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Results for “Manifold sampling”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions

Here we propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We additionally assume that the composition $h\circ F$ defines a continuous selection. Manifold sampling algorithms can be classified as model-based derivative-free methods, in that models of $F$ are combined with particularly sampled information about $h$ to yield local models for use within a trust-region framework. We demonstrate that cluster points of the sequence of iterates generated by the manifold sampling algorithm are Clarke stationary. We consider the tractability of three particular subproblems generated by the manifold sampling algorithm and the extent to which inexact solutions to these subproblems may be tolerated. Numerical results demonstrate that manifold sampling as a derivative-free algorithm is competitive with state-of-the-art algorithms for nonsmooth optimization that utilize first-order information about $f$.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Manifold Sampling for Optimization of Nonconvex Functions That Are Piecewise Linear Compositions of Smooth Components

Here, we develop a manifold sampling algorithm for the minimization of a nonsmooth composite function $f \triangleq \psi + h \circ F$ when $\psi$ is smooth with known derivatives, $h$ is a known, nonsmooth, piecewise linear function, and $F$ is smooth but expensive to evaluate. The trust-region algorithm classifies points in the domain of $h$ as belonging to different manifolds and uses this knowledge when computing search directions. Since $h$ is known, classifying objective manifolds using only the values of $F$ is simple. We prove that all cluster points of the sequence of the manifold sampling algorithm iterates are Clarke stationary; this holds although points evaluated by the algorithm are not assumed to be differentiable and when only approximate derivatives of $F$ are available. Numerical results show that manifold sampling using zeroth-order information about $F$ is competitive with algorithms that employ exact subgradient values from $\partial f$.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Structure-aware methods for expensive derivative-free nonsmooth composite optimization

We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive function. We provide accompanying implementations of these methods: in particular, a novel manifold sampling algorithm (MS-P) with subproblems that are in a sense primal versions of the dual problems solved by previous manifold sampling methods and a method (GOOMBAH) that employs more difficult optimization subproblems. For these two methods, we provide rigorous convergence analysis and guarantees. We demonstrate extensive testing of these methods. Open-source implementations of the methods developed in this manuscript can be found at https://github.com/POptUS/ IBCDFO/.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

CFD Analysis of RLUOB Zone 1 HEPA Filter Plenum and Testing Manifolds

The purpose of this computational fluid dynamics (CFD) analysis is to ensure that Camfil Farr’s upstream and downstream injection and sampling manifolds can meet or exceed the requirements outlined in the ASME AG-1 1997 a(2000) Code on Nuclear Air and Gas Treatment for the testing of HEPA and adsorbent filters. This paper will present a numerical simulation of airflow in the Radiological Laboratory Utility Office Building (RLUOB) zone 1 HEPA filter plenum and testing manifolds using the commercial CFD software ANSYS FLUENT 2020R1. The CFD analysis focuses on the investigation of the air flow distribution and air-aerosol mixing uniformity. The evaluation was done for all steps of the modeling process: grid generation, physics setup, simulation, and post-processing. The mass flow rate in each section of the zone 1 injection and sampling manifolds is also reported.

42 ENGINEERING↗
NASA NTRS1979

Airborne laser induced fluorescence system for measuring OH and other trace gases in the parts-per-quadrillion to parts-per-trillion range

Described in detail is a laser induced fluorescence system which has been successfully interfaced with two aircraft sampling platforms (i.e., Sabreliner jet and an L-188C Electra). This system, which has been under development for four years, presently consists of the following major components: (1) a Nd-Yag laser driven oscillator-amplifier dye laser; (2) a sampling manifold with associated fluorescence detection optics; (3) an OH calibration chamber; (4) a laser beam steering assembly; and (5) sampling electronics and data processing hardware. During the last three years, this system has been flown some 50,000 air miles making tropospheric OH radical measurements over the latitude range of 70 N to 57 S. OH concentrations measured during these flights have ranged from 30 parts-per-quadrillion (3.7 x 10 to the 5th molecules/sq cm) at altitudes of 6 km to 0.8 parts-per-trillion (2.0 x 10 to the 7th molecules/sq cm) at 0.5 km. Computations have been completed which indicate that the existing aircraft system with modest modifications should also be capable of detecting natural tropospheric levels of NO, SO2, CH2O, NO2, HNO2, NO3, H2O2 and CS2 by using both conventional laser-induced fluorescence methodology and multiphoton techniques.

