Engineering PapersSearch

SEARCH · Engineering Papers

Results for “Mathematics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

74 records · Page 2

ResStock Measure Documentation: Residential Variable-Speed Geothermal Heat Pump (4.4 COP, 30.9 EER) With Light Envelope Improvements

This report is part of series describing a variety of different ResStock™ measures. "Measures" refers to energy efficiency retrofits that can be applied to buildings during modeling. This documentation covers the "Residential Variable-Speed Geothermal Heat Pump (4.4 COP, 30.9 EER) with Light Envelope Improvements" measure upgrade methodology and briefly discusses key results. All results can be accessed on the ResStock Open Energy Data Initiative "End-Use Load Profiles for the U.S. Building Stock" data lake and on the data viewer at resstock.nlr.gov.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

UL 1741SC Conformance Development, Evaluation, and Proposal [Slides]

V2G AC is a type of grid interconnection by mobile battery that transforms an EV into a DER with the potential to stabilize the grid and lower costs for electricity. UL 1741SC is a critical new standard to enable grid interconnection of V2G AC-capable vehicles, by defining requirements for V2G AC-intended EVSEs as a gatekeeper between the grid and the EV to support grid safety, such as through redundant voltage trip (namely oversight). EVSE manufacturers need a clear set of conformance test cases and criteria by which to evaluate their equipment and confirm the compliance with UL 1741SC, so that the EVSEs performs as intended for the grid safety. Hence, NLR identified necessary conformance tests and performed the tests identified to understand the maturity.

29 ENERGY PLANNING, POLICY, AND ECONOMY

Deriving the Landauer Principle From the Quantum Shannon Entropy

We derive an expression to determine the equilibrium probability distribution of a quantum state in contact with a noisy thermal environment that formally separates contributions from quantum and classical forms of probabilistic uncertainty. A statistical mechanical interpretation of this probability distribution enables us to derive an expression for the minimum free energy costs for arbitrary (reversible or irreversible) quantum state changes. In conclusion, based on this derivation, we demonstrate that–in contrast to classical systems–the free energy required to erase or reset a qubit depends sensitively on both the fidelity of the target state and on the physical properties of the environment, such as the number of quantum bath states, due primarily to the entropic effects of system-bath entanglement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Internet of Things Data Characterization Process: Pattern of Life Behavioral Data Study

The HoneyBee™ TARDIS LDRD team completed a data scoping study that identified the initial processes and procedures to baseline the normal and expected behaviors during operability and interoperability of Internet of Things (IoT) device networks. This research is the initial step in developing a process (or methodology) to inform a much broader information framework incorporating machine learning to determine device pattern-of-life which enables the detection of abnormal IoT behaviors on an individual device, as well as in the context of a larger network.

97 MATHEMATICS AND COMPUTING

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

General Purpose Data-Driven System Monitoring for Space Operations

Modern space propulsion and exploration system designs are becoming increasingly sophisticated and complex. Determining the health state of these systems using traditional methods is becoming more difficult as the number of sensors and component interactions grows. Data-driven monitoring techniques have been developed to address these issues by analyzing system operations data to automatically characterize normal system behavior. The Inductive Monitoring System (IMS) is a data-driven system health monitoring software tool that has been successfully applied to several aerospace applications. IMS uses a data mining technique called clustering to analyze archived system data and characterize normal interactions between parameters. This characterization, or model, of nominal operation is stored in a knowledge base that can be used for real-time system monitoring or for analysis of archived events. Ongoing and developing IMS space operations applications include International Space Station flight control, satellite vehicle system health management, launch vehicle ground operations, and fleet supportability. As a common thread of discussion this paper will employ the evolution of the IMS data-driven technique as related to several Integrated Systems Health Management (ISHM) elements. Thematically, the projects listed will be used as case studies. The maturation of IMS via projects where it has been deployed, or is currently being integrated to aid in fault detection will be described. The paper will also explain how IMS can be used to complement a suite of other ISHM tools, providing initial fault detection support for diagnosis and recovery.

Satellites