arXiv subjects

Joshua Finkelstein

Publications and source records attributed to Joshua Finkelstein.

14 recordsLinked to original sources

arXiv2026

SEDACS: A Scalable Framework for Complex Chemistry Simulations

Graph-based linear-scaling electronic-structure theory provides a scalable framework for parallel quantum-mechanical molecular dynamics (QMD) simulations by exploiting the nearsightedness of the non-local electronic connectivity in non-metallic systems. When combined with recent shadow molecular dynamics in an extended-Lagrangian formulation, it enables stable long-time simulations of large, chemically active systems. This article introduces the Scalable Ecosystem, Driver, and Analyzer for Complex Chemistry Simulations (SEDACS), which integrates all these advances within a modular, Python-based software package for large-scale QMD simulations driven by external electronic-structure codes. SEDACS provides a tunable, adaptive graph construction in which edges encode the non-local electronic overlap between atoms. This graph is then decomposed into a set of smaller, overlapping subgraphs, where the electronic structure of each of these subgraphs is solved for independently and in parallel using an external electronic-structure code. SEDACS can be coupled to a variety of external electronic-structure solvers with minimal modifications to their software, enabling rapid adoption of the graph-based QMD approach. In this way, SEDACS can greatly extend the capability of existing electronic-structure packages by enabling stable QMD simulations of systems that were previously computationally inaccessible. We demonstrate highly efficient and stable QMD simulations for chemically active systems with tens of thousands of atoms by interfacing SEDACS with an external Fortran-based electronic-structure code based on self-consistent-charge density functional tight-binding theory.

physics.chem-ph↗

arXiv2026

Machine-learned, finite temperature Fermi-operator expansions suitable for GPUs and AI-hardware

We present several finite-temperature recursive Fermi-operator expansion schemes based on the second-order spectral projection (SP2) method. Our approach builds on a previous observation that the electronic structure problem, as formulated through a recursive SP2 expansion, can be mapped onto the architecture of a deep neural network. Using this perspective, we generalize SP2 to finite electronic temperatures by constructing machine learning models that determine optimized recursive expansion coefficients. The same approach is also applied to the prediction of the electronic entropy for fractional occupation numbers. The coefficients are trained for a specified chemical potential and electronic temperature and are not available in closed analytical form. However, by employing an appropriate affine rescaling strategy to the Hamiltonian matrix, we eliminate the need to retrain the model for different temperatures and chemical potentials. Our approach avoids explicit diagonalization and relies solely on highly optimized matrix-matrix multiplication kernels. Compared to state-of-the-art diagonalization, we achieve an order-of-magnitude speedup in the single-particle finite-temperature density matrix calculation for small and moderately sized matrices on modern GPUs and dense matrix multiply units.

quant-ph↗

arXiv2025

Modeling Reactions on the Solid-Liquid Interface With Next Generation Extended Lagrangian Quantum-Based Molecular Dynamics

We present a series of simulations of the oxygen reduction reaction (ORR) using a novel framework for atomistic simulations of surface catalysis under electrochemical bias. The framework makes use of quantum-mechanical extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) simulations, which provide the speed and accuracy required for explicit atomistic treatment of both electrode and electrolyte. Simulations of solvated O$_2$ near nitrogen-doped graphene (NG) were performed to gain insight into the ORR, and different mechanisms were observed, depending on the applied bias. Under higher bias the ORR occurred by an outer-sphere mechanism, without adsorption of O$_2$ to NG. In this mechanism, electron transfer between the catalyst and the O$_2$ was mediated by the solvent. Under lower bias the ORR occurred by an inner-sphere mechanism involving adsorption of O$_2$ to NG, leading to direct electron transfer. Our extensive, all-atom quantum-mechanical molecular dynamics simulations also show clear differences between the kinetics of the ORR on this ideally polarizable electrode and commonly used kinetic theories, leading to new insights regarding mechanistic changes with varied overpotentials. Combining quantum accuracy with explicit solvation and electrostatic potential bias, XL-BOMD opens a route to predictive, atomistic insight into electrocatalytic processes, as demonstrated with the ORR.

physics.chem-ph↗

arXiv2024

Susceptibility Formulation of Density Matrix Perturbation Theory

Density matrix perturbation theory based on recursive Fermi-operator expansions provides a computationally efficient framework for time-independent response calculations in quantum chemistry and materials science. From a perturbation in the Hamiltonian we can calculate the first-order perturbation in the density matrix, which then gives us the linear response in the expectation values for some chosen set of observables. Here we present an alternative, {\it dual} formulation, where we instead calculate the static susceptibility of an observable, which then gives us the linear response in the expectation values for any number of different Hamiltonian perturbations. We show how the calculation of the susceptibility can be performed with the same expansion schemes used in recursive density matrix perturbation theory, including generalizations to fractional occupation numbers and self-consistent linear response calculations, i.e. similar to density functional perturbation theory. As with recursive density matrix perturbation theory, the dual susceptibility formulation is well suited for numerically thresholded sparse matrix algebra, which has linear scaling complexity for sufficiently large sparse systems. Similarly, the recursive computation of the susceptibility also seamlessly integrates with the computational framework of deep neural networks used in artificial intelligence (AI) applications. This integration enables the calculation of quantum response properties that can leverage cutting-edge AI-hardware, such as Nvidia Tensor cores or Google Tensor Processing Units. We demonstrate performance for recursive susceptibility calculations using Nvidia Graphics Processing Units and Tensor cores.

