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Results for “Mathematics of computing”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 505 records · Page 28

Tough Errors Are no Match (TEAM): Optimizing the quantum compiler for noise resilience

This report summarizes Unitary Fund’s contributions to the Department of Energy’s TEAM project (DE-SC0020266) under Thrust 2: Quantum Programming and Compilation. The central outcomes of this work have been the development of Mitiq, an open-source Python toolkit for applying quantum error mitigation (QEM) techniques to noisy quantum programs, and the invention, benchmarking and theoretical investigation of novel QEM techniques. Additional outcomes include the development of other open source software packages for the usage, simulation and control of quantum computers.

97 MATHEMATICS AND COMPUTING↗

Exact signed distance fields using parallel Fast Sweeping Method

Signed distance fields are often used in multiphysics simulations to track material interfaces. We present a simple methodology based on the fast sweeping method to generate the exact signed distance from triangular meshes and linear paths on Cartesian grids. The methodology propagates the closest primitive to the boundary to the rest of the domain following the characteristics. A local upwind criterion is used to decide between the new and existing closest primitive at each grid point while capturing the correct sign of the global function. The methodology has optimal computational complexity and runs efficiently in distributed-memory architectures. We include 2D and 3D test cases along with a resolution study up to 0.512 trillion zones and 1,000 computer cores. The solution strategy can also be applied to other types of meshes or collections of primitives.

97 MATHEMATICS AND COMPUTING↗

FAIR Data and Interpretable AI Framework for Architectured Metamaterials

Our interdisciplinary effort successfully generated FAIR (Findable, Accessible, Interoperable, and Reusable) benchmark datasets for mechanical metamaterials while introducing a novel Artificial Intelligence (AI) framework known as Learning Refined Compositional Rules (LRCR). This framework was specifically designed to bridge the gap across varying computational length scales and extract the underlying physical mechanisms that connect a material's structural geometry to its bulk acoustic properties. Historically, the discovery of such structured materials relied heavily on human intuition or opaque, black-box optimization algorithms that were difficult to generalize. By combining interpretable machine learning techniques with rigorous experimental validation, this project established clear, generalizable design guidelines for tuning wave dispersion and controlling vibrations. Ultimately, the public availability of these structured datasets and algorithms will significantly reduce computational costs and accelerate the design of advanced multi-functional acoustic devices, offering broad societal impacts across fields like aerospace engineering, telecommunications, and biomedical implant design.

36 MATERIALS SCIENCE↗

Xyce™ Parallel Electronic Simulator (V.7.9) Release Notes

The Xyce™ Parallel Electronic Simulator has been written to support the simulation needs of Sandia National Laboratories’ electrical designers. Xyce™ is a SPICE-compatible simulator with the ability to solve extremely large circuit problems on large-scale parallel computing platforms, but also includes support for most popular parallel and serial computers. For up-to-date information not available at the time these notes were produced, please visit the Xyce™ web page at http://xyce.sandia.gov.

42 ENGINEERING↗

Data Center Market Report

The data center market is poised to explode in the coming decade due to undeniable drivers such as continued adoption of generative AI, increased data storage needs, and enterprise integration of AI in numerous industries [1] [2] [3]. Scalable power and increased computational capacity are at the forefront of considerations for hyperscalers, the major cloud service providers in this space. Lawrence Livermore National Laboratory is uniquely poised to help with informed decision making for data center market leaders during this phase of explosive expansion. National grid modeling expertise and cutting edge innovations in computer cooling systems place LLNL in an enviable position for creating economic impact in the data center industry by leveraging its expertise in these areas which can help the data center market keep up with growing demand.

97 MATHEMATICS AND COMPUTING↗

Resilience Through Data-Driven, Intelligent Designed Control: A Formal Methods Approach

The PNNL and GTRI team developed a strategy to integrate temporal logic rule specification for detection of cyber-intrusion in the source code and control algorithms of CPS using advanced cyber-data. The GTRI team utilized its capabilities in rule synthesis and temporal logic specifications for software assurance and verification to detect and predict impact of cyber-intrusions and malware in the computational and control algorithms of cyber-physical systems. The team also developed a testing and verification approach that could be used to validate the suggested approach against a realistic use-case CPS showcasing improvements in system impact prediction performance. Temporal logic offers a compact expression of events in absolute and relative time and has a formalized translation to state machines. As such, temporal logic rules can feasibly be synthesized to any system as a rule engine, with the process being formally verified to be correct. The goal here is to utilize temporal logic rules to detect cyber-attacks and manipulations in the computational algorithms and provide real-time software assurance and verification guarantees.

97 MATHEMATICS AND COMPUTING↗

YOLO for Radio Frequency Signal Classification

Radio frequency signal classification plays a pivotal role in various applications, including spectrum management, wireless security, and cognitive radio. Extant signal classification methods require significant data throughput and are not multilabel. We propose a novel approach to radio frequency signal classification by leveraging the You Only Look Once (YOLO) object detection method. YOLO is a state-of-the-art deep learning model renowned for its real-time object detection capabilities in computer vision applications. We adapt YOLO for signal classification to enable the automatic and efficient identification of various signal types within a power spectral density image. Index Terms—radio-frequency analysis, object detection, neural networks, machine learning, deep learning.

42 ENGINEERING↗

Immersive Visualization for Scientific Data Analysis

We will present the use of immersive visualization at the National Renewable Energy Laboratory (NREL), showcasing how immersive visualization is advancing scientific research and engineering practices and transforming our day-to-day operations. We are leveraging immersive visualization to support scientific discovery and engineering in various domains, including material design, computational fluid dynamics, immersive analytics, grid modernization, digital twins, and situated visualization. We have observed several benefits across four key areas: enhanced spatial judgments, improved understanding through interaction, increased capacity to embed high-dimensional data, and improved collaboration.

immersive analytics↗

Report for the DOE Office of Science Workshop on Envisioning Frontiers in AI and Computing for Biological Research

Artificial intelligence (AI), machine learning (ML), and high-performance computing (HPC) are poised to transform biological research, spurring innovation in biotechnology and biosystems design. "is transformation will bring an explosion of new capabilities to control the expression of genomic information in living organisms and harness that information to invent new biobased technologies (Jinek et al. 2012; NASEM 2025).

59 BASIC BIOLOGICAL SCIENCES↗

Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems

Here, we present a novel physics-informed neural networks (PINNs) framework for modeling interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks for any two subdomains separated by a sharp interface such that the neural networks differ only through their activation functions while the other parameters remain identical. The performance of I-PINNs, conventional PINNs, and other existing domain-decomposition PINNs methods such as extended PINNs (XPINNs) and multi-domain PINN (M-PINN) is compared through several one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems. The results demonstrate that I-PINNs provides a root-mean-square-error accuracy, at least two orders of magnitude better than conventional PINNs and XPINNs at approximately one-tenth of the computational cost of conventional PINNs and half the cost of XPINNs. Additionally, while I-PINNs and M-PINN provide comparable accuracies, M-PINN is found to be approximately 50% more expensive.

42 ENGINEERING↗

PyFaults: A Python Toolkit for Stacking Fault Screening

PyFaults is an open-source Python library designed to model stacking fault disorder in crystalline materials and qualitatively assess the characteristic selective broadening effects in powder X-ray diffraction (PXRD). Here, the main capabilities of PyFaults are presented, including unit cell and supercell model construction, PXRD pattern calculation, assessment against experimental PXRD, and methods for rapid screening of candidate models within a set of possible stacking vectors and fault occurrence probabilities. This program aims to serve as a computationally inexpensive tool for identifying and screening potential stacking fault models in materials with planar disorder. Three diverse case studies, involving GaN, Li2MnO3 and Li3YCl6, are presented to illustrate the program functionality across a range of structure types and stacking fault modalities.

MATHEMATICS AND COMPUTING↗

Z Line VISAR Analysis with the LineVISAR SMASH Class

The Z line VISAR system (ZLV) is a spatially-resolved velocimeter that measures surface velocities in high-energy density experiments on the Z Pulsed Power Facility to facilitate the investigation of fusion, power flow, and dynamic material physics. The data measured in these experiments are analyzed with the LineVISAR SMASH class, a MATLAB software suite that provides tools for data importation, streak image correction, spatiotemporal registration, wrapped phase computation, phase unwrapping, shock handling, and velocity calculation. This report overviews the LineVISAR class, discusses its use, provides example implementations, and supplies analysis specifics not typically recorded in journal publications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Flexible AI Models for Grid Resilience

The rapid growth in size and complexity of artificial intelligence (AI) and machine learning (ML) models has led to increased energy demands, posing a threat to the reliability of the existing power grid. This project addresses the challenge of highly intermittent and energy-intensive inference workloads by (1) developing fidelity-adaptive neural networks capable of dynamic response to grid conditions and (2) integrating these networks with power flow simulations to assess their impact on power grid reliability. We will explore both top-down and bottom-up approaches to create hierarchies of submodels that provide a controlled trade-off between power draw and prediction accuracy. The top-down method utilizes NN pruning to reduce a flagship model into progressively smaller, energy-efficient variants. The bottom-up approach employs geometrically principled weight setting strategies to construct depth-efficient models from the ground up. A real-time hardware-in-the-loop (HIL) platform will be developed to simulate a scaled AC power grid, integrating live AI workload power draw and enabling dynamic model switching in response to grid feedback. This work will provide a novel framework for evaluating the impact of flexible AI/ML workloads on grid performance and establish new methodologies for energy-aware computing in data centers. The outcomes will demonstrate that adaptive AI/ML can play a critical role in improving grid stability while advancing NREL's leadership in energy-efficient computing research.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Practical Probabilistic Programming

Recent advances in probabilistic programming languages (PPLs) have provided the capability for exact inference: computing a closed-form probability distribution for a given probabilistic program. In particular, the new language Roulette uses a language oriented programming (LOP) approach, wherein analysts build new programming languages on top of a set of primitives provided by Roulette, which then translates these structures into a weighted model counting problem which can be solved by automated reasoning tools. However, because Roulette provides few convenience features, developing these new languages is challenging even for expert users. We developed a standard library of common probability functions for Roulette with the goal of improved usability. This included approximation of continuous probability density functions using discrete probability mass functions. We demonstrated this approach by modeling a cosmic ray striking a RAM controller. We found that Roulette provides a powerful interface for highly expressive probabilistic programs to be generated. In collaboration with the NNSA Advanced Simulation and Computing program, which resulted in development of a tool called Circulette, we were able to model complex circuits expressed in Verilog using probabilistic programs with an expressivity not previously possible. Our research question that motivated the development of a Roulette standard library was to determine whether non-experts could use a PPL to model relevant problems regarding radiation effects on microelectronics. This standard library improved the expressivity of Roulette by implementing common probability density functions, mathematical operators on distributions, and support for empirical distributions. While Roulette is a powerful modeling language, the untyped, LOP approach makes error messages difficult to understand and requires expert aid. We recommend further research on Roulette, especially with its error messages, to enable improved usability. At the same time, this project demonstrated that for users familiar with Roulette and the LOP approach, Roulette provides powerful new capabilities that can be integrated with other Sandia modeling capabilities.

97 MATHEMATICS AND COMPUTING↗

Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications

In this work we introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed preconditioner is motivated by the nonlinear two-level overlapping additive Schwarz preconditioner. The neural network parameters are decomposed into groups (subdomains) with overlapping regions. In addition, the network’s feed-forward structure is indirectly imposed through a novel subdomain-wise synchronization strategy and a coarse-level training step. Through a series of numerical experiments, which consider physicsinformed neural networks and operator learning approaches, we demonstrate that the proposed two-level preconditioner significantly speeds up the convergence of the standard (LBFGS) optimizer while also yielding more accurate machine learning models. Moreover, the devised preconditioner is designed to take advantage of model-parallel computations, which can further reduce the training time.

97 MATHEMATICS AND COMPUTING↗

Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. Here we use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.

97 MATHEMATICS AND COMPUTING↗