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At least 649 records · Page 36

Non-Intrusive Parallel-in-Time Solvers for Partial Differential Equations (Final Report)

Many time-dependent problems and simulations are often modeled using Partial Differential Equations. Traditional modeling approaches that use sequential time-stepping are reaching a bottleneck in optimizing efficiency. The Center of Applied Science and Computing at Lawrence Livermore National Laboratory extensively works on parallelizing these algorithms to leverage the increasing computational power from the growing number of processors in computer hardware. In particular, they aim to design non-intrusive algorithms that can generalize to a variety of problems and sizes without requiring additional information from or modifications on the original problems. Multigrid Reduction in Time (MGRIT) is a parallel-in-time algorithm that is designed to be non-intrusive. This project focuses on increasing the efficiency of MGRIT by approximating the coarse-grid operator using machine learning approaches as a means to find the most non-intrusive, or general, solution.

97 MATHEMATICS AND COMPUTING↗

Graph Neural Network-based Tracking as a Service

Recent studies have shown promising results for track finding in dense environments using Graph Neural Network (GNN)-based algorithms. However, GNN-based track finding is computationally slow on CPUs, necessitating the use of coprocessors to accelerate the inference time. Additionally, the large input graph size demands a large device memory for efficient computation, a requirement not met by all computing facilities used for particle physics experiments, particularly those lacking advanced GPUs. Furthermore, deploying the GNN-based track-finding algorithm in a production environment requires the installation of all dependent software packages, exclusively utilized by this algorithm. These computing challenges must be addressed for the successful implementation of GNN-based track-finding algorithm into production settings. In response, we introduce a ``GNN-based tracking as a service'' approach, incorporating a custom backend within the NVIDIA Triton inference server to facilitate GNN-based tracking. This paper presents the performance of this approach using the Perlmutter supercomputer at NERSC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Active Learning for Metamaterial Optimization on HPC and QC Integrated Systems

Active learning algorithms, integrating machine learning, quantum computing and optics simulation in an iterative loop, offer a promising approach to optimizing metamaterials. However, these algorithms can face difficulties in optimizing highly complex structures due to computational limitations. High-performance computing (HPC) and quantum computing (QC) integrated systems can address these issues by enabling parallel computing. In this study, we develop an active learning algorithm working on HPC-QC integrated systems. We evaluate the performance of optimization processes within active learning (i.e., training a machine learning model, problem-solving with quantum computing, and evaluating optical properties through wave-optics simulation) for highly complex metamaterial cases. Our results showcase that utilizing multiple cores on the integrated system can significantly reduce computational time, thereby enhancing the efficiency of optimization processes. Therefore, we expect that leveraging HPC-QC integrated systems helps effectively tackle large-scale optimization challenges in general.

Kim, Seongmin↗

A Minkowski difference-based advancing front packing technique for generating convex noncircular particles in complex domains

In this work, a Minkowski difference-based advancing front approach is proposed to generate convex and non-circular particles in a predefined computational domain. Two specific algorithms are developed to handle the contact conformity of generated particles with the boundaries of the computational domain. The first, called the open form, is used to handle the smooth contact of generated particles with (external) boundaries, while the other, called the closed form, is proposed to handle the internal boundaries of a computational domain with a complex cavity. The Gilbert-Johnson-Keerthi (GJK) method is used to efficiently solve the contact detection between the newly generated particle at the front and existing particles. Furthermore, the problem of one-sided particle lifting, which can cause some defects in the packing structure in existing advancing front methods during packing generation, is highlighted and an effective solution is developed. Several examples of increasing complexity are used to demonstrate the efficiency and applicability of the proposed packing generation approach. The numerical results show that the generated packing is not only more uniform, but also achieves a higher packing density than existing advancing front methods.

42 ENGINEERING↗

Quantum Davidson algorithm for excited states

Abstract Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. However, conventional QKS methodologies depend on a pre-generated subspace through real or imaginary-time evolutions. This subspace is inherently expansive and can be plagued with issues like slow convergence or numerical instabilities, often leading to relatively deep circuits. Our research presents an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuit. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.

97 MATHEMATICS AND COMPUTING↗

QCOR; A Language Extension Specification for the Heterogeneous Quantum-Classical Model of Computation

Quantum computing (QC) is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for QC were designed with fault-tolerant hardware in mind, envisioning stand-alone applications. However, the susceptibility of near-term quantum computers to noise limits their stand-alone utility. To better leverage limited computational strengths of noisy quantum devices, hybrid algorithms have been suggested whereby quantum computers are used in tandem with their classical counterparts in a heterogeneous fashion. This modus operandi calls out for a programming model and a high-level programming language that natively and seamlessly supports heterogeneous quantum-classical hardware architectures in a single-source-code paradigm. Motivated by the lack of such a model, we introduce a language extension specification, called QCOR, which enables single-source quantum-classical programming. Programs written using the QCOR library–based language extensions can be compiled to produce functional hybrid binary executables. After defining QCOR’s programming model, memory model, and execution model, we discuss how QCOR enables variational, iterative, and feed-forward QC. Additionally, QCOR approaches quantum-classical computation in a hardware-agnostic heterogeneous fashion and strives to build on best practices of high-performance computing. The high level of abstraction in the language extension is intended to accelerate the adoption of QC by researchers familiar with classical high-performance computing.

