validation Workflow for Machine Learning Interatomic Potentials for Complex Ceramics
• Predicting hot-electron free energies from ground-state data
• Super-resolution in Molecular Dynamics Trajectory Reconstruction with Bi-Directional Neural Networks
• Transferable empirical pseudopotenials from machine learning
• Construction of Machine Learned Force Fields with Quantum Chemical Accuracy: Applications and Chemical Insights
• Studies of Ni-Cr complexation in FLiBe molten salt using machine learning interatomic potentials
• Nuclear quantum effects in thermal conductivity from centroid molecular dynamics
• Probing the effects of broken symmetries in machine learning
• Segregation, ordering, and precipitation in WTaV-based concentrated refractory alloys
• Probing the state of hydrogen in $\delta$-AlOOH at mantle conditions with machine learning potential
• Training models using forces computed by stochastic electronic structure methods
• Multitask methods for predicting molecular properties from heterogeneous data
• Deep-learning-based prediction of the tetragonal$\to$cubic transition in davemaoite
• DPmoire: A tool for constructing accurate machine learning force fields in moiré systems
• Melting Temperature of Iron Under the Earth's Inner Core Condition from Deep Machine Learning
• A Hessian-Based Assessment of Atomic Forces for Training Machine Learning Interatomic Potentials
• Crystal structure identification with 3D convolutional neural networks with application to high-pressure phase transitions in SiO${}_2$
• Accurate prediction of structural and mechanical properties on amorphous materials enabled through machine-learning potentials: a case study of silicon nitride
• Building nonparametric $n$-body force fields using Gaussian process regression
• Imeall: A Computational Framework for the Calculation of the Atomistic Properties of Grain Boundaries
• Adaptive Exploration and Optimization of Materials Crystal Structures
• Correction of coarse-graining errors by a two-level method: application to the Asakura-Oosawa model
• The phase stability of large-size nanoparticle alloy catalysts at ab initio quality using a nearsighted force-training approach
• Metatensor and metatomic: foundational libraries for interoperable atomistic machine learning
• Shadow molecular dynamics and atomic cluster expansions for flexible charge models
• Size and Quality of Quantum Mechanical Data Sets for Training Neural Network Force Fields for Liquid Water
• Machine learning for structure-property relationships: Scalability and limitations
• Ab initio electron-lattice downfolding: potential energy landscapes, anharmonicity, and molecular dynamics in charge density wave materials
• Training-free hyperparameter optimization of neural networks for electronic structures in matter
• Accurate Molecular Dynamics Enabled by Efficient Physically-Constrained Machine Learning Approaches
• Machine learning potentials for complex aqueous systems made simple
• Prediction rigidities for data-driven chemistry
• Modeling of effective interactions between ligand coated nanoparticles through symmetry functions
• Gaussian Process Regression Adaptive Density-Guided Approach: Towards Calculations of Potential Energy Surfaces for Larger Molecules
• Pre-training, fine-tuning, and distillation (PFD): Automatically generating machine learning force fields from universal models
• Tell machine learning potentials what they are needed for: Simulation-oriented training exemplified for glycine
• Uncertainty Quantification in Atomistic Simulations of Silicon using Interatomic Potentials
• Machine learning for accuracy in density functional approximations
• Active learning for parameter-free multiscale modeling of boundary lubrication
• Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules
• Extending the atomic decomposition and many-body representation, a chemistry-motivated monomer-centered approach for machine learning potentials
• Machine Learning and Materials Informatics: Recent Applications and Prospects
• A smooth basis for atomistic machine learning
• Machine Learning Potentials for Hydrogen Absorption in TiCr${}_2$ Laves Phases
• A classical reactive potential for molecular clusters of sulphuric acid and water
• Fitting to magnetic forces improves the reliability of magnetic Moment Tensor Potentials
