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54 records · Page 2

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING

The Hawaii Meteorology, Energy and Transmission (MET) Toolkit

Reliable long-term resource adequacy and grid planning in Hawaii require precise, multi-decadal meteorological records. This paper introduces the Hawaii Meteorology, Energy and Transmission (MET) Toolkit, a 26-year (2000-2025) high-fidelity atmospheric dataset developed by the National Laboratory of the Rockies (NLR). We present a validation study of the underlying WRF model configurations, comparing the legacy MYNN PBL scheme against an alternative YSU formulation. Using vertical lidar profiles and surface buoy data, our analysis identified a foundational geometric distortion in the legacy NOW-23 Hawaii dataset caused by an incorrect grid projection. When evaluated on a corrected, zero-distortion grid, the YSU scheme demonstrated superior performance in bias and cRMSE compared to the legacy setup. To address these findings, the MET Toolkit has been re-produced as a unified 26-year record using the optimized YSU setup and corrected geometry. This dataset offers the Hawaii power sector a robust, validated, and homogenous reference for future grid resilience and energy integration.

24 POWER TRANSMISSION AND DISTRIBUTION

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING

An attention-based neural ordinary differential equation framework for modeling inelastic processes

To preserve strictly conservative behavior as well as model the variety of dissipative behavior displayed by solid materials, we propose a significant enhancement to the internal state variable-neural ordinary differential equation (ISV-NODE) framework. In this data-driven, physics-constrained modeling framework internal states are inferred rather than prescribed. The ISV-NODE consists of: (a) a stress model dependent on observable deformation and inferred internal state, and (b) a model of the evolution of the internal states. The enhancements to ISV-NODE proposed in this work are multifold: (a) a partially input convex neural network stress potential provides polyconvexity in terms of observed strain while leaving the inferred state unconstrained, and (b) an internal state flow model uses common latent features to inform novel attention-based gating and drives the flow of internal state only in dissipative regimes. We demonstrated that this architecture can accurately model dissipative and conservative behavior across an isotropic, isothermal elastic-viscoelastic-elastoplastic spectrum with three exemplars, while maintaining fundamental principles by design.

97 MATHEMATICS AND COMPUTING

A hybrid Monte Carlo-deterministic second moment method with efficient variance reduction

In this work, we present a hybrid method that combines Monte Carlo with deterministic finite element methods to solve a linear Boltzmann transport equation. Our hybrid method runs orders of magnitude faster than Monte Carlo, without sacrificing accuracy, for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material. We believe that this is the first demonstration of a hybrid Second Moment Method in more than one spatial dimension, the first to consider more than one material, and the first to use variance reduction. Our variance reduction approach arises from an asymptotic analysis in which we show that the magnitude of the scattering source grows without bound. We transform the problem to compute the deviation of the radiation intensity from isotropy. The magnitude of the source in the transformed problem is bounded, and the quality of the hybrid method solution is dramatically improved by a substantial reduction in the variance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Predicting Atomistic Transitions with Transformers

Accurate knowledge of the atomistic transition pathways in materials and material surfaces is crucial for many material science problems. However, conventional simulation techniques used to find these transitions are extremely computationally intensive. Even with large-scale, accelerated material simulations, the computational cost constrains the applicable domain in practice. Machine learning models, with the potential to learn the complex emergent behaviors governing atomistic transitions as a fast surrogate model, have great promise to predict transitions with a vastly reduced computational cost. Here, we demonstrate how transformers can be trained to predict atomistic transitions in nano-clusters. We show how we evaluate physical validity of the predictions and how a multitude of additional, different microstates can be generated by slightly varying the data provided to the model.

36 MATERIALS SCIENCE

Polynomial-time preparation of low-temperature Gibbs states for two-dimensional toric code

In this work, we propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial state, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. We prove that fast mixing at low temperature for the two-dimensional toric code can be achieved by augmenting local jump operators with simple global jump operators, which enable efficient transitions between logical sectors. To establish tight lower bounds on the spectral gap, we introduce a new reduction method that eventually maps the problem to estimating the spectral gap of a perturbed graph Laplacian on a stair graph. Our proof also shows that the Lindblad dynamics with a digitally implemented low-temperature local Davies generator is able to efficiently drive the quantum state toward the ground state manifold.

