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At least 19 records

Progressive Classification Using Support Vector Machines

An algorithm for progressive classification of data, analogous to progressive rendering of images, makes it possible to compromise between speed and accuracy. This algorithm uses support vector machines (SVMs) to classify data. An SVM is a machine learning algorithm that builds a mathematical model of the desired classification concept by identifying the critical data points, called support vectors. Coarse approximations to the concept require only a few support vectors, while precise, highly accurate models require far more support vectors. Once the model has been constructed, the SVM can be applied to new observations. The cost of classifying a new observation is proportional to the number of support vectors in the model. When computational resources are limited, an SVM of the appropriate complexity can be produced. However, if the constraints are not known when the model is constructed, or if they can change over time, a method for adaptively responding to the current resource constraints is required. This capability is particularly relevant for spacecraft (or any other real-time systems) that perform onboard data analysis. The new algorithm enables the fast, interactive application of an SVM classifier to a new set of data. The classification process achieved by this algorithm is characterized as progressive because a coarse approximation to the true classification is generated rapidly and thereafter iteratively refined. The algorithm uses two SVMs: (1) a fast, approximate one and (2) slow, highly accurate one. New data are initially classified by the fast SVM, producing a baseline approximate classification. For each classified data point, the algorithm calculates a confidence index that indicates the likelihood that it was classified correctly in the first pass. Next, the data points are sorted by their confidence indices and progressively reclassified by the slower, more accurate SVM, starting with the items most likely to be incorrectly classified. The user can halt this reclassification process at any point, thereby obtaining the best possible result for a given amount of computation time. Alternatively, the results can be displayed as they are generated, providing the user with real-time feedback about the current accuracy of classification.

Wagstaff, Kiri↗

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗

Similar but Different: Structural and Spectroscopic Characterization of Series of Neodymium, Europium, Americium, and Curium Coordination Complexes

Series of curium, americium, europium, and neodymium complexes with five different polyoxometalate (POM) ligands were structurally and spectroscopically characterized: Na x Cs y H z [M(XW 11 O 39 ) 2 ]· n H 2 O, where M = Nd 3+ , Eu 3+ , Am 3+ , or Cm 3+ and X = B 3+ , Ga 3+ , Si 4+ , Ge 4+ , or P 5+ . This first “serial approach” on transplutonium chemistry was allowed by minimizing the amount of f-element needed per synthesis down to ∼10 μg. This offers a unique opportunity to contrast structural and spectroscopic properties of trivalent actinide with those of lanthanide compounds under identical conditions. The results showcase that although actinide(III) and lanthanide(III) can make isostructural complexes, their solid-state coordination chemistries deviate significantly. The curium and americium compounds were found to be more uniform than their europium and neodymium counterparts, respectively. The particular symmetry of the Cm-POMs also enables the observation of rarely seen emission bands, which hints at vibronic coupling or new emissive pathways. Additionally, the Cm-POM and Eu-POM complexes were characterized via steady-state and time-resolved excitation and emission spectroscopy in solutions containing five different counterions (Li + , Na + , K + , Rb + , or Cs + ), representing 50 combinations of alkali/[M III (XW 11 ) 2 ] n − complexes. The Cm-POMs respond to the alkali counterions by improving symmetry from Li + to Cs + , while the Eu-POMs do the opposite. The luminescence lifetimes of the Cm-POMs also depart from the ideal Kimura equation. Finally, this study provides a rare, and perhaps the most comprehensive, experimental data set comparing heavy actinides and lanthanides via single crystal XRD plus, solution-state, solid-state, and time-resolved emission spectroscopy and demonstrates that lanthanides are only a coarse approximation for actinide elements.

chemical structure↗

Machine learning and TDDFT software for stopping power computation

(SF-24-012) Stopping power describes the rate that a material slows radiation particles passing through it and is useful in designing many technologies. Few organizations can perform new measurements, which require significant resources and rare equipment, and all others rely on coarse approximations rendered from pre-existing data. Methods for computing stopping power in new materials, such as time-dependent density functional theory (TD-DFT), have only recently (circa-2015) become available but are too computationally costly to use frequently enough to have a pronounced impact. We have created a method that opens a pathway to computing stopping power without any need for experimental data by combining electronic structure computations and machine learning.

