Results for “Computer algorithms” — Page 60

DOE OSTI2022

Fast increased fidelity samplers for approximate Bayesian Gaussian process regression

Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H-matrix approximations that scales at O(n log 2 n). We show that this approximation’s Kullback-Leibler divergence to the true posterior can be made arbitrarily small. Though multidimensional GPs could be used with our algorithm, d-dimensional surfaces are modeled as tensor products of univariate GPs to minimize the cost of matrix construction and maximize computational efficiency. We illustrate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and non-synthetic data sets

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Graph Contractions for Calculating Correlation Functions in Lattice QCD

Computing correlation functions for many-particle systems in Lattice QCD is vital to extract nuclear physics observables like the energy spectrum of hadrons such as protons. However, this type of calculation has long been considered to be very challenging and computing-resource intensive because of the complex nature of a hadron composed of quarks with many degrees of freedom. In particular, a correlation function can be calculated through a sum of all possible pairs of quark contractions, each of which is a batched tensor contraction, dictated by Wick's theorem. Because the number of terms of this sum can be very large for any hadronic system of interest, fast evaluation of the sum faces several challenges: an extremely large number of contractions, a huge memory footprint at runtime, and the speed of tensor contractions. In this paper, we present a Lattice QCD analysis software suite, Redstar, which addresses these challenges by utilizing novel algorithmic and software engineering methods targeting modern computing platforms such as many-core CPUs and GPUs. In particular, Redstar represents every term in the sum of a correlation function by a graph, applies efficient graph algorithms to reduce the number of contractions to lower the cost of computations, and minimizes the total memory footprint. Moreover, Redstar carries out the contractions on either CPUs or GPUs utilizing an internal and highly efficient Hadron contraction library. Specifically, we illustrate some important algorithmic optimizations of Redstar, show various key design features of Hadron library, and present the speedup values due to the optimizations along with performance figures for calculating six correlations functions on four computing platforms.

Chen, Jie↗

DOE OSTI2023

Graph Contractions for Calculating Correlation Functions in Lattice QCD

Computing correlation functions for many-particle systems in Lattice QCD is vital to extract nuclear physics observables like the energy spectrum of hadrons such as protons. However, this type of calculation has long been considered to be very challenging and computing-resource intensive because of the complex nature of a hadron composed of quarks with many degrees of freedom. In particular, a correlation function can be calculated through a sum of all possible pairs of quark contractions, each of which is a batched tensor contraction, dictated by Wick's theorem. Because the number of terms of this sum can be very large for any hadronic system of interest, fast evaluation of the sum faces several challenges: an extremely large number of contractions, a huge memory footprint at runtime, and the speed of tensor contractions. In this paper, we present a Lattice QCD analysis software suite, Redstar, which addresses these challenges by utilizing novel algorithmic and software engineering methods targeting modern computing platforms such as many-core CPUs and GPUs. In particular, Redstar represents every term in the sum of a correlation function by a graph, applies efficient graph algorithms to reduce the number of contractions to lower the cost of computations, and minimizes the total memory footprint. Moreover, Redstar carries out the contractions on either CPUs or GPUs utilizing an internal and highly efficient Hadron contraction library. Specifically, we illustrate some important algorithmic optimizations of Redstar, show various key design features of Hadron library, and present the speedup values due to the optimizations along with performance figures for calculating six correlations functions on four computing platforms.

Chen, Jie↗

DOE OSTI2022

Scaling and Benchmarking an Evolutionary Algorithm for Constructing Biophysical Neuronal Models

Single neuron models are fundamental for computational modeling of the brain's neuronal networks, and understanding how ion channel dynamics mediate neural function. A challenge in defining such models is determining biophysically realistic channel distributions. Here, we present an efficient, highly parallel evolutionary algorithm for developing such models, named NeuroGPU-EA. NeuroGPU-EA uses CPUs and GPUs concurrently to simulate and evaluate neuron membrane potentials with respect to multiple stimuli. We demonstrate a logarithmic cost for scaling the stimuli used in the fitting procedure. NeuroGPU-EA outperforms the typically used CPU based evolutionary algorithm by a factor of 10 on a series of scaling benchmarks. We report observed performance bottlenecks and propose mitigation strategies. Finally, we also discuss the potential of this method for efficient simulation and evaluation of electrophysiological waveforms.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

A direct-adjoint approach for material point model calibration with application to plasticity

Here, this paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a single material point serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton–Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Simulating strongly correlated molecules with a superconducting quantum processor

