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DOE OSTI2026

Enhancing ZFP: A Statistical Approach to Understanding and Reducing Error Bias in a Lossy Floating-Point Compression Algorithm

The amount of data generated and gathered in scientific simulations and data collection applications is continuously growing, putting mounting pressure on storage and bandwidth concerns. A means of reducing such issues is data compression; but, lossless data compression is typically ineffective when applied to floating-point data. Thus, users tend to apply a lossy data compressor, which allows for small deviations from the original data. It is essential to understand how the error from lossy compression impacts the accuracy of the data analytics. Thus, we must analyze not only the compression properties but the error as well. In this paper, we provide a statistical analysis of the error caused by ZFP compression, a state-of-the-art, lossy compression algorithm explicitly designed for floating-point data. We show that the error is indeed biased and propose simple modifications to the algorithm to neutralize the bias and further reduce the resulting error.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗

DOE OSTI2024

Exascale-Enabled Models and Algorithms for Microelectronics Applications (MicroEleX) v1

The MicroEleX code package contains a variety of models and algorithms for physical modeling of microelectronic circuitry, including electrostatics, electrodynamics, superconducting physics, micromagnetics, multi-ferroic systems, and quantum transport. MicroEleX leverages the AMReX software framework to provide scalability on GPU-based supercomputing architectures. The code is open source and designed to be algorithmically flexible so developers can incorporate enhanced or customized physics.

Nonaka, Andy↗

DOE OSTI2025

Clustering Algorithm for AM Parts using GSH and EDT with Autoencoder

SAND2025-10103O The Clustering Algorithm for AM Parts Using GSH and (EDT With Autoencoder is a software tool. It uses a clustering algorithm for additive manufacturing (AM) parts using generalized spherical harmonics (GSH) and Euclidean distance transform (EDT) with an autoencoder to quantify material microstructure. The tool offers improved sensitivity to microstructural changes compared to traditional approaches. The tool integrates multiple microstructural properties, such as grain morphology, crystallographic orientation, and material phase information, to provide a comprehensive analysis of material microstructures. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Rodgers, Theron [Sandia National Lab. (SNL-CA), Li↗

DOE OSTI2024

Evaluation of Physical Microphysical Property Retrieval Algorithms During the 2020 IMPACTS Field Campaign

The NASA Investigation of Microphysics and Precipitation for Atlantic Coast Threatening Snowstorms (IMPACTS) field campaign provides high-quality, high-altitude aircraft lidar (532 nm), radar (W-band) and in-cloud microphysical aircraft data taken during wintertime storm events impacting the United States. This study evaluates two mass-dimensional relationships (Brown and Francis (1995, BF95); Heymsfield (2014, H14) and two lidar-radar microphysical retrieval algorithms (Cloudsat and CALIPSO Ice Cloud Property Product (2C-ICE); VarPy (a variational method derived from the satellite lidar-radar data community)) to estimate aircraft-retrieved volume extinction coefficient (σ), ice water content (IWC), and effective radius (r e ) during the 2020 IMPACTS deployment. BF95 and H14 have a close 1:1 correlation (R 2 = 0.98) with in-situ observations of σ. However, only BF95 displays a linear, consistent, and almost temperature-independent low bias for IWC and r e , which likely arises from the environmental conditions used to determine each. Unlike the field-campaign-derived BF95 and H14 relationships, VarPy and 2C-ICE directly ingest the aircraft-based lidar and radar data to simulate σ, IWC, and r e . For all three microphysical parameters, VarPy and 2C-ICE retrieval errors became notably more pronounced around the dendritic growth zone (-15°C to -10°C) and near freezing (≥-5°C), which suggests that both algorithms experience difficulty addressing riming and aggregation processes and with larger particles (dendrites and plates) due in part to their simplified ice particle assumptions. However, the mean-melt diameter ice-particle assumption did yield more accurate IWC estimates, which led to slightly better overall results for VarPy.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Development of a pattern recognition algorithm for reconstructing multi-particle events in the Mu2e detector

