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DOE OSTI2024

Machine-learning based model reduction for partial differential equations

We develop a novel synergistic approach between model reduction and machine learning. The specific goal of this project is to aid in the construction of reduced order models for basis functions that are custom-made to represent the solution of partial differential equations. Partial differential equations (PDEs) are one of the main mathematical tools for describing physical phenomena. However, due to either efficiency or necessity, for many real-world problems, we are interested in constructing reduced order models (ROMs) which focus only on the explicit computation of subsets of the active spatio-temporal scales in the problem, while treating the interaction with the rest of the scales approximately. The task of accurate representation of such interactions (usually called memory terms) constitutes a vast area of research known as model reduction. PI Stinis has significant expertise in the construction of ROMs for complex systems. In addition, in recent work with the project key participant Qadeer, they have utilized machine learning to acquire custom-made basis functions (CBFs) to expand the solutions of PDEs. In the proposed work, we will merge the two concepts by constructing ROMs for subsets of the CBFs needed to represent the solution of a PDE. Specifically, we will use the Mori-Zwanzig model reduction formalism to construct ROMs for subsets of CBFs for nonlinear PDEs of various complexity, as well as investigate the usage of CBFs in the spectral vanishing viscosity method for problems that can form shocks in finite time. The outcome of the research is aimed to be proof-of-concept about a novel synergistic approach between model reduction and machine learning, thus advancing the field of scientific machine learning. Such a capability will benefit the efficient modeling of physical systems appearing in various areas of interest to the DOE.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2024

Coronado National Memorial Disasters: Investigating Geohazards & Slope Failure Susceptibility Utilizing NASA Earth Observations

The Coronado National Memorial (CORO), located in Hereford, Arizona, is situated along the United States' southern border, featuring recently established but still incomplete border barrier roads. This landscape is inherently prone to geohazards, and debris flow due to the steep mountainous topography, complex terrain, monsoonal rains, and freeze/thaw action - and the new infrastructure has exhibited these processes in the form of rockfall, embankment failure, and debris flow. NASA DEVELOP partnered with CORO to conduct a feasibility assessment of Earth observations for identification of geohazards and slope failure susceptibility. Leveraging Earth observations (United States Geological Survey 3D Elevation Program Digital Elevation Model and a locally obtained Light Detection And Ranging-derived Digital Elevation Model) from 2019 to 2023, and geospatial datasets starting from 2008, the study was able to provide tools to determine the focus for damage mitigation, identify areas most susceptible to slope failures, and prioritize at risk assets through three products: change detection maps, slope failure susceptibility maps, and a slope failure prioritization model. With an emphasis on monitoring high-risk areas and prioritizing mitigation efforts, the project addresses a critical gap in remediation strategies and aims to enhance preservation and safety of the region. Results of this study found that (i) the most identifiable areas of change were the road cuts and debris directly adjacent to the roads created for border construction, (ii) areas of highest slope failure susceptibility are located in mountainous areas with erosive geology, and (iii) roads resulting from border construction have approximately twice the risk of slope failure as roads created by the national park service.

Geohazard↗

NASA NTRS1995

Correlations of Different Surface Tests: Tire Behavior Math Model for the High Speed Civil Transport (HSCT) and Michelin Tire Properties Tests for Boeing 777

In the surfaces correlation study, several different volumetric and drainage measurement techniques for classifying surface texture were evaluated as part of a major study to develop and improve methods for predicting tire friction performance on all types of pavement. The objective of the evaluation was to seek relationships between the different techniques, and to relate those results to surface frictional characteristics. We needed to know how each of the tests could be related to each other. Another of my assigned projects was to make a tire behavior math model for the High Speed Civil Transport (HSCT) using the same methods used for the space shuttle a few years ago. A provided third order equation with two variables was used. This model will also be used for studies with the Boeing 777. Only a few changes will be necessary to adapt it for this other aircraft, which is the newest offered by Boeing. In my final project I was involved with testing the tires for this new aircraft using the Aircraft Landing Dynamics Facility (ALDF) test carriage within the carriage house at LaRC. A 50 inch diameter radial tire manufactured by Michelin Aircraft Tire Corporation had to be tested to double overload of 114,000 pounds. The rated load of each tire is 57,000 pounds, but Boeing required tests assuming failure of a companion tire that could have cost Michelin approximately $12 million to build a facility to provide the required test capability. Here at LaRC, only minimum modifications to the facility were required to perform this specific test.

