Parallel Multistream Training of High-Dimensional Neural Network Potentials.

Over the past years high-dimensional neural network potentials (HDNNPs), fitted to accurately reproduce ab initio potential energy surfaces, have become a powerful tool in chemistry, physics and materials science. Here, we focus on the training of the neural networks that lies at the heart of the HDNNP method. We present an efficient approach for optimizing the weight parameters of the neural network via multistream Kalman filtering, using potential energies and forces as reference data. In this procedure, the choice of the free parameters of the Kalman filter can have a significant impact on the fit quality. Carrying out a large parameter study, we determine optimal settings and demonstrate how to optimize training results of HDNNPs. Moreover, we illustrate our HDNNP training approach by revisiting previously presented fits for water and developing a new potential for copper sulfide. This material, accessible in computer simulations so far only via first-principles methods, forms a particularly complex solid structure at low temperatures and undergoes a phase transition to a superionic state upon heating. Analyzing MD simulations carried out with the Cu2S HDNNP, we confirm that the underlying ab initio reference method indeed reproduces this behavior.

• Publication year

  2019

• Venue

  Journal of Chemical Theory and Computation

• Publication date

  2019-04-17

• Fields of study

  Physics, Materials Science, Chemistry, Computer Science, Medicine

• Identifiers
  DOI 10.1021/acs.jctc.8b01092PMID 30995035
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Library-Based LAMMPS Implementation of High-Dimensional Neural Network Potentials.

  2019cited by this paper
• Density anomaly of water at negative pressures from first principles

  2018cited by this paper
• Automatic selection of atomic fingerprints and reference configurations for machine-learning potentials.

  2018cited by this paper
• Machine learning for molecular and materials science

  2018cited by this paper
• Constructing first-principles phase diagrams of amorphous LixSi using machine-learning-assisted sampling with an evolutionary algorithm.

  2018cited by this paper
• First Principles Neural Network Potentials for Reactive Simulations of Large Molecular and Condensed Systems.

  2017cited by this paper
• wACSF-Weighted atom-centered symmetry functions as descriptors in machine learning potentials.

  2017cited by this paper
• Compound Copper Chalcogenide Nanocrystals.

  2017cited by this paper
• Accurate Neural Network Description of Surface Phonons in Reactive Gas–Surface Dynamics: N2 + Ru(0001)

  2017cited by this paper
• An implementation of artificial neural-network potentials for atomistic materials simulations: Performance for TiO2

  2016cited by this paper
• Neural network molecular dynamics simulations of solid-liquid interfaces: water at low-index copper surfaces.

  2016cited by this paper
• Structure of aqueous NaOH solutions: insights from neural-network-based molecular dynamics simulations.

  2016cited by this paper
• Perspective: Machine learning potentials for atomistic simulations.

  2016cited by this paper
• How van der Waals interactions determine the unique properties of water

  2016cited by this paper
• Machine learning: Trends, perspectives, and prospects

  2015cited by this paper
• Constructing high‐dimensional neural network potentials: A tutorial review

  2015cited by this paper
• Machine learning for quantum mechanics in a nutshell

  2015cited by this paper
• Representing the potential-energy surface of protonated water clusters by high-dimensional neural network potentials.

  2015cited by this paper
• High-Dimensional Neural Network Potentials for Organic Reactions and an Improved Training Algorithm.

  2015cited by this paper
• Representing potential energy surfaces by high-dimensional neural network potentials

  2014cited by this paper
• Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials

  2014cited by this paper
• The mechanism of ultrafast structural switching in superionic copper (I) sulphide nanocrystals

  2013cited by this paper
• A Full-Dimensional Neural Network Potential-Energy Surface for Water Clusters up to the Hexamer

  2013cited by this paper
• Neural network potentials for metals and oxides – First applications to copper clusters at zinc oxide

  2013cited by this paper
• An introduction to the tools hosted in the Bilbao Crystallographic Server

  2012cited by this paper
• Construction of high-dimensional neural network potentials using environment-dependent atom pairs.

