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DOE OSTI2018

New structures of Fe3S for rare-earth-free permanent magnets

We applied adaptive genetic algorithm (AGA) to search for low-energy crystal structures of Fe 3 S. A number of structures with energies lower than that of the experimentally reported Pnma and I-4 structures have been obtained from our AGA searches. These low-energy structures can be classified as layer-motif and column-motif structures. In the column-motif structures, Fe atoms self-assemble into rods with bcc type of underlying lattice, which are separated by the holes terminated by S atoms. In the layer-motif structures, the bulk Fe is broken into slabs of several layers passivated by S atoms. Magnetic properties calculations showed that the column-motif structures exhibit reasonably high uniaxial magnetic anisotropy. In addition, we examined the effect of Co doping to Fe 3 S and found magnetic anisotropy can be enhanced through Co doping.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Tutorial: Machine-Learning-Based CREASE-2D Analysis of 2D SAXS Profiles to Characterize Anisotropic Nanostructures in Soft Materials

We present a tutorial to guide users on how to extend the Computational Reverse Engineering Analysis of Scattering Experiments-2D (CREASE-2D) framework to interpret their experimental two-dimensional small-angle scattering (SAS) data from soft materials (e.g., polymers, peptide amphiphiles, biomolecular fibrils). Unlike most traditional SAS analysis approaches, which typically rely on azimuthally averaged onedimensional (1D) profiles, CREASE-2D utilizes the complete 2D scattering profile to reveal information about anisotropy in the structure. In past applications, CREASE has provided insights into complex structural features, including the cross-sectional shapes of assembled nanostructures and dispersity in these features, which are difficult to discern with existing analytical models. While (1D- ) CREASE has been applied to SANS and SAXS data, this tutorial shares the steps for implementing CREASE-2D using an example of a dipeptide solution system, for which we have SAXS data. We present details for these steps involved in using CREASE-2D to interpret SAXS profiles: how to preprocess SAXS data, define relevant structural features, generate three-dimensional real-space structures for specific values of these features, train a machine learning (ML) surrogate model to predict scattering profiles for given structural features, and optimize these features using genetic algorithms (GA). Then, we use these steps to interpret complex 2DSAXS data collected from dipeptide solutions that, in microscopy images, exhibit nanoscale structures that could be elliptical tubes/ flat tapes/cylinders or a combination of these cross sections. Open-source codes, computational hardware, and software requirements, as well as the strengths and limitations of this protocol, are also presented. We expect researchers working with (soft) biomaterials, peptide amphiphiles, amphiphilic polymer solutions, polymer nanocomposites, and blends of particles/polymers will find this CREASE-2D method and this tutorial of use.

CREASE↗

DOE OSTI2022

Trajectory design via unsupervised probabilistic learning on optimal manifolds

Abstract This article illustrates the use of unsupervised probabilistic learning techniques for the analysis of planetary reentry trajectories. A three-degree-of-freedom model was employed to generate optimal trajectories that comprise the training datasets. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. We find that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. Using the diffusion coordinates on the graph of training samples, the probabilistic framework subsequently augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path planning algorithm. In this framework, the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time.

42 ENGINEERING↗

DOE OSTI2026

CVEVOLVE

CVEvolve is an agentic AI system for autonomous algorithm discovery for scientific data processing. It creates workflows where large language model agents freely set up and configure development environments and evaluation harnesses, develop and improve data processing algorithms with designed exploration-exploitation balancing mechanisms, log history and findings in a structured database, and run holdout testing to ensure algorithm generalizability. CVEvolve offers a zero-code interface and does not require users to provide structured data and evaluation scripts.

Cherukara, MatthewJoseph [Argonne National Laborat↗

DOE OSTI2014

Machine Learning Toolkit for Extreme Scale

Support Vector Machines (SVM) is a popular machine learning technique, which has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. MaTEx undertakes the challenge of designing a scalable parallel SVM training algorithm for large scale systems, which includes commodity multi-core machines, tightly connected supercomputers and cloud computing systems. Several techniques are proposed for improved speed and memory space usage including adaptive and aggressive elimination of samples for faster convergence , and sparse format representation of data samples. Several heuristics for earliest possible to lazy elimination of non-contributing samples are considered in MaTEx. In many cases, where an early sample elimination might result in a false positive, low overhead mechanisms for reconstruction of key data structures are proposed. The proposed algorithm and heuristics are implemented and evaluated on various publicly available datasets

Source record↗

DOE OSTI2014

Machine Learning Toolkit for Extreme Scale

Source record↗

DOE OSTI2018

Predicting phase behavior of grain boundaries with evolutionary search and machine learning

