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DOE OSTI2016

An Icosahedral Quasicrystal and Its 1/0 Crystalline Approximant in the Ca–Au–Al System

A new icosahedral quasicrystalline phase, CaAu 4.5–x Al 1.5+x [0.11 ≤ x ≤ 0.40(6); CaAu 4.4 Al 1.6 , a QC = 5.383(4) Å, and Pm35], and its lowest-order 1/0 cubic crystalline approximant phase, CaAu 3+x Al 1–x [0 ≤ x ≤ 0.31(1); a = 9.0766(5)–9.1261(8) Å, Pa3(No. 205), and Pearson symbol cP40], have been discovered in the Ca-poor region of the Ca–Au–Al system. In the crystalline approximant, eight [Au 3–x Al 1+x ] tetrahedra fill the unit cell, and each tetrahedron is surrounded by four Ca atoms, thus forming a three-dimensional network of {Ca 4/4 [Au 3–x Al 1+x ]} tetrahedral stars. Here, a computational study of Au and Al site preferences concurs with the experimental results, which indicate a preference for near-neighbor Au–Al interactions over Au–Au and Al–Al interactions. Analysis of the electronic density of states and the associated crystal orbital Hamilton population curves was used to rationalize the descriptions of CaAu 4.5–x Al 1.5+x [0.11 ≤ x ≤ 0.46(6)] and CaAu 3+x Al 1–x [0 ≤ x ≤ 0.31(1)] as polar intermetallic species, whereby Ca atoms engage in polar covalent bonding with the electronegative, electron-deficient [Au 3–x Al 1+x ] tetrahedral clusters and the observed phase width of the crystalline approximant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

The double pentaladder integral to all orders

We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N = 4 super-Yang-Mills theory. We provide exact, finite-coupling formulas for the basic double pentaladder integrals as a single Mellin integral over hypergeometric functions. For particular choices of the dual conformal cross ratios, we can evaluate the integral at weak coupling to high loop orders in terms of multiple polylogarithms. We argue that the integrals are exponentially suppressed at strong coupling. Here in this paper, we describe the space of functions that contains all such double pentaladder integrals and their derivatives, or coproducts. This space, a prototype for the space of Steinmann hexagon functions, has a simple algebraic structure, which we elucidate by considering a particular discontinuity of the functions that localizes the Mellin integral and collapses the relevant symbol alphabet. This function space is endowed with a coaction, both perturbatively and at finite coupling, which mixes the independent solutions of the hypergeometric differential equation and constructively realizes a coaction principle of the type believed to hold in the full Steinmann hexagon function space.

1/N Expansion↗

DOE OSTI2019

SUSPECT: MINLP special structure detector for Pyomo

We present SUSPECT, an open source toolkit that symbolically analyzes mixed-integer nonlinear optimization problems formulated using the Python algebraic modeling library Pyomo. We present the data structures and algorithms used to implement SUSPECT. SUSPECT works on a directed acyclic graph representation of the optimization problem to perform: bounds tightening, bound propagation, monotonicity detection, and convexity detection. We show how the tree-walking rules in SUSPECT balance the need for lightweight computation with effective special structure detection. SUSPECT can be used as a standalone tool or as a Python library to be integrated in other tools or solvers. Here, we highlight the easy extensibility of SUSPECT with several recent convexity detection tricks from the literature. We also report experimental results on the MINLPLib 2 dataset.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Impact of bowtie filter and object position on the two-dimensional noise power spectrum of a clinical MDCT system