Ward, Logan↗

The influence of gamma prime on the recrystallization of an oxide dispersion strengthened superalloy - MA 6000E

The requirement of large, recrystallized, highly elongated grains is of primary importance to the development of suitable high temperature properties in oxide dispersion strengthened-superalloys. In the present study the recrystallization behavior of MA 6000E, a recently developed Y2O3 strengthened superalloy produced by mechanical alloying, was examined using transmission and replication microscopy. Gradient and isothermal annealing treatments were applied to extruded and hot rolled products. It was found that conversion from a very fine (0.2 micron) grain structure to a coarse (approximately 10 mm) grain structure is controlled by the dissolution of the gamma prime phase, while grain shape was controlled primarily by the thermal gradient. The fine uniform oxide dispersion appeared to have only a secondary influence in determining the grain shape as columnar grains could be grown transverse to the working direction by appropriate application of the thermal gradient.

Hotzler, R. K.↗

Ash loading and insolation at Hanford, Washington during and after the eruption of Mount St. Helens

The effects of volcanic ash suspended in the atmosphere on the incident solar radiation was monitored at the Hanford Meteorological Station (HMS) subsequent to the major eruption of Mount St. Helens on May 18, 1980. Passage of the ash plume over Hanford resulted in a very dramatic decrease of solar radiation intensity to zero. A reduction in visibility to less than 1 km was observed, as great quantities of ash fell out of the plume onto the ground. Ash loading in the atmosphere remained very high for several days following the eruption, primarily as a result of resuspension from the surface. Visibilities remained low (2 to 8 km) during this period. Estimates of atmospheric turbidity were made from the ratio of diffuse-to-direct solar radiation; these turbidities were used to estimate extinction along a horizontal path, a quantity which can be related to visibility. Comparisons of observed and estimated visibilities were very good, in spite of the rather coarse approximations used in the estimates. Atmospheric clarity and visibility improved to near pre-eruption conditions following a period of rain showers. The diffuse-to-direct ratio of solar radiation provided a useful index for estimating volcanic ash loading of the atmosphere.

Laulainen, N. S.↗

Igneous inclusions from ordinary chondrites: High temperature cumulates and a shock melt

We report microprobe, instrumental neutron activation analysis, and radiochemical neutron activation analysis data for three large igneous inclusions in the Yamato (Y-)75097, Y-793241, and Y-794046 ordinary chondrites. The inclusions in the first two chondrites are troctolitic cumulates that have undergone appreciable reactions with their hosts either during emplacement and/or cooling. Olivine-spinel Fe-Mg exchange pairs in these two inclusions record equilibration temperatures of about 710 C, and these temperatures are similar to those exhibited by mineral pairs in the Y-75097 and Y-793241 hosts. The inclusion in Y-794046 is texturally unique, consisting of fine-grained, randomly distributed olivines, coarse (approximately 2 mm) fascicular pyroxene laths, and angular pockets of maskelynite/plagioclase feldspar. The phase compositions are readily interpreted as having resulted from extremely rapid, essentially isochemical cooling to temperatures less than 1000 C of a melt with an initial temperature greater than 1670 C. We suggest that this igneous inclusion formed in-situ by shock.

Sack, Richard O.↗

Advanced analysis technique for the evaluation of linear alternators and linear motors

A method for the mathematical analysis of linear alternator and linear motor devices and designs is described, and an example of its use is included. The technique seeks to surpass other methods of analysis by including more rigorous treatment of phenomena normally omitted or coarsely approximated such as eddy braking, non-linear material properties, and power losses generated within structures surrounding the device. The technique is broadly applicable to linear alternators and linear motors involving iron yoke structures and moving permanent magnets. The technique involves the application of Amperian current equivalents to the modeling of the moving permanent magnet components within a finite element formulation. The resulting steady state and transient mode field solutions can simultaneously account for the moving and static field sources within and around the device.

Holliday, Jeffrey C.↗

A IAB-Complex Iron Meteorite Containing Low-Ca Clinopyroxene: Northwest Africa 468 and its Relationship to Iodranites and Formation by Impact Melting