The study of grain boundary phase transitions is an emerging field until recently dominated by experiments. The major bottleneck in the exploration of this phenomenon with atomistic modeling has been the lack of a robust computational tool that can predict interface structure. Here we develop a computational tool based on evolutionary algorithms that performs efficient grand-canonical grain boundary structure search and we design a clustering analysis that automatically identifies different grain boundary phases. Its application to a model system of symmetric tilt boundaries in Cu uncovers an unexpected rich polymorphism in the grain boundary structures. We find new ground and metastable states by exploring structures with different atomic densities. Our results demonstrate that the grain boundaries within the entire misorientation range have multiple phases and exhibit structural transitions, suggesting that phase behavior of interfaces is likely a general phenomenon.

36 MATERIALS SCIENCE↗

DOE OSTI2024

GeoThermalCloud: Cloud Fusion of Big Data and Multi-Physics Models using Machine Learning for Discovery, Exploration, and Development of Hidden Geothermal Resources

The primary goals of this project are exploring hidden geothermal resources in the U.S.A. and designing profitable enhanced geothermal systems (EGS). Many processes and parameters control geothermal exploration and energy production from geothermal fields. Diverse datasets (e.g., geology, geochemistry, geophysics, satellite, airborne geophysics) are available to help characterize subsurface geothermal conditions. Sparse and multi-scale characteristics of these datasets prohibit properly leveraging these datasets for geothermal exploration and profitable EGS design. Recent advancements in machine learning (ML) promise to resolve these issues. The tremendous challenges and risks of geothermal exploration and production bring the demand for novel ML methods and tools that can (1) analyze large field datasets, (2) assimilate model simulations (large inputs and outputs), (3) process sparse datasets, (4) perform transfer learning (between sites with different exploratory levels), (5) extract hidden geothermal signatures in the field and simulation data, (6) label geothermal resources and processes, (7) identify high-value data acquisition targets, and (8) guide geothermal exploration and production by selecting optimal exploration, production, and drilling strategies. To address these necessities, ML-based geothermal resources exploration and enhanced geothermal systems (EGS) design tools have been developed. The exploration tool is called GeoThermalCloud and EGS design tool is called GeoDT-ML. GeoThermalCloud (https://github.com/SmartTensors/GeoThermalCloud.jl) utilizes a LANL unsupervised ML platform called SmartTensors (https://tensors.lanl.gov/) to automate data analyses and interpretations by extracting hidden signatures to identify geothermal prospects. Also, it enables the identification of critical measurements needed to identify geothermal resource signatures. Alternatively, GeoDT-ML (https://github.com/SmartTensors/GeoThermalCloud.jl/tree/master/EGS) is an ML-based alternative to GeoDT (https://github.com/GeoDesignTool/GeoDT.git), a fast, simplified multi-physics solver to evaluate EGS project designs in uncertain geologic systems. GeoDT-ML leverages recent advances in deep learning and high-performance computing. It is a faster and simpler version of GeoDT. To make this project a success, we used capabilities of LANL, PNNL, Google, Stanford, and Julia Computing. We analyzed eight datasets of the U.S.A. using GeothermalCloud and demonstrated potential highly prospective geothermal resources and identified key factors defining highly prospective sites. The first data set includes 44 locations in southwest New Mexico and 18 geological, hydrogeological, geophysical, geothermal, geochemical attributes. We defined low- and medium-temperature hydrothermal systems and discovered a new highly prospective site. The second data set analyzed 18 shallow water chemistry attributes at 14,342 locations in the Great Basin. It demarcated modestly, moderately, and highly prospective sites including key attributes for each type of prospectivity. The third data set analyzed Utah FORGE data including satellite (InSAR), geophysical (gravity, seismic), geochemical, and geothermal attributes. Here, we performed prospectivity analysis to identify future drilling locations using geological, geochemical, and geophysical attributes. Maps of temperature at depth and heat flow are constructed based on the available data. Prospectivity maps were generated, and drilling locations were proposed for future geothermal field exploration. The fourth data set analyzed 21 attributes at 120 locations in Tularosa Basin, New Mexico; data comes from past play fairway analyses in this region. ML analyses identified geothermal signatures associated with modestly, moderately, and highly hydrothermal systems. We also defined dominant attributes and spatial distribution of the geothermal signatures. The fifth, sixth, seventh, and eighth datasets include Tohatchi Springs, New Mexico, Hawaii, Brady site, Nevada, and EGS Collab, respectively. Moreover, we coupled GeothermalCloud and magnetotellurics data to pinpoint drilling locations for developing geothermal projects in the Tularosa Basin, New Mexico. GeothermalCloud found potential prospective locations for geothermal resources near White Sands Missile Range and McGregor Range at Fort Bliss. Magnetotellurics data determined the potential depth (~1800m) of geothermal prospects at McGregor Range based on apparent resistivity structures/layers in the subsurface. The McGregor Range consists of three resistivity layers and two resistivity structures. Magnetotellurics data also helps identify that the western portion of the McGregor Range has thick and low-resistivity earth materials. The low resistivity to the west is most likely for a fault system. Assuming temperature is consistent with a geothermal reservoir, the west-central part of the McGregor Range has the highest geothermal potential because of the increase in porosity and associated permeability attributed to the interpreted fault system. Also, we devised a coupling strategy between a process model and GeothermalCloud to characterize hydrogeological conditions and geothermal conditions, respectively. The process model characterizes hydrogeological and geothermal conditions on highly prospective geothermal sites provided by GeothermalCloud. We developed a physics-informed neural network (PINN) version of the Burns equation that can be easily coupled with GeothermalCloud. Furthermore, we performed an optimal design decision maximizing the economic value of an EGS power plant. This study optimized the range of well spacing between injection and production wells maximizing net present value in dollars (NPV). For this task, we used the GeoDT to simulate the Utah FORGE EGS development cycle from the initial well design to the end of production. Next, we accomplished another crucial task, which is predicting permeability of geothermal reservoirs. Predicting permeability of geothermal reservoirs is a non-trivial task because of huge computational runtime of simulation and lack of measurements. To avoid these limitations, we used easy-to-measure chemical concentrations in the subsurface as measurement data and convolutional neural network based ML model of a high-fidelity model. Next, we predicted permeability using Markov chain Monte Carlo simulation. We found that Markov chain Monte Carlo simulation predicts permeability with a high certainty if the prediction zone in the simulation area has chemical concentration data. Finally, we analyzed the DOE funded INGENIOUS and GeoDAWN projects data. For discovering hidden geothermal systems in the Great Basin, the INGENIOUS project accumulated old data, collected new data, and released them in 2022. The dataset includes a total of 24 geological, geophysical, and geochemical attributes. Data resolution and scale significantly vary prohibiting an appropriate usage. To avoid such limitations, we brought all data in the same resolution and scale by applying the inverse distance weighting interpolation technique for predicting data in unsampled locations. Subsequently, we analyzed LiDAR data of the GeoDAWN project. We received data in tiles format. The DOE’s overarching goal is to use ML on LiDAR data for finding favorable geological structures (e.g., step up faults in Brady, Nevada). To serve the purpose, we need to label favorable geologic structures that correspond to LiDAR data. We wrote an algorithm to label the LiDAR data with the favorable geologic structures.