Roman, Ivan↗

NASA NTRS2017

Characterizing DebriSat Fragments: So Many Fragments, So Much Data, and So Little Time

To improve prediction accuracy, the DebriSat project was conceived by NASA and DoD to update existing standard break-up models. Updating standard break-up models require detailed fragment characteristics such as physical size, material properties, bulk density, and ballistic coefficient. For the DebriSat project, a representative modern LEO spacecraft was developed and subjected to a laboratory hypervelocity impact test and all generated fragments with at least one dimension greater than 2 mm are collected, characterized and archived. Since the beginning of the characterization phase of the DebriSat project, over 130,000 fragments have been collected and approximately 250,000 fragments are expected to be collected in total, a three-fold increase over the 85,000 fragments predicted by the current break-up model. The challenge throughout the project has been to ensure the integrity and accuracy of the characteristics of each fragment. To this end, the post hypervelocity-impact test activities, which include fragment collection, extraction, and characterization, have been designed to minimize handling of the fragments. The procedures for fragment collection, extraction, and characterization were painstakingly designed and implemented to maintain the post-impact state of the fragments, thus ensuring the integrity and accuracy of the characterization data. Each process is designed to expedite the accumulation of data, however, the need for speed is restrained by the need to protect the fragments. Methods to expedite the process such as parallel processing have been explored and implemented while continuing to maintain the highest integrity and value of the data. To minimize fragment handling, automated systems have been developed and implemented. Errors due to human inputs are also minimized by the use of these automated systems. This paper discusses the processes and challenges involved in the collection, extraction, and characterization of the fragments as well as the time required to complete the processes. The objective is to provide the orbital debris community an understanding of the scale of the effort required to generate and archive high quality data and metadata for each debris fragment 2 mm or larger generated by the DebriSat project.

Shiotani, B.↗

DOE OSTI2025

Identifying Vehicle Signals in Continuous Seismic Data Using Unsupervised Machine-Learning Techniques

Seismic sensors deployed near roadways effectively capture ground vibrations generated by passing vehicles. Although both traditional and machine‐learning algorithms have been utilized for analyzing such signals, independent validation of detected vehicle events remains limited. We applied two unsupervised machine‐learning algorithms, uniform manifold approximation and projection for dimension reduction, and hierarchical density‐based spatial clustering of applications with noise, to continuous seismic data collected along a road on the main campus of Oak Ridge National Laboratory. The algorithms identified seven distinct cluster labels across the entire dataset. By comparing these cluster labels with precipitation records from a nearby weather station and image‐derived labels from a local camera system, we identified one cluster associated with rainfall and another with vehicle activity. Our algorithms identified a greater number of vehicle‐related labels compared to the camera‐derived labels because seismic data are unaffected by poor lighting conditions. The arrival times of the newly detected vehicle signals corresponded well with the road’s speed limit, supporting our findings. Our algorithm outperformed the short‐term average/long‐term average method and k‐means clustering. Our results suggest that seismic data, when analyzed with machine‐learning algorithms, can complement existing vehicle monitoring systems, particularly under challenging environmental conditions.

Chai, Chengping [Oak Ridge National Laboratory (OR↗

DOE OSTI2022

OPALCO - Decatur Island Solar and Energy Storage Project: An Assessment of Battery Technical Performance

Orcas Power & Light Cooperative (OPALCO) is a member-owned, nonprofit cooperative utility that provides energy services to approximately 11,200 customers across 20 islands in San Juan County, Washington. OPALCO’s mostly hydroelectric power is generated by Bonneville Power Administration and delivered to the islands by submarine cables. In 2016, as part of the second round of funding from the Washington state Clean Energy Fund, OPALCO received a $1 million matching grant to support a project that deployed a 504-kW LG community photovoltaic (PV) system in combination with a 1 MW/2 MWh lithium-iron-phosphate battery energy storage system (BESS) on Decatur Island, Washington. The Decatur Island Substation is essential to ensuring reliable energy for the residents of the San Juan Islands as it is the point of interconnection with the mainland transmission system. The BESS, in combination with the community solar array, will deliver an innovative method to both defer the costly upgrade of the transmission system and allow for other high-value applications intended to benefit the utility and its customers. In 2018, Pacific Northwest National Laboratory (PNNL) completed a preliminary economic assessment for several identified use cases in collaboration with OPALCO. Between August 2021 and May 2022, extensive testing was conducted, and the results were used to assess the technical performance of the BESS subjected to actual field operations. Both reference performance and use case tests were performed: (a) Reference performance tests assess the general technical capabilities of the BESS, such as energy capacity, round-trip efficiency (RTE), ramp rate, and signal tracking capability. These are the first tests performed (baseline) and are repeated after use case tests (post cycle). A standardized U.S. Department of Energy (DOE) energy storage performance protocol was used to characterize the BESS, including representative duty cycle profiles, test procedure guidance, and calculation guidance for determining key characteristics. (b) Use case tests examine the performance of the BESS for specific use cases using duty cycles developed by PNNL in collaboration with OPALCO. Four use cases were selected for testing: 1) demand charge reduction, 2) load shaping, 3) outage mitigation, and 4) transmission deferral. The use case duty cycles were developed based on utility and site-specific characteristics in addition to the technical characteristics and physical capabilities of the BESS. Use case tests were performed between the baseline and post cycle tests. This report describes the BESS and its components, presents testing and performance analysis results, and shares key insights and lessons learned from this project. Outcomes of the tests and analyses will help OPALCO understand the performance of the Decatur Island BESS in its current state and design appropriate operational strategies for this and other BESSs over the long term.

14 SOLAR ENERGY↗

DOE OSTI2023

Stability of Kuramoto networks subject to large and small fluctuations from heterogeneous and spatially correlated noise

Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise. In this article, we focus on the assessment of fluctuations resulting from heterogeneous and spatially correlated noise inputs on Kuramoto model networks. We evaluate the typical, small fluctuations near synchronized states and connect the network variance to the overlap between stable modes of synchronization and the input noise covariance. Going beyond small to large fluctuations, we introduce the indicator mode approximation that projects the dynamics onto a single amplitude dimension. Such an approximation allows for estimating rates of fluctuations to saddle instabilities, resulting in phase slips between connected oscillators. Statistics for both regimes are quantified in terms of effective noise amplitudes that are compared and contrasted for several noise models. In conclusion, bridging the gap between small and large fluctuations, we show that a larger network variance does not necessarily lead to higher rates of large fluctuations.

42 ENGINEERING↗

DOE OSTI2025

On the Sampling-Based Computation of Nash Equilibria Under Uncertainty via the Nikaido–Isoda Function

We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be L 0 -Lipschitz continuous and convex, given rival decisions with convex and closed player-specific feasibility sets. To address this problem, we consider minimizing a suitably defined value function defined using the Nikaido–Isoda function. Such an avenue does not necessitate either monotonicity properties of the concatenated gradient map or potentiality requirements on the game but does require a suitable regularity requirement under which a stationary point is a Nash equilibrium. We design and analyze a sampling-enabled projected-gradient-response method, reliant on inexact resolution of a player-level best-response subproblem. Here, by deriving suitable Lipschitzian guarantees on the value function, we derive both asymptotic guarantees for the sequence of generated iterates as well as rate and complexity guarantees for computing a stationary point by appropriate choices of the sampling rate and inexactness sequence.