Northwest Africa 468 (NWA 468) is a new ungrouped, silicate-rich member of the IAB complex of nonmagmatic iron meteorites. The silicates contain relatively coarse (approximately 300 micron-size) grains of low-Ca clinopyroxene with polysynthetic twinning and inclined extinction. Low-Ca clinopyroxene is indicative of quenching from high temperatures (either from protoenstatite in a few seconds or high-temperature clinoenstatite in a few hours). It seems likely that NWA 468 formed by impact melting followed by rapid cooling to less than or equal to 660 C. After the loss of a metal-sulfide melt from the silicates, sulfide was reintroduced, either from impact-mobilized FeS or as an S2 vapor that combined with metallic Fe to produce FeS. The O-isotopic composition (delta O-17 = -1.39 %) indicates that the precursor material of NWA 468 was a metal-rich (e.g., CR) carbonaceous chondrite. Lodranites are similar in bulk chemical and O-isotopic composition to the silicates in NWA 468; the MAC 88177 lodranite (which also contains low-Ca clinopyroxene) is close in bulk chemical composition. Both NWA 468 and MAC 88177 have relatively low abundances of REE (rare earth elements) and plagiophile elements. Siderophiles in the metal-rich areas of NWA 468 are similar to those in the MAC 88177 whole rock; both samples contain low Ir and relatively high Fe, Cu and Se. Most unweathered lodranites contain approximately 20 - 38 wt. % metallic Fe-Ni. These rocks may have formed in an analogous manner to NWA 468 (i.e., by impact melting of metal-rich carbonaceous-chondrite precursors) but with less separation of metal-rich melts from silicates.

Rubin, Alan E.↗

Millimeter-Wave Localizers for Aircraft-to-Aircraft Approach Navigation

Aerial refueling technology for both manned and unmanned aircraft is critical for operations where extended aircraft flight time is required. Existing refueling assets are typically manned aircraft, which couple to a second aircraft through the use of a refueling boom. Alignment and mating of the two aircraft continues to rely on human control with use of high-resolution cameras. With the recent advances in unmanned aircraft, it would be highly advantageous to remove/reduce human control from the refueling process, simplifying the amount of remote mission management and enabling new operational scenarios. Existing aerial refueling uses a camera, making it non-autonomous and prone to human error. Existing commercial localizer technology has proven robust and reliable, but not suited for aircraft-to-aircraft approaches like in aerial refueling scenarios since the resolution is too coarse (approximately one meter). A localizer approach system for aircraft-to-aircraft docking can be constructed using the same modulation with a millimeterwave carrier to provide high resolution. One technology used to remotely align commercial aircraft on approach to a runway are ILS (instrument landing systems). ILS have been in service within the U.S. for almost 50 years. In a commercial ILS, two partially overlapping beams of UHF (109 to 126 MHz) are broadcast from an antenna array so that their overlapping region defines the centerline of the runway. This is called a localizer system and is responsible for horizontal alignment of the approach. One beam is modulated with a 150-Hz tone, while the other with a 90-Hz tone. Through comparison of the modulation depths of both tones, an autopilot system aligns the approaching aircraft with the runway centerline. A similar system called a glide-slope (GS) exists in the 320-to-330MHz band for vertical alignment of the approach. While this technology has been proven reliable for millions of commercial flights annually, its UHF nature limits its ability to operate beyond the 1-to-2-meter precisions associated with commercial runway width. A prototype ILS-type system operates at millimeter-wave frequencies to provide automatic and robust approach control for aerial refueling. The system allows for the coupling process to remain completely autonomous, as a boom operator is no longer required. Operating beyond 100 GHz provides enough resolution and a narrow enough beamwidth that an approach corridor of centimeter scales can be maintained. Two modules were used to accomplish this task. The first module is a localizer/glide-slope module that can be fitted on a refueling aircraft. This module provides the navigation beams for aligning the approaching aircraft. The second module is navigational receiver fitted onto the approaching aircraft to be re fueled that can detect the approach beams. Since unmanned aircraft have a limited payload size and limited electrical power, the receiver portion was implemented in CMOS (complementary metal oxide semiconductor) technology based on a super-regenerative receiver (SRR) architecture. The SRR achieves mW-level power consumption and chip sizes less than l mm2. While super-regenerative techniques have small bandwidths that limit use in communication systems, their advantages of high sensitivity, low complexity, and low power make them ideal in this situation where modulating tones of less than 1 kHz are used.