97 MATHEMATICS AND COMPUTING

Revealing the Hidden Third Dimension of Point Defects in Two-Dimensional MXenes

Point defects govern many important functional properties of two-dimensional (2D) materials. However, resolving the three-dimensional (3D) arrangement of these defects in multi-layer 2D materials remains a fundamental challenge, hindering rational defect engineering. Here, we overcome this limitation using an artificial intelligence-guided electron microscopy workflow to map the 3D topology and clustering of atomic vacancies in Ti3C2TX MXene. Our approach reconstructs the 3D coordinates of vacancies across hundreds of thousands of lattice sites, generating robust statistical insight into their distribution that can be correlated with specific synthesis pathways. This large-scale data enables us to classify a hierarchy of defect structures-from isolated vacancies to nanopores-revealing their preferred formation and interaction mechanisms, as corroborated by molecular dynamics simulations. This work provides a generalizable framework for understanding and ultimately controlling point defects across large volumes, paving the way for the rational design of defect-engineered functional 2D materials.

2D materials

Frontier Job-Centric Telemetry Dataset

Comprehensive analysis of high-performance computing (HPC) systems requires linking workload execution to system behavior. This kind of analysis is vital for diagnosing performance issues, managing capacity, detecting anomalous workloads, and understanding how applications interact with system hardware. This job-centric telemetry dataset unifies scheduler job records with node-level measurements, enabling direct association between workloads and their corresponding power, thermal, and performance characteristics. It contains sanitized, scheduler related metadata for 152,400 individual jobs that ran on the Frontier supercomputer and ended on selected days throughout 2024 and 2025, a subpopulation of ~6.8% of the total number of allocated jobs with non-zero run time on the system over that same period. Each is linked with files that contain telemetry time series records of the power utilization and temperature behavior of its allocated nodes and their processors during the run time of the job. Where available, a portion of the job files also contain network performance time series. Jobs are sampled from select days that reflect normal levels of user activity and possess job size distributions with large numbers of leadership class jobs (>20% of Frontier nodes). Jobs in this dataset attempt to best represent successful user workflows.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

Crustal Deformation and Gravitational Effects From Dynamic Ocean Mass Redistribution Impact Projected Sea‐Level Change

As the climate warms, associated changes in ocean dynamics will redistribute sea‐water mass within the ocean, contributing to relative sea‐level change. This mass redistribution will cause additional sea‐level changes due to gravitational self‐attraction, deformation of the solid Earth, and shifts in the Earth's rotation axis (GRD), which are not incorporated in sea‐level projections. Using CMIP6 climate model output, we quantify relative sea‐level changes induced by GRD from ocean‐dynamic mass loading through 2100. These effects act to amplify projected ocean‐dynamic sea‐level patterns, causing sea‐level rise in coastal regions, particularly along wide continental shelves and at high latitudes. On average, the magnitude of such GRD‐induced sea‐level change is equivalent to ∼15% of the signal due to dynamic ocean mass redistribution. Although our results show substantial inter‐model spread, they reveal that GRD‐induced relative sea‐level changes from ocean mass redistribution represent a non‐negligible component of regional sea‐level change and should be considered in projections.

58 GEOSCIENCES

Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is #BQP-complete in the worst case. In this work, we introduce QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

97 MATHEMATICS AND COMPUTING

The cluster decomposition of the configurational energy of multicomponent alloys

Abstract The cluster expansion method (CEM) is a widely used lattice-based technique in the study of multicomponent alloys. Despite its prevalent use, a clear understanding of expansion terms is lacking. We present a modern mathematical formalism of the CEM and introduce thecluster decomposition—a unique and basis-independent decomposition for functions of the atomic configuration in a crystal. We identify the cluster decomposition as an invariant ANOVA decomposition; and demonstrate how functional analysis of variance and sensitivity analysis can be used to interpret interactions among species. Furthermore, we show how the mathematical structure of the cluster decomposition enables numerical evaluation that scales with the number of clusters and is independent of the number of species. Overall, our work enables rigorous interpretations of interactions among species, provides opportunities to explore parameter estimation beyond linear regression, introduces a numerical efficient implementation, and enables analysis of cluster expansions based on established mathematical and statistical principles.

Chemistry

Electronic structure prediction of medium and high entropy alloys across composition space

We propose machine learning (ML) models to predict the electron density — the fundamental unknown of a material’s ground state — across the composition space of concentrated alloys. From this, other physical properties can be inferred, enabling accelerated exploration. A significant challenge is that the number of descriptors and sampled compositions required for accurate prediction grows rapidly with species. To address this, we employ Bayesian Active Learning (AL), which minimizes training data requirements by leveraging uncertainty quantification capabilities of Bayesian Neural Networks. Compared to the strategic tessellation of the composition space, Bayesian-AL reduces the number of training data points by a factor of 2.5 for ternary (SiGeSn) and 1.7 for quaternary (CrFeCoNi) systems. We also introduce easy-to-optimize, body-attached-frame descriptors, which respect physical symmetries while keeping descriptor-vector size nearly constant as alloy complexity increases. Our ML models demonstrate high accuracy and generalizability in predicting both electron density and energy across composition space.

materials science

Modeling Occupant Core Temperatures Across the Boston Building Stock to Advance Public Health

