Results for “97 MATHEMATICS AND COMPUTING” — Page 4

DOE OSTI2025

Data-Conforming Data-Driven Control: Avoiding Premature Generalizations Beyond Data

Data-driven and adaptive control approaches face the problem of introducing sudden distributional shifts beyond the distribution of data encountered during learning. Therefore, they are prone to invalidating the very assumptions used in their own construction. This is due to the linearity of the underlying system, inherently assumed and formulated in most data-driven control approaches, which may falsely generalize the behavior of the system beyond the behavior experienced in the data. This article seeks to mitigate these problems by enforcing consistency of the newly designed closed-loop systems with data and slowing down any distributional shifts in the joint state-input space. This is achieved through incorporating affine regularization terms and linear matrix inequality constraints to data-driven approaches, resulting in convex semi-definite programs that can be efficiently solved by standard software packages. We discuss the optimality conditions of these programs and then conclude this article with a numerical example that further highlights the problem of premature generalization beyond data and shows the effectiveness of our proposed approaches in enhancing the safety of data-driven control methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Argonne Leadership Computing Facility 2024 Operational Assessment Report

This Operational Assessment Report describes how the Argonne Leadership Computing Facility (ALCF) met or exceeded every goal set by DOE for the calendar year (CY) 2024. In CY 2024, the ALCF operated Polaris, an AMD and NVIDIA-based Hewlett Packard Enterprise (HPE) Apollo 6500 Gen10+ system that provides a powerful platform for breakthrough science and prepares applications and workloads for Aurora, Argonne National Laboratory’s Intel-HPE exascale computer. Since going into production in August 2022, Polaris has supported research teams from the DOE Exascale Computing Project (ECP), which concluded in 2024, and from ALCF’s Aurora Early Science Program (ESP). Polaris delivered a total of 2555.7K node-hours to 17 Innovative and Novel Computational Impact on Theory and Experiment (INCITE) 2024 projects and 601.6K node-hours to ASCR Leadership Computing Challenge (ALCC) projects (12 of which were awarded during the 2023–2024 ALCC year and 11 of which were awarded during the 2024–2025 ALCC year), as well as providing substantial time for Director’s Discretionary (DD) projects (966.2K node-hours). As Table ES.1 shows, Polaris performed exceptionally well in terms of overall availability (97.7 percent), scheduled availability (99.6 percent), and utilization (94.7 percent; Table 2.1). In CY 2024, ALCF supported more than 2,000 users. As of March 18, 2025, ALCF’s users have published 254 papers in peer-reviewed journals and technical proceedings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs. To this end, here we present a large dataset of qubit-based quantum Hamiltonians. The dataset, called HamLib (for Hamiltonian Library), is freely available online and contains problem sizes ranging from 2 to 1000 qubits. HamLib includes problem instances of the Heisenberg model, Fermi-Hubbard model, Bose-Hubbard model, molecular electronic structure, molecular vibrational structure, MaxCut, Max- k -SAT, Max- k -Cut, QMaxCut, and the traveling salesperson problem. The goals of this effort are (a) to save researchers time by eliminating the need to prepare problem instances and map them to qubit representations, (b) to allow for more thorough tests of new algorithms and hardware, and (c) to allow for reproducibility and standardization across research studies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Impact Report: Quantum Systems Accelerator

The Quantum Systems Accelerator (QSA) is a U.S. National Quantum Information Science Research Center established in August 2020 and funded by the Department of Energy (DOE) Office of Science. QSA is composed of 15 partner institutions— universities and national laboratories—bringing together pioneers of many of today’s unique quantum information science (QIS) and engineering capabilities. Led by Lawrence Berkeley National Laboratory (Berkeley Lab), with Sandia National Laboratories (Sandia Labs) as the lead partner, 250+ QSA researchers are catalyzing U.S. leadership in a fast-growing field that seeks solutions to the Nation’s and the world’s most pressing problems by harnessing the laws of quantum mechanics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Green's function methods for multiphysics simulations (Final Report)

Green's functions are important tools for analyzing mathematical properties of partial differential equations (PDEs), and for numerically solving PDEs, especially when equations for the same operator but with multiple right hand sides need to be solved simultaneously. This proposal aims at developing efficient and accurate numerical methods for computing Green's functions, which can be used to tackle a challenging question in multiphysics simulation of DOE-mission science problems: how to couple quantum physics with classical physics. The key mathematical difficulty is properly formulate a "boundary condition" for the region described by quantum physics, and conventional approaches often model such boundary conditions in an empirical way. The proposed Green's function methods use the Dirichlet-to-Neumann map to formulate a boundary condition that is non-empirical and can couple the quantum and classical regions in an in principle exact way. The key ingredient of the new methods is to construct the Dirichlet-to-Neumann map in an efficient, accurate and versatile manner. The new methods have provably low complexity and are ideally suited for massively parallel and emerging many-core computational systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A Roadmap for Reaching the Potential of Brain-Derived Computing

Neuromorphic computing is a critical future technology for the computing industry, but it has yet to achieve its promise and has struggled to establish a cohesive research community. A large part of the challenge is that full realization of the potential of brain inspiration requires advances in both device hardware, computing architectures, and algorithms. This simultaneous development across technology scales is unprecedented in the computing field. This article presents a strategy, framed by market and policy pressures, for moving past these current technological and cultural hurdles to realize its full impact across technology. Achieving the full potential of brain-derived algorithms as well as post-complementary metal-oxide-semiconductor (CMOS) scaling neuromorphic hardware requires appropriately balancing the near-term opportunities of deep learning applications with the long-term potential of less understood opportunities in neural computing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

