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DOE OSTI2024

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics↗

NASA NTRS1999

Control of Meridional Flow by a Non-Uniform Rotational Magnetic Field

The diffusive mass transfer of species during crystal growth in vertical ampoules is significantly affected by fluid flow in the liquid mother phase (melt). For electrically conductive melts, an elegant way of remotely inducing and controlling this flow is by utilizing a uniform rotational magnetic field (RMF) in the transverse direction. It induces an azimuthal flow which tends to homogenize the thermal and solutal fields. The rotating field also reduces the diffusion boundary layer, stabilizes temperature fluctuations, and promotes better overall crystal growth. For moderate strengths of the applied magnetic field (2-20 m Tesla) with frequencies of up to 400 Hz, the induced secondary meridional flow becomes significant. It typically consists of one roll at the bottom of the liquid column and a second roll (vortex) at the top. The flow along the centerline (ampoule axis) is directed from the growing solid (interface) towards the liquid (melt). In case of convex interfaces (e.g. in floating zone crystal growth) such flow behavior is beneficial since it suppresses diffusion at the center. However, for concave interfaces (e.g. vertical Bridgman crystal growth) such a flow tends to exacerbate the situation in making the interface shape more concave. It would be beneficial to have some control of this meridional flow- for example, a single recirculating cell with controllable direction and flow magnitude will make this technique even more attractive for crystal growth. Such flow control is a possibility if a non-uniform PNE field is utilized for this purpose. Although this idea has been proposed earlier, it has not been conclusively demonstrated so far. In this work, we derive the governing equations for the fluid dynamics for such a system and obtain solutions for a few important cases. Results from parallel experimental measurements of fluid flow in a mercury column subjected to non-uniform RMF will also be presented.

Mazuruk, Konstantin↗

DOE OSTI2025

Superadditivity at large charge

The weak gravity conjecture has been invoked to conjecture that the dimensions of charged operators in a CFT should obey a superadditivity relation (sometimes referred to as convexity). In this paper, we study superadditivity of the operator spectrum in theories expanded about the semi-classical saddle point that dominates correlators of large charge operators. We explore this in two contexts. The first is a model with two scalar fields that carry different charges, at a non-trivial Wilson-Fisher fixed point. A careful analysis of the semi-classics for this two field model demonstrates that ‘quantum’ violations of superadditivity (those not forbidden by the conjecture) persist in the large charge regime. We then turn to study the general properties of CFTs at large charge as bottom-up EFTs. By a trial and error procedure we come up with a seemingly consistent family of examples violating the conjecture. In so doing the presence of a genuine dilaton field appears necessary. On the one hand our result demonstrates that the superadditivity conjecture cannot be proven purely on the basis of a bottom-up analysis. On the other hand, the need for a dilaton, with the corresponding infinite fine tuning, indicates the conjecture-violating EFTs are unlikely to be UV completable.

effective field theories↗

NASA NTRS1998

Summary of Research Report

Ten papers, published in various publications, on buckling, and the effects of imperfections on various structures are presented. These papers are: (1) Buckling mode localization in elastic plates due to misplacement in the stiffner location; (2) On vibrational imperfection sensitivity on Augusti's model structure in the vicinity of a non-linear static state; (3) Imperfection sensitivity due to elastic moduli in the Roorda Koiter frame; (4) Buckling mode localization in a multi-span periodic structure with a disorder in a single span; (5) Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling; (6) Derivation of multi-dimensional ellipsoidal convex model for experimental data; (7) Passive control of buckling deformation via Anderson localization phenomenon; (8)Effect of the thickness and initial im perfection on buckling on composite cylindrical shells: asymptotic analysis and numerical results by BOSOR4 and PANDA2; (9) Worst case estimation of homology design by convex analysis; (10) Buckling of structures with uncertain imperfections - Personal perspective.

