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DOE OSTI2023

Semantic embedding for quantum algorithms

The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation’s realizing dynamics. As quantum computing matures, a similar need has developed for an assurance of the correctness of high-level quantum algorithmic reasoning. Parallel to this need, many quantum algorithms have been unified and improved using quantum signal processing (QSP) and quantum singular value transformation (QSVT), which characterize the ability, by alternating circuit ansätze, to transform the singular values of sub-blocks of unitary matrices by polynomial functions. However, while the algebraic manipulation of polynomials is simple (e.g., compositions and products), the QSP/QSVT circuits realizing analogous manipulations of their embedded polynomials are non-obvious. This work constructs and characterizes the runtime and expressivity of QSP/QSVT protocols where circuit manipulation maps naturally to the algebraic manipulation of functional transforms (termed semantic embedding). In this way, QSP/QSVT can be treated and combined modularly, purely in terms of the functional transforms they embed, with key guarantees on the computability and modularity of the realizing circuits. We also identify existing quantum algorithms whose use of semantic embedding is implicit, spanning from distributed search to proofs of soundness in quantum cryptography. The methods used, based in category theory, establish a theory of semantically embeddable quantum algorithms, and provide a new role for QSP/QSVT in reducing sophisticated algorithmic problems to simpler algebraic ones.

Physics↗
DOE OSTI2016

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Massively parallel solvers for elliptic partial differential equations in numerical weather and climate prediction

The demand for substantial increases in the spatial resolution of global weather and climate prediction models makes it essential to use numerically efficient and highly scalable algorithms to solve the equations of large-scale atmospheric fluid dynamics. For stability and efficiency reasons, several of the operational forecasting centres, in particular the Met Office and the European Centre for Medium-Range Weather Forecasts (ECMWF) in the UK, use semi-implicit semi-Lagrangian time-stepping in the dynamical core of the model. The additional burden with this method is that a three-dimensional elliptic partial differential equation (PDE) for the pressure correction has to be solved at every model time step and this often constitutes a significant proportion of the time spent in the dynamical core. In global models, this PDE must be solved in a thin spherical shell. To run within tight operational time-scales, the solver has to be parallelized and there seems to be a (perceived) misconception that elliptic solvers do not scale to large processor counts and hence implicit time-stepping cannot be used in very high-resolution global models. After reviewing several methods for solving the elliptic PDE for the pressure correction and their application in atmospheric models, we demonstrate the performance and very good scalability of Krylov subspace solvers and multigrid algorithms for a representative model equation with more than 1010 unknowns on 65 536 cores on the High-End Computing Terascale Resource (HECToR), the UK's national supercomputer. Here, we tested and optimized solvers from two existing numerical libraries (the Distributed and Unified Numerics Environment (DUNE) and Parallel High Performance Preconditioners (hypre)) and implemented both a conjugate gradient solver and a geometric multigrid algorithm based on a tensor-product approach, which exploits the strong vertical anisotropy of the discretized equation. We study both weak and strong scalability and compare the absolute solution times for all methods; in contrast to one-level methods, the multigrid solver is robust with respect to parameter variations.

58 GEOSCIENCES↗
DOE OSTI2019

Parallel beamlet dose calculation via beamlet contexts in a distributed multi‐GPU framework