  2012cited by this paper
• High chalcocite Cu2S: a solid-liquid hybrid phase.

  2012cited by this paper
• Assembled monolayer nanorod heterojunctions.

  2011cited by this paper
• Observation of Transient Structural-Transformation Dynamics in a Cu2S Nanorod

  2011cited by this paper
• α-Chalcocite Nanoparticle Synthesis and Stability

  2011cited by this paper
• Fast and accurate modeling of molecular atomization energies with machine learning.

  2011cited by this paper
• Atom-centered symmetry functions for constructing high-dimensional neural network potentials.

  2011cited by this paper
• Size Dependence of a Temperature-Induced Solid-Solid Phase Transition in Copper(I) Sulfide

  2011cited by this paper
• A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu.

  2010cited by this paper
• Efficient sampling of atomic configurational spaces.

  2009cited by this paper
• Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons.

  2009cited by this paper
• Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks.

  2009cited by this paper
• Synthesis and photovoltaic application of copper(I) sulfide nanocrystals.

  2008cited by this paper
• Generalized neural-network representation of high-dimensional potential-energy surfaces.

  2007cited by this paper
• Bilbao Crystallographic Server: I. Databases and crystallographic computing programs

  2006cited by this paper
• Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups.

  2006cited by this paper
• Neural Network Models of Potential Energy Surfaces:  Prototypical Examples.

  2005cited by this paper
• Time series prediction with a weighted bidirectional multi-stream extended Kalman filter

  2004cited by this paper
• A New Approach to Linear Filtering and Prediction Problems

  2002cited by this paper
• Machine learning for science: state of the art and future prospects.

  2001cited by this paper
• Kalman Filtering and Neural Networks

  2001cited by this paper
• A signal processing framework based on dynamic neural networks with application to problems in adaptation, filtering, and classification

  1998cited by this paper
• Generalized Gradient Approximation Made Simple.

  1996cited by this paper
• Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

  1996cited by this paper
• Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.

  1996cited by this paper
• Ab initio molecular dynamics for liquid metals.

  1995cited by this paper
• A Limited Memory Algorithm for Bound Constrained Optimization

  1995cited by this paper
• Projector augmented-wave method.

  1994cited by this paper
• Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium.

  1994cited by this paper
• Training feedforward networks with the Marquardt algorithm

  1994cited by this paper
• Adaptive, global, extended Kalman filters for training feedforward neural networks

  1994cited by this paper
• Fast parallel algorithms for short-range molecular dynamics

  1993cited by this paper
• Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density.

  1988cited by this paper
• Density-functional exchange-energy approximation with correct asymptotic behavior.

  1988cited by this paper
• Learning representations by back-propagating errors

  1986cited by this paper
• The crystal structures of low chalcocite and djurleite

  1979cited by this paper
• Crystal Structure of Low Chalcocite

  1971cited by this paper
• A New Approach to Variable Metric Algorithms

  1970cited by this paper
• The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations

  1970cited by this paper
• ON THE STATISTICAL DISTRIBUTION OF COPPER IONS IN THE STRUCTURE OF β -CHALCOCITE

  1965cited by this paper
• Distribution of Atoms in High Chalcocite, Cu2S

  1963cited by this paper
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters

  1963cited by this paper
• New Results in Linear Filtering and Prediction Theory

  1961cited by this paper
• A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES

  1944cited by this paper

• Machine learning interatomic potentials for lithium battery electrolyte design

  2026cites this paper
• Transition from Vehicular to Structural Ionic Transport in Electrified Alkali Aqueous Solutions.

  2026cites this paper
• Machine-learning interatomic potentials for interfaces in all-solid-state batteries: Perspectives on training data, model selection, and validation

  2026cites this paper
• Oxygen vacancy diffusion in davemaoite (CaSiO3 perovskite): Implications for the redox equilibrium and the electrical conductivity of Earth’s lower mantle

  2026cites this paper
• Machine-Learning Ice Spectra: From 1 to 256 Features.

