arXiv subjects

Nicolas Bock

Publications and source records attributed to Nicolas Bock.

At least 19 recordsLinked to original sources

arXiv2024

Hybrid programming-model strategies for GPU offloading of electronic structure calculation kernels

To address the challenge of performance portability, and facilitate the implementation of electronic structure solvers, we developed the Basic Matrix Library (BML) and Parallel, Rapid O(N) and Graph-based Recursive Electronic Structure Solver (PROGRESS) libraries. BML implements linear algebra operations necessary for electronic structure kernels using a unified user interface for various matrix formats (dense, sparse) and architectures (CPUs, GPUs). Focusing on Density Functional Theory (DFT) and Tight-Binding (TB) models, PROGRESS implements several solvers for computing the single-particle density matrix and relies on BML. In this paper, we describe the general strategies used for these implementations on various computer architectures, using OpenMP target functionalities on GPUs, in conjunction with third-party libraries to handle performance critical numerical kernels. We demonstrate the portability of this approach and its performance on benchmark problems.

physics.comp-ph↗

arXiv2023

On-Surface Carbon Nitride Growth from Polymerization of 2,5,8-Triazido-s-heptazine

Carbon nitrides have recently come into focus for photo- and thermal catalysis, both as support materials for metal nanoparticles as well as photocatalysts themselves. While many approaches for the synthesis of three-dimensional carbon nitride materials are available, only top-down approaches by exfoliation of powders lead to thin film flakes of this inherently two-dimensional material. Here, we describe an in situ on-surface synthesis of monolayer 2D carbon nitride films, as a first step towards precise combination with other 2D materials. Starting with a single monomer precursor, we show that 2,5,8-triazido-s-heptazine (TAH) can be evaporated intact, deposited on a single crystalline Au(111) or graphite support, and activated via azide decomposition and subsequent coupling to form a covalent polyheptazine network. We demonstrate that the activation can occur in three pathways, via electrons (X-ray illumination), photons (UV illumination) and thermally. Our work paves the way to coat materials with extended carbon nitride networks which are, as we show, stable under ambient conditions.

cond-mat.mtrl-sci↗

arXiv2021

Performance Optimizations of Recursive Electronic Structure Solvers targeting Multi-Core Architectures (LA-UR-20-26665)

As we rapidly approach the frontiers of ultra large computing resources, software optimization is becoming of paramount interest to scientific application developers interested in efficiently leveraging all available on-Node computing capabilities and thereby improving a requisite science per watt metric. The scientific application of interest here is the Basic Math Library (BML) that provides a singular interface for linear algebra operation frequently used in the Quantum Molecular Dynamics (QMD) community. The provisioning of a singular interface indicates the presence of an abstraction layer which in-turn suggests commonalities in the code-base and therefore any optimization or tuning introduced in the core of code-base has the ability to positively affect the performance of the aforementioned library as a whole. With that in mind, we proceed with this investigation by performing a survey of the entirety of the BML code-base, and extract, in form of micro-kernels, common snippets of code. We introduce several optimization strategies into these micro-kernels including 1.) Strength Reduction 2.) Memory Alignment for large arrays 3.) Non Uniform Memory Access (NUMA) aware allocations to enforce data locality and 4.) appropriate thread affinity and bindings to enhance the overall multi-threaded performance. After introducing these optimizations, we benchmark the micro-kernels and compare the run-time before and after optimization for several target architectures. Finally we use the results as a guide to propagating the optimization strategies into the BML code-base. As a demonstration, herein, we test the efficacy of these optimization strategies by comparing the benchmark and optimized versions of the code.

cs.PF↗

arXiv2016

Graph-based linear scaling electronic structure theory

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

physics.comp-ph↗

arXiv2015

A $N$-Body Solver for Square Root Iteration

We develop the Sparse Approximate Matrix Multiply ($\tt SpAMM$) $n$-body solver for first order Newton Schulz iteration of the matrix square root and inverse square root. The solver performs recursive two-sided metric queries on a modified Cauchy-Schwarz criterion, culling negligible sub-volumes of the product-tensor for problems with structured decay in the sub-space metric. These sub-structures are shown to bound the relative error in the matrix-matrix product, and in favorable cases, to enjoy a reduced computational complexity governed by dimensionality reduction of the product volume. A main contribution is demonstration of a new, algebraic locality that develops under contractive identity iteration, with collapse of the metric-subspace onto the identity's plane diagonal, resulting in a stronger $\tt SpAMM$ bound. Also, we carry out a first order {Fr\'{e}chet} analyses for single and dual channel instances of the square root iteration, and look at bifurcations due to ill-conditioning and a too aggressive $\tt SpAMM$ approximation. Then, we show that extreme $\tt SpAMM$ approximation and contractive identity iteration can be achieved for ill-conditioned systems through regularization, and we demonstrate the potential for acceleration with a scoping, product representation of the inverse factor.