Nikaido-Isoda function↗

DOE OSTI2025

Strong Correlation DMRG and DFT

This project developed new ways to improve computer simulations of materials where electrons interact strongly with each other, a challenge for today’s most widely used method, density functional theory (DFT). We used an exact numerical method, the density matrix renormalization group (DMRG), to create highly accurate reference results for simple model systems, and used these to test DFT, prove when it will converge, and even train machine-learned functionals. We also invented new kinds of localized basis functions (“gausslets” and “multi-sliced gausslets”) and a “sliced-basis” approach that make high-accuracy simulations faster and more practical. These methods were applied to extended hydrogen systems, enabling the direct derivation of accurate low-energy models from first-principles calculations. We also introduced a new formalism, Conditional-Probability DFT, which could bypass traditional approximations. The tools and results from this work, including open-source software releases, will help scientists design and understand complex quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Extrapolation of Type Ia Supernova Spectra into the Near-infrared Using Principal Component Analysis

Abstract We present a method of extrapolating the spectroscopic behavior of Type Ia supernovae (SNe Ia) in the near-infrared (NIR) wavelength regime up to 2.30 μ m using optical spectroscopy. Such a process is useful for accurately estimating K-corrections and other photometric quantities of SNe Ia in the NIR. A principal component analysis is performed on data consisting of Carnegie Supernova Project I & II optical and NIR FIRE spectra to produce models capable of making these extrapolations. This method differs from previous spectral template methods by not parameterizing models strictly by photometric light-curve properties of SNe Ia, allowing for more flexibility of the resulting extrapolated NIR flux. A difference of around −3.1% to −2.7% in the total integrated NIR flux between these extrapolations and the observations is seen here for most test cases including Branch core-normal and shallow-silicon subtypes. However, larger deviations from the observation are found for other tests, likely due to the limited high-velocity and broad-line SNe Ia in the training sample. Maximum-light principal components are shown to allow for spectroscopic predictions of the color-stretch light-curve parameter, s BV , within approximately ±0.1 units of the value measured with photometry. We also show these results compare well with NIR templates, although in most cases the templates are marginally more fitting to observations, illustrating a need for more concurrent optical+NIR spectroscopic observations to truly understand the diversity of SNe Ia in the NIR.

Astronomy & Astrophysics↗

DOE OSTI2025

Decomposing Cloud Radiative Feedbacks by Cloud-Top Phase

Changes in cloud scattering properties and emissivity that arise from atmospheric warming cause substantial radiative feedbacks in model projections of anthropogenic climate change, and the relative importance of the underlying mechanisms is poorly understood. One leading hypothesis is that ice-to-liquid conversions cause clouds to optically thicken, producing a major negative feedback. We test this hypothesis by developing a method to decompose cloud radiative feedbacks by cloud-top phase. The method is applied to an ensemble of six state-of-the-art global climate models run with prescribed sea surface temperature. In these simulations, the global mean of the net cloud scattering and emissivity feedback from cloud-phase conversions ranges from −0.17 to −0.01 W m −2 K −1 , while the overall net cloud feedback ranges from 0.02 to 0.91 W m −2 K −1 . The multimodel mean of the cloud scattering and emissivity feedback from cloud-phase conversions is approximately 19% of the magnitude of the multimodel mean of the overall cloud feedback (−0.10 vs 0.52 W m −2 K −1 ). These results indicate that cloud-phase conversions cause a robust negative feedback by changing cloud scattering and emissivity, but this mechanism makes a modest contribution to the overall cloud feedback at the global scale.