Many of the biggest challenges in expanding the nation’s access to clean and low-cost energy resources are fundamentally chemistry or materials challenges. An important case is the development of new catalysts for the up-conversion of cheap and readily available materials such as methane or water into materials suitable for use as a fuel such as methanol or oxygen. To understand and exploit such processes, computer simulations of chemical reactions provide a natural complement to experimental studies. Unfortunately, most catalytic reactions involve so-called “strongly correlated” molecules which are notoriously difficult to study with simulation algorithms that can be executed on existing (classical) computers. The recent growth in quantum information science offers an alternative potential route for simulating these difficult systems. As a result, an increasing number of computational chemists are becoming interested in quantum computing. At the same time, quantum information scientists have identified chemistry simulation as a possible first demonstration of a quantum computer providing an improvement over a classical computer. The objective of this project is to accurately simulate strongly correlated molecules on a quantum processor. To meet the high challenges of this objective, new hybrid quantum/classical algorithms will be co-designed with advanced quantum gate developments and computed on customized quantum hardware. Some of the developed techniques will be transferable to study other molecular systems, while the project as a whole will help define better strategies for advancing the quantum simulation of matter more generally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Seascape Interface Control Document (V. 2)

This paper serves as the Interface Control Document (ICD) for the Seascape automated test harness developed at Sandia National Laboratories. The primary purposes of the Seascape system are: (1) provide a place for accruing large, curated, labeled data sets useful for developing and evaluating detection and classification algorithms (including, but not limited to, supervised machine learning applications) (2) provide an automated structure for specifying, running and generating reports on algorithm performance. Seascape uses GitLab, Nexus, Solr, and Banana, open source codes, together with code written in the Python language, to automatically provision and configure computational nodes, queue up jobs to accomplish algorithms test runs against the stored data sets, gather the results and generate reports which are then stored in the Nexus artifact server.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

NWChem: Past, present, and future

Specialized computational chemistry packages have permanently reshaped the landscape of chemical sciences by providing tools to support and guide the experimental effort and for prediction of chemical and materials properties. In this regard, a special role has been played by electronic structure packages where complex chemical and materials processes can be modeled using first-principle-driven methodologies. Over the last few decades, the rapid development of computing technologies and a tremendous increase in computational power has offered a unique chance to study complex chemical transformations using sophisticated and predictive many-body techniques to describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, a critical role has been played by novel parallel algorithms capable of taking advantage of computational resources to address polynomial scaling of electronic structure methods. NWChem was among the first electronic structure codes that focused on delivering scalable performance for electronic structure simulations. Herein, we briefly review the NWChem suite of computational codes including its history, design principles, parallel tools, current capabilities, outreach and outlook.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Optimal Power Flow in DC Networks with Robust Feasibility and Stability Guarantees

With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and operational constraint satisfaction are of concern. Most existing DC network optimal power flow (DN-OPF) formulations assume exact knowledge of loading conditions and do not provide stability guarantees. Here, in contrast, this paper studies a DN-OPF formulation which considers both stability and operational constraint satisfaction under uncertainty. The need to account for a range of uncertainty realizations in this paper's robust optimization formulation results in a challenging semi-infinite program (SIP). The proposed solution algorithm reformulates this SIP into a computationally tractable problem by constructing a tight convex inner approximation of the stability set using sufficient conditions for the existence of a feasible and stable power flow solution. Optimal generator set-points are obtained by optimizing over the proposed convex stability set. The validity and effectiveness of the propose algorithm is demonstrated through various DC networks adapted from IEEE test cases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Seascape Interface Control Document (V.1)

This paper serves as the Interface Control Document (ICD) for the Seascape automated test harness developed at Sandia National Laboratories. The primary purposes of the Seascape system are: (1) provide a place for accruing large, curated, labeled data sets useful for developing and evaluating detection and classification algorithms (including, but not limited to, supervised machine learning applications) (2) provide an automated structure for specifying, running and generating reports on algorithm performance. Seascape uses GitLab, Nexus, Solr, and Banana, open source codes, together with code written in the Python language, to automatically provision and configure computational nodes, queue up jobs to accomplish algorithms test runs against the stored data sets, gather the results and generate reports which are then stored in the Nexus artifact server.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Seascape Interface Control Document

This paper serves as the Interface Control Document (ICD) for the Seascape automated test harness developed at Sandia National Laboratories. The primary purposes of the Seascape system are: (1) provide a place for accruing large, curated, labeled data sets useful for developing and evaluating detection and classification algorithms (including, but not limited to, supervised machine learning applications) (2) provide an automated structure for specifying, running and generating reports on algorithm performance. Seascape uses GitLab, Nexus, Solr, and Banana, open source software, together with code written in the Python language, to automatically provision and configure computational nodes, queue up jobs to accomplish algorithms test runs against the stored data sets, gather the results and generate reports which are then stored in the Nexus artifact server.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Stealthy Cyber Anomaly Detection On Large Noisy Multi-material 3D Printer Datasets Using Probabilistic Models

As Additive Layer Manufacturing (ALM) becomes pervasive in industry, its applications in safety critical component manufacturing are being explored and adopted. However, ALM's reliance on embedded computing renders it vulnerable to tampering through cyber-attacks. Sensor instrumentation of ALM devices allows for rigorous process and security monitoring, but also results in a massive volume of noisy data for each run. As such, in-situ, near-real-time anomaly detection is very challenging. The ideal algorithm for this context is simple, computationally efficient, minimizes false positives, and is accurate enough to resolve small deviations. In this paper, we present a probabilistic-model-based approach to address this challenge. To test our approach, we analyze current measurements from a polymer composite 3D printer during emulated tampering attacks. Our results show that our approach can consistently and efficiently locate small changes in the presence of substantial operational noise.