Tang, Adrian J.↗

Multigrid solvers on parallel computers

Massively parallel computers, as considered in this investigation, are not yet available. However, a large-scale parallel computer cannot usefully be designed before the hypothetical algorithms which will employ it are studied. Most of the studies of parallel partial differential equations (PDE) solvers are based on solution techniques much slower (on sequential machines) than multigrid methods. Multigrid methods are highly parallelizable. Each of their processes can simultaneously be performed at all grid points. The present investigation is concerned with a preliminary exploration of the potential of multigrid, or, more generally, Multi-Level Adaptive Techniques (MLAT) on computers with many processors. Basic processes are considered, taking into account coarse-grid approximation, relaxation, coarse-grid corrections, full multigrid algorithms, nonlinear problems and eigenvalue problems, fine-to-coarse correction, and chains of problems. Details of parallel multigrid processing are also examined.

Brandt, A.↗

A quasi-meshfree method for constructing boundary-aware reproducing bases on geometrically complex domains using manifold geodesics

In many applications, physical domains are geometrically complex making it challenging to perform coarse-scale approximation. A defeaturing process is often used to simplify the domain in preparation for approximation and analysis at the coarse scale. In this paper, a methodology is presented for constructing a coarse-scale reproducing basis on geometrically complex domains given an initial fine-scale mesh of the fully featured domain. The initial fine-scale mesh can be of poor quality and extremely refined. The construction of the basis functions begins with a coarse-scale covering of the domain and generation of weighting functions with local support. Manifold geodesics are used to define distances within the local support for general applicability to non-convex domains. Conventional moving least squares is used to construct the coarse-scale reproducing basis. Applications in quasi-interpolation and linear elasticity are presented.

97 MATHEMATICS AND COMPUTING↗

Spatially Local Surrogate Modeling of Subgrid-Scale Effects in Idealized Atmospheric Flows: A Deep Learned Approach Using High-Resolution Simulation Data

Abstract We introduce a machine learned surrogate model from high-resolution simulation data to capture the subgrid-scale effects in dry, stratified atmospheric flows. We use deep neural networks (NNs) to model the spatially local state differences between a coarse-resolution simulation and a high-resolution simulation. The setup enables the capture of both dissipative and antidissipative effects in the state differences. The NN model is able to accurately capture the state differences in offline tests outside the training regime. In online tests intended for production use, the NN-coupled coarse simulation has higher accuracy over a significant period of time compared to the coarse-resolution simulation without any correction. We provide evidence of the capability of the NN model to accurately capture high-gradient regions in the flow field. With the accumulation of the errors, the NN-coupled simulation becomes computationally unstable after approximately 90 coarse simulation time steps. Insights gained from these surrogate models further pave the way for formulating stable, complex, physics-based spatially local NN models which are driven by traditional subgrid-scale turbulence closure models. Significance Statement Flows in the atmosphere are highly chaotic and turbulent, comprising flow structures of broad scales. For effective computational modeling of atmospheric flows, the effects of the small- and large-scale structures need to be captured by the simulations. Capturing the small-scale structures requires fine-resolution simulations. Even with the current state-of-the-art supercomputers, it can be prohibitively expensive to simulate these flows when computed for the entire earth over climate time scales. Thus, it is necessary to focus on the larger-scale structures using a coarse-resolution simulation while capturing the effects of the smaller-scale structures using some parameterization (approximation) scheme and incorporating it into the coarse-resolution simulation. We use machine learning to model the effects of the small-scale structures (subgrid-scale effects) in atmospheric flows. Data from a fine-resolution simulation is used to compute the missing subgrid-scale effects in coarse-resolution simulations. We then use machine learning models to approximate these differences between the coarse- and fine-resolution simulations. We see improved accuracy for the coarse-resolution simulations when corrected using these machine learned models.

54 ENVIRONMENTAL SCIENCES↗

Algebraic Nonoverlapping Domain Decomposition Methods for Stabilized FEM and FV Discretizations

We consider preconditioning methods for convection dominated fluid flow problems based on a nonoverlapping Schur complement domain decomposition procedure for arbitrary triangulated domains. The triangulation is first partitioned into a number of subdomains and interfaces which induce a natural 2 x 2 partitioning of the p.d.e. discretization matrix. We view the Schur complement induced by this partitioning as an algebraically derived coarse space approximation. This avoids the known difficulties associated with the direct formation of an effective coarse discretization for advection dominated equations. By considering various approximations of the block factorization of the 2 x 2 system, we have developed a family of robust preconditioning techniques. A computer code based on these ideas has been developed and tested on the IBM SP2 using MPI message passing protocol. A number of 2-D CFD calculations will be presented for both scalar advection-diffusion equations and the Euler equations discretized using stabilized finite element and finite volume methods. These results show very good scalability of the preconditioner for various discretizations as the number of processors is increased while the number of degrees of freedom per processor is fixed.