Purpose Dose calculation is one of the most computationally intensive, yet essential tasks in the treatment planning process. With the recent interest in automatic beam orientation and arc trajectory optimization techniques, there is a great need for more efficient model‐based dose calculation algorithms that can accommodate hundreds to thousands of beam candidates at once. Foundational work has shown the translation of dose calculation algorithms to graphical processing units ( GPU s), lending to remarkable gains in processing efficiency. But these methods provide parallelization of dose for only a single beamlet, serializing the calculation of multiple beamlets and under‐utilizing the potential of modern GPU s. In this paper, the authors propose a framework enabling parallel computation of many beamlet doses using a novel beamlet context transformation and further embed this approach in a scalable network of multi‐ GPU computational nodes. Methods The proposed context‐based transformation separates beamlet‐local density and TERMA into distinct beamlet contexts that independently provide sufficient data for beamlet dose calculation. Beamlet contexts are arranged in a composite context array with dosimetric isolation, and the context array is subjected to a GPU collapsed‐cone convolution superposition procedure, producing the set of beamlet‐specific dose distributions in a single pass. Dose from each context is converted to a sparse representation for efficient storage and retrieval during treatment plan optimization. The context radius is a new parameter permitting flexibility between the speed and fidelity of the dose calculation process. A distributed manager‐worker architecture is constructed around the context‐based GPU dose calculation approach supporting an arbitrary number of worker nodes and resident GPU s. Phantom experiments were executed to verify the accuracy of the context‐based approach compared to Monte Carlo and a reference CPU ‐ CCCS implementation for single beamlets and broad beams composed by addition of beamlets. Dose for representative 4 π beam sets was calculated in lung and prostate cases to compare its efficiency with that of an existing beamlet‐sequential GPU ‐ CCCS implementation. Code profiling was also performed to evaluate the scalability of the framework across many networked GPU s. Results The dosimetric accuracy of the context‐based method displays <1.35% and 2.35% average error from the existing serialized CPU ‐ CCCS algorithm and Monte Carlo simulation for beamlet‐specific PDD s in water and slab phantoms, respectively. The context‐based method demonstrates substantial speedup of up to two orders of magnitude over the beamlet‐sequential GPU ‐ CCCS method in the tested configurations. The context‐based framework demonstrates near linear scaling in the number of distributed compute nodes and GPU s employed, indicating that it is flexible enough to meet the performance requirements of most users by simply increasing the hardware utilization. Conclusions The context‐based approach demonstrates a new expectation of performance for beamlet‐based dose calculation methods. This approach has been successful in accelerating the dose calculation process for very large‐scale treatment planning problems ‐ such as automatic 4 π IMRT beam orientation and VMAT arc trajectory selection, with hundreds of thousands of beamlets ‐ in clinically feasible timeframes. The flexibility of this framework makes it as a strong candidate for use in a variety of other very large‐scale treatment planning tasks and clinical workflows.

Neph, Ryan↗
DOE OSTI2021

Neuromorphic Graph Algorithms

Graph algorithms enable myriad large-scale applications including cybersecurity, social network analysis, resource allocation, and routing. The scalability of current graph algorithm implementations on conventional computing architectures are hampered by the demise of Moore’s law. We present a theoretical framework for designing and assessing the performance of graph algorithms executing in networks of spiking artificial neurons. Although spiking neural networks (SNNs) are capable of general-purpose computation, few algorithmic results with rigorous asymptotic performance analysis are known. SNNs are exceptionally well-motivated practically, as neuromorphic computing systems with 100 million spiking neurons are available, and systems with a billion neurons are anticipated in the next few years. Beyond massive parallelism and scalability, neuromorphic computing systems offer energy consumption orders of magnitude lower than conventional high-performance computing systems. We employ our framework to design and analyze new spiking algorithms for shortest path and dynamic programming problems. Our neuromorphic algorithms are message-passing algorithms relying critically on data movement for computation. For fair and rigorous comparison with conventional algorithms and architectures, which is challenging but paramount, we develop new models of data-movement in conventional computing architectures. This allows us to prove polynomial-factor advantages, even when we assume a SNN consisting of a simple grid-like network of neurons. To the best of our knowledge, this is one of the first examples of a rigorous asymptotic computational advantage for neuromorphic computing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Rexsss Performance Analysis: Domain Decomposition Algorithm Implementations for Resilient Numerical Partial Differential Equation Solvers

The future of extreme-scale computing is expected to magnify the influence of soft faults as a source of inaccuracy or failure in solutions obtained from distributed parallel computations. The development of resilient computational tools represents an essential recourse for understanding the best methods for absorbing the impacts of soft faults without sacrificing solution accuracy. The Rexsss (Resilient Extreme Scale Scientific Simulations) project pursues the development of fault resilient algorithms for solving partial differential equations (PDEs) on distributed systems. Performance analyses of current algorithm implementations assist in the identification of runtime inefficiencies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method to solve the Navier–Stokes equations, with a highly parallel fast multipole method (fmm) as numerical engine, and match the current record in mesh size for this application, a cube of computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the fft algorithm as the numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the fmm-based vortex method achieving 74% parallel efficiency on 4096 processes (one gpu per mpi process, 3 gpus per node of the tsubame-2.0 system). The fft-based spectral method is able to achieve just 14% parallel efficiency on the same number of mpi processes (using only cpu cores), due to the all-to-all communication pattern of the fft algorithm. The calculation time for one time step was 108 s for the vortex method and 154 s for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex-method calculations to date.