Purpose: Noise characteristics of clinical multidetector CT (MDCT) systems can be quantified by the noise power spectrum (NPS). Although the NPS of CT has been extensively studied in the past few decades, the joint impact of the bowtie filter and object position on the NPS has not been systematically investigated. This work studies the interplay of these two factors on the two dimensional (2D) local NPS of a clinical CT system that uses the filtered backprojection algorithm for image reconstruction. Methods: A generalized NPS model was developed to account for the impact of the bowtie filter and image object location in the scan field-of-view (SFOV). For a given bowtie filter, image object, and its location in the SFOV, the shape and rotational symmetries of the 2D local NPS were directly computed from the NPS model without going through the image reconstruction process. The obtained NPS was then compared with the measured NPSs from the reconstructed noise-only CT images in both numerical phantom simulation studies and experimental phantom studies using a clinical MDCT scanner. The shape and the associated symmetry of the 2D NPS were classified by borrowing the well-known atomic spectral symbols s, p, and d, which correspond to circular, dumbbell, and cloverleaf symmetries, respectively, of the wave function of electrons in an atom. Finally, simulated bar patterns were embedded into experimentally acquired noise backgrounds to demonstrate the impact of different NPS symmetries on the visual perception of the object. Results: (1) For a central region in a centered cylindrical object, an s-wave symmetry was always present in the NPS, no matter whether the bowtie filter was present or not. In contrast, for a peripheral region in a centered object, the symmetry of its NPS was highly dependent on the bowtie filter, and both p-wave symmetry and d-wave symmetry were observed in the NPS. (2) For a centered region-ofinterest (ROI) in an off-centered object, the symmetry of its NPS was found to be different from that of a peripheral ROI in the centered object, even when the physical positions of the two ROIs relative to the isocenter were the same. (3) The potential clinical impact of the highly anisotropic NPS, caused by the interplay of the bowtie filter and position of the image object, was highlighted in images of specific bar patterns oriented at different angles. The visual perception of the bar patterns was found to be strongly dependent on their orientation. Conclusions: The NPS of CT depends strongly on the bowtie filter and object position. Even if the location of the ROI with respect to the isocenter is fixed, there can be different symmetries in the NPS, which depend on the object position and the size of the bowtie filter. For an isolated off-centered object, the NPS of its CT images cannot be represented by the NPS measured from a centered object.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2 → 5 amplitude in planar N = 4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N -particle MHV amplitude in this region to a function, we specialize to N = 7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the well-studied six-gluon case. As an application of our results, we explicitly compute the seven-gluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.

1/N expansion↗

DOE OSTI2012

MOGO: Model-Oriented Global Optimization of Petascale Applications

The MOGO project was initiated under in 2008 under the DOE Program Announcement for Software Development Tools for Improved Ease-of-Use on Petascale systems (LAB 08-19). The MOGO team consisted of Oak Ridge National Lab, Argonne National Lab, and the University of Oregon. The overall goal of MOGO was to attack petascale performance analysis by developing a general framework where empirical performance data could be efficiently and accurately compared with performance expectations at various levels of abstraction. This information could then be used to automatically identify and remediate performance problems. MOGO was be based on performance models derived from application knowledge, performance experiments, and symbolic analysis. MOGO was able to make reasonable impact on existing DOE applications and systems. New tools and techniques were developed, which, in turn, were used on important DOE applications on DOE LCF systems to show significant performance improvements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

The one-loop six-dimensional hexagon integral with three massive corners

We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum of 24 terms involving only one basic function, which is a simple linear combination of logarithms, dilogarithms, and trilogarithms of uniform degree three transcendentality. Our method uses differential equations to determine the symbol of the function, and an algorithm to reconstruct the latter from its symbol. It is known that six-dimensional hexagon integrals are closely related to scattering amplitudes in N = 4 super Yang-Mills theory, and we therefore expect our result to be helpful for understanding the structure of scattering amplitudes in this theory, in particular at two loops.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Symbol alphabets in QCD and flag cluster algebras

The full 245-letter symbol alphabet for all planar massless two-loop six-point Feynman integrals was recently determined in arXiv:2412.19884 and arXiv:2501.01847. In a parallel mathematical development, it was shown in arXiv:2408.14956 that there is an embedding of the cluster algebra associated to the partial flag variety $\mathcal{Fl}$ $2,n-2;n$ , which describes the kinematics of n massless particles, into that of the Grassmannian Gr(n–2, 2n–4). In this paper we connect these developments by showing that most of the rational symbol letters can be expressed in terms of flag cluster variables, and that all of the algebraic symbol letters arise from infinite mutation sequences.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

HyKKT: a hybrid direct-iterative method for solving KKT linear systems

Here, we propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the LBLT factorization where L is a lower triangular matrix and B is 1×1 or 2×2 block diagonal. However, this requires pivoting, which substantially increases communication cost and degrades performance on GPUs. Our approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solver on the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach on large optimal power flow problems and show that it can efficiently utilize GPUs and outperform LBL T factorization of the full system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

An Interactive Visualization Tool for Large-Scale Building Stock Modeling

Recent advancements in data science and high-performance computing are making it easier to run millions of building simulations, but meaningful visualization of such large datasets remains a challenge. This paper presents a new tool developed to view the results of large-scale OpenStudio simulations of national, regional, or local building stocks. The tool processes millions of simulations to calculate measure savings, utility bills, carbon emissions, primary energy, and cost-effectiveness metrics at a high geographic resolution. Interactive visualizations of the building characteristics, consumption, and measure savings data include proportional symbol maps and histogram plots and can be filtered by any building characteristic.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

An Interactive Visualization Tool for Large-Scale Building Stock Modeling: Preprint

big data↗

DOE OSTI2017

Rapid multiphase-field model development using a modular free energy based approach with automatic differentiation in MOOSE/MARMOT

In this paper, we present a novel rapid phase-field model development capability using a modular free energy based approach in the finite element based MOOSE framework. The phase-field equations are implemented in a general form as separate code form the model specific data such as the thermodynamic free energy density and mobility functions. This isolates researchers from complicated code and allows them to focus on implementing new material models. In addition, using a native symbolic differentiation algorithm, all required derivatives of the free energy density are automatically determined, removing sources for potential human error, and guaranteeing optimally preconditioned equation systems through fully populated Jacobian matrices. Free energy terms contributing to a phase-field model are abstracted into self contained objects that can be combined at will at simulation run time. Combining multiple chemical and mechanical free energy contributions allows the construction of coupled phase-field, mechanics, and multiphase models. Through just-in-time compilation, we greatly reduce the computational time required to evaluate the differentiated expressions. Lastly, we demonstrate the new capability on a variety of example simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Kinetic Alfvén Turbulence: Electron and Ion Heating by Particle-in-cell Simulations

Three-dimensional particle-in-cell simulations of the forward cascade of decaying kinetic Alfvén turbulence have been carried out as an initial-value problem on a collisionless, homogeneous, magnetized, electron–ion plasma model with β{sub e}=β{sub i}=0.50 and m {sub i}/m {sub e} = 100, where subscripts e and i represent electrons and ions, respectively. Initial anisotropic narrowband spectra of relatively long-wavelength modes with approximately gyrotropic distributions in k{sub ⊥} undergo a forward cascade to broadband spectra of magnetic fluctuations at shorter wavelengths. Maximum electron and ion heating rates are computed as functions of the initial fluctuating magnetic field energy density ε{sub o} on the range 0.05<ε{sub o}<0.50. In contrast to dissipation by whistler turbulence, the maximum ion heating rate due to kinetic Alfvén turbulence is substantially greater than the maximum electron heating rate. Furthermore, ion heating as well as electron heating due to kinetic Alfvén turbulence scale approximately with ε {sub o}. Finally, electron heating leads to anisotropies of the type T{sub ∥e}>T{sub ⊥e}, where the parallel and perpendicular symbols refer to directions parallel and perpendicular, respectively, to the background magnetic field, whereas the heated ions remain relatively isotropic. This implies that, for the range of ε {sub o} values considered, the Landau wave–particle resonance is a likely heating mechanism for the electrons and may also contribute to ion heating.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Ternary Bismuthide SrPtBi 2 : Computation and Experiment in Synergism to Explore Solid-State Materials