• Temperature effects on the point defects formation in [111] W by neutron induced collision cascade
• Machine-learning enabled optimization of atomic structures using atoms with fractional existence
• Iterative charge equilibration for fourth-generation high-dimensional neural network potentials
• Automated atomistic simulations of dissociated dislocations with ab initio accuracy
• Locality of Interatomic Forces in Tight Binding Models for Insulators
• Cluster-based multidimensional scaling embedding tool for data visualization
• Fast proper orthogonal descriptors for many-body interatomic potentials
• Equivariant Neural Networks for Spin Dynamics Simulations of Itinerant Magnets
• Developing Potential Energy Surfaces for Graphene-based 2D-3D Interfaces from Modified High Dimensional Neural Networks for Applications in Energy Storage
• Nonlinear Elasticity from Atomistic Mechanics
• Interpolating many-body wave functions for accelerated molecular dynamics on the near-exact electronic surface
• AI-accelerated Materials Informatics Method for the Discovery of Ductile Alloys
• Constitutive relations for plasticity of amorphous carbon
• Efficient moment tensor machine-learning interatomic potential for accurate description of defects in Ni-Al Alloys
• Reliable computational prediction of supramolecular ordering of complex molecules under electrochemical conditions
• Graph-neural-network predictions of solid-state NMR parameters from spherical tensor decomposition
• $\Delta$-model correction of Foundation Model based on the models own understanding
• Efficient Generation of Stable Linear Machine-Learning Force Fields with Uncertainty-Aware Active Learning
• Molecular Dipole Moment Learning via Rotationally Equivariant Gaussian Process Regression with Derivatives in Molecular-orbital-based Machine Learning
• A Fully Quantum-Mechanical Treatment for Kaolinite
• Neural-networks model for force prediction in multi-principal-element alloys
• Aqueous Solution Chemistry In Silico and the Role of Data Driven Approaches
• Equivariant Machine Learning Interatomic Potentials with Global Charge Redistribution
• Machine learning based modeling of disordered elemental semiconductors: understanding the atomic structure of a-Si and a-C
• Benchmarking CHGNet Universal Machine Learning Interatomic Potential Against DFT and EXAFS: Case of Layered WS2 and MoS2
• Efficient ensemble uncertainty estimation in Gaussian Processes Regression
• Morphological evolution via surface diffusion learned by convolutional, recurrent neural networks: extrapolation and prediction uncertainty
• Machine learning interatomic potential for predicting the thermal properties of uranium nitride
• On-the-fly machine learning-augmented constrained AIMD to design new routes from glassy carbon to quenchable amorphous diamond with low pressure and temperature
• Reconstructions and Dynamics of $\beta$-Lithium Thiophosphate Surfaces
• Active-learning-based efficient prediction of ab-initio atomic energy: a case study on a Fe random grain boundary model with millions of atoms
• Rigorous body-order approximations of an electronic structure potential energy landscape
• Insights into one-body density matrices using deep learning
• Modeling refractory high-entropy alloys with efficient machine-learned interatomic potentials: defects and segregation
• Compressing and forecasting atomic material simulations with descriptors
• Superconductor discovery in the emerging paradigm of Materials Informatics
• Learning intermolecular forces at liquid-vapor interfaces
• Deep Learning Inter-atomic Potential for Thermal and Phonon Behaviour of Silicon Carbide with Quantum Accuracy
• Critical assessment of machine-learned repulsive potentials for the Density Functional based Tight-Binding method: a case study for pure silicon
• EOSnet: Embedded Overlap Structures for Graph Neural Networks in Predicting Material Properties
• Determining ground states of alloy by a symmetry-based classification
• Inversion of the chemical environment representations
• The impact of static distortion waves on superlubricity
• Equivariant Tensor Network Potentials
• Embedding quantum statistical excitations in a classical force field
• Modeling Chemical Exfoliation of Non-van der Waals Chromium Sulfides by Machine Learning Interatomic Potentials and Monte Carlo Simulations
