Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales

Propelled partly by the Materials Genome Initiative, and partly by the algorithmic developments and the resounding successes of data-driven efforts in other domains, informatics strategies are beginning to take shape within materials science. These approaches lead to surrogate machine learning models that enable rapid predictions based purely on past data rather than by direct experimentation or by computations/simulations in which fundamental equations are explicitly solved. Data-centric informatics methods are becoming useful to determine material properties that are hard to measure or compute using traditional methods—due to the cost, time or effort involved—but for which reliable data either already exists or can be generated for at least a subset of the critical cases. Predictions are typically interpolative, involving fingerprinting a material numerically first, and then following a mapping (established via a learning algorithm) between the fingerprint and the property of interest. Fingerprints, also referred to as “descriptors”, may be of many types and scales, as dictated by the application domain and needs. Predictions may also be extrapolative—extending into new materials spaces—provided prediction uncertainties are properly taken into account. This article attempts to provide an overview of some of the recent successful data-driven “materials informatics” strategies undertaken in the last decade, with particular emphasis on the fingerprint or descriptor choices. The review also identifies some challenges the community is facing and those that should be overcome in the near future.

/pdf/machine-learning-in-materials-informatics-recent-km20z9ojry.pdf

Machine learning in materials informatics: recent applications and prospects

Force fields developed with machine learning methods in tandem with quantum mechanics are beginning to find merit, given their (i) low cost, (ii) accuracy, and (iii) versatility. Recently, we proposed one such approach, wherein, the vectorial force on an atom is computed directly from its environment. Here, we discuss the multistep workflow required for their construction, which begins with generating diverse reference atomic environments and force data, choosing a numerical representation for the atomic environments, down selecting a representative training set, and lastly the learning method itself, for the case of Al. The constructed force field is then validated by simulating complex materials phenomena such as surface melting and stress–strain behavior, that truly go beyond the realm of ab initio methods, both in length and time scales. To make such force fields truly versatile an attempt to estimate the uncertainty in force predictions is put forth, allowing one to identify areas of poor performance...

http://pubs.acs.org/doi/pdf/10.1021/acs.jpcc.6b10908

Machine Learning Force Fields: Construction, Validation, and Outlook

Emerging machine learning (ML)-based approaches provide powerful and novel tools to study a variety of physical and chemical problems. In this contribution, we outline a universal strategy to create ML-based atomistic force fields, which can be used to perform high-fidelity molecular dynamics simulations. This scheme involves (1) preparing a big reference dataset of atomic environments and forces with sufficiently low noise, e.g., using density functional theory or higher-level methods, (2) utilizing a generalizable class of structural fingerprints for representing atomic environments, (3) optimally selecting diverse and non-redundant training datasets from the reference data, and (4) proposing various learning approaches to predict atomic forces directly (and rapidly) from atomic configurations. From the atomistic forces, accurate potential energies can then be obtained by appropriate integration along a reaction coordinate or along a molecular dynamics trajectory. Based on this strategy, we have created model ML force fields for six elemental bulk solids, including Al, Cu, Ti, W, Si, and C, and show that all of them can reach chemical accuracy. The proposed procedure is general and universal, in that it can potentially be used to generate ML force fields for any material using the same unified workflow with little human intervention. Moreover, the force fields can be systematically improved by adding new training data progressively to represent atomic environments not encountered previously. A machine learning-based strategy for calculating atomic force fields could expand the range of molecular dynamics simulations. Molecular dynamics simulations are a powerful tool for exploring how atomic-scale chemical and physical processes evolve over time. To perform such simulations, an initial atomic configuration needs to be defined, and atomic forces are input for each time step. Whilst quantum mechanics-based methods for calculating the fields are available, these approaches cannot easily be applied to large systems over long timescales. A team of researchers from the University of Connecticut, led by Rampi Ramprasad, now present a general and universal strategy for using machine learning-based methods to generate highly accurate atomic force fields that may provide a pathway for performing efficient molecular dynamics simulations on nanometer-sized systems over several nanoseconds.

/pdf/a-universal-strategy-for-the-creation-of-machine-learning-20w4k0zgz2.pdf

A universal strategy for the creation of machine learning-based atomistic force fields

Simulations based on solving the Kohn-Sham (KS) equation of density functional theory (DFT) have become a vital component of modern materials and chemical sciences research and development portfolios. Despite its versatility, routine DFT calculations are usually limited to a few hundred atoms due to the computational bottleneck posed by the KS equation. Here we introduce a machine-learning-based scheme to efficiently assimilate the function of the KS equation, and by-pass it to directly, rapidly, and accurately predict the electronic structure of a material or a molecule, given just its atomic configuration. A new rotationally invariant representation is utilized to map the atomic environment around a grid-point to the electron density and local density of states at that grid-point. This mapping is learned using a neural network trained on previously generated reference DFT results at millions of grid-points. The proposed paradigm allows for the high-fidelity emulation of KS DFT, but orders of magnitude faster than the direct solution. Moreover, the machine learning prediction scheme is strictly linear-scaling with system size.

/pdf/solving-the-electronic-structure-problem-with-machine-3b5i7abnrs.pdf

Solving the electronic structure problem with machine learning

Force fields developed with machine learning methods in tandem with quantum mechanics are beginning to find merit, given their (i) low cost, (ii) accuracy, and (iii) versatility. Recently, we proposed one such approach, wherein, the vectorial force on an atom is computed directly from its environment. Here, we discuss the multi-step workflow required for their construction, which begins with generating diverse reference atomic environments and force data, choosing a numerical representation for the atomic environments, down selecting a representative training set, and lastly the learning method itself, for the case of Al. The constructed force field is then validated by simulating complex materials phenomena such as surface melting and stress-strain behavior - that truly go beyond the realm of $ab\ initio$ methods both in length and time scales. To make such force fields truly versatile an attempt to estimate the uncertainty in force predictions is put forth, allowing one to identify areas of poor performance and paving the way for their continual improvement.

Rohit Batra

Papers

Machine learning in materials informatics: recent applications and prospects

Machine Learning Force Fields: Construction, Validation, and Outlook

A universal strategy for the creation of machine learning-based atomistic force fields

Solving the electronic structure problem with machine learning

Machine learning force fields: Construction, validation, and outlook