Mu2e is an upcoming experiment at Fermilab and its main goal is to search for the Charged Lepton Flavor Violation (CLFV) in the coherent transition of a muon into an electron on an Al target. In Mu2e, multi-particle events can occur simultaneously within the same time region and it is crucial to accurately identify each particle track, including signals, to improve the robustness of track finding methods and enhance reconstruction efficiency. ¯p annihilation is one of the background events and produces multiple particles that can mimic signal events. Additionally, photons from radiative pion captures can produce a γ → $e+e−$ pair, which can be used to calibrate the Mu2e momentum scale and the resolution. The Mu2e track reconstruction sequence begins by grouping hits produced in the tracker based on time and z coordinate information, called TimeCluster, and selected hits are processed to reconstruct helices and determine their momentum. The current pattern recognition algorithms identify a single helix per TimeCluster for single track events. A new pattern recognition algorithm is being developed to reconstruct multi-particle events and its features for finding multiple tracks and the current evaluation results are reported.

Kitagawa, H. [Pisa U.]↗

DOE OSTI2025

Simultaneous prediction of structural properties in epitaxially–grown GaN with quantum and conventional multi–output learning algorithms

Hundreds of GaN thin film crystal plasma–assisted molecular beam epitaxy synthesis experiment records spanning two decades were organized into a dataset correlating the growth experiment design parameters with discrete, binary determinations of crystallinity and surface morphology. Conventional data science techniques as well as both quantum and classical multi–output supervised machine learning algorithms were implemented to investigate the relationships between the operating parameter data and the structural figures of merit. Correlation coefficients, decision tree nodes, p–values, and SHAP values all support substrate temperature and gallium effusion cell conditions as being statistically significant for simultaneously influencing GaN crystallinity and surface morphology. Here, a conventional deep neural network learned best from the data, followed by a quantum–classical hybrid gradient boosting algorithm. When combined with calculations of uncertainty intervals based on VennAbers predictors, machine learning predictions of both structural properties show good agreement with results reported in published experimental literature.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Algorithms and file structures to extend and enhance liquid chromatography and ion mobility mass spectrometry workflows (CRADA Final Report)

The purpose of this project was to continue supporting customizations of algorithms and raw data file structures to enhance software workflows for liquid chromatography (LC), mass spectrometry (MS) and ion mobility mass spectrometry (IM-MS)-based protein and metabolite characterization. PNNL worked with Agilent to design, implement, evaluate, and demonstrate new algorithms and integrated them as functionalities into the PNNL-PreProcessor software. The project augmented PNNL’s capabilities to analyze complex proteomics and metabolomics samples. These capabilities are directly beneficial to DOE and PNNL efforts to characterize and analyze these compounds in microbial and plant communities. The project assisted Agilent in further developing improved instrument-software solutions combining liquid chromatography and ion mobility with mass spectrometry for widespread applications in life sciences and other fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Randomized Algorithms for Linear Solvers

Recently, randomized algorithms in numerical linear algebra, specifically those centered around random sketching, have gained traction in primarily theoretical research due to their potential to significantly reduce problem dimensionality at the cost of an O(1) multiplicative distortion factor. It has been assumed that this sketching can be done efficiently, but thorough investigation into how precisely to do it has been neglected. Moreover, the theory-based community has argued for sketching’s ability to reduce computational cost via complexity analysis, but has not researched how it affects the stability of the algorithms. At Sandia, efficient linear solvers that scale well on modern HPC architectures while maintaining stability are imperative for practical applications. In this LDRD, we developed a random sketching strategy that is substantially faster than existing ones, and demonstrate its superior performance in practice on a NVIDIA H100 GPU. Moreover, we show how this can be used to significantly outperform existing linear least squares solvers while improving the solver’s stability as well. Additionally, we demonstrate how this sketching strategy can be used to make a fast, stable QR factorization that can subsequently be used in s-step and block Krylov solvers. Finally, we incorporate a sketching-based block orthogonalization scheme into s-step GMRES, which is stable and faster than existing approaches on the Perlmutter supercomputer.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Radio Frequency Algorithms

Final Technical Report for DOE SC0019287 award titled Radio Frequency Algorithms. This project supported the design, simulation, analysis, and optimization of robust algorithms to configure, optimize, and control Radio Frequency and Low-Level RF systems for several modern accelerator systems.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Fundamental Algorithmic Research for Quantum Computing (FAR‐QC) (Final report)