Climate change↗

DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Improved Prediction of Cold-Air Pools in the Weather Research and Forecasting Model Using a Truly Horizontal Diffusion Scheme for Potential Temperature

The terrain-following vertical coordinate system used by many atmospheric models, including the Weather Research and Forecasting (WRF) Model, is prone to errors in regions of complex terrain. These errors stem, in part, from the calculation of horizontal gradients within the diffusion term of the momentum or scalar evolution equations. In WRF, such gradients can be calculated along coordinate surfaces, or using metric terms that help account for grid skewness. However, neither of these options ensures a truly horizontal gradient calculation, especially if a grid cell is skewed enough that the heights of the neighboring grid points used in the calculation fall outside the vertical range of the cell. In this work, an improved scheme that uses Taylor series approximations to vertically interpolate variables to the level necessary for a truly horizontal gradient calculation is implemented in WRF for the diffusion of potential temperature. The scheme is validated using an atmosphere-at-rest configuration, in which spurious flows develop only as a result of numerical errors and can thus be used as a proxy for model performance. Following validation, the method is applied to the simulation of cold-air pools (CAPs), which occur in regions of complex terrain and are characterized by strong near-surface temperature gradients. Using the truly horizontal scheme, idealized simulations demonstrate reduced numerical mixing in a quiescent CAP, and a realistic case study in the Columbia River basin shows a reduction in positive wind speed bias by up to roughly 20% compared to observations from the Second Wind Forecast Improvement Project.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

FY21 Status report on the CMVB and CNWG International Collaborations

The ART-GCR Methods area includes an international collaboration work package that covers the tasks defined for the Computational Methods Validation and Benchmark (CMVB)and Civil Nuclear Energy Research and Development Working Group (CNWG) projects. This report summarizes the status of the FY21 tasks and planned FY22 DOE contributions. The CMVB Project Arrangement (PA) is not yet formally approved by all signatories, and no work has therefore been performed in FY21 at INL related to this activity. The CNWG activities inFY21 consisted of the simulation of the High Temperature Test Reactor (HTTR) Loss Of Forced Cooling (LOFC) experimental with the Idaho National Laboratory (INL) codes Griffin, BISON and RELAP-7 based on the Multiphysics Object-Oriented Simulation Environment (MOOSE).It was found that the multiphysics coupled suite is capable of simulating all the important phenomena occurring during the Depressurized Loss of Forced Cooling (DLOFC) experiments showing promising agreement with the measurements given the number of uncertainties and approximations introduced into the model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Asymptotic preserving methods for fluid electron-fluid models in the large magnetic field limit with mathematically guaranteed properties (Final Report)

The current manuscript is a final report on the activities carried out under the Project LDRD-CIS #226834. In scientific terms, the work reported in this manuscript is a continuation of the efforts started with Project LDRD-express #223796 with final report of activities SAND2021-11481, see [83]. In this section we briefly explain what pre-existing developments motivated the current body of work and provide an overview of the activities developed with the funds provided. The overarching goal of the current project LDRD-CIS #226834 and the previous project LDRD-express #223796 is the development of numerical methods with mathematically guaranteed properties in order to solve the Euler-Maxwell system of plasma physics and generalizations thereof. Even though Project #223796 laid out general foundations of space and time discretization of Euler-Maxwell system, overall, it was focused on the development of numerical schemes for purely electrostatic fluid-plasma models. In particular, the project developed a family of schemes with mathematically guaranteed robustness in order to solve the Euler-Poisson model. This model is an asymptotic limit where only electrostatic response of the plasma is considered. Its primary feature is the presence of a non-local force, the electrostatic force, which introduces effects with infinite speed propagation into the problem. Even though instantaneous propagation of perturbations may be considered nonphysical, there are plenty of physical regimes of technical interest where such an approximation is perfectly valid.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

