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DOE OSTI2023

Multinucleon structure and dynamics via quantum computing

We propose a framework for computing the structure and dynamics for second-quantized many-nucleon Hamiltonians on quantum computers. We develop an oracle-based Hamiltonian input model that computes the many-nucleon states and nonzero Hamiltonian matrix elements of the many-nucleon system. With our Fock-state based input model, we show how to implement the sparse matrix simulation algorithms to calculate the dynamics of the second-quantized many-nucleon Hamiltonian. Based on the dynamics simulation methods, we also present the methodology for structure calculations of the many-nucleon system. In this work, we provide an explicit circuit design of our input model of the second-quantized Hamiltonian within a direct encoding scheme that maps the occupation of each available single-particle state in the many-nucleon state to the state of specific qubit in a quantum register. Here, we analyze our method and provide the asymptotic cost in computing resources for structure and dynamics calculations of many-nucleon systems. For pedagogical purposes, we demonstrate our input model with two model problems in restricted model spaces.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Uncovering multiscale structure-property correlations via active learning in scanning tunneling microscopy

Atomic arrangements and local sub-structures fundamentally influence emergent material functionalities. These structures are conventionally probed using spatially resolved studies and the property correlations are deciphered by a researcher based on sequential explorations, thereby limiting the efficiency and scope. Here we demonstrate a multi-scale Bayesian deep-learning based framework that automatically correlates material structure with its electronic properties using scanning tunneling microscopy (STM) measurements in real-time. Its predictions are used to autonomously direct exploration toward regions of the sample that optimize a given material property. This method is deployed on a low-temperature ultra-high vacuum STM to understand the structure-property relationship in a europium-based semimetal, EuZn 2 As 2 , a promising candidate relevant to magnetism-driven topological phenomena. The framework employs a sparse-sampling approach to efficiently construct the scalar-property space using minimal measurements, about 1–10% of the data required in standard hyperspectral methods. Moreover, we formulate the problem hierarchically across length scales, implementing autonomous workflow to locate mesoscopic and atomic structures that correspond to a target material property. This framework offers the choice to design scalar-property from the spectroscopic data to steer sample exploration. Our findings reveal correlations of the electronic properties unique to surface terminations, local defect density, and point defects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1987

Automated problem scheduling and reduction of synchronization delay effects

It is anticipated that in order to make effective use of many future high performance architectures, programs will have to exhibit at least a medium grained parallelism. A framework is presented for partitioning very sparse triangular systems of linear equations that is designed to produce favorable preformance results in a wide variety of parallel architectures. Efficient methods for solving these systems are of interest because: (1) they provide a useful model problem for use in exploring heuristics for the aggregation, mapping and scheduling of relatively fine grained computations whose data dependencies are specified by directed acrylic graphs, and (2) because such efficient methods can find direct application in the development of parallel algorithms for scientific computation. Simple expressions are derived that describe how to schedule computational work with varying degrees of granularity. The Encore Multimax was used as a hardware simulator to investigate the performance effects of using the partitioning techniques presented in shared memory architectures with varying relative synchronization costs.

Saltz, Joel H.↗

DOE OSTI2025

Sparse measurement medical CT reconstruction using multi-fused block matching denoising priors

A major challenge for medical X-ray CT imaging is reducing the number of X-ray projections to lower radiation dosage and reduce scan times without compromising image quality. However these under-determined inverse imaging problems rely on the formulation of an expressive prior model to constrain the solution space while remaining computationally tractable. Traditional analytical reconstruction methods like Filtered Back Projection (FBP) often fail with sparse measurements, producing artifacts due to their reliance on the Shannon-Nyquist Sampling Theorem. Consensus Equilibrium, which is a generalization of Plug and Play, is a recent advancement in Model-Based Iterative Reconstruction (MBIR), has facilitated the use of multiple denoisers are prior models in an optimization free framework to capture complex, non-linear prior information. However, 3D prior modelling in a Plug and Play approach for volumetric image reconstruction requires long processing time due to high computing requirement. Instead of directly using a 3D prior, this work proposes a BM3D Multi Slice Fusion (BM3D-MSF) prior that uses multiple 2D image denoisers fused to act as a fully 3D prior model in Plug and Play reconstruction approach. Our approach does not require training and are thus able to circumvent ethical issues related with patient training data and are readily deployable in varying noise and measurement sparsity levels. In addition, reconstruction with the BM3D-MSF prior achieves similar reconstruction image quality as fully 3D image priors, but with significantly reduced computational complexity. We test our method on clinical CT data and demonstrate that our approach improves reconstructed image quality.

