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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↗

DOE OSTI2020

Symmetry reduction of tensor networks in many-body theory: I. Automated symbolic evaluation of SU(2) algebra

Abstract The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. SU (2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

Tichai, A.↗

DOE OSTI2025

Discovering nuclear models from symbolic machine learning

Numerous phenomenological nuclear models have been proposed to describe specific observables within different regions of the nuclear chart. However, developing a unified model that describes the complex behavior of all nuclei remains an open challenge. Here, we explore whether symbolic Machine Learning (ML) can rediscover traditional nuclear physics models or identify alternatives with improved simplicity, fidelity, and predictive power. To address this challenge, we developed a Multi-objective Iterated Symbolic Regression approach that handles symbolic regressions over multiple target observables, accounts for experimental uncertainties and is robust against high-dimensional problems. As a proof of principle, we applied this method to describe the nuclear binding energies and charge radii of light and medium mass nuclei. Our approach identified simple analytical relationships based on the number of protons and neutrons, providing interpretable models with precision comparable to state-of-the-art nuclear models. Additionally, we integrated this ML-discovered model with an existing complementary model to estimate the limits of nuclear stability. These results highlight the potential of symbolic ML to develop accurate nuclear models and guide our description of complex many-body problems.

Nuclear structure↗

DOE OSTI2014

Discriminating chaotic and stochastic dynamics through the permutation spectrum test

In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Beyond 100 Gb/s: Capacity, Flexibility, and Network Optimization

Here, we discuss building blocks that enable the exploitation of optical capacities beyond 100 Gb/s. Optical networks will benefit from more flexibility and agility in their network elements, especially from coherent transceivers. To achieve capacities of 400 Gb/s and more, coherent transceivers will operate at higher symbol rates. This will be made possible with higher bandwidth components using new electro-optic technologies implemented with indium phosphide and silicon photonics. Digital signal processing will benefit from new algorithms. Multi-dimensional modulation, of which some formats are already in existence in current flexible coherent transceivers, will provide improved tolerance to noise and fiber nonlinearities. Constellation shaping will further improve these tolerances while allowing a finer granularity in the selection of capacity. Frequency-division multiplexing will also provide improved tolerance to the nonlinear characteristics of fibers. Algorithms with reduced computation complexity will allow the implementation, at speeds, of direct pre-compensation of nonlinear propagation effects. Advancement in forward error correction will shrink the performance gap with Shannon's limit. At the network control and management level, new tools are being developed to achieve a more efficient utilization of networks. This will also allow for network virtualization, orchestration, and management. Lastly, FlexEthernet and FlexOTN will be put in place to allow network operators to optimize capacity in their optical transport networks without manual changes to the client hardware.

47 OTHER INSTRUMENTATION↗

DOE OSTI2016

Profiling Production OpenSHMEM Applications, In: OpenSHMEM 2016: OpenSHMEM and Related Technologies. Enhancing OpenSHMEM for Hybrid Environments

Developing high performance OpenSHMEM applications routinely involves gaining a deeper understanding of software execution, yet there are numerous hurdles to gathering performance metrics in a production environment. Most OpenSHMEM performance profilers rely on the PSHMEM interface but PSHMEM is an optional and often unavailable feature. We present a tool that generates direct measurement performance profiles of OpenSHMEM applications even when PSHMEM is unavailable. The tool operates on dynamically linked and statically linked application binaries, does not require debugging symbols, and functions regardless of compiler optimization level. Integrated in the TAU Performance System, the tool uses automatically-generated wrapper libraries that intercept OpenSHMEM API calls to gather performance metrics with minimal overhead. Dynamically linked applications may use the tool without modifying the application binary in any way.

Computer Science↗

DOE OSTI2020

PDQ Users Manual Version 1 for PDQ Code Version 1.12

PDQ is a tool for the management of the input and execution of batch jobs for simulation codes that use a text based input system. It accomplishes this goal by operating at two levels. First, it takes input file templates (commonly known at LANL as input deck templates) and creates multiple instantiations by performing substitutions of data from table files into symbols (variables) found in the template. Second, it provides commands to submit the created files to the SLURM batch system for execution. These two activities taken together produce a whole that is greater than the sum of its parts and provides an elegant way of executing studies across multiple similar simulations while minimizing the risk of typographical errors in the input files.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

On the Goldbach Conjecture

This note proposes a confirmation proof of Goldbach’s Conjecture from 1742 [gol]: Can every even integer n > 2 be represented as the sum of 2 prime numbers? First, I present an analysis of the nature of multiplication as description length reduction for addition. This allows to explain prime numbers from first principles rather than by definition. Then, I use this analysis to derive that any natural number n must be representable by n – 1 unique two-summand additions. Given that an explicit formula for the number of primes smaller n is unknown, I formulate the contraposition to the conjecture. I then count the maximum number of possible unique additions when the summands are both non-prime or 1 and when one summand is non-prime, prime or 1 and the other is non-prime or 1. This is done using a case distinction for even and odd n. The counting is facilitated by finding the maximum number of positions a plus symbol can be placed into the unary representation of n, given the constraints. The main result is that no even n ≥ 8 exists where all n – 1 additions can be formulated without including the case of the addition of two primes. A side result is that any odd integer n can be represented by 1 addition of 2 primes if and only if n – 2 is prime.

97 MATHEMATICS AND COMPUTING↗