• Maximum volume simplex method for automatic selection and classification of atomic environments and environment descriptor compression
• Accelerated lignocellulosic molecule adsorption structure determination
• Predictive power of polynomial machine learning potentials for liquid states in 22 elemental systems
• Kinetics of orbital ordering in cooperative Jahn-Teller models: Machine-learning enabled large-scale simulations
• Application-specific machine-learned interatomic potentials: exploring the trade-off between DFT convergence, MLIP expressivity, and computational cost
• Multi-head committees enable direct uncertainty prediction for atomistic foundation models
• Atomistic Simulations of Oxide-Water Interfaces using Machine Learning Potentials
• Fine-Tuning Unifies Foundational Machine-learned Interatomic Potential Architectures at ab initio Accuracy
• Titanium-hydrogen interaction at megabar pressure
• Accessing negative Poisson`s ratio of graphene by machine learning interatomic potentials
• On the equivalence of molecular graph convolution and molecular wave function with poor basis set
• Particle Swarm Based Hyper-Parameter Optimization for Machine Learned Interatomic Potentials
• Steerable Wavelet Scattering for 3D Atomic Systems with Application to Li-Si Energy Prediction
• Localized Coulomb Descriptors for the Gaussian Approximation Potential
• Adaptive-precision potentials for large-scale atomistic simulations
• Free energy profiles for chemical reactions in solution from high-dimensional neural network potentials: The case of the Strecker synthesis
• Machine-Learning Surrogate Model for Accelerating the Search of Stable Ternary Alloys
• Unveiling the Lithium-Ion Transport Mechanism in Li2ZrCl6 Solid-State Electrolyte via Deep Learning-Accelerated Molecular Dynamics Simulations
• Dynamical Heterogeneity in Supercooled Water and its Spectroscopic Fingerprints
• Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schrödinger Equation
• Gaussian processes for choosing laser parameters for driven, dissipative Rydberg aggregates
• Structural Characterization of Grain Boundaries and Machine Learning of Grain Boundary Energy and Mobility
• Machine learning interatomic potential for the low-modulus Ti-Nb-Zr alloys in the vicinity of dynamical instability
• Large-scale cooperative sulfur vacancy dynamics in two-dimensional MoS2 from machine learning interatomic potentials
• Guest Editorial: Special Topic on Software for Atomistic Machine Learning
• Atomistic Graph Neural Networks for metals: Application to bcc iron
• Rapid Exploration of Optimization Strategies on Advanced Architectures using TestSNAP and LAMMPS
• High-performance descriptor for magnetic materials: Accurate discrimination of magnetic structure
• Ab initio machine learning in chemical compound space
• Symmetry- and Gradient-enhanced Gaussian Process Regression for the Active Learning of Potential Energy Surfaces in Porous Materials
• Testing Outlier Detection Algorithms for Identifying Early-Stage Solute Clusters in Atom Probe Tomography
• Accurate Machine Learning Interatomic Potentials for Polyacene Molecular Crystals: Application to Single Molecule Host-Guest Systems
• Discovery of Novel Silicon Allotropes with Optimized Band Gaps to Enhance Solar Cell Efficiency through Evolutionary Algorithms and Machine Learning
• Viscosity, breakdown of Stokes-Einstein relation and dynamical heterogeneity in supercooled liquid Ge${}_2$Sb${}_2$Te${}_5$ from simulations with a neural network potential
• Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired Neural Networks for the 3D microstructure evolution of materials via Cahn-Hilliard flow
• Machine Learning Force Field for Thermal Oxidation of Silicon
• Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions
• Parameterizing empirical interatomic potentials for predicting thermophysical properties via an irreducible derivative approach: the case of ThO${}_2$ and UO${}_2$
• Structure and thermodynamics of defects in Na-feldspar from a neural network potential
• Zero Shot Molecular Generation via Similarity Kernels
• Efficient sampling of atomic configurational spaces
• Machine Learning Accelerated Computational Surface-Specific Vibrational Spectroscopy Reveals Oxidation Level of Graphene in Contact with Water
• Data Fusion of Deep Learned Molecular Embeddings for Property Prediction
• Low-rank matrix and tensor approximations for compression of machine-learning interatomic potentials
• Efficient GPU-Accelerated Training of a Neuroevolution Potential with Analytical Gradients
• Atomistic understanding of hydrogen bubble-induced embrittlement in tungsten enabled by machine learning molecular dynamics
• Point-Pattern Matching Technique for Local Structural Analysis in Condensed Matter
• Towards Improved Quantum Machine Learning for Molecular Force Fields
• Quantitative analysis of the prediction performance of a Convolutional Neural Network evaluating the surface elastic energy of a strained film
• GeoT: A Geometry-aware Transformer for Reliable Molecular Property Prediction and Chemically Interpretable Representation Learning
• Nanoindentation induced plasticity in equiatomic MoTaW alloys by experimentally guided machine learning molecular dynamics simulations
• Orbital Mixer: Using Atomic Orbital Features for Basis Dependent Prediction of Molecular Wavefunctions
• The Homunculus Brain and Categorical Logic
• FaVAD: A software workflow for characterisation and visualizing of defects in crystalline structures
• Symmetry-broken ground state and phonon mediated superconductivity in Kagome CsV${}_3$Sb${}_5$
• Flexible dual-branched message passing neural network for quantum mechanical property prediction with molecular conformation
• Probing the Temporal Response of Liquid Water to a THz Pump Pulse Using Machine Learning-Accelerated Non-Equilibrium Molecular Dynamics
• Locality of Interatomic Interactions in Self-Consistent Tight Binding Models
• On Simulating Thin-Film Processes at the Atomic Scale Using Machine Learned Force Fields
• Radiation damage and phase stability of Al${}_x$CrCuFeNi${}_y$ alloys using a machine-learned interatomic potential
• A general formalism for machine-learning models based on multipolar-spherical harmonics
• Standing Wave Decomposition Gaussian Process
• Mapping the Structure of Oxygen-Doped Wurtzite Aluminum Nitride Coatings From Ab Initio Random Structure Search and Experiments
• First Principles Validation of Energy Barriers in Ni${}_{75}$Al${}_{25}$
• An Electrostatic Spectral Neighbor Analysis Potential (eSNAP) for Lithium Nitride
• Machine-Learned Potentials for Solvation Modeling
• Machine-Learned Bond-Order Potential for Exploring the Configuration Space of Carbon
• Structural transitions in dense disordered silicon from quantum-accurate ultra-large-scale simulations
• Modular hybrid machine learning and physics-based potentials for scalable modeling of van der Waals heterostructures
• Crystal Nucleation in Eutectic Al-Si Alloys by Machine-Learned Molecular Dynamics
• Representing spherical tensors with scalar-based machine-learning models
• Active Δ-learning with universal potentials for global structure optimization
• The Photochemical Birth of the Hydrated Electron in Liquid Water
• Resolving the Body-Order Paradox of Machine Learning Interatomic Potentials
• First principles interatomic potential for tungsten based on Gaussian process regression
• Scalable Data-Driven Basis Selection for Linear Machine Learning Interatomic Potentials
• Thermal conductivities of monolayer graphene oxide from machine learning molecular dynamics simulations
• Multi-objective optimization and quantum hybridization of equivariant deep learning interatomic potentials
• Self-consistency error correction for accurate machine learning potentials from variational Monte Carlo
• Machine-learning force-field models for dynamical simulations of metallic magnets
• Fine-tuning of universal machine-learning interatomic potentials for high-entropy alloys with application to 2D (Mo,Ta,Nb,W,V)S${}_2$
• Benchmarking Chemically Scalable Machine-Learning Interatomic Potentials for Large-Scale Simulations of Multicomponent Alloys
• Automated Prediction of Thermodynamic Properties via Bayesian Free-Energy Reconstruction from Molecular Dynamics
• High-pressure melting and elastic behavior of vanadium and niobium based on ab initio and machine learning molecular dynamics
• Accelerating Complex Materials Discovery with Universal Machine-Learning Potential-Driven Structure Prediction
• Experimental Evidence of Quantum Drude Oscillator Behavior in Liquids Revealed with Probabilistic Iterative Boltzmann Inversion
• Scalable Training of Neural Network Potentials for Complex Interfaces Through Data Augmentation
