Since the classical molecular dynamics simulator LAMMPS was released as an open source code in 2004, it has become a widely-used tool for particle-based modeling of materials at length scales ranging from atomic to mesoscale to continuum. Reasons for its popularity are that it provides a wide variety of particle interaction models for different materials, that it runs on any platform from a single CPU core to the largest supercomputers with accelerators, and that it gives users control over simulation details, either via the input script or by adding code for new interatomic potentials, constraints, diagnostics, or other features needed for their models. As a result, hundreds of people have contributed new capabilities to LAMMPS and it has grown from fifty thousand lines of code in 2004 to a million lines today. In this paper several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers. We also highlight some capabilities recently added to the code which were enabled by this flexibility, including dynamic load balancing, on-the-fly visualization, magnetic spin dynamics models, and quantum-accuracy machine learning interatomic potentials. Program Summary: Program Title: Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) CPC Library link to program files: https://doi.org/10.17632/cxbxs9btsv.1 Developer's repository link: https://github.com/lammps/lammps Licensing provisions: GPLv2 Programming language: C++, Python, C, Fortran Supplementary material: https://www.lammps.org Nature of problem: Many science applications in physics, chemistry, materials science, and related fields require parallel, scalable, and efficient generation of long, stable classical particle dynamics trajectories. Within this common problem definition, there lies a great diversity of use cases, distinguished by different particle interaction models, external constraints, as well as timescales and lengthscales ranging from atomic to mesoscale to macroscopic. Solution method: The LAMMPS code uses parallel spatial decomposition, distributed neighbor lists, and parallel FFTs for long-range Coulombic interactions [1]. The time integration algorithm is based on the Størmer-Verlet symplectic integrator [2], which provides better stability than higher-order non-symplectic methods. In addition, LAMMPS supports a wide range of interatomic potentials, constraints, diagnostics, software interfaces, and pre- and post-processing features. Additional comments including restrictions and unusual features: This paper serves as the definitive reference for the LAMMPS code. References: [1] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 117 (1995) 1–19. [2] L. Verlet, Computer experiments on classical fluids: I. Thermodynamical properties of Lennard–Jones molecules, Phys. Rev. 159 (1967) 98–103.
The final review for the FY21 Advanced Simulation and Computing (ASC) Computational Systems and Software Environments (CSSE) L2 Milestone #7840 was conducted on August 25th, 2021 at Sandia National Laboratories in Albuquerque, New Mexico. The review committee/panel unanimously agreed that the milestone has been successfully completed, exceeding expectations on several of the key deliverables.
Rendezvous algorithms encode a communication pattern that is useful when processors sending data do not know who the receiving processors should be, or vice versa. The idea is to define an intermediate decomposition where datums from different sending processors can ”rendezvous” to perform a computation, in a manner that both the senders and eventual receivers of the results can identify the appropriate rendezvous processor. Originally designed for interpolating between overlaid grids with independent parallel decompositions (Plimpton et al., 2004), we have recently found rendezvous algorithms useful for a variety of operations in particle- or grid-based simulation codes when running large problems on large numbers of processors. In particular, we show they can perform well when a load-balanced intermediate decomposition is randomized and not spatial, requiring all-to-all communication to move data between processors. In this case rendezvous algorithms leverage the large bisection communication bandwidths which parallel machines provide. We describe how rendezvous algorithms work in a scientific computing context and give specific examples for molecular dynamics and Direct Simulation Monte Carlo codes which result in dramatic performance improvements versus simpler algorithms which do not scale as well. We explain how a generic rendezvous algorithm can be implemented, and also point out similarities with the MapReduce paradigm popularized by Google and Hadoop.
Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction and other dissipative interactions. The resistance to rolling and spinning or twisting torque that stops a sphere also changes the microstructure of a granular packing of frictional spheres by increasing the number of constraints on the degrees of freedom of motion. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a pressure-controlled protocol. Mechanically stable packings are achievable at volume fractions and average coordination numbers as low as 0.53 and 2.5, respectively, when the particles experience high resistance to sliding, rolling, and twisting. Only when the particle model includes rolling and twisting friction were experimental volume fractions reproduced.
Hyperdynamics (HD) is a method for accelerating the timescale of standard molecular dynamics (MD). It can be used for simulations of systems with an energy potential landscape that is a collection of basins, separated by barriers, where transitions between basins are infrequent. HD enables the system to escape from a basin more quickly while enabling a statistically accurate renormalization of the simulation time, thus effectively boosting the timescale of the simulation. In the work of Kim et al. [J. Chem. Phys. 139, 144110 (2013)], a local version of HD was formulated, which exploits the intrinsic locality characteristic typical of most systems to mitigate the poor scaling properties of standard HD as the system size is increased. Here, we discuss how both HD and local HD can be formulated to run efficiently in parallel. We have implemented these ideas in the LAMMPS MD code, which means HD can be used with any interatomic potential LAMMPS supports. Together, these parallel methods allow simulations of any size to achieve the time acceleration offered by HD (which can be orders of magnitude), at a cost of 2-4× that of standard MD. As examples, we performed two simulations of a million-atom system to model the diffusion and clustering of Pt adatoms on a large patch of the Pt(100) surface for 80 μs and 160 μs.
In traditional molecular dynamics (MD) simulations, atoms and coarse-grained particles are modeled as point masses interacting via isotropic potentials. For studies where particle shape plays a vital role, more complex models are required. In this paper we describe a spectrum of approaches for modeling aspherical particles, all of which are now available (some recently) as options within the LAMMPS MD package. Broadly these include two classes of models. In the first, individual particles are aspherical, either via a pairwise anisotropic potential which implicitly assigns a simple geometric shape to each particle, or in a more general way where particles store internal state which can explicitly define a complex geometric shape. In the second class of models, individual particles are simple points or spheres, but rigid body constraints are used to create composite aspherical particles in a variety of complex shapes. We discuss parallel algorithms and associated data structures for both kinds of models, which enable dynamics simulations of aspherical particle systems across a wide range of length and time scales. We also highlight parallel performance and scalability and give a few illustrative examples of aspherical models in different contexts.
The Direct Simulation Monte Carlo (DSMC) method has been used for more than 50 years to simulate rarefied gases. The advent of modern supercomputers has brought higher-density near-continuum flows within range. This in turn has revived the debate as to whether the Boltzmann equation, which assumes molecular chaos, can be used to simulate continuum flows when they become turbulent. In an effort to settle this debate, two canonical turbulent flows are examined, and the results are compared to available continuum theoretical and numerical results for the Navier-Stokes equations.
The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief barrier to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method's inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird's 1994 formulation. Here, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We give a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.
Simulating energetic materials with complex microstructure is a grand challenge, where until recently, an inherent gap in computational capabilities had existed in modelling grain-scale effects at the microscale. We have enabled a critical capability in modelling the multiscale nature of the energy release and propagation mechanisms in advanced energetic materials by implementing, in the widely used LAMMPS molecular dynamics (MD) package, several novel coarse-graining techniques that also treat chemical reactivity. Our innovative algorithmic developments rooted within the dissipative particle dynamics framework, along with performance optimisations and application of acceleration technologies, have enabled extensions in both the length and time scales far beyond those ever realised by atomistic reactive MD simulations. In this paper, we demonstrate these advances by modelling a shockwave propagating through a microstructured material and comparing performance with the state-of-the-art in atomistic reactive MD techniques. As a result of this work, unparalleled explorations in energetic materials research are now possible.
We provide a demonstration that gas-kinetic methods incorporating molecular chaos can simulate the sustained turbulence that occurs in wall-bounded turbulent shear flows. The direct simulation Monte Carlo method, a gas-kinetic molecular method that enforces molecular chaos for gas-molecule collisions, is used to simulate the minimal Couette flow at Re=500. The resulting law of the wall, the average wall shear stress, the average kinetic energy, and the continually regenerating coherent structures all agree closely with corresponding results from direct numerical simulation of the Navier-Stokes equations. These results indicate that molecular chaos for collisions in gas-kinetic methods does not prevent development of molecular-scale long-range correlations required to form hydrodynamic-scale turbulent coherent structures.
The computational power of HPC is beyond our comprehension when we hear that 5 quadrillion computations can happen in a matter of seconds, or that machine learning is changing the way everything works. But none of that happens in a vacuum, and the teams behind the scenes—the developers of the hardware, the operating systems, the data transfer protocols, and the applications themselves—are the unsung heroes of a world where faster is better and you'd better hope there's no bug in the software or the hardware to slow you down. HPC is most successful when all these aspects work together seamlessly. The stories that follow are a tribute to the hardworking teams behind the scenes.
Analog resistive memories promise to reduce the energy of neural networks by orders of magnitude. However, the write variability and write nonlinearity of current devices prevent neural networks from training to high accuracy. We present a novel periodic carry method that uses a positional number system to overcome this while maintaining the benefit of parallel analog matrix operations. We demonstrate how noisy, nonlinear TaOx devices that could only train to 80% accuracy on MNIST, can now reach 97% accuracy, only 1% away from an ideal numeric accuracy of 98%. On a file type dataset, the TaOx devices achieve ideal numeric accuracy. In addition, low noise, linear Li1-xCoO2 devices train to ideal numeric accuracies using periodic carry on both datasets.
Resistive memory crossbars can dramatically reduce the energy required to perform computations in neural algorithms by three orders of magnitude when compared to an optimized digital ASIC [1]. For data intensive applications, the computational energy is dominated by moving data between the processor, SRAM, and DRAM. Analog crossbars overcome this by allowing data to be processed directly at each memory element. Analog crossbars accelerate three key operations that are the bulk of the computation in a neural network as illustrated in Fig 1: vector matrix multiplies (VMM), matrix vector multiplies (MVM), and outer product rank 1 updates (OPU)[2]. For an NxN crossbar the energy for each operation scales as the number of memory elements O(N2) [2]. This is because the crossbar performs its entire computation in one step, charging all the capacitances only once. Thus the CV2 energy of the array scales as array size. This fundamentally better than trying to read or write a digital memory. Each row of any NxN digital memory must be accessed one at a time, resulting in N columns of length O(N) being charged N times, requiring O(N3) energy to read a digital memory. Thus an analog crossbar has a fundamental O(N) energy scaling advantage over a digital system. Furthermore, if the read operation is done at low voltage and is therefore noise limited, the read energy can even be independent of the crossbar size, O(1) [2].
We provide the first demonstration that molecular-level methods based on gas kinetic theory and molecular chaos can simulate turbulence and its decay. The direct simulation Monte Carlo (DSMC) method, a molecular-level technique for simulating gas flows that resolves phenomena from molecular to hydrodynamic (continuum) length scales, is applied to simulate the Taylor-Green vortex flow. The DSMC simulations reproduce the Kolmogorov -5/3 law and agree well with the turbulent kinetic energy and energy dissipation rate obtained from direct numerical simulation of the Navier-Stokes equations using a spectral method. This agreement provides strong evidence that molecular-level methods for gases can be used to investigate turbulent flows quantitatively.
Biological neural networks continue to inspire new developments in algorithms and microelectronic hardware to solve challenging data processing and classification problems. Here, we survey the history of neural-inspired and neuromorphic computing in order to examine the complex and intertwined trajectories of the mathematical theory and hardware developed in this field. Early research focused on adapting existing hardware to emulate the pattern recognition capabilities of living organisms. Contributions from psychologists, mathematicians, engineers, neuroscientists, and other professions were crucial to maturing the field from narrowly-tailored demonstrations to more generalizable systems capable of addressing difficult problem classes such as object detection and speech recognition. Algorithms that leverage fundamental principles found in neuroscience such as hierarchical structure, temporal integration, and robustness to error have been developed, and some of these approaches are achieving world-leading performance on particular data classification tasks. In addition, novel microelectronic hardware is being developed to perform logic and to serve as memory in neuromorphic computing systems with optimized system integration and improved energy efficiency. Key to such advancements was the incorporation of new discoveries in neuroscience research, the transition away from strict structural replication and towards the functional replication of neural systems, and the use of mathematical theory frameworks to guide algorithm and hardware developments.
The Rayleigh-Taylor instability (RTI) is investigated using the Direct Simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, two-dimensional and three-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode-perturbed interfaces between two atmospheric-pressure monatomic gases. The DSMC simulations reproduce all qualitative features of the RTI and are in reasonable quantitative agreement with existing theoretical and empirical models in the linear, nonlinear, and self-similar regimes. At late times, the instability is seen to exhibit a self-similar behavior, in agreement with experimental observations. For the conditions simulated diffusion can influence the initial instability growth significantly.
Resistive memories enable dramatic energy reductions for neural algorithms. We propose a general purpose neural architecture that can accelerate many different algorithms and determine the device properties that will be needed to run backpropagation on the neural architecture. To maintain high accuracy, the read noise standard deviation should be less than 5% of the weight range. The write noise standard deviation should be less than 0.4% of the weight range and up to 300% of a characteristic update (for the datasets tested). Asymmetric nonlinearities in the change in conductance vs pulse cause weight decay and significantly reduce the accuracy, while moderate symmetric nonlinearities do not have an effect. In order to allow for parallel reads and writes the write current should be less than 100 nA as well.
In this paper, the Rayleigh-Taylor instability (RTI) is investigated using the direct simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, fully resolved two-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode perturbed interfaces between two atmospheric-pressure monatomic gases as a function of the Atwood number and the gravitational acceleration. The DSMC simulations reproduce many qualitative features of the growth of the mixing layer and are in reasonable quantitative agreement with theoretical and empirical models in the linear, nonlinear, and self-similar regimes. In some of the simulations at late times, the instability enters the self-similar regime, in agreement with experimental observations. Finally, for the conditions simulated, diffusion can influence the initial instability growth significantly.
International Conference for High Performance Computing, Networking, Storage and Analysis, SC
Brown, W.M.; Semin, Andrey; Hebenstreit, Michael; Khvostov, Sergey; Raman, Karthik; Plimpton, Steven J.
Electrical power efficiency is a primary concern in designing modern HPC systems. Common strategies to improve CPU power efficiency rely on increased parallelism within a processor that is enabled both by an increase in the vector capabilities within the core and also the number of cores within a processor. Although many-core processors have been available for some time, achieving power-efficient performance has been challenging due to the offload model. Here, we evaluate performance of the molecular dynamics code LAMMPS on two new Intel® processors including the second generation many-core Intel® Xeon Phi™ processor that is available as a bootable CPU. We describe our approach to measure power consumption out-of-band and software optimizations necessary to achieve energy efficiency. We analyze benefits from Intel® Advanced Vector Extensions 512 instructions and demonstrate increased simulations rates with over 9X the CPU+DRAM power efficiency when compared to the unoptimized code on previous generation processors.