Davis, D. D.↗
DOE OSTI2024

Optimization on Manifolds via Graph Gaussian Processes

This paper integrates manifold learning techniques within a Gaussian process upper confidence bound algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

Bayesian optimization↗
DOE OSTI2022

Derivative-free optimization of a rapid-cycling synchrotron

Here, we develop and solve a constrained optimization model to identify an integrable optics rapid-cycling synchrotron lattice design that performs well in several capacities. Our model encodes the design criteria into 78 linear and nonlinear constraints, as well as a single nonsmooth objective, where the objective and some constraints are defined from the output of Synergia, an accelerator simulator. We detail the difficulties of the 23-dimensional simulation-constrained decision space and establish that the space is nonempty. We use a derivative-free manifold sampling algorithm to account for structured nondifferentiability in the objective function. Our numerical results quantify the dependence of solutions on constraint parameters and the effect of the form of objective function.

43 PARTICLE ACCELERATORS↗
NASA NTRS1998

Development of an Atmospheric Pressure Ionization Mass Spectrometer

A commercial atmospheric pressure ionization mass spectrometer (APIMS) was purchased from EXTREL Mass Spectrometry, Inc. (Pittsburgh, PA). Our research objectives were to adapt this instrument and develop techniques for real-time determinations of the concentrations of trace species in the atmosphere. The prototype instrument is capable of making high frequency measurements with no sample preconcentrations. Isotopically labeled standards are used as an internal standard to obtain high precision and to compensate for changes in instrument sensitivity and analyte losses in the sampling manifold as described by Bandy and coworkers. The prototype instrument is capable of being deployed on NASA C130, Electra, P3, and DC8 aircraft. After purchasing and taking delivery by June 1994, we assembled the mass spectrometer, data acquisition, and manifold flow control instrumentation in electronic racks and performed tests.

Source record↗
DOE OSTI2025

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems↗
NASA NTRSDate not supplied

Sample Processor for Life on Icy Worlds (SPLIce): Monolithic Manifold-Based System to Recover, Prepare, and Deliver Samples and Standards to Instrumentation Suites for Ocean World Life-Search Missions

A claim of life detection on one of the solar system’s icy ocean worlds would necessitate extraordinarily convincing evidence. Limited energy availability in the oceans of such bodies as Europa and Enceladus argues for microbes as most probable among possible life forms, but evidence of their existence in the surface layers of an icy moon or in a frozen plume ejected into space could take various forms, pointing to instrumentation suites as a preferred means to detect diverse molecular and morphological life indicators. Multiple disparate categories of positive detections could provide truly convincing evidence from samples that may be only a few micro-liters. SPLIce’s Foundation. Teams led by NASA’s Ames Research Center have developed and operated numerous small, live-biology and astrobiology science payloads in space over two decades. Since 2016, we have adapted and augmented their biological sample-handling systems to create compact, robust search-for-life fluidic processors designed to function after a decade or more in transit, in environments with very little gravity and lots of radiation: up to 100’s of kilorads.

