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DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

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arXiv 2017年

作者： Wang, Han Zhang, Linfeng Han, Jiequn Weinan, E. Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform molecular dynamics. Potential applications of DeePMD-kit span from finite molecules to extended systems and from metallic systems to chemically bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical molecular dynamics and quantum (path-integral) molecular dynamics packages, i.e., LAMMPS and the i-PI, respectively. Thus, upon training, the potential energy and force field models can be used to perform efficient molecular simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interatomic potential energy and forces of a water model using data obtained from density functional theory. We demonstrate that the resulted molecular dynamics model reproduces accurately the structural information contained in the original model. Copyright © 2017, The Authors. All rights reserved.

关键词： Potential energy

Particle swarm optimization with local search for height-map surface reconstruction from point clouds in reverse engineering

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Neural Computing and Applications 2024年 1-20页

作者： Gálvez, Akemi Fister, Iztok Deb, Suash Fister, Iztok Iglesias, Andrés Dept. of Applied Mathematics and Computational Sciences E.T.S.I. Caminos Canales y Puertos University of Cantabria Avda. de los Castros s/n Santander39005 Spain Faculty of Pharmaceutical Sciences Toho University 2-2-1 Miyama Funabashi274-8510 Japan Faculty of Electrical Engineering and Computer Science University of Maribor Koroska cesta 34 Maribor2000 Slovenia IT & Educational Consultant Ranchi India Distinguished Professorial Associate Decision Sciences and Modeling Program Victoria University Melbourne Australia

Surface reconstruction is a classical process in industrial engineering and manufacturing, particularly in reverse engineering, where the goal is to obtain a digital model from a physical object. For that purpose, the real object is typically scanned or digitized and the resulting point cloud is then fitted to mathematical surfaces through numerical optimization. The choice of the approximating functions is crucial for the accuracy of the process. Real-world objects such as manufactured workpieces often require complex nonlinear approximating functions, which are not well suited for standard numerical methods. In a previous paper presented at the ISMSI 2023 conference, we addressed this issue by using manually selected approximation functions via optimization through the cuckoo search algorithm with Lévy flights. Building upon that work, this paper presents an enhanced and extended method for surface reconstruction by using height-map surfaces obtained through a combination of exponential, polynomial and logarithmic functions. A feasible approach for this goal is to consider continuous bivariate distribution functions, which ensures consistent models along with good mathematical properties for the output shapes, such as smoothness and integrability. However, this approach leads to a difficult multivariate, constrained, multimodal continuous nonlinear optimization problem. To tackle this issue, we apply particle swarm optimization, a popular swarm intelligence technique for continuous optimization. The method is hybridized with a local search procedure for further improvement of the solutions and applied to a benchmark of 15 illustrative examples of point clouds fitted to different surface models. The performance of the method is analyzed through several computational experiments. The numerical and graphical results show that the method is able to recover the shape of the point clouds accurately and automatically. Furthermore, our approach outperforms other alternati

关键词： Particle swarm optimization (PSO)

Deep Potential generation scheme and simulation protocol for the Li10GeP2S12-type superionic conductors

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arXiv 2020年

作者： Huang, Jianxing Zhang, Linfeng Wang, Han Zhao, Jinbao Cheng, Jun Weinan, E. State Key Laboratory of Physical Chemistry of Solid Surfaces iChEM College of Chemistry and Chemical Engineering Xiamen University Xiamen361005 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China Department of Mathematics Princeton University PrincetonNJ08544 United States

Solid-state electrolyte materials with superior lithium ionic conductivities are vital to the next-generation Li-ion batteries. Molecular dynamics could provide atomic scale information to understand the diffusion process of Li-ion in these superionic conductor materials. Here we implement the Deep Potential Generator (DP-GEN) to set up an efficient protocol to automatically generate interatomic potentials for Li10GeP2S12-type solid-state electrolyte materials (Li10GeP2S12, Li10SiP2S12 and Li10SnP2S12). The reliability and accuracy of the fast interatomic potentials are validated. With the potentials, we extend the simulation of diffusion process to a wide temperature range (300K-1000K) and systems with large size (~1000 atoms). Important technical aspects like the statistical error and size effect are carefully investigated and benchmark tests including the effect of density functional, thermal expansion and configurational disorder are performed. The computed data that considering these factors agrees well with the experimental results and we find that the 3 structures shows different behaviors with respect to configurational disorder. Our work paves the way for further research on computation screening of solid-state electrolyte materials. Copyright © 2020, The Authors. All rights reserved.

关键词： Solid electrolytes

A deep potential model with long-range electrostatic interactions

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arXiv 2021年

作者： Zhang, Linfeng Wang, Han Muniz, Maria Carolina Panagiotopoulos, Athanassios Z. Car, Roberto Weinan, E. DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States School of Mathematical Sciences Peking University Beijing100871 China AI for Science Institute Beijing China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei+core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the deep potential long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples, the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal. © 2021, CC BY.