quant-ph↗

arXiv2024

Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs

In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI/ML hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure theory, $S^{-1}$. This factorization of $S^{-1}$, written as $ZZ^T=S^{-1}$, is used to transform the general matrix eigenvalue problem into a standard matrix eigenvalue problem. Here we present a mixed precision iterative refinement algorithm where $Z$ is given recursively using matrix-matrix multiplications and can be computed with high performance on Tensor cores. To understand the performance and accuracy of Tensor cores, comparisons are made to GPU-only implementations in single and double precision. Additionally, we propose a non-parametric stopping criteria which is robust in the face of lower precision floating point operations. The algorithm is particularly useful when we have a good initial guess to $Z$, for example, from previous time steps in quantum-mechanical molecular dynamics simulations or from a previous iteration in a geometry optimization.

physics.comp-ph↗

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

A fast, dense Chebyshev solver for electronic structure on GPUs

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes ($\lesssim$ 5000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm [W. Liang et al, J. Chem. Phys. 2003] whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. This improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller ($\lesssim$ 1000) matrix sizes. Lastly, we apply our technique to a model system with a high density of states around the Fermi level which typically presents significant challenges.

physics.chem-ph↗

arXiv2022

A Methodology to Generate Crystal-based Molecular Structures for Atomistic Simulations

We propose a systematic method to construct crystal-based molecular structures often needed as input for computational chemistry studies. These structures include crystal ``slabs" with periodic boundary conditions (PBCs) and non-periodic solids such as Wulff structures. We also introduce a method to build crystal slabs with orthogonal PBC vectors. These methods are integrated into our code, Los Alamos Crystal Cut (LCC), which is open source and thus fully available to the community. Examples showing the use of these methods are given throughout the manuscript.

cond-mat.mtrl-sci↗

arXiv2022

Quantum perturbation theory using Tensor cores and a deep neural network

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e. dense matrix-matrix multiplications, in mixed precision arithmetics which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree-Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

physics.comp-ph↗

arXiv2021

Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

In light of the recently published complete set of statistically correct Gronbech-Jensen (GJ) methods for discrete-time thermodynamics, we revise a differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has at least weak second order accuracy in the applied time step. It further helps identify a novel half-step velocity, which simultaneously produces both correct kinetic statistics and correct transport measures for any of the statistically sound GJ methods. Explicit algorithmic expressions are given for the integration of the new half-step velocity into the GJ set of methods. Numerical simulations, including quantum-based molecular dynamics (QMD) using the QMD suite LATTE, highlight the discussed properties of the algorithms as well as exhibit the direct application of robust, time step independent stochastic integrators to quantum-based molecular dynamics.

physics.comp-ph↗

arXiv2021

Quantum-based Molecular Dynamics Simulations Using Tensor Cores

Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency, but with the caveat that they were designed for tensor contractions (matrix-matrix multiplications) using only low-precision floating point operations. In spite of this, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born-Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on the tensor cores of a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born-Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.

physics.comp-ph↗

arXiv2021

Mixed Precision Fermi-Operator Expansion on Tensor Cores From a Machine Learning Perspective

We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for half-precision floating point operations on Nvidia's A100 tensor core units. The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem. We demonstrate how this network can be accelerated by optimizing the weight and bias values to substantially reduce the number of layers required for convergence. We also show how this machine learning approach can be used to optimize the coefficients of the recursive Fermi-operator expansion to accurately represent fractional occupation numbers of the electronic states at finite temperatures.

physics.comp-ph↗

arXiv2020

The Challenge of Stochastic St{\o}rmer-Verlet Thermostats Generating Correct Statistics

In light of the recently developed complete GJ set of single random variable stochastic, discrete-time St{\o}rmer-Verlet algorithms for statistically accurate simulations of Langevin equations, we investigate two outstanding questions: 1) Are there any algorithmic or statistical benefits from including multiple random variables per time-step, and 2) are there objective reasons for using one or more methods from the available set of statistically correct algorithms? To address the first question, we assume a general form for the discrete-time equations with two random variables and then follow the systematic, brute-force GJ methodology by enforcing correct thermodynamics in linear systems. It is concluded that correct configurational Boltzmann sampling of a particle in a harmonic potential implies correct configurational free-particle diffusion, and that these requirements only can be accomplished if the two random variables per time step are identical. We consequently submit that the GJ set represents all possible stochastic St{\o}rmer-Verlet methods that can reproduce time-step-independent statistics of linear systems. The second question is thus addressed within the GJ set. Based in part on numerical simulations of complex molecular systems, and in part on analytic scaling of time, we analyze the apparent difference in stability between different methods. We attribute this difference to the inherent time scaling in each method, and suggest that this scaling may lead to inconsistencies in the interpretation of dynamical and statistical simulation results. We therefore suggest that the method with the least inherent time-scaling, the GJ-I/GJF-2GJ method, be preferred for statistical applications where spurious rescaling of time is undesirable.

cond-mat.stat-mech↗

arXiv2019

Comparison of Modern Langevin Integrators for Simulations of Coarse-Grained Polymer Melts

For a wide range of phenomena, current computational ability does not always allow for fully atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining (CG) is an established approach to alleviate the impact of computational limits while retaining the same algorithms used in atomistic simulations. It is of importance to understand how algorithms such as Langevin integrators perform on non-trivial CG molecular systems, and in particular how large of an integration time step can be used without introducing unacceptable amounts of error into averaged quantities of interest. To investigate this, we examined three different Langevin integrators on a CG polymer melt: the recently developed BAOAB method by Leimkuhler and Matthews, the Gronbech-Jensen and Farago method, or G-JF, and the frequently used Brunger-Brooks-Karplus integrator, also known as BBK. We compute and analyze key statistical properties for each. Our results indicate that the three integrators perform similarly when using a small friction parameter; however, outside of this regime the use of large integration steps produces significant deviations from the predicted diffusivity and steady-state distributions for all integration methods examined with the exception of G-JF.

physics.comp-ph↗