math.NA↗

arXiv2014

Solvers for $\mathcal{O} (N)$ Electronic Structure in the Strong Scaling Limit

We present a hybrid OpenMP/Charm++ framework for solving the $\mathcal{O} (N)$ Self-Consistent-Field eigenvalue problem with parallelism in the strong scaling regime, $P\gg{N}$, where $P$ is the number of cores, and $N$ a measure of system size, i.e. the number of matrix rows/columns, basis functions, atoms, molecules, etc. This result is achieved with a nested approach to Spectral Projection and the Sparse Approximate Matrix Multiply [Bock and Challacombe, SIAM J.~Sci.~Comput. 35 C72, 2013], and involves a recursive, task-parallel algorithm, often employed by generalized $N$-Body solvers, to occlusion and culling of negligible products in the case of matrices with decay. Employing classic technologies associated with generalized $N$-Body solvers, including over-decomposition, recursive task parallelism, orderings that preserve locality, and persistence-based load balancing, we obtain scaling beyond hundreds of cores per molecule for small water clusters ([H${}_2$O]${}_N$, $N \in \{ 30, 90, 150 \}$, $P/N \approx \{ 819, 273, 164 \}$) and find support for an increasingly strong scalability with increasing system size $N$.

math.NA↗

arXiv2014

An N-Body Solution to the Problem of Fock Exchange

We report an N-Body approach to computing the Fock exchange matrix with and without permutational symmetry. The method achieves an O(N lg N) computational complexity through an embedded metric-query, allowing hierarchical application of direct SCF criteria. The advantages of permutational symmetry are found to be 4-fold for small systems, but decreasing with increasing system size and/or more permissive neglect criteria. This work sets the stage for: (1) the introduction of range queries in multi-level multipole schemes for rank reduction, and (2) recursive task parallelism.

cs.DS↗

arXiv2013

Thermal electronic excitations in liquid metals

Thermal electronic excitations in metal crystals are calculated by starting with a reference structure for the nuclei: the crystal structure of the appropriate phase. Here we explain the corresponding theory for metal liquids, starting with an appropriate reference structure for a liquid. We explain the significance of these structures, and we briefly review how to find them and calculate their properties. Then we examine the electronic densities of states for liquid structures of Na, Al, and Cu, comparing them to their crystal forms. Next we explain how to calculate the dominant electronic thermal excitation term, considering issues of accuracy that do not arise in the crystal theory. Finally we briefly discuss the contribution from the interaction between excited electrons and moving nuclei.

cond-mat.mtrl-sci↗

arXiv2012

An Optimized Sparse Approximate Matrix Multiply for Matrices with Decay

We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with decay that achieves an $\mathcal{O} (n \log n)$ computational complexity with respect to matrix dimension $n$. We find that the max norm of the error achieved with a \SpAMM{} tolerance below $2 \times 10^{-8}$ is lower than that of the single-precision {\tt SGEMM} for dense quantum chemical matrices, while outperforming {\tt SGEMM} with a cross-over already for small matrices ($n \sim 1000$). Relative to naive implementations of \SpAMM{} using Intel's Math Kernel Library ({\tt MKL}) or AMD's Core Math Library ({\tt ACML}), our optimized version is found to be significantly faster. Detailed performance comparisons are made for quantum chemical matrices with differently structured sub-blocks. Finally, we discuss the potential of improved hardware prefetch to yield 2--3x speedups.

math.NA↗

arXiv2011

Extended Lagrangian free energy molecular dynamics

Extended free energy Lagrangians are proposed for first principles molecular dynamics simulations at finite electronic temperatures for plane-wave pseudopotential and local orbital density matrix based calculations. Thanks to the extended Lagrangian description the electronic degrees of freedom can be integrated by stable geometric schemes that conserve the free energy. For the local orbital representations both the nuclear and electronic forces have simple and numerically efficient expressions that are well suited for reduced complexity calculations. A rapidly converging recursive Fermi operator expansion method that does not require the calculation of eigenvalues and eigenfunctions for the construction of the fractionally occupied density matrix is discussed. An efficient expression for the Pulay force that is valid also for density matrices with fractional occupation occurring at finite electronic temperatures is also demonstrated.

physics.chem-ph↗

arXiv2011

Energy momentum conservation effects on two-particle correlation functions

Two particle correlations are used to extract information about the characteristic size of the system in proton-proton and heavy ion collisions. The size of the system can be extracted from the Bose-Einstein quantum mechanical effect for identical particles. However there are also long range correlations that shift the baseline of the correlation function from the expected flat behavior. A possible source of these correlations is the conservation of energy and momentum, especially for small systems, where the energy available for particle production is limited. A new technique, first used by the STAR collaboration, of quantifying these long range correlations using energy-momentum conservation considerations is presented in this talk. Using Monte Carlo simulations of proton-proton collisions at 900 GeV, it is shown that the baseline of the two particle correlation function can be described using this technique.

hep-ex↗

arXiv2010

Fast Multiplication of Matrices with Decay

A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize within the matrix space through truncation or rank reduction. Matrix truncation (element dropping) is compared to SpAMM for quantum chemical matrices with approximate exponential and algebraic decay. For matched errors in the electronic total energy, SpAMM is found to require fewer to far fewer floating point operations relative to dropping. The challenges and opportunities afforded by this new approach are discussed, including the potential for high performance implementations.

cs.DS↗

arXiv2010

Liquid state properties from first principles DFT calculations: Static properties

In order to test the Vibration-Transit (V-T) theory of liquid dynamics, ab initio density functional theory (DFT) calculations of thermodynamic properties of Na and Cu are performed and compared with experimental data. The calculations are done for the crystal at T = 0 and T_m, and for the liquid at T_m. The key theoretical quantities for crystal and liquid are the structural potential and the dynamical matrix, both as function of volume. The theoretical equations are presented, as well as details of the DFT computations. The properties compared with experiment are the equilibrium volume, the isothermal bulk modulus, the internal energy and the entropy. The agreement of theory with experiment is uniformly good. Our primary conclusion is that the application of DFT to V-T theory is feasible, and the resulting liquid calculations achieve the same level of accuracy as does ab initio lattice dynamics for crystals. Moreover, given the well established reliability of DFT, the present results provide a significant confirmation of V-T theory itself.

cond-mat.stat-mech↗

arXiv2010

Femtoscopy and energy-momentum conservation effects in proton-proton collisions at 900 GeV in ALICE

Two particle correlations are used to extract information about the characteristic size of the system for proton-proton collisions at 900 GeV measured by the ALICE (A Large Ion Collider experiment) detector at CERN. The correlation functions obtained show the expected Bose-Einstein effect for identical particles, but there are also long range correlations present that shift the baseline from the expected flat behavior. A possible source of these correlations is the conservation of energy and momentum, especially for small systems, where the energy available for particle production is limited. A new technique, first introduced by the STAR collaboration, of quantifying these long range correlations using energy-momentum conservation considerations is presented here. It is shown that the baseline of the two particle correlation function can be described using this technique.

hep-ex↗

arXiv2009

Optimized network clustering by jumping sub-optimal dendrograms

We propose a method to improve community division techniques in networks that are based on agglomeration by introducing dendrogram jumping. The method is based on iterations of sub-optimal dendrograms instead of optimization of each agglomeration step. We find the algorithm to exhibit excellent scaling behavior of its computational complexity. In its present form the algorithm scales as $\mathcal{O} (N^{2})$, but by using more efficient data structures it is possible to achieve a scaling of $\mathcal{O} (N \log^{2} N)$. We compare our results with other methods such as the greedy algorithm and the extremal optimization method. We find modularity values larger than the greedy algorithm and values comparable to the extremal optimization method.

physics.soc-ph↗

arXiv2009

An improved model for the transit entropy of monatomic liquids

In the original formulation of vibration-transit (V-T) theory for monatomic liquid dynamics, the transit contribution to entropy was taken to be a universal constant, calibrated to the constant-volume entropy of melting. This model suffers two deficiencies: (a) it does not account for experimental entropy differences of 2% among elemental liquids, and (b) it implies a value of zero for the transit contribution to internal energy. The purpose of this paper is to correct these deficiencies. To this end, the V-T equation for entropy is fitted to an overall accuracy of 0.1% to the available experimental high temperature entropy data for elemental liquids. The theory contains two nuclear motion contributions: (a) the dominant vibrational contribution S_{vib}(T/θ_0), where T is temperature and θ_0 is the vibrational characteristic temperature, and (b) the transit contribution S_{tr}(T/θ_{tr}), where θ_{tr} is a scaling temperature for each liquid. The appearance of a common functional form of S_{tr} for all the liquids studied is a property of the experimental data, when analyzed via the V-T formula. The resulting S_{tr} implies the correct transit contribution to internal energy. The theoretical entropy of melting is derived, in a single formula applying to normal and anomalous melting alike. An ab initio calculation of θ_0, based on density functional theory, is reported for liquid Na and Cu. Comparison of these calculations with the above analysis of experimental entropy data provides verification of V-T theory. In view of the present results, techniques currently being applied in ab initio simulations of liquid properties can be employed to advantage in the further testing and development of V-T theory.

cond-mat.other↗

arXiv2008

Quantitative Calculations for Black Hole Production at the Large Hadron Collider

The framework of Large Extra Dimensions provides a way to explain why gravity is weaker compared to the other forces in nature. A consequence of this model is the possible production of D-dimensional Black Holes in high energy p-p collisions at the Large Hadron Collider. The present work uses the CATFISH Black Hole generator to study quantitatively how these events could be observed in the hadronic channel at mid-rapidity using a particle tracking detector.

hep-ph↗

arXiv2008

Cache oblivious storage and access heuristics for blocked matrix-matrix multiplication

We investigate effects of ordering in blocked matrix--matrix multiplication. We find that submatrices do not have to be stored contiguously in memory to achieve near optimal performance. Instead it is the choice of execution order of the submatrix multiplications that leads to a speedup of up to four times for small block sizes. This is in contrast to results for single matrix elements showing that contiguous memory allocation quickly becomes irrelevant as the blocksize increases.

cs.DS↗