Yoginath, Srikanth↗

DOE OSTI2024

Compressing branch-and-bound trees

A branch-and-bound (BB) tree certifies a dual bound on the value of an integer program. In this work, we introduce the tree compression problem (TCP): Given a BB tree T that certifies a dual bound, can we obtain a smaller tree with the same (or stronger) bound by either (1) applying a different disjunction at some node in T or (2) removing leaves from T? Here we believe such post-hoc analysis of BB trees may assist in identifying helpful general disjunctions in BB algorithms. We initiate our study by considering computational complexity and limitations of TCP. We then conduct experiments to evaluate the compressibility of realistic branch-and-bound trees generated by commonly-used branching strategies, using both an exact and a heuristic compression algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

On the use of a multigrid-reduction-in-time algorithm for multiscale convergence of turbulence simulations

Simulations of turbulent flow present challenges in terms of accuracy and affordability on modern highly-parallel computer architectures. A multigrid-reduction-in-time algorithm is used to provide a framework for separately evolving different scales of turbulence and for parallelizing the temporal domain, thereby increasing the concurrency. It is hypothesized that the space–time locality of the small scales of turbulence can be used to circumvent difficulties in applying temporal multigrid to flows dominated by inertial physics. For algorithms that fall well short of spectral accuracy (fourth-order is used in this work) attention must be paid to the accuracy of features on scales transferred between multigrid levels. Numerical experiments were performed using implicit large-eddy simulation. Results from applying the approach to an infinite-Reynolds number Taylor–Green flow and a double-shear flow at a Reynolds number of 11650 provide strong evidence that the approach has merit. The multigrid-reduction-in-time framework can be used to parallelize the temporal domain of a high-Reynolds-number turbulent flow and permit independent convergence of different scales. Establishing this foundation allows for future research in reducing the wall-clock time to solve turbulent flows while retaining the same accuracy as sequential solvers. In conclusion, current performance results from parallelizing the temporal domain are not competitive with those from sequential-in-time methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

PySpawn: Software for Nonadiabatic Quantum Molecular Dynamics

The ab initio multiple spawning (AIMS) method enables nonadiabatic quantum molecular dynamics simulations in an arbitrary number of dimensions, with potential energy surfaces provided by electronic structure calculations performed on-the-fly. However, the intricacy of the AIMS algorithm complicates software development, deployment on modern shared computer resources, and post-simulation data analysis. PySpawn is a nonadiabatic molecular dynamics software package that addresses these issues. Here, the program is designed to be easily interfaced with electronic structure software, and an interface to the TeraChem software package is described here. PySpawn introduces a task-based reorganization of the AIMS algorithm, allowing fine-grained restart capability and setting the stage for efficient parallelization in a future release. PySpawn includes a user-friendly and interactive Python analysis module that will enable novice users to painlessly adopt AIMS. As a demonstration of PySpawn’s simulation capability and analysis module, we report complete active space self-consistent field–based AIMS simulations of the 1,2- dithienyl-1,2-dicyanoethene molecule, a promising molecular photoswitch.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function $f_{NTU}$(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. Here, the new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Quantum Solver Using Singular Value Decomposition for Computational Fluid Dynamics

Numerical solutions for fluid flow problems are challenging and have been focus of Computational Fluid Dynamics (CFD) research for past several decades. The advent of quantum computing promises exponential speedup in comparison to existing classical methods and alleviate computational constraints posed by CFD problems. Although solutions for most problems of interest in fluid dynamics using quantum computing are distant, recent advances in algorithms, software and hardware provide a path towards realizing this goal. Quantum linear solver algorithms (QLSA) such as Harrow–Hassidim–Lloyd (HHL) and Variational Quantum Linear Solver (VQLS) have been successfully implemented to solve for canonical problems such as Hele-Shaw flow. However, these algorithms still suffer to scale and address problems with ill-conditioned Jacobians. In the current paper, we alleviate these restrictions with a new quantum solver based on Singular Value Decomposition (SVD) and simulate flow past a 2D cylinder. The fidelity of the SVD based quantum solver in predicting the flow past 2D cylinder is computed along with an assessment of errors. Classical and quantum solutions for the flow are compared for different resolutions. Finally, we discuss variation in the solutions based on number of shots used.

Gottiparthi, Kalyan [ORNL] (ORCID:0000000213540255↗