97 MATHEMATICS AND COMPUTING↗

fp-tools

The output of a molecular dynamics simulation is a data file containing properties of the motion of the simulated particles as a function of time (e.g., positions, velocities). From this output, scientists can extract various properties which give insight into the physics of the system; for example, the radial distribution function can be computed from the particle positions, which gives insight into how close the system is to melting or freezing. Many publicly available codes to perform molecular dynamics simulations exist and have been well adopted by the scientific community (e.g., LAMMPS, VASP). However, it remains standard practice for scientists to write their own post-processing scripts to extract various properties of interest from the molecular dynamics simulation data. Since in many cases scientists are interested in the same set of “textbook” properties, there is a large duplication of effort in writing these post-processing scripts. Our proposed code, FP-Tools, is a C++ toolkit designed to help scientists extract and analyze quantities of interest from the output of a molecular dynamics simulation, eliminating the need for them to write these codes themselves and thus reducing this duplication of effort. The quantities which are computed by our code are well documented in the literature (either in publications or textbooks), and the algorithms we implement to compute these properties are also well known in the field. We are not introducing new science or methods here; rather, our primary goal is to provide a useful tool to the community in the form of a well-documented, easy to use package.

Hartman, Leah↗

Data-Driven Computation of Probabilistic Marching Cubes for Efficient Visualization of Level-Set Uncertainty

Uncertainty visualization is an important emerging research area. Being able to visualize data uncertainty can help scientists improve trust in analysis and decision-making. However, visualizing uncertainty can add computational overhead, which can hinder the efficiency of analysis. In this paper, we propose novel data-driven techniques to reduce the computational requirements of the probabilistic marching cubes (PMC) algorithm. PMC is an uncertainty visualization technique that studies how uncertainty in data affects level-set positions. However, the algorithm relies on expensive Monte Carlo (MC) sampling for the multivariate Gaussian uncertainty model because no closed-form solution exists for the integration of multivariate Gaussian. In this work, we propose the eigenvalue decomposition and adaptive probability model techniques that reduce the amount of MC sampling in the original PMC algorithm and hence speed up the computations. Our proposed methods produce results that show negligible differences compared with the original PMC algorithm demonstrated through metrics, including root mean squared error, maximum error, and difference images. We demonstrate the performance and accuracy evaluations of our data-driven methods through experiments on synthetic and real datasets.

Athawale, Tushar↗

GentenMPI: Distributed Memory Sparse Tensor Decomposition

GentenMPl is a toolkit of sparse canonical polyadic (CP) tensor decomposition algorithms that is designed to run effectively on distributed-memory high-performance computers. Its use of distributed-memory parallelism enables it to efficiently decompose tensors that are too large for a single compute node's memory. GentenMPl leverages Sandia's decades-long investment in the Trilinos solver framework for much of its parallel-computation capability. Trilinos contains numerical algorithms and linear algebra classes that have been optimized for parallel simulation of complex physical phenomena. This work applies these tools to the data science problem of sparse tensor decomposition. In this report, we describe the use of Trilinos in GentenMPl, extensions needed for sparse tensor decomposition, and implementations of the CP-ALS (CP via alternating least squares) and GCP-SGD (generalized CP via stochastic gradient descent) sparse tensor decomposition algorithms. We show that GentenMPl can decompose sparse tensors of extreme size, e.g., a 12.6-terabyte tensor on 8192 computer cores. We demonstrate that the Trilinos backbone provides good strong and weak scaling of the tensor decomposition algorithms.

97 MATHEMATICS AND COMPUTING↗

Fast Data Processing for Hyperspectral Sensors on Small Platforms

Hyperspectral imaging is a very promising technology for nuclear proliferation detection. However, due to size and weight restrictions, small hyperspectral platforms such as satellites and small drones lack the on-board computing resources for accurate, real-time analysis of the enormous flow of data that a continuously operating hyperspectral sensor generates. This severely limits satellite systems, which can collect far more data than what they can telemeter, and hinders the ability of all platforms to adapt their missions on the fly in response to observations. This program addresses the hyperspectral data processing challenge through development of new, fast and accurate algorithms that produce data products in real time. The algorithms circumvent the major computational bottlenecks in existing processing streams, and would be incorporated in lightweight, power-efficient single-board computer systems. The toolkit of fast algorithms will be immediately useful in current and future hyperspectral systems being built by the Government and by private industry, including drone-based systems and satellite constellations that acquire timely global imagery.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Benchmarking Coordination Number Prediction Algorithms on Inorganic Crystal Structures

