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arXiv:1209.6630 · Journal of Computational Chemistry

Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond

Anthony Scemama, Michel Caffarel, Emmanuel Oseret, William Jalby

Published Jan 3, 2013• 36 citations
arXivHTMLPDF

Abstract

Various strategies to implement efficiently quantum Monte Carlo (QMC) simulations for large chemical systems are presented. These include: (i) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), (ii) the possibility of keeping the memory footprint minimal, (iii) the important enhancement of single-core performance when efficient optimization tools are used, and (iv) the definition of a universal, dynamic, fault-tolerant, and load-balanced framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC=Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056, and 1731 electrons). Using 10-80 k computing cores of the Curie machine (GENCI-TGCC-CEA, France), QMC=Chem has been shown to be capable of running at the petascale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large-scale QMC simulations for future exascale platforms with a comparable level of efficiency is expected to be feasible.

DOI
10.1002/jcc.23216

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Various strategies to implement efficiently quantum Monte Carlo (QMC) simulations for large chemical systems are presented. These include: (i) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), (ii) the possibility of keeping the memory footprint minimal, (iii) the important enhancement of single-core performance when efficient optimization tools are used, and (iv) the definition of a universal, dynamic, fault-tolerant, and load-balanced framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC=Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056, and 1731 electrons). Using 10-80 k computing cores of the Curie machine (GENCI-TGCC-CEA, France), QMC=Chem has been shown to be capable of running at the petascale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large-scale QMC simulations for future exascale platforms with a comparable level of efficiency is expected to be feasible.
The exponential growth in computer power over the past few decades has been a huge boon to computational chemistry, physics, biology, and materials science. Now, a standard workstation or Linux cluster can calculate semi-quantitative properties of moderately sized systems. The next step in computational science is developing better algorithms which allow quantitative calculations of a system's properties. A relatively new class of algorithms, known collectively as Quantum Monte Carlo (QMC), has the potential to quantitatively calculate the properties of molecular systems. Furthermore, QMC scales as O(N3)O(N^3)O(N3) or better. This makes possible very high-level calculations on systems that are too large to be examined using standard high-level methods. This thesis develops (1) an efficient algorithm for determining "on-the-fly" the statistical error in serially correlated data, (2) a manager-worker parallelization algorithm for QMC that allows calculations to run on heterogeneous parallel computers and computational grids, (3) a robust algorithm for optimizing Jastrow functions which have singularities for some parameter values, and (4) a proof-of-concept demonstrating that it is possible to find transferable parameter sets for large classes of compounds.
With advances in algorithms and growing computing powers, quantum Monte Carlo (QMC) methods have become a leading contender for high accuracy calculations for the electronic structure of realistic systems. The performance gain on recent HPC systems is largely driven by increasing parallelism: the number of compute cores of a SMP and the number of SMPs have been going up, as the Top500 list attests. However, the available memory as well as the communication and memory bandwidth per element has not kept pace with the increasing parallelism. This severely limits the applicability of QMC and the problem size it can handle. OpenMP/MPI hybrid programming provides applications with simple but effective solutions to overcome efficiency and scalability bottlenecks on large-scale clusters based on multi/many-core SMPs. We discuss the design and implementation of hybrid methods in QMCPACK and analyze its performance on current HPC platforms characterized by various memory and communication hierarchies.
Quantum chemistry is a useful tool that provides insight into the properties and behavior of chemical systems. Modern software packages have made quantum chemistry methods more easily accessible, and the continued increase in available computational resources has allowed them to be applied to larger systems at higher levels of theory. Two significant problems that the field faces are the high computational complexity of high-level methods and the shift toward parallelism in high performance computing architectures. This work examines the treatment of weakly interacting molecular systems with the fixed-node diffusion Monte Carlo (DMC) method. DMC and other quantum Monte Carlo (QMC) methods offer a possible solution to both of the aforementioned problems: they can produce near-exact results with a lower scaling (with respect to problem size) than other similarly-accurate methods, and they are inherently parallel, so there is little additional cost associated with distributing the work of a single QMC calculation across a large number of processing units. The only error in DMC that is not systematically improvable is the constraint of a fixed nodal surface of the many-particle wave function of the system being studied. There are many cases in which a single Slater determinant trial function is sufficient to obtain accurate results, but there are others in which more sophisticated multi-determinant trial functions are necessary. Furthermore, it is non-trivial to generate nodal surfaces of similar quality for isolated and interacting molecules, so cancellation of errors is not guaranteed. We examine the use of different single- and multi-determinant trial functions in DMC calculations on small chemical systems with the goal of further understanding how to construct appropriate trial functions for molecules and clusters.
Over the past two decades, continuum quantum Monte Carlo (QMC) has proved to be an invaluable tool for predicting of the properties of matter from fundamental principles. By solving the Schrödinger equation through a stochastic projection, it achieves the greatest accuracy and reliability of methods available for physical systems containing more than a few quantum particles. QMC enjoys scaling favorable to quantum chemical methods, with a computational effort which grows with the second or third power of system size. This accuracy and scalability has enabled scientific discovery across a broad spectrum of disciplines. The current methods perform very efficiently at the terascale. The quantum Monte Carlo Endstation project is a collaborative effort among researchers in the field to develop a new generation of algorithms, and their efficient implementations, which will take advantage of the upcoming petaflop architectures. Some aspects of these developments are discussed here. These tools will expand the accuracy, efficiency and range of QMC applicability and enable us to tackle challenges which are currently out of reach. The methods will be applied to several important problems including electronic and structural properties of water, transition metal oxides, nanosystems and ultracold atoms.
For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation have evolved to require the minimum amount of logic and rely heavily on computationally efficient library-based matrix algebra and optimised paging schemes. In this regard, the recent development of exact stochastic quantum chemical algorithms to reduce computational scaling and memory overhead requires a contrasting algorithmic philosophy, but one which when implemented efficiently can achieve higher accuracy/cost ratios with small random errors. Additionally, they can exploit the continuing trend for massive parallelisation which hinders the progress of deterministic high-level quantum chemical algorithms. In the Quantum Monte Carlo community, stochastic algorithms are ubiquitous but the discrete Fock space of quantum chemical methods is often unfamiliar, and the methods introduce new concepts required for algorithmic efficiency. In this paper, we explore these concepts and detail an algorithm used for Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which is implemented and available in MOLPRO and as a standalone code, and is designed for high-level parallelism and linear-scaling with walker number. Many of the algorithms are also in use in, or can be transferred to, other stochastic quantum chemical methods and implementations. We apply these algorithms to the strongly correlated chromium dimer to demonstrate their efficiency and parallelism.
Quantum Monte Carlo (QMC) methods deliver highly accurate electronic structure calculations but are computationally intensive. The quantum Monte Carlo kernel library (QMCkl) provides a modular, portable collection of high-performance kernels implementing the core building blocks of QMC calculations. It offers a C-compatible application programming interface, supports the TREXIO standard for input, and covers essential QMC kernels including atomic and molecular orbitals, cusp corrections, the Jastrow factor, and the necessary derivatives also to perform variational and structural optimization. QMCkl separates algorithmic development from hardware-specific tuning by combining human-readable reference implementations with performance-optimized kernels that produce identical numerical results. The library enables consistent, efficient, and reproducible simulations across different QMC codes and architectures and achieves substantial speedups in the evaluation of the energy and its derivatives. Beyond QMC, QMCkl can accelerate deterministic quantum chemistry workflows and visualization tools, promoting cross-code interoperability and simplifying high-performance scientific software development.