Elishakoff, Isaac↗

NASA NTRSDate not supplied

Development of Langmuir and Spatially Resolved OES Diagnostics for Arc Jet Shock and Boundary Layer Measurements Relevant to Atmospheric Re-Entry Environments

The second-generation miniature Arc Jet Research Chamber (mARC) ground testing facility at NASA Ames requires physical characterization of its supersonic plasma flow to verify numerical models and material sample testing. Two types of plasma diagnostics will be utilized: Langmuir probes and optical emission spectroscopy (OES). Several single and triple Langmuir probes have been constructed and will be inserted parallel to the flow via a sweep arm to measure post-shock electron temperature and number density along radial profiles at different axial distances. Due to the high heat flux (200-3000 W/cm2) sweep durations are necessarily short (< 0.1 s). Measuring these properties near the probe surface provide characterization of the post-shock environment. This is an important metric for validating coupled CFD-material codes, and will provide insight into longstanding thermocouple anomalies attributed to charging of heatshield surfaces. An OES system has also been assembled to obtain spatially resolved density and temperature for various flow species. The system consists of a convex lens that forms an image of the plasma onto a 16-channel linear fiber array, which will simultaneously capture the spectra from sixteen different locations. The light emission from the plasma is then focused by a spherical mirror into a spectrometer and recorded with a camera. These measurements non-intrusively provide a new spatially resolved flow characterization capability. This will initially be used to resolve issues with shock radiation interference in pyrometer measurements of material surface temperature. The design of each diagnostic and any initial results will be discussed.

Ethan Main-Loam Leong↗

NASA NTRS1992

The shape of asteroid 1917 Cuyo

Lightcurves obtained for 1917 Cuyo at solar phase angles near 54 degrees have an amplitude delta m = 0.44 mag. However, convex-profile inversion of the lightcurves yields an estimate of the asteroid's mean cross section (C, a 2-D average of the 3-D shape) that is only slightly noncircular, with an elongation approximately 1.15. The estimate of C undoubtedly contains systematic errors, the most severe of which could arise from non-equatorial viewing/illumination geometry. However, Cuyo's radar echo shows very little variation in bandwidth vs. rotation phase, supporting the hypothesis that this asteroid's elongation is rather modest.

Ostro, Steven J.↗

DOE OSTI2021

Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

This paper introduces the scaled boundary cubature (SBC) scheme for accurate and efficient integration of functions over polygons and two-dimensional regions bounded by parametric curves. Over two-dimensional domains, the SBC method reduces integration over a region bounded by m curves to integration over m regions (referred to as curved triangular regions), where each region is bounded by two line segments and a curve. With proper (counterclockwise) orientation of the boundary curves, the scheme is applicable to convex and nonconvex domains. Additionally, for star-convex domains, a tensor-product cubature rule with positive weights and integration points in the interior of the domain is obtained. If the integrand is homogeneous, we show that this new method reduces to the homogeneous numerical integration scheme; however, the SBC scheme is more versatile since it is equally applicable to both homogeneous and non-homogeneous functions. This paper also introduces several methods for smoothing integrands with point singularities and near-singularities. When these methods are used, highly efficient integration of weakly singular functions is realized. Finally, the SBC method is applied to a number of benchmark problems, which reveal its broad applicability and superior performance (in terms of time to generate a rule and accuracy per cubature point) when compared to existing methods for integration.

42 ENGINEERING↗

NASA NTRS2002

Diffractive optical elements on non-flat substrates using electron beam lithography

The present disclosure describes a technique for creating diffraction gratings on curved surfaces with electron beam lithography. The curved surface can act as an optical element to produce flat and aberration-free images in imaging spectrometers. In addition, the fabrication technique can modify the power structure of the grating orders so that there is more energy in the first order than for a typical grating. The inventors noticed that by using electron-beam lithography techniques, a variety of convex gratings that are well-suited to the requirements of imaging spectrometers can be manufactured.