Instrumentation suite↗
NASA NTRS2001

Beagle 2: The Next Exobiology Mission to Mars

Beagle 2 is a 60 kg probe (with a 30 kg lander) developed in the United Kingdom for inclusion on the European Space Agency's 2003 Mars Express. Beagle 2 will deliver to the Martian surface a payload which consists of a high percentage of science instruments to landed spacecraft mass. Beagle 2 will be launched in June, 2003 with Mars Express on a Soyuz-Fregat rocket from the Baikonur Cosmodrome in Kazakhstan. Beagle 2 will land on Mars on December 26, 2003 in the Isidis Planitia basin (approximately 10 degrees N and 275 degrees W), a large sedimentary basin that overlies the boundary between ancient highlands and northern plains. Isidis Planitia, the third largest basin on Mars, which is possibly filled with sediment deposited at the bottom of long-standing lakes or seas, offers an ideal environment for preserving traces of life. Beagle 2 was developed to search for organic material and other volatiles on and below the surface of Mars in addition to the study of the inorganic chemistry and mineralogy. Beagle 2 will utilize a mechanical mole and grinder to obtain samples from below the surface, under rocks and inside rocks. A pair of stereo cameras will image the landing site along with a microscope for examination of surface and rock samples. Analyses will include both rock and soil samples at various wavelengths, X-ray spectrometer and Mossbauer spectrometer as well as a search for organics and other light element species (e.g. carbonates and water) and measurement of their isotopic compositions. Beagle 2 has as its focus the goal of establishing whether evidence for life existed in the past on Mars at the Isidis Planitia site or at least establishing if the conditions were ever suitable. Carbonates and organic components were first recognized as existing on Mars when they were found in the Martian meteorite Nakhla. Romanek et al showed the carbonates in ALH84001 were formed at low temperatures. McKay et al noted possible evidence of early life on Mars within the ALH84001 meteorite. Thomas-Keprta et al showed the magnetite biomarkers in ALH84001's carbonates are indistinguishable from those formed by magnetotactic bacteria found on Earth. Gibson et al showed there was significant evidence for liquid water and biogenic products present on Mars across a 3.9 billion year period. A mechanical arm (PAW) operates from the lander and is used for science operations along with sample acquisition. Instruments attached to the PAW include: stereo cameras, Mossbauer instrument, X-ray fluorescence instrument, microscope, environmental sensors, rock corer/grinder, a spoon, mirror, brushes, a mole attachment for acquisition of subsurface to depths of 1 to 2 meters and an illumination device. Each camera has 14 filters which have been optimized for mineralogy composition, dust and water vapor detection. The microscope's camera is designed for viewing the size and shape of dust particles, rock surfaces, microfossils, and characteristics of the samples prior to introduction into the gas analysis package (GAP). The camera has a resolution of 4 microns/pixel, features four color capability (red, green, blue and UV (ultraviolet) fluoresence), a depth of focus of 40 micrometers and translation stage of +3 millimeters. The heart of the Beagle 2's life detection package is the gas analysis package (GAP), which consists of a mass spectrometer with collectors at fixed masses for precise isotopic ratio measurements and voltage scanning for spectral analysis. Primary aim of the GAP is to search for the presence of bulk constituents, individual species, and isotopic fractionations for both extinct and extent life along with studying the low-temperature geochemistry of the hydrogen, carbon, nitrogen and oxygen components on Mars from both the surface and atmosphere. GAP is a magnetic sector mass spectrometer with the range of 1 to 140 amu which can be operated in both the static and dynamic modes. A triple Faraday collector array will be used for C, N and O ratios along with a double Faraday array for H/D. Pulse counting electron multiplier will be utilized for noble gases and selected organics. Anticipated detection limits are at the picomole level for operation in the static mode of operation and high precision isotopic measurements will be made in the dynamic mode. Sample processing and preparation system consists of reaction vessels along with references. Sample ovens capable of being heated are attached to the manifold for sample combustion. Surface, subsurface materials and interior rock specimens will be combusted in pure oxygen gas at various temperature intervals to release organic matter and volatiles. Combustion process will permit detection of all forms and all atoms of carbon present in the samples. A chemical processing system is capable of a variety of conversion reactions. Gases are manipulated either by cryogenic or chemical reactions and passed through the gas handling portion of the vacuum system. There are two modes of operation: quantitative analysis and precise isotopic measurements. Additional information is contained in the original extended abstract.

Gibson, Everett K., Jr.↗
DOE OSTI2025

Generative learning of densities on manifolds

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps , a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Double diffusion maps↗
NASA NTRS1986

Observations of the J = 10 manifold of the pure rotational band of phosphine on Saturn

Saturn was observed in the vicinity of the J = 10 manifold of the pure rotational band of phosphine on 1984 July 10 and 12 from NASA's Kuiper Airborne Observatory with the facility far-infrared cooled grating spectrometer. On each night observations of the full disk plus rings were made at 4 to 6 discrete wavelengths which selectively sampled the manifold and the adjacent continuum. The previously reported detection of this manifold is confirmed. After subtraction of the flux due to the rings, the data are compared with disk-averaged models of Saturn. It is found that PH3 must be strongly depleted above the thermal inversion (approx. 70 mbar). The best fitting models consistent with other observational constaints indicate that PH3 is significantly depleted at even deeper atmospheric levels ( or = 500 mbar), implying an eddy diffusion coefficient for Saturn of 10 to the 4 cm sq/sec.

Haas, M. R.↗
NASA NTRS1985

Observations of the J = 10 manifold of the pure rotational band of phosphine on Saturn

Saturn was observed in the vicinity of the J = 10 manifold of the pure rotational band of phosphine on 1984 July 10 and 12 from NASA's Kuiper Airborne Observatory with the facility far-infrared cooled grating spectrometer. On each night observations of the full disk plus rings were made at 4 to 6 discrete wavelengths which selectively sampled the manifold and the adjacent continuum. The previously reported detection of this manifold is confirmed. After subtraction of the flux due to the rings, the data are compared with disk-averaged models of Saturn. It is found that PH3 must be strongly depleted above the thermal inversion (approx. 70 mbar). The best fitting models consistent with other observational constraints indicate that PH3 is significantly depleted at even deeper atmospheric levels (or = 500 mbar), implying an eddy diffusion coefficient for Saturn of 10 to the 4 cm sq/sec.

Haas, M. R.↗
DOE OSTI2018

Derivative-free robust optimization by outer approximations

We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We demonstrate the practical benefits of the algorithm on a new class of test problems.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1970

Economic gas chromatograph system for subambient pressure gas sampling

Gas chromatograph sampling system consists of a manifold with a gas-sample valve, a minimum-volume pressure transducer with a portable monitor, a vacuum-source valve, and a sample inlet valve. Increased accuracy of analysis is obtained by better control of sample size.

Mitchell, S. M.↗