RePED 250: Manufacturing and Market Analysis of High-Temperature Alternators

The novel repetitive pulsed electric drill 250 (RePED 250) has the potential to greatly lower the costs and drilling times of geothermal projects. This tool discharges electric pulses through hard rock formations, shattering the rock in tension and allowing it to be quickly removed. One hurdle in bringing this technology to market is the RePED 250 downhole alternator. This component is essential for supplying power to the electronic drilling tool. There are currently no downhole tools on the market that meet the RePED 250 alternator's high temperature and power requirements. This report focuses on the path to commercialization for this novel alternator technology being developed as part of the RePED 250 project. One aim of this work is to identify the geothermal market size for the RePED 250 alternator, as well as other potential markets for this technology outside of geothermal. The geothermal market is very small, with only approximately 13 wells drilled in the United States each year. The worldwide market is several times this size and growing each year. The ability of the RePED 250 technology to drastically reduce the cost of geothermal projects may also lead to an increase in this market size. Technology developed for the high-temperature, high-power RePED 250 alternator can also be used to create high-temperature and high-power motors. These motors and alternators will have potential applications in oil and gas drilling, a $300 billion dollar industry in the United States alone, as well as in more distant industries such as aircraft, weapon systems, space exploration, and electric vehicles. Other aspects of the RePED 250 alternator's path to commercialization are also analyzed, including the supply chain for production materials and potential manufacturing methods. The supply chain and manufacturing practices for low-temperature motors and alternators are well established and require relatively minor changes for the high-temperature and high-power RePED 250 alternator. Sourcing for high-temperature materials has been identified, as well as potential supply chain risks. These most notably include electrical steel and high-temperature samarium cobalt (SmCo) magnets. Overall, these risks are not expected to be significant at the likely manufacturing scale required for the RePED 250.

15 GEOTHERMAL ENERGY↗

NASA NTRS1978

Mars synthetic topographic mapping

Topographic contour maps of Mars are compiled by synthesizing data acquired from various scientific experiments of the Mariner 9 mission, including S-band radio occultation, the UV spectrometer, the IR radiometer, the IR interferometer spectrometer, and television imagery, as well as earth-based radar information. The entire planet is mapped at scales of 1:25,000,000 and 1:5,000,000 using Mercator, Lambert, and polar stereographic map projections. For the computation of map projections, a biaxial spheroid figure is adopted. The semimajor and semiminor axes are 3393.4 and 3375.7 km, respectively, with a polar flattening of 0.0052. For the computation of elevations, a topographic datum is defined by a gravity field described in terms of spherical harmonics of fourth order and fourth degree combined with a 6.1-mbar occultation pressure surface. This areoid can be approximated by a triaxial ellipsoid with semimajor axes of A = 3394.6 km and B = 3393.3 km and a semiminor axis of C = 3376.3 km. The semimajor axis A intersects the Martian surface at longitude 105 deg W. The dynamic flattening of Mars is 0.00525. The contour interval of the maps is 1 km. For some prominent features where overlapping pictures from Mariner 9 are available, local contour maps at relatively larger scales were also compiled by photogrammetric methods on stereo plotters.

Wu, S. S. C.↗

NASA NTRS1990

Physical conditions in photodissociation regions - Application to galactic nuclei

A procedure is outlined which determines the physical characteristics of the neutral interstellar medium in the nuclei of luminous galaxies. The method uses millimeter and IR observations to find the mass and density of the molecular and atomic gas components as well as the UV flux incident on clouds. The area and volume filling factors and approximate number of clouds and cloud radii are also found. For the Galactic center, about 100 clouds of radius about 0.4 pc and density about 100,000/cu cm are found within about 5 pc. The atomic gas temperature is about 700 K and the FUV field on clouds is about 100,000 times the local Galactic FUV field. The flux is consistent with a central source of luminosity of 2-3 x 10 to the 7th solar. Roughly 100,000 clouds of radius roughly 0.4 pc are found within the roughly 330 pc nuclear region of M82. The large number of clouds produces a projected area filling factor approaching unity. Cloud heating may be dominated by an intense interstellar UV flux.

Wolfire, Mark G.↗