Maker, Paul D.↗

NASA NTRS2007

Weather Research and Forecasting Model Sensitivity Comparisons for Warm Season Convective Initiation

Mesoscale weather conditions can significantly affect the space launch and landing operations at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS). During the summer months, land-sea interactions that occur across KSC and CCAFS lead to the formation of a sea breeze, which can then spawn deep convection. These convective processes often last 60 minutes or less and pose a significant challenge to the forecasters at the National Weather Service (NWS) Spaceflight Meteorology Group (SMG). The main challenge is that a "GO" forecast for thunderstorms and precipitation at the Shuttle Landing Facility is required at the 90 minute deorbit decision for End Of Mission (EOM) and at the 30 minute Return To Launch Site (RTLS) decision. Convective initiation, timing, and mode also present a forecast challenge for the NWS in Melbourne, FL (MLB). The NWS MLB issues such tactical forecast information as Terminal Aerodrome Forecasts (TAF5), Spot Forecasts for fire weather and hazardous materials incident support, and severe/hazardous weather Watches, Warnings, and Advisories. Lastly, these forecasting challenges can also affect the 45th Weather Squadron (45 WS), which provides comprehensive weather forecasts for shuttle launch, as well as ground operations, at KSC and CCAFS. The need for accurate mesoscale model forecasts to aid in their decision making is crucial. This study specifically addresses the skill of different model configurations in forecasting warm season convective initiation. Numerous factors influence the development of convection over the Florida peninsula. These factors include sea breezes, river and lake breezes, the prevailing low-level flow, and convergent flow due to convex coastlines that enhance the sea breeze. The interaction of these processes produces the warm season convective patterns seen over the Florida peninsula. However, warm season convection remains one of the most poorly forecast meteorological parameters. To determine which configuration options are best to address this specific forecast concern, the Weather Research and Forecasting (WRF) model, which has two dynamical cores - the Advanced Research WRF (ARW) and the Non-hydrostatic Mesoscale Model (NMM) was employed. In addition to the two dynamical cores, there are also two options for a "hot-start" initialization of the WRF model - the Local Analysis and Prediction System (LAPS; McGinley 1995) and the Advanced Regional Prediction System (ARPS) Data Analysis System (ADAS; Brewster 1996). Both LAPS and ADAS are 3- dimensional weather analysis systems that integrate multiple meteorological data sources into one consistent analysis over the user's domain of interest. This allows mesoscale models to benefit from the addition of highresolution data sources. Having a series of initialization options and WRF cores, as well as many options within each core, provides SMG and MLB with considerable flexibility as well as challenges. It is the goal of this study to assess the different configurations available and to determine which configuration will best predict warm season convective initiation.

Watson, Leela R.↗

NASA NTRS1985

The Influence of Low Frequency Mechanical Vibrations on the Growth of Single Crystals

The optimum conditions for crystal growth are usually achieved either by suppressing convective fluid flows (e.g., by the use of a low-gravity environment) or by over-riding thermal and solutal convection by the use of a strong stirring action. A novel stirring technique has been developed which involves subjecting a vertical crucible to a circle in a horizontal plane (without rotation). Use of an amplitude of 3 mm at a frequency of approx 6 Hz produced complete mixing of a non-uniform aqueous liquid in a few seconds. The mixing action involved the downward flow of liquid in the outer annulus of the liquid, driven by surface waves. When the downward flowing liquid reaches the bottom of the crucible, it is reflected in a central, upward flowing spiral. This flow pattern should be beneficial for crystal growth by the Bridgman method since it will sweep impurities away from the walls and produce a more convex solid-liquid interface. Initial attempts to apply the new stirring technique to CdTe crystal growth did not show significant improvement in the number of crystals nucleated, but the interface shape appeared to be close to that predicted.

Feigelson, R. S.↗

DOE OSTI2020

Computational modeling and neutron imaging to understand interface shape and solute segregation during the vertical gradient freeze growth of BaBrCl:Eu