Hossain, Maliha [ORNL]↗

NASA NTRS1981

An empirical investigation of methods for nonsymmetric linear systems

The present investigation is concerned with a comparison of methods for solving linear algebraic systems which arise from finite difference discretizations of the elliptic convection-diffusion equation in a planar region Omega with Dirichlet boundary conditions. Such linear systems are typically of the form Ax = b where A is an N x N sparse nonsymmetric matrix. In a discussion of discretizations, it is assumed that a regular rectilinear mesh of width h has been imposed on Omega. The discretizations considered include central differences, upstream differences, and modified upstream differences. Six methods for solving Ax = b are considered. Three variants of Gaussian elimination have been chosen as representatives of state-of-the-art software for direct methods under different assumptions about pivoting. Three iterative methods are also included.

Sherman, A. H.↗

DOE OSTI2025

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

CodEx: A Modular Framework for Joint Temporal De-Blurring and Tomographic Reconstruction

In many computed tomography (CT) imaging applications, it is important to rapidly collect data from an object that is moving or changing with time. Tomographic acquisition is generally assumed to be step-and-shoot, where the object is rotated to each desired angle, and a view is taken. However, step-and-shoot acquisition is slow and can waste photons, so in practice fly-scanning is done where the object is continuously rotated while collecting data. However, this can result in motion-blurred views and consequently reconstructions with severe motion artifacts. In this paper, we introduce CodEx, a modular framework for joint de-blurring and tomographic reconstruction that can effectively invert the motion blur introduced in sparse view fly-scanning. The method is a synergistic combination of a novel acquisition method with a novel non-convex Bayesian reconstruction algorithm. CodEx works by encoding the acquisition with a known binary code that the reconstruction algorithm then inverts. Using a well chosen binary code to encode the measurements can improve the accuracy of the inversion process. The CodEx reconstruction method uses the alternating direction method of multipliers (ADMM) to split the inverse problem into iterative deblurring and reconstruction sub-problems, making reconstruction practical to implement. Here we present reconstruction results on both simulated and binned experimental data to demonstrate the effectiveness of our method.

42 ENGINEERING↗

DOE OSTI2025

Learning Physically Interpretable Atmospheric Models From Data With WSINDy

The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional methods. However, many of the current data-driven approaches employ highly parameterized neural networks, often resulting in uninterpretable models and limited gains in scientific understanding. In this work, we address the interpretability problem by explicitly discovering partial differential equations governing atmospheric phenomena, identifying symbolic mathematical models with direct physical interpretations. The purpose of this paper is to demonstrate that, in particular, the weak-form sparse identification of nonlinear dynamics (WSINDy) algorithm can learn effective atmospheric models from both simulated and assimilated data. Our approach adapts the standard WSINDy algorithm to work with high-dimensional fluid data of arbitrary spatial dimension.

58 GEOSCIENCES↗

DOE OSTI2019

Complex Sources and Impacts on Remediation and Monitoring Approaches

Remedy selection, implementation, and coordination with tank farm activities for adjacent waste sites need to be facilitated by a technically defensible description of sources and their relative strength and temporal contributions to groundwater contamination. Detailed data describing contaminant source releases are typically not available, so source locations are highly uncertain. Furthermore, data on sources and model parameters are not readily available through direct measurements. Instead, source data are often derived by extrapolation from a few direct and/or indirect measurements, while model parameters are commonly estimated using inverse modeling or calibration methods. Because the conceptual model of sources will influence the mass and timing of the flux of contaminants to groundwater, uncertainty in the source terms should be considered. Even though a best-fit model can often be identified, it may not be the best representation of the sources given the sparse, uncertain nature of the data used for estimating source terms. To support future feasibility studies, a systematic approach is needed for identifying remediation and monitoring activities appropriate under conditions of uncertainty. In this study, an integrated assessment of alternative conceptual model elements has been examined using the B-Complex site in the Hanford Central Plateau to demonstrate how multiple sources in a waste management complex can be described to identify their relative contributions to groundwater. The heterogeneous structure of the system is modeled based on available field information on the lithological data for both the vadose zone and aquifer. The approach includes a simulation assessment and linkages to site data, with an uncertainty analysis applied to evaluate the effects of source term uncertainty on contaminant mass flux to groundwater. An integrated assessment of alternative conceptual model elements was evaluated to identify how parameter uncertainty impacts both temporal and spatial uncertainties associated with vadose zone source terms. Modeling scenarios identify important characteristics of remediation target zones to provide context for how surface barriers, in situ remedies, and water-table treatment zones can be designed to account for source dynamics. Ramifications for remediation and monitoring are discussed within the context of the source term uncertainty. The described approach facilitates systematically addressing alternative conceptual model questions in relation to remediation and monitoring and supports the remedial investigation/ feasibility study process and the remediation strategy development for the Hanford Central Plateau.