15 GEOTHERMAL ENERGY↗

DOE OSTI2013

Pulmonary lobe segmentation based on ridge surface sampling and shape model fitting

Purpose: Performing lobe-based quantitative analysis of the lung in computed tomography (CT) scans can assist in efforts to better characterize complex diseases such as chronic obstructive pulmonary disease (COPD). While airways and vessels can help to indicate the location of lobe boundaries, segmentations of these structures are not always available, so methods to define the lobes in the absence of these structures are desirable. Methods: The authors present a fully automatic lung lobe segmentation algorithm that is effective in volumetric inspiratory and expiratory computed tomography (CT) datasets. The authors rely on ridge surface image features indicating fissure locations and a novel approach to modeling shape variation in the surfaces defining the lobe boundaries. The authors employ a particle system that efficiently samples ridge surfaces in the image domain and provides a set of candidate fissure locations based on the Hessian matrix. Following this, lobe boundary shape models generated from principal component analysis (PCA) are fit to the particles data to discriminate between fissure and nonfissure candidates. The resulting set of particle points are used to fit thin plate spline (TPS) interpolating surfaces to form the final boundaries between the lung lobes. Results: The authors tested algorithm performance on 50 inspiratory and 50 expiratory CT scans taken from the COPDGene study. Results indicate that the authors' algorithm performs comparably to pulmonologist-generated lung lobe segmentations and can produce good results in cases with accessory fissures, incomplete fissures, advanced emphysema, and low dose acquisition protocols. Dice scores indicate that only 29 out of 500 (5.85%) lobes showed Dice scores lower than 0.9. Two different approaches for evaluating lobe boundary surface discrepancies were applied and indicate that algorithm boundary identification is most accurate in the vicinity of fissures detectable on CT. Conclusions: The proposed algorithm is effective for lung lobe segmentation in absence of auxiliary structures such as vessels and airways. The most challenging cases are those with mostly incomplete, absent, or near-absent fissures and in cases with poorly revealed fissures due to high image noise. However, the authors observe good performance even in the majority of these cases.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2019

StructureDistiller: Structural relevance scoring identifies the most informative entries of a contact map

Protein folding and structure prediction are two sides of the same coin. Contact maps and the related techniques of constraint-based structure reconstruction can be considered as unifying aspects of both processes. We present the Structural Relevance (SR) score which quantifies the information content of individual contacts and residues in the context of the whole native structure. The physical process of protein folding is commonly characterized with spatial and temporal resolution: some residues are Early Folding while others are Highly Stable with respect to unfolding events. We employ the proposed SR score to demonstrate that folding initiation and structure stabilization are subprocesses realized by distinct sets of residues. The example of cytochrome c is used to demonstrate how StructureDistiller identifies the most important contacts needed for correct protein folding. This shows that entries of a contact map are not equally relevant for structural integrity. The proposed StructureDistiller algorithm identifies contacts with the highest information content; these entries convey unique constraints not captured by other contacts. Identification of the most informative contacts effectively doubles resilience toward contacts which are not observed in the native contact map. Furthermore, this knowledge increases reconstruction fidelity on sparse contact maps significantly by 0.4 Å.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

CP2K: An Electronic Structure and Molecular Dynamics Software Package - Quickstep: Efficient and Accurate Electronic Structure Calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular and biological systems. It is especially aimed at massively-parallel and linear-scaling electronic structure methods and state-of-the-art ab-initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension. TDK has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 716142). VRR has been supported by the Swiss National Science Foundation in the form of Ambizione grant No. PZ00P2 174227 and RZK by the Natural Sciences and Engineering Research Council of Canada (NSERC) through Discovery Grants (RGPIN-2016-0505). GKS and CJM are supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. UK based work was funded under the embedded CSE programme of the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk), grants eCSE03-011, eCSE06-6, eCSE08-9, eCSE13-17 and the EPSRC (EP/P022235/1) grant “Surface and Interface Toolkit for the Materials Chemistry Community". Computational resources were provided by the Swiss National Supercomputing Centre (CSCS) and Compute Canada. The generous allocation of computing time on the FPGA-based supercomputer “Noctua" at PC2 is kindly acknowledged.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Visual Analytics of Heterogeneous Data Using Hypergraph Learning

For real-world learning tasks (e.g., classification), graph-based models are commonly used to fuse the information distributed in diverse data sources, which can be heterogeneous, redundant, and incomplete. Thesemodels represent the relations in different datasets as pairwise links. However, these links cannot deal with high-order relations which connect multiple objects (e.g., in public health datasets, more than two patient groups admitted by the same hospital in 2014). In this article, we propose a visual analytics approach forthe classification on heterogeneous datasets using the hypergraph model. The hypergraph is an extension to traditional graphs in which a hyperedge connects multiple vertices instead of just two. We model various high-order relations in heterogeneous datasets as hyperedges and fuse different datasets with a unified hypergraph structure. We use the hypergraph learning algorithm for predicting missing labels in the datasets.To allow users to inject their domain knowledge into the model-learning process, we augment the traditional learning algorithm in a number of ways. In addition, we also propose a set of visualizations which enable the user to construct the hypergraph structure and the parameters of the learning model interactively during the analysis. Here, we demonstrate the capability of our approach via two real-world cases.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Active Learning Guided Computational Discovery of Plant-Based Redoxmers for Organic Nonaqueous Redox Flow Batteries

Organic nonaqueous redox flow batteries (ONRFBs) are promising energy storage devices due to their scalability and reliance on sourceable materials. However, finding suitable redox-active organic molecules (redoxmers) for these batteries remains a challenge. Using plant-based compounds as precursors for these redoxmers can decrease their costs and environmental toxicity. In this computational study, flavonoid molecules have been examined as potential redoxmers for ONRFBs. Flavone and isoflavone derivatives were selected as catholyte (positive charge carrier) and anolyte (negative charge carrier) molecules, respectively. To drive their redox potentials to the opposite extremes, in silico derivatization was performed using a novel algorithm to generate a library of > 40000 candidate molecules that penalizes overly complex structures. A multiobjective Bayesian optimization based active learning algorithm was then used to identify best redoxmer candidates in these search spaces. Furthermore, our study provides methodologies for molecular design and optimization of natural scaffolds and highlights the need of incorporating expert chemistry awareness of the natural products and the basic rules of synthetic chemistry in machine learning.