Computer Science↗
DOE OSTI2015

ZettaBricks: A Language Compiler and Runtime System for Anyscale Computing

This grant supported the ZettaBricks and OpenTuner projects. ZettaBricks is a new implicitly parallel language and compiler where defining multiple implementations of multiple algorithms to solve a problem is the natural way of programming. ZettaBricks makes algorithmic choice a first class construct of the language. Choices are provided in a way that also allows our compiler to tune at a finer granularity. The ZettaBricks compiler autotunes programs by making both fine-grained as well as algorithmic choices. Choices also include different automatic parallelization techniques, data distributions, algorithmic parameters, transformations, and blocking. Additionally, ZettaBricks introduces novel techniques to autotune algorithms for different convergence criteria. When choosing between various direct and iterative methods, the ZettaBricks compiler is able to tune a program in such a way that delivers near-optimal efficiency for any desired level of accuracy. The compiler has the flexibility of utilizing different convergence criteria for the various components within a single algorithm, providing the user with accuracy choice alongside algorithmic choice. OpenTuner is a generalization of the experience gained in building an autotuner for ZettaBricks. OpenTuner is a new open source framework for building domain-specific multi-objective program autotuners. OpenTuner supports fully-customizable configuration representations, an extensible technique representation to allow for domain-specific techniques, and an easy to use interface for communicating with the program to be autotuned. A key capability inside OpenTuner is the use of ensembles of disparate search techniques simultaneously; techniques that perform well will dynamically be allocated a larger proportion of tests.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Parallelization techniques for quantum simulation of fermionic systems

Mapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum processor to enable (or impede) parallelization of the resulting Hamiltonian-simulation algorithm. It is shown that this problem can be mapped to a path coloring problem on a graph constructed from the particular choice of encoding fermions onto qubits and the fermionic interactions onto paths. The basic version of this problem is called the weak coloring problem. Taking into account the fine-grained details of the mapping yields what is called the strong coloring problem, which leads to improved parallelization performance. A variety of illustrative analytical and numerical examples are presented to demonstrate the amount of improvement for both weak and strong coloring-based parallelizations. Our results are particularly important for implementation on near-term quantum processors where minimizing circuit depth is necessary for algorithmic feasibility.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

CONRAD—A software framework for cone-beam imaging in radiology

Purpose: In the community of x-ray imaging, there is a multitude of tools and applications that are used in scientific practice. Many of these tools are proprietary and can only be used within a certain lab. Often the same algorithm is implemented multiple times by different groups in order to enable comparison. In an effort to tackle this problem, the authors created CONRAD, a software framework that provides many of the tools that are required to simulate basic processes in x-ray imaging and perform image reconstruction with consideration of nonlinear physical effects.Methods: CONRAD is a Java-based state-of-the-art software platform with extensive documentation. It is based on platform-independent technologies. Special libraries offer access to hardware acceleration such as OpenCL. There is an easy-to-use interface for parallel processing. The software package includes different simulation tools that are able to generate up to 4D projection and volume data and respective vector motion fields. Well known reconstruction algorithms such as FBP, DBP, and ART are included. All algorithms in the package are referenced to a scientific source.Results: A total of 13 different phantoms and 30 processing steps have already been integrated into the platform at the time of writing. The platform comprises 74.000 nonblank lines of code out of which 19% are used for documentation. The software package is available for download at http://conrad.stanford.edu. To demonstrate the use of the package, the authors reconstructed images from two different scanners, a table top system and a clinical C-arm system. Runtimes were evaluated using the RabbitCT platform and demonstrate state-of-the-art runtimes with 2.5 s for the 256 problem size and 12.4 s for the 512 problem size.Conclusions: As a common software framework, CONRAD enables the medical physics community to share algorithms and develop new ideas. In particular this offers new opportunities for scientific collaboration and quantitative performance comparison between the methods of different groups.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2020

DEEP Solar: Data DrivEn Modeling and Analytics for Enhanced System Layer ImPlementation

Realizing the SETO 2030 mission of reducing solar energy costs to 3-5 c/kWh will require innovative enabling research on effective, cost-efficient integration of local PV within distribution systems. However, the intermittent and variable nature of PVs compels operators to impose conservative hosting capacity constraints. Given the extremely high variability of (intermittent and unpredictable) solar energy generation, relaxing the capacity constraints (which are currently around 15%) and achieving 100% or greater integration of renewables will require a fundamental transformation of the power grid via the utilization of exponentially larger amounts of AMI enabled fine-grained data. To address the challenges in increasing the penetration of renewable energy based DERs, this project envisions an Enhanced System Layer (ESL) at the distribution network level that is reliable, cost-effective and scalable to millions of Distributed Energy Resources (DERs)/devices. This includes developing: 1) Transformative and highly scalable machine learning based predictive analytics tools that plug into distribution system planning and provide real-time situational awareness at the distribution level for short and long-term operational planning. The tools will be built using novel data-driven energy models of millions of active nodes with AMI, 2) Adaptive stochastic analysis and optimization algorithms for real-time grid operations, 3) Dynamic Scenario Analysis using parallel Cloudenabled implementations with < 1 minute computational cycle times.

14 SOLAR ENERGY↗
DOE OSTI2013

SLOAVx: Scalable LOgarithmic AlltoallV Algorithm for Hierarchical Multicore Systems

Scientific applications use collective communication operations in Message Passing Interface (MPI) for global synchronization and data exchanges. Alltoall and AlltoallV are two important collective operations. They are used by MPI jobs to exchange messages among all of MPI processes. AlltoallV is a generalization of Alltoall, supporting messages of varying sizes. However, the existing MPI AlltoallV implementation has linear complexity, i.e., each process has to send messages to all other processes in the job. Such linear complexity can result in sub optimal scalability of MPI applications when they are deployed on millions of cores. To address above challenge, in this paper, we introduce a new Scalable LOgarithmic AlltoallV algorithm, named SLOAV, for MPI AlltoallV collective operation. SLOAV aims to achieve global exchange of small messages of different sizes in a logarithmic number of rounds. Furthermore, given the prevalence of multicore systems with shared memory, we design a hierarchical AlltoallV algorithm based on SLOAV by leveraging the advantages of shared memory, which is referred to as SLOAVx. Compared to SLOAV, SLOAVx significantly reduces the inter-node communication, thus improving the entire system performance and mitigating the impact of message latency. We have implemented and embedded both algorithms in Open MPI. Our evaluation on large-scale computer systems shows that for the 8-byte and 1024-process MPI Alltoallv operation, the SLOAV can reduce the latency by as much as 86.4%, when compared to the state-of-the-art, and SLOAVx can further optimize the SLOAV by up to 83.1% in terms of message latency on multicore systems. In addition, experiments with NAS Parallel Benchmark (NPB) demonstrate that our algorithms are very effective for real-world applications.

Computer Science↗
DOE OSTI2019

Optimization of Condensed Matter Physics Application with OpenMP Tasking Model

The Density Matrix Renormalization Group (DMRG++) is a condensed matter physics application used to study superconductivity properties of materials. It’s main computations consist of calculating hamiltonian matrix which requires sparse matrix-vector multiplications. This paper presents task-based parallelization and optimization strategies of the Hamiltonian algorithm. The algorithm is implemented as a mini-application in C++ and parallelized with OpenMP. The optimization leverages tasking features, such as dependencies or priorities included in the OpenMP standard 4.5. The code refactoring targets performance as much as programmability. The optimized version achieves a speedup of 8.0× with 8 threads and 20.5× with 40 threads on a Power9 computing node while reducing the memory consumption to 90 MB with respect to the original code, by adding less than ten OpenMP directives.

Criado, Joel↗
DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Asynchronously parallel optimization solver for finding multiple minima

This paper proposes and analyzes an asynchronously parallel optimization algorithm for finding multiple, high-quality minima of nonlinear optimization problems. Our multistart algorithm considers all previously evaluated points when determining where to start or continue a local optimization run. Theoretical results show that, under certain assumptions, the algorithm almost surely starts a finite number of local optimization runs and identifies, or has a single local optimization run converging to, every minimum. The algorithm is applicable to general optimization settings, but our numerical results focus on the case when derivatives are unavailable. In numerical tests, a PYTHON implementation of the algorithm is shown to yield good approximations of many minima (including a global minimum), and this ability scales well with additional resources. Our implementation’s time to solution is shown also to scale well even when the time to evaluate the function evaluation is highly variable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams

A new, alternative set of interpretation rules of Feynman–Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mE{sub h} after 10{sup 6} Monte Carlo steps.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries

Highlights: •An algorithm for partitioning computational meshes is proposed. •The Morton order space-filling curve is modified to achieve improved locality. •A spatial locality metric is defined to compare results with existing approaches. •Results indicate improved performance of the algorithm in complex geometries. -- Abstract: A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton order curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

High-Performance Computation of Distributed-Memory Parallel 3D Voronoi and Delaunay Tessellation

Computing a Voronoi or Delaunay tessellation from a set of points is a core part of the analysis of many simulated and measured datasets: N-body simulations, molecular dynamics codes, and LIDAR point clouds are just a few examples. Such computational geometry methods are common in data analysis and visualization; but as the scale of simulations and observations surpasses billions of particles, the existing serial and shared-memory algorithms no longer suffice. A distributed-memory scalable parallel algorithm is the only feasible approach. The primary contribution of this paper is a new parallel Delaunay and Voronoi tessellation algorithm that automatically determines which neighbor points need to be exchanged among the subdomains of a spatial decomposition. Other contributions include periodic and wall boundary conditions, comparison of our method using two popular serial libraries, and application to numerous science datasets.

97 MATHEMATICS AND COMPUTING↗