In this work we apply continuum models to analyze phase change, heat transfer, fluid flow, solute transport, and segregation in order to understand prior neutron imaging observations of the vertical gradient freeze growth of Eu-doped BaBrCl. The models provide a rigorous framework in which to understand the mechanisms that are responsible for the complicated evolution of interface shape and dopant distribution in the growth experiment. We explain how a transition in the solid/liquid interface shape from concave to convex is driven by changes in radial heat transfer caused by furnace design. We also provide a mechanistic explanation of how dynamic growth conditions and changes of the flow structure in the melt result in complicated segregation patterns in this system. A growth pause caused by controller lock-up is shown to result in a band of solute depletion in accordance with classical theory. However, changing flow patterns during growth result in a non-monotonic axial distribution of solute that cannot be explained by simple application of classical segregation models. We assert that the approach presented here, namely the use of rigorous models in conjunction advanced diagnostics, such as neutron imaging, provides an exciting path forward for process optimization and control, accelerating the incremental advances that have, in the past, typically relied on empiricism, experience, and intuition.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Quantifying Dynamic Signal Spread in Real-Time High-Energy X-ray Diffraction

Abstract Measured intensity in high-energy monochromatic X-ray diffraction (HEXD) experiments provides information regarding the microstructure of the crystalline material under study. The location of intensity on an areal detector is determined by the lattice spacing and orientation of crystals so that changes in the heterogeneity of these quantities are reflected in the spreading of diffraction peaks over time. High temporal resolution of such dynamics can now be experimentally observed using technologies such as the mixed-mode pixel array detector (MM-PAD) which facilitates in situ dynamic HEXD experiments to study plasticity and its underlying mechanisms. In this paper, we define and demonstrate a feature computed directly from such diffraction time series data quantifying signal spread in a manner that is correlated with plastic deformation of the sample. A distinguishing characteristic of the analysis is the capability to describe the evolution from the distinct diffraction peaks of an undeformed alloy sample through to the non-uniform Debye–Scherrer rings developed upon significant plastic deformation. We build on our previous work modeling data using an overcomplete dictionary by treating temporal measurements jointly to improve signal spread recovery. We demonstrate our approach in simulations and on experimental HEXD measurements captured using the MM-PAD. Our method for characterizing the temporal evolution of signal spread is shown to provide an informative means of data analysis that adds to the capabilities of existing methods. Our work draws on ideas from convolutional sparse coding and requires solving a coupled convex optimization problem based on the alternating direction method of multipliers.

Engineering↗

NASA NTRS2011

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

Acikmese, Behcet↗

NASA NTRS2000

Distribution of expansins in graviresponding maize roots

To test if expansins, wall loosening proteins that disrupt binding between microfibrils and cell wall matrix, participate in the differential elongation of graviresponding roots, Zea mays L. cv. Merit roots were gravistimulated and used for immunolocalization with anti-expansin. Western blots showed cross-reaction with two proteins of maize, one of the same mass as cucumber expansin (29 kDa), the second slightly larger (32 kDa). Maize roots contained mainly the larger protein, but both were found in coleoptiles. The expansin distribution in cucumber roots and hypocotyls was similar to the distribution in maize. Roots showed stronger expansin signals on the expanding convex side than the concave flank as early as 30 min after gravistimulation. Treatment with brefeldin A, a vesicle transport inhibitor, or the auxin transport inhibitor, naphthylphthalamic acid, showed delayed graviresponse and the appearance of differential staining. Our results indicate that expansins may be transported and secreted to cell walls via vesicles and function in wall expansion.

Non-NASA Center↗

DOE OSTI2024

Using Convex Optimization to Efficiently Apportion Tracer and Pollutant Sources From Point Concentration Observations

Abstract Rivers transport elements, minerals, chemicals, and pollutants produced in their upstream basins. A sample from a river is a mixture of all of its upstream sources, making it challenging to pinpoint the contribution from each individual source. Here, we show how a nested sample design and convex optimization can be used to efficiently unmix downstream samples of a well‐mixed, conservative tracer in a steady state system into the contributions of their upstream sources. Our approach is significantly faster than previous methods. We represent the river's sub‐catchments, defined by sampling sites, using a directed acyclic graph. This graph is used to build a convex optimization problem which, thanks to its convexity, can be quickly solved to global optimality—in under a second on desktop hardware for data sets of ∼100 samples or fewer. Uncertainties in the upstream predictions can be generated using Monte Carlo resampling. We provide an open‐source implementation of this approach in Python. The inputs required are straightforward: a table containing sample locations and observed tracer concentrations, along with a D8 flow‐direction raster map. As a case study, we use this method to map the elemental geochemistry of sediment sources for rivers draining the Cairngorms mountains, UK. This method could be extended to non‐conservative and non‐steady state tracers. We also show, theoretically, how multiple tracers could be simultaneously inverted to recover upstream run‐off or erosion rates as well as source concentrations. Overall, this approach can provide valuable insights to researchers in various fields, including water quality, geochemical exploration, geochemistry, hydrology, and wastewater epidemiology.