  2026cites this paper
• Insights into Ethylene Deep Oxidation on Pd–Au Bimetallic Catalysts: From Surface Dynamics to Pathway Selectivity

  2026cites this paper
• Quantitative composition‑annealing temperature map of stacking‑fault energy in CoCrNi medium‑entropy alloys unveiled by first‑principles neural‑network potentials

  2026cites this paper
• Atomistic simulation of Guinier–Preston zone nucleation kinetics in Al–Cu alloys: A neural network-driven kinetic Monte Carlo approach

  2025cites this paper
• Machine Learning Molecular Dynamics Simulations of Materials with Complex Structures

  2025influential citation
• A Portable Data Set for Borophene Growth Modeling with Reactive Neural Network Potentials

  2025cites this paper
• Foundation models for metallurgy?

  2025cites this paper
• dpdata: A Scalable Python Toolkit for Atomistic Machine Learning Data Sets

  2025cites this paper
• Theoretical study of large-scale graphene on the Cu(111) surface using machine learning potential.

  2025cites this paper
• Insights into the Structure and Dynamics of Water at Co3O4${\rm Co}_3{\rm O}_4$ (001) Using a High‐Dimensional Neural Network Potential

  2025cites this paper
• Molecular dynamics modeling in catalyst layer development for PEM fuel cell

  2025cites this paper
• Machine Learning Committee Neural Network Potential Energy Surfaces for Two-Dimensional Metal–Organic Frameworks

  2025cites this paper
• Machine learning interatomic potential can infer electrical response

  2025cites this paper
• Free energy profiles for chemical reactions in solution from high-dimensional neural network potentials: The case of the Strecker synthesis.

  2025cites this paper
• Transferability and expansion of the clayNN model

  2025cites this paper
• Applications of machine learning in surfaces and interfaces

  2025cites this paper
• Molecular dynamics simulation of failure and micro-plasticity of calcium silicate hydrate based on deep potential

  2025cites this paper
• ABFML: A problem-oriented package for rapidly creating, screening, and optimizing new machine learning force fields.

  2025cites this paper
• Exploring structures of nanoclusters combining high-dimensional neural network potentials with unsupervised machine learning algorithms

  2025cites this paper
• A Neural Network Interatomic Potential for the Ternary α-Fe-C-H System: Toward Million-Atom Simulations of Hydrogen Embrittlement in Steel

  2025cites this paper
• Development and application of a high-dimensional neural network potential for boron carbide

  2025cites this paper
• Machine Learning Potential Analysis of Structural Transition in Cu and Ag Nanoparticles: From Icosahedral to Face-Centered Cubic

  2025cites this paper
• Modeling Gas Adsorption and Mechanistic Insights into Flexibility in Isoreticular Metal–Organic Frameworks Using High-Dimensional Neural Network Potentials

  2025cites this paper
• Nuclear quantum effects at the liquid/vapor interface from neural-network based path integral molecular dynamics simulations.

  2025cites this paper
• A Theoretical Study on the Structural Evolution of Ru–Zn Bimetallic Nanoparticles

  2025cites this paper
• Machine learning interatomic potential reveals hydrogen embrittlement origins at general grain boundaries in α-iron

  2025cites this paper
• Molecular dynamics simulations of the sputtering of boron and boron oxide surfaces

  2025cites this paper
• Understanding the Synergistic Co-Mo Effect in Maraging Steels: Redistribution of Solute Atoms

  2025cites this paper
• Development of interatomic potential and effect of ordering on defect properties in CrMnV

  2025cites this paper
• The structure of liquid carbon elucidated by in situ X-ray diffraction

  2025cites this paper
• Machine-learning interatomic potentials from a users perspective: a comparison of accuracy, speed and data efficiency

  2025cites this paper
• Evidence and origin of anomalous diffusion of Ag+ ion in amorphous silica: A molecular dynamics study with neural network interatomic potentials.

  2025cites this paper
• Data-driven atomistic modeling of crystalline and glassy solid-state electrolytes.

  2025cites this paper
• Phonon dispersion filter: A physics-inspired feature selection for machine learning potentials

  2025cites this paper
• Achieving Empirical Potential Efficiency with DFT Accuracy: A Neuroevolution Potential for the $\alpha$-Fe--C--H System

  2025cites this paper
• ReMLP-NET: A Neural Network Interaction Potential for Molecular Energy Prediction.

  2025cites this paper
• Non-Arrhenius Li-ion transport and grain-size effects in argyrodite solid electrolytes

  2025cites this paper
• Accelerating Global Optimization of Cerium Oxide Nanocluster Structures with High-Dimensional Neural Network Potential.

  2025cites this paper
• Predictive Quantum Vibrational Spectra through Active Learning 4G-NNPs.

  2025cites this paper
• Investigation of solid-state diffusion bonding of Al–Cu interfaces of metal joints using molecular dynamics simulations

  2025cites this paper
• Data-Efficient Equivariant NNPs Enable DFT-Accurate Simulations and Implicit Solvation Free Energies

  2025cites this paper
• Microscopic dynamics of enhanced glass-forming ability with minor oxygen addition in bulk metallic glasses.

  2025cites this paper
• An iterative and automatic collective variable optimization scheme via unsupervised feature selection with CUR matrix decomposition.

  2025cites this paper
• Exploring structures of Pd clusters on hydrogenated ceria surface using High-Dimensional neural network potential

  2025cites this paper
• The evolution of machine learning potentials for molecules, reactions and materials.

  2025cites this paper
• A highly transferable and efficient machine learning interatomic potentials study of α-Fe–C binary system

  2024influential citation
• Machine-learning-assisted deciphering of microstructural effects on ionic transport in composite materials: A case study of Li7La3Zr2O12-LiCoO2

  2024cites this paper
• Introduction to machine learning potentials for atomistic simulations

  2024cites this paper
• The role of the water contact layer on hydration and transport at solid/liquid interfaces

  2024cites this paper
• Rich proton dynamics and phase behaviours of nanoconfined ices

  2024cites this paper
• Highly efficient and transferable interatomic potentials for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si28.svg" display="inline" id="d1e1011"><mml:mi>α</mml:mi></mml:math>-iron and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si28.svg" display="inline" id=

  2024cites this paper
• A high-dimensional neural network potential for Co3O4

  2024influential citation
• Surface stratification determines the interfacial water structure of simple electrolyte solutions

  2024cites this paper
• Structure and Dynamics of the Magnetite(001)/Water Interface from Molecular Dynamics Simulations Based on a Neural Network Potential

  2024cites this paper
• Utilizing Wyckoff Sites to Construct Machine-Learning-Driven Interatomic Potentials for Crystalline Materials: A Case Study on α-Alumina

  2024cites this paper
• Infrared Spectra Prediction for Diazo Groups Utilizing a Machine Learning Approach with Structural Attention Mechanism

  2024cites this paper
• Machine-Learned Potentials by Active Learning from Organic Crystal Structure Prediction Landscapes

  2024cites this paper
• Modeling martensitic transformation temperatures in Zirconia–Ceria solid solutions using machine learning interatomic potentials

  2024influential citation
• Data-Efficient Active Learning for Thermodynamic Integration: Acidity Constants of BiVO4 in Water.

  2024cites this paper
• Temperature and structure measurements of heavy-ion-heated diamond using in situ X-ray diagnostics

  2024cites this paper
• The wetting of H2O by CO2.

  2024cites this paper
• Thermodynamics of alkali feldspar solid solutions with varying Al-Si order: atomistic simulations using a neural network potential

  2024cites this paper
• Superdiffusive Rotation of Interfacial Water on Noble Metal Surface.

  2024cites this paper
• Elaboration of a neural-network interatomic potential for silica glass and melt

  2024cites this paper
• Effects of Nonequilibrium Atomic Structure on Ionic Diffusivity in LLZO: A Classical and Machine Learning Molecular Dynamics Study

  2024cites this paper
• Five-Site Water Models for Ice and Liquid Water Generated by a Series-Parallel Machine Learning Strategy.

  2024cites this paper
• Investigation of the cross sections for electron collision ionization of complex molecules

  2024cites this paper
• Homogeneous nucleation of undercooled Al-Ni melts via a machine-learned interaction potential.

  2024cites this paper
• Stability and lifetime of diffusion-trapped oxygen in oxide-derived copper CO2 reduction electrocatalysts

  2024cites this paper
• Exploring the stable structures of cerium oxide nanoclusters using high-dimensional neural network potential

  2024cites this paper
• Exploring the Premelting Transition through Molecular Simulations Powered by Neural Network Potentials

  2024cites this paper
• Exploring the frontiers of condensed-phase chemistry with a general reactive machine learning potential

  2024cites this paper
• Machine learning the electric field response of condensed phase systems using perturbed neural network potentials

  2024cites this paper
• Unsupervised identification of crystal defects from atomistic potential descriptors

  2024cites this paper
• Adaptive loss weighting for machine learning interatomic potentials

  2024cites this paper
• Atomistic simulations of nuclear fuel UO2 with machine learning interatomic potentials

  2024cites this paper
• Structure and thermodynamics of defects in Na-feldspar from a neural network potential

  2024cites this paper
• Long Time Scale Molecular Dynamics Simulation of Magnesium Hydride Dehydrogenation Enabled by Machine Learning Interatomic Potentials

  2024cites this paper
• High-Throughput Exploration of Ti-V-Nb-Mo Carbide MXenes Using Neural Network Potentials and Their Evaluation as Catalysts for Hydrogen Evolution Reaction.

  2024cites this paper
• Cartesian atomic cluster expansion for machine learning interatomic potentials

  2024influential citation
• Evaluation of Rate Coefficients in the Gas Phase Using Machine-Learned Potentials.

  2024cites this paper
• Automatic feature selection and weighting in molecular systems using Differentiable Information Imbalance

  2024cites this paper
• Development of Machine Learning Atomistic Potential for Molecular Simulation of Hematite–Water Interfaces

  2024cites this paper
• Scaling Molecular Dynamics with ab initio Accuracy to 149 Nanoseconds per Day

  2024cites this paper
• Neural network-assisted model of interfacial fluids with explicit coarse-grained molecular structures.

  2024cites this paper
• Machine-learning-accelerated structure prediction of PtSnO nanoclusters under working conditions.

  2024cites this paper
• Efficiency, accuracy, and transferability of machine learning potentials: Application to dislocations and cracks in iron

  2024cites this paper
• Atomistic modeling of nucleation kinetics of Guinier–Preston zones in Al–Cu alloys: Two formation scenarios and prediction of the time-temperature-transformation diagram

  2024cites this paper
• Automatic feature selection and weighting using Differentiable Information Imbalance

  2024cites this paper
• Probing degradation at solid-state battery interfaces using machine-learning interatomic potential

  2024cites this paper
• Modeling Chemical Exfoliation of Non-van der Waals Chromium Sulfides by Machine Learning Interatomic Potentials and Monte Carlo Simulations

  2023cites this paper
• Machine-learned interatomic potentials: Recent developments and prospective applications

  2023cites this paper
• Hydrogen atom scattering at the Al2O3(0001) surface: a combined experimental and theoretical study.

  2023cites this paper
• Highly efficient and transferable interatomic potentials for {\alpha}-iron and {\alpha}-iron/hydrogen binary systems using deep neural networks

  2023cites this paper
• The kinetics of the ice-water interface from ab initio machine learning simulations.

  2023cites this paper
• Force training neural network potential energy surface models

  2023cites this paper