A combination of theoretical calculation and the experimental synthesis to explore the new ternary compound is demonstrated in the Sr–Pt–Bi system. Because Pt–Bi is considered as a new critical charge-transfer pair for superconductivity, it inspired us to investigate the Sr–Pt–Bi system. With a thorough calculation of all the known stable/metastable compounds in the Sr–Pt–Bi system and crystal structure predictions, the thermodynamic stability of hypothetical stoichiometry, SrPtBi2, is determined. Following the high-temperature synthesis and crystallographic analysis, the first ternary bismuthide in Sr–Pt–Bi, SrPtBi2 was prepared, and the stoichiometry was confirmed experimentally. SrPtBi 2 crystallizes in the space group Pnma (S.G. 62, Pearson Symbol oP48), which matches well with theoretical prediction using an adaptive genetic algorithm. Using first-principles calculations, we demonstrate that the orthorhombic structure has lower formation energies than other 112 structure types, such as tetragonal BaMnBi 2 (CuSmP 2 ) and LaAuBi 2 (CuHfSi 2 ) structure types. The bonding analysis indicates that the Pt–Bi interactions play a critical role in structural stability. The physical property measurements show the metallic properties at the low temperature, which agrees with the electronic structure assessment.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Robust Explanations using Diverse Adversarially Trained Ensembles, Multi-Modal Contrastive Learning, and Attribution-based Confidence Metrics

The primary objective of this project is to strengthen the trustworthiness of AI systems by designing algorithms that make their internal decision-making processes more understandable to human users. This involves creating clear, interpretable explanations for AI decisions and developing metrics to assess these explanations' validity and reliability. Significant progress has been achieved through (i) developing symbolic explanations, (ii) generating meaningful interpretive insights, (iii) establishing accuracy and confidence metrics, and (iv) devising methods to evaluate the knowledge boundaries of AI models. To date, the research findings have been shared in peer-reviewed publications, with accompanying scientific and technical information (STI) detailed below.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Machine Learning-Based Anomaly Detection for Load Forecasting Under Cyberattacks

Accurate load forecasting can create both economic and reliability benefits for power system operators. However, the cyberattack on load forecasting may mislead operators to make unsuitable operational decisions for the electricity delivery. To effectively and accurately detect these cyberattacks, this paper develops a machine learning-based anomaly detection (MLAD) methodology. First, load forecasts provided by neural networks are used to reconstruct the benchmark and scaling data by using the k-means clustering. Second, the cyberattack template is estimated by the naive Bayes classification based on the cumulative distribution function and statistical features of the scaling data. Finally, the dynamic programming is utilized to calculate both the occurrence and parameter of one cyberattack on load forecasting data. Here, a widely used symbolic aggregation approximation method is compared with the developed MLAD method. Numerical simulations on the publicly load data show that the MLAD method can effectively detect cyberattacks for load forecasting data with relatively high accuracy. Also, the robustness of MLAD is verified by thousands of attack scenarios based on Monte Carlo simulation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Infidelity Associated with Eliminating the Bus Resonator

This summer project started out to quantify the error associated with an approximate model of a superconducting circuit, where two qubits are dispersively coupled through a bus resonator. Understanding this error helps us decide if the approximate model is sufficient for the purpose of optimal control. We find out that the error of the approximate model covers up a nontrivial problem of the underlying circuit, which limits the fidelity of two-qubit gates under 99% for practical parameters. This suggests that high fidelity gates of this circuit cannot be achieved through optimal control alone, and changes of the parameters/design of the circuits appear necessary. Additionally, to carry out the algebra involved, a symbolic commutator algebra package HamMaker is developed in Julia. The package is capable of automating some difficult algebra in optimal control that previously had to be performed by hand. Within this work, HamMaker has been used to derived some simple but nontrivial corrections to the existing effective Hamiltonian.

74 ATOMIC AND MOLECULAR PHYSICS↗