25 ENERGY STORAGE↗

DOE OSTI2016

CRYSTAL CHEMISTRY OF THREE-COMPONENT WHITE DWARFS AND NEUTRON STAR CRUSTS: PHASE STABILITY, PHASE STRATIFICATION, AND PHYSICAL PROPERTIES

A systematic search for multicomponent crystal structures is carried out for five different ternary systems of nuclei in a polarizable background of electrons, representative of accreted neutron star crusts and some white dwarfs. Candidate structures are “bred” by a genetic algorithm and optimized at constant pressure under the assumption of linear response (Thomas–Fermi) charge screening. Subsequent phase equilibria calculations reveal eight distinct crystal structures in the T = 0 bulk phase diagrams, five of which are complicated multinary structures not previously predicted in the context of compact object astrophysics. Frequent instances of geometrically similar but compositionally distinct phases give insight into structural preferences of systems with pairwise Yukawa interactions, including and extending to the regime of low-density colloidal suspensions made in a laboratory. As an application of these main results, we self-consistently couple the phase stability problem to the equations for a self-gravitating, hydrostatically stable white dwarf, with fixed overall composition. To our knowledge, this is the first attempt to incorporate complex multinary phases into the equilibrium phase-layering diagram and mass–radius-composition dependence, both of which are reported for He–C–O and C–O–Ne white dwarfs. Finite thickness interfacial phases (“interphases”) show up at the boundaries between single-component body-centered cubic (bcc) crystalline regions, some of which have lower lattice symmetry than cubic. A second application—quasi-static settling of heavy nuclei in white dwarfs—builds on our equilibrium phase-layering method. Tests of this nonequilibrium method reveal extra phases that play the role of transient host phases for the settling species.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Recent Advances in Small Angle X-ray Scattering for Superlattice Study

Small-angle x-ray scattering is used for the structure determination of superlattice for its superior resolution, nondestructive nature, and high penetration power of x rays. With the advent of high brilliance x-ray sources and innovative computing algorithms, there have been notable advances in small angle x-ray scattering analysis of superlattices. High brilliance x-ray beams have made data analyses less model-dependent. Additionally, novel data acquisition systems are faster and more competitive than ever before, enabling a more accurate mapping of the superlattices' reciprocal space. Fast and high-throughput computing systems and algorithms also make possible advanced analysis methods, including iterative phasing algorithms, non-parameterized fitting of scattering data with molecular dynamics simulations, and the use of machine learning algorithms. As a result, solving nanoscale structures with high resolutions has become an attainable task. In this review, we highlight new developments in the field and introduce their applications for the analysis of nanoscale ordered structures, including nanoparticle supercrystals, nanoscale lithography patterns, and supramolecular self-assemblies. Particularly, we highlight the reciprocal space mapping techniques and the use of iterative phase retrieval algorithms. We also cover coherent-beam-based small angle x-ray scattering techniques such as ptychography and ptycho-tomography in view of the traditional small angle x-ray scattering perspective.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix

We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimal block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Ordering Traces Logically to Identify Lateness in Message Passing Programs

Event traces are valuable for understanding the behavior of parallel programs. However, automatically analyzing a large parallel trace is difficult, especially without a specific objective. We aid this endeavor by extracting a trace's logical structure, an ordering of trace events derived from happened-before relationships, while taking into account developer intent. Using this structure, we can calculate an operation's delay relative to its peers on other processes. The logical structure also serves as a platform for comparing and clustering processes as well as highlighting communication patterns in a trace visualization. We present an algorithm for determining this idealized logical structure from traces of message passing programs, and we develop metrics to quantify delays and differences among processes. We implement our techniques in Ravel, a parallel trace visualization tool that displays both logical and physical timelines. Rather than showing the duration of each operation, we display where delays begin and end, and how they propagate. As a result, we apply our approach to the traces of several message passing applications, demonstrating the accuracy of our extracted structure and its utility in analyzing these codes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Ordering Traces Logically to Identify Lateness in Parallel Programs

Event traces are a valuable tool for understanding the behavior of parallel programs. Automatically analyzing a large trace, however, especially without a specific objective, is difficult. We aid this process by extracting a trace’s logical structure, an ordering of events derived from their happened before relationships. From this perspective, we can calculate delays relative to peers rather than duration and determine where they begin and how they propagate. The logical structure also acts as a platform for comparing and clustering processes as well as showing communication patterns in a trace visualization. We present an algorithm for determining this idealized logical structure from a trace and develop metrics to quantify delays and differences among processes. We implement this in our novel trace visualizer, Ravel, and apply our approach to several applications, demonstrating the accuracy of our extracted structure and its utility in analyzing these codes.

97 MATHEMATICS AND COMPUTING↗