This document is the final technical report for the "Fundamental Algorithmic Research for Quantum Computing" (FAR-QC) project at Dartmouth College (PI: J. Whitfield, co-PI: L. Viola). It details the project's primary scientific accomplishments from 2019 to 2025, focusing on advances in quantum simulation algorithms, resource-efficient fermionic encodings, bosonic topology, and optimization methods for near-term quantum devices. The report also summarizes project impacts, including software development (Quiqbox.jl), workforce training, and a complete list of resulting publications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Selection Algorithm Improvement for MicroBooNE

Data selection is an extremely important part of data analysis for any experiment. Finding a physics result is often the result of sifting through a massive amount of data, keeping data that we believe to be signal and throwing out data we do not. This process is called data selection. Creating a selection algorithm is an intensive process that must balance keeping enough data to have statistics and maximizing the signal purity of that data. In this study, we used three different reconstruction tools, Pandora, WireCell, and LANTERN, for the MicroBooNE experiment in conjunction to improve the selection algorithm for analysis. For the case of this study, we look into the charged current N proton 0 pions (CCNp0$\pi$) interaction channel. This is the dominant channel for the Short Baseline Neutrino (SBN) program and is expected to be a large contributor to the Deep Underground Neutrino Experiment (DUNE). We first investigated each of the three tools to find out more about their strengths and weaknesses as reconstructions. We then put together a direct comparison of the three methods to find which method or combination of methods would return the best result for us. While the study is ongoing, we have learned a lot about data selection for the experiment and the differences between the reconstruction tools.

Dillon, Brayden [Michigan State U.]↗

DOE OSTI2026

Frameworks, Algorithms, and Scalable Technologies for Mathematics (FASTMath) SciDAC Institute

As computational models scale to larger computers, the rate at which they produce data has far outstripped the same computers ability to write that data and further the file systems ability to store that data. Almost all of the SciDAC applications, but especially those related to fusion solve very large scale PDEs whose scientific output his impacted by this problem. To gain access to dynamics in an exascale simulation that are not identifiable a priori and to make that dynamical data available to machine learning requires fundamental research in the area of in situ data data analytics. Here data analytics includes compression, visualization, uncertainty quantification, and machine learning. This in situ data analytics will enable on-the-fly spatial and temporal compression of solution dynamics, expose that space-time compressed field to machine learning algorithms that have been specialized to work with dynamically evolving data (existing machine learning algorithms treat data sets as static), greatly improving the opportunity for machine learning to provide feedback to the compression, all within an ongoing simulation, without the need to write data to files. The same concepts are also being applied to uncertainty quantification and multi-fidelity modeling which have similar needs for spatial and temporal compression of the ongoing exascale simulation to perform either without the typical, unacceptable writing of data to files.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

A large-scale benchmarking of deterministic and stochastic derivative-free optimization algorithms

This presentation summarizes our work in the PrOMMiS project on benchmarking of data-driven optimization algorithms and their applications in self-driving laboratories. This work supports the broader project goal of accelerating the identification of promising separation methods and operating conditions for critical minerals separation processes. We present a systematic benchmarking study of 42 data-driven optimization algorithms on a broad collection of 502 test problems. The results identify BAM, GLCCLUSTER, and MULTIMIN as the most effective optimization solvers, with BAM showing the highest overall performance and solving more than 80% of the benchmark problems. The study also shows that no single solver consistently outperforms the others across all problem types, indicating that our future laboratory applications may benefit from using a small set of strong solvers rather than relying on a single method. The presentation also illustrates an in-silico chemical reactor case study showing that data-driven optimization methods can guide autonomous experimentation in a self-driving laboratory and identify optimal operating conditions within a small number of experiments. Overall, the results provide a basis for selecting efficient optimization methods and demonstrate the practical use of data-driven optimization in self-driving laboratory workflows.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Algorithm-guided experimentation for autonomous AI systems in self-driving laboratories

36 MATERIALS SCIENCE↗

DOE OSTI2026

Hardware Implementation of Grover's Search Algorithm

Grover's algorithm searches through an unstructured database, offering a quadratic speedup over classical search algorithms. We implement it, as well as two deterministic variants, on IBM (Kingston) and IQM (Garnet) hardware. Additionally, we test dynamical decoupling as an error mitigation technique. We compare our results to a classical, brute force approach to evaluate current hardware capabilities.

Pressman, Daniel [Fermilab]↗