Barnes, Richard↗

DOE OSTI2023

Investigating Inherent Numerical Stabilization for the Moist, Compressible, Non‐Hydrostatic Euler Equations on Collocated Grids

This study investigates inherent numerical dissipation due to upwind fluxes and reconstruction strategies for collocated Finite-Volume integration of the Euler equations. Idealized supercell simulations are used without any explicit dissipation. Flux terms are split into: mass flux, pressure, and advected quantities. They are computed with the following upwind strategies: central, advectively upwind, and acoustically upwind. This is performed for third and ninth-order-accurate reconstructions with and without Weighted Essentially Non-Oscillatory limiting. Acoustic-only upwinding for pressure and mass flux terms and advective-only upwinding for advected quantities is the most flexible simplification found. It reduces data movement and computations. Assuming a constant speed of sound in acoustic upwinding gives similar results to using the true speed of sound. Dissipation from upwind adapts automatically to grid spacing, time step, reconstruction accuracy, and flow smoothness. While stability is maintained even at 21st-order spatial accuracy, there is a limit to the spatial order of accuracy for which upwinding alone can create a realizable solution in the conditions of this study. Convex combinations of upwind and central solutions for flux terms also reduced dissipation, but as the central proportion grows, solutions become physically unrealizable. The range of length scales of the kinetic energy spectra can be extended along k −5/3 to smaller spatial scales by reducing dissipation either with higher-order reconstructions or using convex combinations of upwind and central fluxes. However, not all extensions of the length scale range along k −5/3 exhibit physically realizable solutions, even though the spectra appear to be physical.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1992

Cartography of asteroids and comet nuclei from low resolution data

High resolution images of non-spherical objects, such as Viking images of Phobos and the anticipated Galileo images of Gaspra, lend themselves to conventional planetary cartographic procedures: control network analysis, stereophotogrammetry, image mosaicking in 2D or 3D, and airbrush mapping. There remains the problem of a suitable map projection for bodies which are extremely elongated or irregular in shape. Many bodies will soon be seen at lower resolution (5-30 pixels across the disk) in images from speckle interferometry, the Hubble Space Telescope, ground-based radar, distinct spacecraft encounters, and closer images degraded by smear. Different data with similar effective resolutions are available from stellar occultations, radar or lightcurve convex hulls, lightcurve modeling of albedo variations, and cometary jet modeling. With such low resolution, conventional methods of shape determination will be less useful or will fail altogether, leaving limb and terminator topography as the principal sources of topographic information. A method for shape determination based on limb and terminator topography was developed. It has been applied to the nucleus of Comet Halley and the jovian satellite Amalthea. The Amalthea results are described to give an example of the cartographic possibilities and problems of anticipated data sets.

Stooke, Philip J.↗

DOE OSTI2022

Multi-service battery energy storage system optimization and control

Battery energy storage systems (BESS) have become fundamental part of modern power systems due to their capability to provide multiple grid services. As the renewable penetration increases, BESS procurement is also expected to increase where it is envisioned to play a systematic and strategical role in power systems planning and operation. Hence, in this paper we present a multiple grid service procurement and operation for BESS - ranging from energy arbitrage, reserve/regulation services, power factor correction, and demand management. The proposed framework considers an optimal multi-temporal dimension, designed to be operable for both planning and real-time operation. Moreover, non-linearity inherent to BESS services and uncertainty associated to market forecasts variables are addressed using techniques such as polyhedral norms and robust optimization approaches. Here, the developed model is tested using a utility-scaled BESS and the obtained results show the effectiveness of the systematic BESS multi-service planning and operation approach.

25 ENERGY STORAGE↗