Rockhold, Mark L.↗

DOE OSTI2019

Complex Sources and Impacts on Remediation and Monitoring Approaches - 19058

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1993

Implementing abstract multigrid or multilevel methods

Multigrid methods can be formulated as an algorithm for an abstract problem that is independent of the partial differential equation, domain, and discretization method. In such an abstract setting, problems not arising from partial differential equations can be treated. A general theory exists for linear problems. The general theory was motivated by a series of abstract solvers (Madpack). The latest version was motivated by the theory. Madpack now allows for a wide variety of iterative and direct solvers, preconditioners, and interpolation and projection schemes, including user callback ones. It allows for sparse, dense, and stencil matrices. Mildly nonlinear problems can be handled. Also, there is a fast, multigrid Poisson solver (two and three dimensions). The type of solvers and design decisions (including language, data structures, external library support, and callbacks) are discussed. Based on the author's experiences with two versions of Madpack, a better approach is proposed. This is based on a mixed language formulation (C and FORTRAN + preprocessor). Reasons for not using FORTRAN, C, or C++ (individually) are given. Implementing the proposed strategy is not difficult.

Douglas, Craig C.↗

NASA NTRS2011

Experiments in Reconstructing Twentieth-Century Sea Levels

One approach to reconstructing historical sea level from the relatively sparse tide-gauge network is to employ Empirical Orthogonal Functions (EOFs) as interpolatory spatial basis functions. The EOFs are determined from independent global data, generally sea-surface heights from either satellite altimetry or a numerical ocean model. The problem is revisited here for sea level since 1900. A new approach to handling the tide-gauge datum problem by direct solution offers possible advantages over the method of integrating sea-level differences, with the potential of eventually adjusting datums into the global terrestrial reference frame. The resulting time series of global mean sea levels appears fairly insensitive to the adopted set of EOFs. In contrast, charts of regional sea level anomalies and trends are very sensitive to the adopted set of EOFs, especially for the sparser network of gauges in the early 20th century. The reconstructions appear especially suspect before 1950 in the tropical Pacific. While this limits some applications of the sea-level reconstructions, the sensitivity does appear adequately captured by formal uncertainties. All our solutions show regional trends over the past five decades to be fairly uniform throughout the global ocean, in contrast to trends observed over the shorter altimeter era. Consistent with several previous estimates, the global sea-level rise since 1900 is 1.70 +/- 0.26 mm/yr. The global trend since 1995 exceeds 3 mm/yr which is consistent with altimeter measurements, but this large trend was possibly also reached between 1935 and 1950.

Ray, Richard D.↗

DOE OSTI2024

Symbolic diagnostics to interpret and analyze neural network models

Embedded machine-learned models (EMLMs) have the promise to improve the predictive accuracy of engineering simulators in environments of national interest. EMLMs often comprise complex input-output maps (e.g., neural networks), which make them unamenable to rigorous analysis and generally difficult to interpret. In the face of decades of theory, this lack of interpretability is a significant barrier to building confidence in these models. This work outlines an approach to interpret EMLMs using sparse polynomial regression for comparison with theoretical understanding. To do so, we build on the concept of Locally Interpretable Model-agnostic Explanations (LIME) using physics-informed clustering, prototype selection, and library construction. While general, we demonstrate our method on tensor-basis neural networks used in Reynolds-Averaged Navier-Stokes simulations of hypersonic fluid flows. Results are presented for a simulated toy model and for direct numerical simulations (DNS) of turbulent flows over a flat plate.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

Performance issues for iterative solvers in device simulation

Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.