The future of computing beyond Moore’s Law

Moore’s Law is a techno-economic model that has enabled the information technology industry to double the performance and functionality of digital electronics roughly every 2 years within a fixed cost, power and area. Advances in silicon lithography have enabled this exponential miniaturization of electronics, but, as transistors reach atomic scale and fabrication costs continue to rise, the classical technological driver that has underpinned Moore’s Law for 50 years is failing and is anticipated to flatten by 2025. Here, this article provides an updated view of what a post-exascale system will look like and the challenges ahead, based on our most recent understanding of technology roadmaps. It also discusses the tapering of historical improvements, and how it affects options available to continue scaling of successors to the first exascale machine. Lastly, this article covers the many different opportunities and strategies available to continue computing performance improvements in the absence of historical technology drivers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Good Practices for High-Quality Scientific Computing

Experimental and observational sciences have developed robust practices for conducting experiments, maintaining their instruments, and record keeping for provenance. Computational science has only recently begun to confront the issue of quality of their instrument, the software, and the credibility of their scientific output. Most of the available literature in software engineering relates to enterprise software. While it can inform practices in scientific software, adjustments are usually needed. From time to time quality conscious practitioners have published collections of best practices for scientific software. Here, this article provides one more such list but with updated suggestions, motivated by the need to keep up with the rapid changes in the computing industry.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

SIERRA/Aero Theory Manual - Version 4.58

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment.

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DOE OSTI2020

SIERRA/Aero User Manual - Version 4.58

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment.

42 ENGINEERING↗

DOE OSTI2021

Intelligent Sampling for Surrogate Modeling, Hyperparameter Optimization, and Data Analysis

Sampling techniques are used in many fields, including design of experiments, image processing, and graphics. The techniques in each field are designed to meet the constraints specific to that field such as uniform coverage of the range of each dimension or random samples that are at least a certain distance apart from each other. When an application imposes new constraints, for example, by requiring samples in a non-rectangular domain or the addition of new samples to an existing set, a common solution is to modify the algorithm currently in use, often with less than satisfactory results. As an alternative, we propose the concept of intelligent sampling, where we devise algorithms specifically tailored to meet our sampling needs, either by creating new algorithms or by modifying suitable algorithms from other fields. Surprisingly, both qualitative and quantitative comparisons indicate that some relatively simple algorithms can be easily modified to meet the many sampling requirements of surrogate modeling, hyperparameter optimization, and data analysis; these algorithms outperform their more sophisticated counterparts currently in use, resulting in better use of time and computer resources.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

SIERRA/Aero User Manual (V.5.2)

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment.

42 ENGINEERING↗

DOE OSTI2022

SIERRA/Aero Theory Manual (V.5.6)

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment.

42 ENGINEERING↗

DOE OSTI2022

SIERRA/Aero User Manual (V.5.6)

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment.

42 ENGINEERING↗

DOE OSTI2021

Toward a Seamless Integration of Computing, Experimental, and Observational Science Facilities: A Blueprint to Accelerate Discovery

The Department of Energy, Office of Science operates world-leading facilities for experimental, observational, and computational science. DOE supercomputing facilities will reach performance at the scale of ExaFLOPs in the coming years, enabling new vistas of scale and precision for large scale simulations and data analysis. Experimental scientific facilities are undergoing similar upgrades that will lead to higher data rates and correspondingly larger computational demands, and will increase the need for near-real-time processing and resilient support for more complex workflows. A transformation of science is underway, with workloads at supercomputing facilities increasingly driven by this explosion of data from instruments and experimental facilities, as well as the accelerating use of Artificial Intelligence (AI) as a tool for scientific discovery. A seamless integration of computing, networking, instruments, and experimental facilities is required to support these emerging workloads and open up a new frontier of U.S. leadership in scientific discovery. We propose to accomplish this by providing frictionless access to the ASCR supercomputing facilities. We describe our vision of combining the power of ASCR supercomputers and networking infrastructure into an integrated scalable fabric, available to end user scientists via interfaces that aim to automate and simplify access to high performance computing systems. This will enable unprecedented computational science capabilities for experimental and observational facilities, and will create new opportunities to combine large simulations and modeling with experimental facility data analysis. This blueprint for creating an integrated network of computational and experimental facilities will provide an enriched discovery environment and open doors for new scientific communities to access the DOE’s world-leading computing and networking capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Experience of Migrating a Parallel Graph Coloring Program from CUDA to SYCL

We describe the experience of converting a CUDA implementation of a parallel graph coloring algorithm to SYCL. The goals are for our work to be useful to application and compiler developers by providing a detailed description of migration paths between CUDA and SYCL. We will describe how CUDA functions are mapped to SYCL functions. Evaluating the CUDA and SYCL implementations of the algorithm shows that the performance of SYCL and CUDA kernels are comparable over the test graph set on NVIDIA P100 and V100 GPUs. The SYCL program also allows for performance evaluation with the OpenCL and Level Zero interfaces and power profiling on an Intel GPU computing platform.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA/Aero Theory Manual - V.5.10

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment.

42 ENGINEERING↗