• Exact average many-body interatomic interaction model for random alloys
• From Local Atomic Environments to Molecular Information Entropy
• Efficient interpolation of molecular properties across chemical compound space with low-dimensional descriptors
• Development of data-driven spd tight-binding models of Fe -- parameterisation based on QSGW and DFT calculations including information about higher-order elastic constants
• Atomistic Global Optimization X: A Python package for optimization of atomistic structures
• Deep Residual Networks Learn the Geodesic Curve in the Wasserstein Space
• Robust recognition and exploratory analysis of crystal structures via Bayesian deep learning
• Machine learning dynamics of phase separation in correlated electron magnets
• Machine learning approaches for analyzing and enhancing molecular dynamics simulations
• Pushing the limits of atomistic simulations towards ultra-high temperature: a machine-learning force field for ZrB2
• Nanoindentation simulations for copper and tungsten with adaptive-precision potentials
• Thermal transport and phase transitions of zirconia by on-the-fly machine-learned interatomic potentials
• REANN: A PyTorch-based End-to-End Multi-functional Deep Neural Network Package for Molecular, Reactive and Periodic Systems
• Deep machine learning potentials for multicomponent metallic melts: development, predictability and compositional transferability
• A2I Transformer: Permutation-equivariant attention network for pairwise and many-body interactions with minimal featurization
• Systematic global structure search of bismuth-based binary systems under pressure using machine learning potentials
• Neural Polarization: Toward Electron Density for Molecules by Extending Equivariant Networks
• Gradient-based grand canonical optimization enabled by graph neural networks with fractional atomic existence
• Compressing local atomic neighbourhood descriptors
• Dynamically polarisable force-fields for surface simulations via multi-output classification Neural Networks
• Machine learning approach for vibronically renormalized electronic band structures
• Accelerating a hybrid continuum-atomistic fluidic model with on-the-fly machine learning
• Active Learning of a Neural Network Potential for Large-Scale Atomistic Simulations of Polymer Electrolyte Membranes
• Assessing zero-shot generalisation behaviour in graph-neural-network interatomic potentials
• Graph Neural Network for Hamiltonian-Based Material Property Prediction
• Cluster Fragments in Amorphous Phosphorus and their Evolution under Pressure
• Macro-Dipole-Constrainted Learning of Atomic Charges for Accurate Electrostatic Potentials at Electrochemical Interfaces
• Active learning of potential-energy surfaces of weakly-bound complexes with regression-tree ensembles
• Superheated solid state induced by a single collision event
• Improved capabilities of the TurboGAP code for radiation induced cascade simulations: an illustration with silicon
• Surfing multiple conformation-property landscapes via machine learning: Designing magnetic anisotropy
• Machine Learning Study of Surface Reconstructions of the Cu${}_2$O(111) Surface
• Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems
• The ground state of CuInP${}_2$S${}_6$ thin films: A study of the deep potential method
• Fast and accurate quasi-atom method for simultaneous atomistic and continuum simulation of solids
• Machine learning of electronic structure and atomistic properties from the external potential
• Faster Molecular Dynamics with Neural Network Potentials via Distilled Multiple Time-Stepping and Non-Conservative Forces
• Detect the Interactions that Matter in Matter: Geometric Attention for Many-Body Systems
• Critical point for de-mixing of binary hard spheres
• QM/MM Methods for Crystalline Defects. Part 3: Machine-Learned Interatomic Potentials
• Efficient Data Selection Methods for the Development of Machine Learned Potentials
• Interpolation and extrapolation of global potential energy surfaces for polyatomic systems by Gaussian processes with composite kernels
• Smooth Overlap of Spin Orientations: Machine Learning Exchange Fields for Ab-initio Spin Dynamics
• NQCDynamics.jl: A Julia Package for Nonadiabatic Quantum Classical Molecular Dynamics in the Condensed Phase
• Pairwise interactions for Potential energy surfaces and Atomic forces with Deep Neural network