Barth, Timothy J.↗

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

Patera, Anthony T.↗

Shadow Molecular Dynamics and Atomic Cluster Expansions for Flexible Charge Models

Here, a shadow molecular dynamics scheme for flexible charge models is presented where the shadow Born–Oppenheimer potential is derived from a coarse-grained approximation of range-separated density functional theory. The interatomic potential, including the atomic electronegativities and the charge-independent short-range part of the potential and force terms, is modeled by the linear atomic cluster expansion (ACE), which provides a computationally efficient alternative to many machine learning methods. The shadow molecular dynamics scheme is based on extended Lagrangian (XL) Born–Oppenheimer molecular dynamics (BOMD). XL-BOMD provides stable dynamics while avoiding the costly computational overhead associated with solving an all-to-all system of equations, which normally is required to determine the relaxed electronic ground state prior to each force evaluation. To demonstrate the proposed shadow molecular dynamics scheme for flexible charge models using atomic cluster expansion, we emulate the dynamics generated from self-consistent charge density functional tight-binding (SCC-DFTB) theory using a second-order charge equilibration (QEq) model. The charge-independent potentials and electronegativities of the QEq model are trained for a supercell of uranium oxide (UO 2 ) and a molecular system of liquid water. The combined ACE+XL-QEq molecular dynamics simulations are stable over a wide range of temperatures both for the oxide and for the molecular systems and provide a precise sampling of the Born–Oppenheimer potential energy surfaces. Accurate ground Coulomb energies are produced by the ACE-based electronegativity model during an NVE simulation of UO 2 , predicted to be within 1 meV of those from SCC-DFTB on average during comparable simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assessing the Atmospheric Response to Subgrid Surface Heterogeneity in the Single-Column Community Earth System Model, Version 2 (CESM2)

Land-atmosphere interactions are central to the evolution of the atmospheric boundary layer and the subsequent formation of clouds and precipitation. Existing global climate models represent these connections with bulk approximations on coarse spatial scales, but observations suggest that small-scale variations in surface characteristics and co-located turbulent and momentum fluxes can significantly impact the atmosphere. Recent model development efforts have attempted to capture this phenomenon by coupling existing representations of subgrid-scale (SGS) heterogeneity between land and atmosphere models. Such approaches are in their infancy and it is not yet clear if they can produce a realistic atmospheric response to surface heterogeneity. Here, we implement a parameterization to capture the effects of SGS heterogeneity in the Community Earth System Model (CESM2), and compare single-column simulations against high-resolution Weather Research and Forecasting (WRF) large-eddy simulations (LESs), which we use as a proxy for observations. The CESM2 experiments increase the temperature and humidity variances in the lowest atmospheric levels, but the response is weaker than in WRF-LES. In part, this is attributed to an underestimate of surface heterogeneity in the land model due to a lack of SGS meteorology, a separation between deep and shallow convection schemes in the atmosphere, and a lack of explicitly represented mesoscale secondary circulations. These results highlight the complex processes involved in capturing the effects of SGS heterogeneity and suggest the need for parameterizations that communicate their influence not only at the surface but also vertically.

54 ENVIRONMENTAL SCIENCES↗

A Grad-Shafranov model for compact quasisymmetric stellarators

A Grad-Shafranov equation (GSE) valid for compact quasisymmetric stellarators is derived by an asymptotic expansion around a vacuum field carried to first order. We obtain an equation for the existence of flux surfaces leading up to the GSE. The flux surface label must simultaneously satisfy the existence equation and the GSE, which generally leads to an overdetermined problem. We show how the overdetermined problem can be resolved within our model for a class of hybrid devices similar to that studied by Henneberg and Plunk [Phys. Rev. Res. 6, L022052 (2024)]. We are also able to solve the existence equation for flux surfaces analytically in the most general case by introducing a special coordinate system. This will enable us to carry out an optimization seeking to minimize the error in our GSE while obeying the flux surface existence equation, which will allow us to find solutions outside the class of hybrid devices. This will allow for a coarse-grained approximate search in the space of quasisymmetric equilibria that should be faster than a conventional stellarator optimization. Nevertheless, it would still be necessary to fine-tune the approximate solutions using conventional tools to obtain a more precise optimized equilibrium.

Nikulsin, N. (ORCID:0000000318611777)↗