Coordination numbers and geometries form a theoretical framework for understanding and predicting materials properties. Algorithms to determine coordination numbers automatically are increasingly used for machine learning and automatic structural analysis. In this work, we introduce MaterialsCoord, a benchmark suite containing 56 experimentally-derived crystal structures (spanning elements, binaries, and ternary compounds) and their corresponding coordination environments as described in the research literature. We also describe CrystalNN, a novel algorithm for determining near neighbors. We compare CrystalNN against 7 existing near-neighbor algorithms on the MaterialsCoord benchmark, finding CrystalNN to perform similarly to several well-established algorithms. For each algorithm, we also assess computational demand and sensitivity towards small perturbations that mimic thermal motion. Finally, we investigate the similarity between bonding algorithms when applied to the Materials Project database. Finally, we expect that this work will aid the development of coordination prediction algorithms as well as improve structural descriptors for machine learning and other applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Scattering using real-time path integrals

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While imaginary time treatments of scattering are possible, imaginary time is not a natural framework for treating scattering problems. More importantly, quantum algorithms for calculating path integrals require real-time evolution. Purpose: Here, we test a recently introduced method for performing direct calculations of scattering observables using real-time path integrals in order to understand the challenges facing real-time path integral calculations of scattering observables. Method: The computations are based on a new interpretation of the path integral as the expectation value of a potential functional on cylinder sets of continuous paths with respect to a complex probability distribution. The method can in principle be applied to arbitrary short-range potentials. Results: The method is applied to compute matrix elements of Møller wave operators applied to narrow wave packets. These are used to calculate half-shell sharp-momentum transition matrix elements for one-dimensional potential scattering. The calculations for half-shell transition operator matrix elements converge to the numerical solution of the Lippmann-Schwinger equation. Conclusions: This work presents a proof in principle that scattering observables can be computed using real-time Feynman path integrals. While the computational method is not efficient, it can be improved. It provides a laboratory for studying quantum computational algorithms that are applicable to scattering problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Master State Distributed Estimator (masde)

The MSE technology provides a distributed state estimation scheme for power utilities by making it a real time dynamic system, versus the static snapshot method used today. This will allow utilities to verify power grid readings and identify false data on the communication network. The prevailing method of estimation takes all the data from the system into a single load flow equation at the utilities command center. This becomes a large algorithm that is very time consuming to solve, providing the engineers only snap shots of the system. The MFD distributes an algorithm to devises that are already installed at various locations on the power grid. This allows for much faster computer times because the algorithms contain magnitudes less data. When each distributed estimator completes its calculation, it sends the results back to the master device to check against all other distributed estimators.

Reen, DylanW.↗

Progress on the National Solar Radiation Data Base (NSRDB): A new DNI computation

This study introduces a new technique to compute direct normal irradiance (DNI) for improving the National Solar Radiation Data Base (NSRDB). A finite-surface integration algorithm is developed to compute solar radiation in differential solid angles and efficiently infer its contribution to a surface perpendicular to the solar direction. A lookup table of cloud bi-directional transmittance distribution function (BTDF) is developed by use of the discrete ordinates radiative transfer (DISORT) model for possible solar and observing directions and various cloud optical and microphysical properties. In each solar incident direction, DNI is given by the cloud BTDFs from approximately 200 differential solid angles. The simulated DNI is calibrated and evaluated using surface observations at the National Renewable Energy Laboratory's (NREL's) Solar Energy Research Laboratory (SRRL) and the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) facility.

54 ENVIRONMENTAL SCIENCES↗

Implementing and Benchmarking the Locally Competitive Algorithm on the Loihi 2 Neuromorphic Processor

Neuromorphic processors have garnered considerable interest in recent years for their potential in enabling energy-efficient and high-speed computing. The Locally Competative Algorithm (LCA) has been utilized for power efficient sparse coding on neuromophic processors, including the first Loihi processor \cite{appletospikes, loihi1}. With the Loihi 2 processor enabling custom neuron models and graded spike communication, more complex implementations of LCA are possible \cite{loihi2}. We present a new implementation of LCA designed for the Loihi 2 processor and perform an initial set of benchmarks comparing it to LCA on CPU and GPU devices. In these experiments LCA on Loihi 2 is faster and orders of magnitude more efficient, while maintaining similar reconstruction quality. We find this performance improvement increases as the LCA parameters are tuned towards greater representation sparsity. Our study highlights the potential of neuromorphic processors, particularly Loihi 2, in enabling intelligent,autonomous, real-time processing on small robots, satellite where there are strict SWaP (small, lightweighr, and low-power) requirement. By demonstrating the superior performance of LCA on Loihi 2 compared to conventional computing device, our study suggests that Loihi 2 could be a valuable tool in advancing these types of applications. Overall, our study highlights the potential of neuromorphic processors for efficient and accurate data processing on resource-constrained devices.

Parpart, Gavin G.↗

An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation

Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in terms of chip size and error rates. Shallow quantum circuits with uncomplicated topologies are essential for successful applications in the NISQ era. In this work, based on matrix analysis, we derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The depth of the compressed circuits is independent of simulation time and grows linearly with the number of spins. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond O(10 3 ) spins. The resulting quantum circuits have a simple nearest-neighbor topology, which makes them ideally suited for NISQ devices.

Hamiltonian simulation↗