Fan, Qing↗

DOE OSTI2018

Comparison of sparse domain approaches for 4D SPECT dynamic image reconstruction

Purpose: Dynamic imaging (DI) provides additional diagnostic information in emission tomography in comparison to conventional static imaging at the cost of being computationally more challenging. Dynamic single photon emission computed tomography (SPECT) reconstruction is particularly difficult because of the limitations in the sampling geometry present in most existing scanners. We have developed an algorithm Spline Initialized Factor Analysis of Dynamic Structures (SIFADS) that is a matrix factorization method for reconstructing the dynamics of tracers in tissues and blood directly from the projections in dynamic cardiac SPECT, without first resorting to any 3D reconstruction. Methods: SIFADS is different from "pure" factor analysis in dynamic structures (FADS) in that it employs a dedicated spline-based pre-initialization. In this paper, we analyze the convergence properties of SIFADS and FADS using multiple metrics. The performances of the two approaches are evaluated for numerically simulated data and for real dynamic SPECT data from canine and human subjects. Results: For SIFADS, metrics analyzed for reconstruction algorithm convergence show better features of the metric curves vs iterations. In addition, SIAFDS provides better tissue segmentations than that from pure FADS. Measured computational times are also typically better for SIFADS implementations than those with pure FADS. Conclusion: The analysis supports the utility of the pre-initialization of a factorization algorithm for better dynamic SPECT image reconstruction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1991

Lanczos eigensolution method for high-performance computers

The theory, computational analysis, and applications are presented of a Lanczos algorithm on high performance computers. The computationally intensive steps of the algorithm are identified as: the matrix factorization, the forward/backward equation solution, and the matrix vector multiples. These computational steps are optimized to exploit the vector and parallel capabilities of high performance computers. The savings in computational time from applying optimization techniques such as: variable band and sparse data storage and access, loop unrolling, use of local memory, and compiler directives are presented. Two large scale structural analysis applications are described: the buckling of a composite blade stiffened panel with a cutout, and the vibration analysis of a high speed civil transport. The sequential computational time for the panel problem executed on a CONVEX computer of 181.6 seconds was decreased to 14.1 seconds with the optimized vector algorithm. The best computational time of 23 seconds for the transport problem with 17,000 degs of freedom was on the the Cray-YMP using an average of 3.63 processors.

Bostic, Susan W.↗

DOE OSTI2022

Probing for the Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement

We report thatpProbing is a general technique that is used to reduce the variance of the Hutchinson stochastic estimator for the trace of the inverse of a large, sparse matrix A. The variance of the estimator is the sum of the squares of the off-diagonal elements of A -1 . Therefore, this technique computes probing vectors that when used in the estimator annihilate the largest off-diagonal elements. For matrices that display decay of the magnitude of |A$^{-1}_{ij}$| with the graph distance between nodes i and j, this is achieved through graph coloring of increasing powers A k . Equivalently, when a matrix stems from a lattice discretization, it is computationally beneficial to find a distance-k coloring of the lattice. Previously, a hierarchical coloring was proposed so that k can be increased at runtime as needed without discarding previous work. In this work, we study probing for the more general problem of computing the trace of a permutation of A -1 , say PA -1 . The motivation comes from lattice quantum chromodynamics (QCD), where we need to construct “disconnected diagrams” to extract flavor-separated generalized parton functions. In lattice QCD, where the matrix has a four-dimensional toroidal lattice structure, these nonlocal operators correspond to a PA -1 , where P is the permutation relating to some displacement $\vec{p}$ in one or more dimensions. We focus on a single dimension displacement (p), but our methods are general. We show that probing on A k or (PA) k does not annihilate the largest magnitude elements. To resolve this issue, our displacement-based probing works on PA k using a new coloring scheme that works directly on appropriately displaced neighborhoods on the lattice. We prove lower bounds on the number of colors needed and study the effect of this scheme on variance reduction, both theoretically and experimentally on a real-world lattice QCD calculation. We achieve orders of magnitude speedup over the unprobed or the naively probed methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Early Inference of Nuclear Technology-Directed Research Activities of Authors from Scientific Publications

Nuclear research articles can provide information about early nuclear proliferation indicators such as influential research entities and technology capability levels of a country, but detection of nuclear activities typically occurs after they have started. We investigate the extent to which nuclear research articles can be used to infer whether a research entity will acquire or develop a nuclear technology before it happens. Early detection of nuclear proliferation or technology development indicators from data is challenging due to partial observability, sparse and unlabeled information, and confounding signals from multiple concurrent activities. This paper presents the early detection problem as a sequential decision-making, goal inference problem, where the objective is to characterize and predict an individual’s, organization’s, or a country’s intent (unobserved goal-directed behavior) towards developing a nuclear capability from partially observed sequences of their research publications, using inverse reinforcement learning and Bayesian goal inference methods. A computational framework is presented, and its application demonstrated using 29,196 Scopus records for a case study related to a civil nuclear capability. The case study results serve as a proof-of-concept demonstration for inference of technology-directed research activity of authors who publish in the nuclear domain. The inference method, combined with advanced computing, may be used to assess and monitor activities pertaining to early developmental stages of a nuclear technology or capability, which in turn can help to identify and prioritize activities with nuclear proliferation potential for further investigation.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