关键词： Electrostatics

Density-based and transport-based core-periphery structures in networks

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Physical Review E 2014年第3期89卷 032810-032810页

作者： Sang Hoon Lee Mihai Cucuringu Mason A. Porter Oxford Centre for Industrial and Applied Mathematics Mathematical Institute University of Oxford Oxford OX2 6GG United Kingdom Program in Applied and Computational Mathematics (PACM) Princeton University Fine Hall Washington Road Princeton New Jersey 08544-1000 USA Department of Mathematics University of California Los Angeles Los Angeles California 90095 USA CABDyN Complexity Centre University of Oxford Oxford OX1 1HP United Kingdom

Networks often possess mesoscale structures, and studying them can yield insights into both structure and function. It is most common to study community structure, but numerous other types of mesoscale structures also exist. In this paper, we examine core-periphery structures based on both density and transport. In such structures, core network components are well-connected both among themselves and to peripheral components, which are not well-connected to anything. We examine core-periphery structures in a wide range of examples of transportation, social, and financial networks—including road networks in large urban areas, a rabbit warren, a dolphin social network, a European interbank network, and a migration network between counties in the United States. We illustrate that a recently developed transport-based notion of node coreness is very useful for characterizing transportation networks. We also generalize this notion to examine core versus peripheral edges, and we show that the resulting diagnostic is also useful for transportation networks. To examine the properties of transportation networks further, we develop a family of generative models of roadlike networks. We illustrate the effect of the dimensionality of the embedding space on transportation networks, and we demonstrate that the correlations between different measures of coreness can be very different for different types of networks.

关键词： MESOSCALE convective complexes -- Computer simulation COMMUNITY organization TRANSPORTATION SOCIAL networks DENSITY MARKOV processes DEPENDENCY (Imperialism)

Publisher’s Note: “Enhanced damping of ion acoustic waves in dense plasmas” [Phys. Plasmas 18, 014505 (2011)]

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Physics of Plasmas 2011年第3期18卷

作者： S. Son Sung Joon Moon 118 Caleb Lane Princeton New Jersey 08540 USA 2Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

This article was originally published online on 11 January 2011 with an error in S. Son’s affiliation. AIP apologizes for this error.

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DP Compress: a Model Compression Scheme for Generating Efficient Deep Potential Models

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arXiv 2021年

作者： Lu, Denghui Jiang, Wanrun Chen, Yixiao Zhang, Linfeng Jia, Weile Wang, Han Chen, Mohan HEDPS CAPT College of Engineering Peking University Beijing100871 China Songshan Lake Materials Laboratory Guangdong Dongguan523808 China Institute of Physics Chinese Academy of Sciences Beijing100190 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Beijing Institute of Big Data Research Beijing100871 China Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China

Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via deep neural networks to predict the energy and atomic forces, resulting in lower running efficiency as compared to the typical empirical force fields. Herein, we report a model compression scheme for boosting the performance of the Deep Potential (DP) model, a deep learning based PES model. This scheme, we call DP Compress, is an efficient post-processing step after the training of DP models (DP Train). DP Compress combines several DP-specific compression techniques, which typically speed up DP-based molecular dynamics simulations by an order of magnitude faster, and consume an order of magnitude less memory. We demonstrate that DP Compress is sufficiently accurate by testing a variety of physical properties of Cu, H2O, and Al-Cu-Mg systems. DP Compress applies to both CPU and GPU machines and is publicly available online. Copyright © 2021, The Authors. All rights reserved.

关键词： Molecular dynamics

Algebraic Constraints and Algorithms for Common Lines in Cryo-EM

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arXiv 2024年

作者： Muller, Tommi Duncan, Adriana L. Verbeke, Eric J. Kileel, Joe Mathematical Institute University of Oxford OxfordOX2 6GG United Kingdom Department of Mathematics University of Texas at Austin AustinTX78712 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Oden Institute University of Texas at Austin AustinTX78712 United States

We revisit the topic of common lines between projection images in single particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain 2n × n matrix storing properly-scaled basis vectors for the common lines between n projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated to the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental *** Codes 90C26, 14Q30 © 2024, CC BY.

关键词： Clustering algorithms

On the non stationary Navier-Stokes equations with an external force

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Advances in Differential Equations 1999年第5期4卷 697-730页

作者： Cannone, Marco Planchon, Fabrice UMR 7599 du CNRS UFR Mathématiques Université Denis Diderot Paris VII 75251 Paris Cedex 05 2 Place Jussieu France Program for Applied and Computational Mathematics Princeton University Princeton NJ 08544-1000 United States

We present two different existence and uniqueness algorithms for constructing global mild solutions in C([0, T);L3(ℝ3)) to the Cauchy problem for the Navier-Stokes equations with an external force.

We present two different existence and uniqueness algorithms for constructing global mild solutions in C([0, T);L³(ℝ³)) to the Cauchy problem for the Navier-Stokes equations with an external force.

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