In recent history, extreme heat has been the cause of most deaths from a natural disaster. Exposure to extreme heat can aggravate preexisting conditions, increase hospitalization, and even cause death. Thus, modeling the thermal resilience of households across the United States will allow for a quantitative assessment of the health and safety risks posed by extreme heat. For the first time, we simulate occupant comfort in representative households across Boston by combining the granular results of the ResStock(TM) model with a two-node heat strain model. This model calculates occupants' core body temperature in each simulated household over a year. We compare the simulated core temperatures to two public health metrics: hyperthermia and heat stroke. Our results show for households in Boston that do not have or use aid conditioning, thousands potentially experience many dangerous heat events each summer and these events can last for more than a day at a time. These heat events peak during the late afternoon and evening, just as residents are coming home, cooking meals, and trying to go to sleep. We have found that multi-family buildings, renters, and low-income homes in more airtight and insulated homes are the most at risk for these events. These results demonstrate the scale and urgency of exposure to extreme heat.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

Mechanical, Electrochemical & Thermal Models - Training (CRADA CRD-19-00798 Final Report)

Under the proposed effort in partnership with Hyundai Motor Company (HMC), the National Renewable Energy Laboratory (NLR) will host Dr. Jaeyoung Lim from HMC for a period of one year to jointly develop mathematical models for battery cells and modules subject to mechanical crush. NLR will assist with the development of mathematical models that Dr. Lim will incorporate into his research effort on new concepts of mobility with electric vehicles.

33 ADVANCED PROPULSION SYSTEMS

NanoPSD: A software for automatic detection of Nano-Particle Shape Distribution in electron microscopy images

Accurate quantification of the size and morphology of nanoparticles from electron microscopy (EM) images is essential to understand growth mechanisms, surface reactivity, and functional behavior in nanoscale materials. Manual analysis remains slow, subjective, and difficult to reproduce in large datasets. We introduce NanoPSD (Nano-Particle Shape Distribution), an open-source and fully automated framework for quantitative particle detection and morphology analysis from EM images. NanoPSD integrates adaptive contrast enhancement, polarity-agnostic scale-bar detection, Optical Character Recognition (OCR)-based calibration, and classical segmentation via Otsu thresholding with morphological refinement. Particle contours are used to extract geometric descriptors, including equivalent circular diameter, aspect ratio, circularity, and solidity, enabling automated classification into spherical, rod-like, and aggregate morphologies. The framework supports both single-image and batch processing, generating publication-quality visualizations, LaTeX-ready tables, and structured comma-separated values (CSV) datasets. As a demonstration, we applied NanoPSD to plasma-synthesized nanoparticle samples diagnosed via transmission electron microscopy (TEM). The code produced statistically robust size and morphology distributions spanning a few to tens of nanometers with minimal user supervision. The pipeline demonstrates high reproducibility and scalability, processing large image collections with consistent calibration and output formatting. Its modular design enables seamless integration of future deep-learning-based segmentation models, providing a pathway toward intelligent, data-driven electron microscopy analysis.

36 MATERIALS SCIENCE

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

97 MATHEMATICS AND COMPUTING

Dimensional Reduction Guides Electronic Structure Evolution in the A n Cu 4–n SnS 4 Semiconductor Series

The search for new functional materials with tunable properties remains a central challenge in chemistry, particularly for applications in energy and electronics. In this work, we present a framework for predictive crystal design in alkali metal chalcogenides that enables controlled dimensional reduction of a parent covalent motif, yielding a broad range of electronic structures, which systematically evolve from one parent to the other. We present 11 new members of the A n Cu 4–n SnS 4 family (A = alkali metal; n = 0–4), which reduce the three-dimensional (3D) covalent network of Cu 4 SnS 4 into various 3D, 2D, 1D, and 0D [Cu 4–n SnS 4 ] n− motifs through the substitution of Cu with alkali metals of various radii. The end members of the family set the range in achievable band gaps at 0.99 eV for fully covalent Cu 4 SnS 4 (n = 0) and 3.38 eV for K 4 SnS 4 (n = 4) with 0D [SnS 4 ] n− tetrahedra. As the dimensionality of [Cu 4–n SnS 4 ] n− systematically reduces within A n Cu 4–n SnS 4 (n = 1–3), a stepwise increase in band gap energy occurs through a gradual decrease in the energy of the valence band maximum and an increase in the conduction band minimum, with an increase in the effective masses of charge carriers. Furthermore, irrespective of the alkali metal, the thermal stability decreases with decreasing [Cu 4–n SnS 4 ] n− dimensionality within the quaternary members. Most importantly, we demonstrate that predictable crystal structure and property evolution for a given composition space is possible by deriving a general formula based on substituting the covalent metals of a parent structure with alkali metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH