2HOT: An Improved Parallel Hashed Oct-Tree N-Body Algorithm for Cosmological Simulation

We report on improvements made over the past two decades to our adaptive treecode N-body method (HOT). A mathematical and computational approach to the cosmological N-body problem is described, with performance and scalability measured up to 256k ($2^{18}$) processors. We present error analysis and scientific application results from a series of more than ten 69 billion ($4096^3$) particle cosmological simulations, accounting for $4 \times 10^{20}$ floating point operations. These results include the first simulations using the new constraints on the standard model of cosmology from the Planck satellite. Our simulations set a new standard for accuracy and scientific throughput, while meeting or exceeding the computational efficiency of the latest generation of hybrid TreePM N-body methods.Comment: 12 pages, 8 figures, 77 references; To appear in Proceedings of SC '1

Accelerating scientific codes by performance and accuracy modeling

Scientific software is often driven by multiple parameters that affect both accuracy and performance. Since finding the optimal configuration of these parameters is a highly complex task, it extremely common that the software is used suboptimally. In a typical scenario, accuracy requirements are imposed, and attained through suboptimal performance. In this paper, we present a methodology for the automatic selection of parameters for simulation codes, and a corresponding prototype tool. To be amenable to our methodology, the target code must expose the parameters affecting accuracy and performance, and there must be formulas available for error bounds and computational complexity of the underlying methods. As a case study, we consider the particle-particle particle-mesh method (PPPM) from the LAMMPS suite for molecular dynamics, and use our tool to identify configurations of the input parameters that achieve a given accuracy in the shortest execution time. When compared with the configurations suggested by expert users, the parameters selected by our tool yield reductions in the time-to-solution ranging between 10% and 60%. In other words, for the typical scenario where a fixed number of core-hours are granted and simulations of a fixed number of timesteps are to be run, usage of our tool may allow up to twice as many simulations. While we develop our ideas using LAMMPS as computational framework and use the PPPM method for dispersion as case study, the methodology is general and valid for a range of software tools and methods

Frequency adaptive metadynamics for the calculation of rare-event kinetics

The ability to predict accurate thermodynamic and kinetic properties in biomolecular systems is of both scientific and practical utility. While both remain very difficult, predictions of kinetics are particularly difficult because rates, in contrast to free energies, depend on the route taken and are thus not amenable to all enhanced sampling methods. It has recently been demonstrated that it is possible to recover kinetics through so called `infrequent metadynamics' simulations, where the simulations are biased in a way that minimally corrupts the dynamics of moving between metastable states. This method, however, requires the bias to be added slowly, thus hampering applications to processes with only modest separations of timescales. Here we present a frequency-adaptive strategy which bridges normal and infrequent metadynamics. We show that this strategy can improve the precision and accuracy of rate calculations at fixed computational cost, and should be able to extend rate calculations for much slower kinetic processes.Comment: 15 pages, 2 figures, 2 table

By-passing the Kohn-Sham equations with machine learning

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields, ranging from materials science to biochemistry to astrophysics. Machine learning holds the promise of learning the kinetic energy functional via examples, by-passing the need to solve the Kohn-Sham equations. This should yield substantial savings in computer time, allowing either larger systems or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. Both improved accuracy and lower computational cost with this method are demonstrated by reproducing DFT energies for a range of molecular geometries generated during molecular dynamics simulations. Moreover, the methodology could be applied directly to quantum chemical calculations, allowing construction of density functionals of quantum-chemical accuracy

Reducing memory requirements for large size LBM simulations on GPUs

The scientific community in its never-ending road of larger and more efficient computational resources is in need of more efficient implementations that can adapt efficiently on the current parallel platforms. Graphics processing units are an appropriate platform that cover some of these demands. This architecture presents a high performance with a reduced cost and an efficient power consumption. However, the memory capacity in these devices is reduced and so expensive memory transfers are necessary to deal with big problems. Today, the lattice-Boltzmann method (LBM) has positioned as an efficient approach for Computational Fluid Dynamics simulations. Despite this method is particularly amenable to be efficiently parallelized, it is in need of a considerable memory capacity, which is the consequence of a dramatic fall in performance when dealing with large simulations. In this work, we propose some initiatives to minimize such demand of memory, which allows us to execute bigger simulations on the same platform without additional memory transfers, keeping a high performance. In particular, we present 2 new implementations, LBM-Ghost and LBM-Swap, which are deeply analyzed, presenting the pros and cons of each of them.This project was funded by the Spanish Ministry of Economy and Competitiveness (MINECO): BCAM Severo Ochoa accreditation SEV-2013-0323, MTM2013-40824, Computación de Altas Prestaciones VII TIN2015-65316-P, by the Basque Excellence Research Center (BERC 2014-2017) pro- gram by the Basque Government, and by the Departament d' Innovació, Universitats i Empresa de la Generalitat de Catalunya, under project MPEXPAR: Models de Programació i Entorns d' Execució Paral·lels (2014-SGR-1051). We also thank the support of the computing facilities of Extremadura Research Centre for Advanced Technologies (CETA-CIEMAT) and NVIDIA GPU Research Center program for the provided resources, as well as the support of NVIDIA through the BSC/UPC NVIDIA GPU Center of Excellence.Peer ReviewedPostprint (author's final draft

Development of an object-oriented finite element program: application to metal-forming and impact simulations

During the last 50 years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. In the same time, the finite element method has become a widely used tool for researchers and engineers. Recent advances in computational software have made possible to solve more physical and complex problems such as coupled problems, nonlinearities, high strain and high-strain rate problems. In this field, an accurate analysis of large deformation inelastic problems occurring in metal-forming or impact simulations is extremely important as a consequence of high amount of plastic flow. In this presentation, the object-oriented implementation, using the C++ language, of an explicit finite element code called DynELA is presented. The object-oriented programming (OOP) leads to better-structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. The most significant advantage of OOP is in the modeling of complex physical systems such as deformation processing where the overall complex problem is partitioned in individual sub-problems based on physical, mathematical or geometric reasoning. We first focus on the advantages of OOP for the development of scientific programs. Specific aspects of OOP, such as the inheritance mechanism, the operators overload procedure or the use of template classes are detailed. Then we present the approach used for the development of our finite element code through the presentation of the kinematics, conservative and constitutive laws and their respective implementation in C++. Finally, the efficiency and accuracy of our finite element program are investigated using a number of benchmark tests relative to metal forming and impact simulations