Hasan Metin Aktulga

Parallel reactive molecular dynamics: Numerical methods and algorithmic techniques

Molecular dynamics modeling has provided a powerful tool for simulating and understanding diverse systems - ranging from materials processes to biophysical phenomena. Parallel formulations of these methods have been shown to be among the most scalable scientific computing applications. Many instances of this class of methods rely on a static bond structure for molecules, rendering them infeasible for reactive systems. Recent work on reactive force fields has resulted in the development of ReaxFF, a novel bond order potential that bridges quantum-scale and classical MD approaches by explicitly modeling bond activity (reactions) and charge equilibration. These aspects of ReaxFF pose significant challenges from a computational standpoint, both in sequential and parallel contexts. Evolving bond structure requires efficient dynamic data structures. Minimizing electrostatic energy through charge equilibration requires the solution of a large sparse linear system with a shielded electrostatic kernel at each sub-femtosecond long time-step. In this context, reaching spatio-temporal scales of tens of nanometers and nanoseconds, where phenomena of interest can be observed, poses significant challenges. In this paper, we present the design and implementation details of the Purdue Reactive Molecular Dynamics code, PuReMD. PuReMD has been demonstrated to be highly efficient (in terms of processor performance) and scalable. It extends current spatio-temporal simulation capability for reactive atomistic systems by over an order of magnitude. It incorporates efficient dynamic data structures, algorithmic optimizations, and effective solvers to deliver low per-time-step simulation time, with a small memory footprint. PuReMD is comprehensively validated for performance and accuracy on up to 3375 cores on a commodity cluster (Hera at LLNL-OCF). Potential performance bottlenecks to scalability beyond our experiments have also been analyzed. PuReMD is available over the public domain and has been used to model diverse systems, ranging from strain relaxation in Si-Ge nanobars, water-silica surface interaction, and oxidative stress in lipid bilayers (bio-membranes).

Reactive Molecular Dynamics: Numerical Methods and Algorithmic Techniques

Modeling atomic and molecular systems requires computation-intensive quantum mechanical methods such as, but not limited to, density functional theory [R. A. Friesner, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 6648-6653]. These methods have been successful in predicting various properties of chemical systems at atomistic scales. Due to the inherent nonlocality of quantum mechanics, the scalability of these methods ranges from O(

Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations

N^3

Improving the scalability of a symmetric iterative eigensolver for multi-core platforms

) to O(

PuReMD-GPU: A reactive molecular dynamics simulation package for GPUs

N^7

Topology-aware mappings for large-scale eigenvalue problems

) depending on the method used and approximations involved. This significantly limits the size of simulated systems to a few thousand atoms, even on large scale parallel platforms. On the other hand, classical approximations of quantum systems, although computationally (relatively) easy to implement, yield simpler models that lack essential chemical properties such as reactivity and charge transfer. The recent work of van Duin et al. [J. Phys. Chem. A, 105 (2001), pp. 9396-9409] overcomes the limitations of nonreactive classical molecular dynamics (MD) approximations by carefully incorporating limited nonlocality (to mimic quantum behavior) through an empirical bond order potential. This reactive classical MD method, called ReaxFF, achieves essential quantum properties, while retaining the computational simplicity of classical MD, to a large extent. Implementation of reactive force fields presents significant algorithmic challenges. Since these methods model bond breaking and formation, efficient implementations must rely on complex dynamic data structures. Charge transfer in these methods is accomplished by minimizing electrostatic energy through charge equilibration. This requires the solution of large linear systems (

Parallel eigenvalue calculation based on multiple shift-invert Lanczos and contour integral based spectral projection method

10^8

Exploring the future of out-of-core computing with compute-local non-volatile memory

degrees of freedom and beyond) with shielded electrostatic kernels at each time-step. Individual time-steps are themselves typically in the range of tenths of femtoseconds, requiring optimizations within and across time-steps to scale simulations to nanoseconds and beyond, where interesting phenomena may be observed. In this paper, we present implementation details of sPuReMD (serial Purdue reactive molecular dynamics program), a unique reactive classical MD code. We describe various data structures, and the charge equilibration solver at the core of the simulation engine. This Krylov subspace solver relies on a preconditioner based on incomplete LU factorization with thresholds (ILUT), specially targeted to our application. We comprehensively validate the performance and accuracy of sPuReMD on a variety of hydrocarbon systems. In particular, we show excellent per-time-step time, linear time scaling in system size, and a low memory footprint. sPuReMD is a freely distributed software with GPL and is currently being used to model diverse systems ranging from oxidative stress in biomembranes to strain relaxation in Si-Ge nanorods.

Identifying statistical dependence in genomic sequences via mutual information estimates

Obtaining highly accurate predictions on the properties of light atomic nuclei using the configuration interaction (CI) approach requires computing a few extremal Eigen pairs of the many-body nuclear Hamiltonian matrix. In the Many-body Fermion Dynamics for nuclei (MFDn) code, a block Eigen solver is used for this purpose. Due to the large size of the sparse matrices involved, a significant fraction of the time spent on the Eigen value computations is associated with the multiplication of a sparse matrix (and the transpose of that matrix) with multiple vectors (SpMM and SpMM_T). Existing implementations of SpMM and SpMM_T significantly underperform expectations. Thus, in this paper, we present and analyze optimized implementations of SpMM and SpMM_T. We base our implementation on the compressed sparse blocks (CSB) matrix format and target systems with multi-core architectures. We develop a performance model that allows us to understand and estimate the performance characteristics of our SpMM kernel implementations, and demonstrate the efficiency of our implementation on a series of real-world matrices extracted from MFDn. In particular, we obtain 3-4 speedup on the requisite operations over good implementations based on the commonly used compressed sparse row (CSR) matrix format. The improvements in the SpMM kernel suggest we may attain roughly a 40% speed up in the overall execution time of the block Eigen solver used in MFDn.

Efficient global optimization of reactive force-field parameters

We describe an efficient and scalable symmetric iterative eigensolver developed for distributed memory multi‐core platforms. We achieve over 80% parallel efficiency by major reductions in communication overheads for the sparse matrix‐vector multiplication and basis orthogonalization tasks. We show that the scalability of the solver is significantly improved compared to an earlier version, after we carefully reorganize the computational tasks and map them to processing units in a way that exploits the network topology. We discuss the advantage of using a hybrid OpenMP/MPI programming model to implement such a solver. We also present strategies for hiding communication on a multi‐core platform. We demonstrate the effectiveness of these techniques by reporting the performance improvements achieved when we apply our solver to large‐scale eigenvalue problems arising in nuclear structure calculations. Because sparse matrix‐vector multiplication and inner product computation constitute the main kernels in most iterative methods, our ideas are applicable in general to the solution of problems involving large‐scale symmetric sparse matrices with irregular sparsity patterns. Copyright