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DOE OSTI2018

A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows

A geometric multigrid algorithm is introduced for solving nonsymmetric linear systems resulting from the discretization of the variable density Navier–Stokes equations on nonuniform structured rectilinear grids and high-Reynolds number flows. The restriction operation is defined such that the resulting system on the coarser grids is symmetric, thereby allowing for the use of efficient smoother algorithms. To achieve an optimal rate of convergence, the sequence of interpolation and restriction operations are determined through a dynamic procedure. A parallel partitioning strategy is introduced to minimize communication while maintaining the load balance between all processors. To test the proposed algorithm, we consider two cases: 1) homogeneous isotropic turbulence discretized on uniform grids and 2) turbulent duct flow discretized on stretched grids. Testing the algorithm on systems with up to a billion unknowns shows that the cost varies linearly with the number of unknowns. This O (N) behavior confirms the robustness of the proposed multigrid method regarding ill-conditioning of large systems characteristic of multiscale high-Reynolds number turbulent flows. The robustness of our method to density variations is established by considering cases where density varies sharply in space by a factor of up to 104, showing its applicability to two-phase flow problems. Strong and weak scalability studies are carried out, employing up to 30,000 processors, to examine the parallel performance of our implementation. Excellent scalability of our solver is shown for a granularity as low as 104 to 105 unknowns per processor. At its tested peak throughput, it solves approximately 4 billion unknowns per second employing over 16,000 processors with a parallel efficiency higher than 50%.

Computer Science↗

DOE OSTI2016

The Ce-Ni-Si system as a representative of the rare earth-Ni-Si family: Isothermal section and new rare-earth nickel silicides

The Ce-Ni-Si system has been investigated at 870/1070 K by X-ray and microprobe analyses. The existence of the known compounds, i.e.: Ce{sub 2}Ni{sub 15.8}Si{sub 1.2} (Th{sub 2}Ni{sub 17}-type), Ce{sub 2}Ni{sub 15-14}Si{sub 2-3} (Th{sub 2}Zn{sub 17}-type), CeNi{sub 8.6}Si{sub 2.4} (BaCd{sub 11}-type), CeNi{sub 8.8}Si{sub 4.2} (LaCo{sub 9}Si{sub 4}-type), CeNi{sub 6}Si{sub 6} (CeNi{sub 6}Si{sub 6}-type), CeNi{sub 5}Si{sub 1-0.3} (TbCu{sub 7}-type), CeNi{sub 4}Si (YNi{sub 4}Si-type), CeNi{sub 2}Si{sub 2} (CeGa{sub 2}Al{sub 2}-type), Ce{sub 2}Ni{sub 3}Si{sub 5} (U{sub 2}Co{sub 3}Si{sub 5}-type), Ce{sub 3}Ni{sub 6}Si{sub 2} (Ce{sub 3}Ni{sub 6}Si{sub 2}-type), Ce{sub 3}Ni{sub 4}Si{sub 4} (U{sub 3}Ni{sub 4}Si{sub 4}-type), CeNiSi{sub 2} (CeNiSi{sub 2}-type), ~CeNi{sub 1.3}Si{sub 0.7} (unknown type structure), Ce{sub 6}Ni{sub 7}Si{sub 4} (Pr{sub 6}Ni{sub 7}Si{sub 4}-type), CeNiSi (LaPtSi-type), CeNi{sub 0.8-0.3}Si{sub 1.2-1.7} (AlB{sub 2}-type), ~Ce{sub 2}Ni{sub 2}Si (unknown type structure), ~Ce{sub 4.5}Ni{sub 3.5}Si{sub 2} (unknown type structure), Ce{sub 15}Ni{sub 7}Si{sub 10} (Pr{sub 15}Ni{sub 7}Si{sub 10}-type), Ce{sub 5}Ni{sub 1.85}Si{sub 3} (Ce{sub 5}Ni{sub 1.85}Si{sub 3}-type), Ce{sub 6}Ni{sub 1.4}Si{sub 3.4} (Ce{sub 6}Ni{sub 1.67}Si{sub 3}-type), Ce{sub 7}Ni{sub 2}Si{sub 5} (Ce{sub 7}Ni{sub 2}Si{sub 5}-type) and Ce{sub 3}NiSi{sub 3} (Y{sub 3}NiSi{sub 3}-type) has been confirmed in this section. Moreover, the type structure has been determined for ~Ce{sub 2}Ni{sub 2}Si (Mo{sub 2}NiB{sub 2}-type Ce{sub 2}Ni{sub 2.5}Si{sub 0.5}) and ~Ce{sub 4.5}Ni{sub 3.5}Si{sub 2} (W{sub 3}CoB{sub 3}-type Ce{sub 3}Ni{sub 3-2.7}Si{sub 1-1.3}) and new ternary phases Ce{sub 2}Ni{sub 6.25}Si{sub 0.75} (Gd{sub 2}Co{sub 7}-type), CeNi{sub 7-7.6}Si{sub 6-5.4} (GdNi{sub 7}Si{sub 6}-type) and ~Ce{sub 27}Ni{sub 42}Si{sub 31} (unknown type structure) have been identified in this system. Quasi-binary phases, solid solutions, were detected at 870/1070 K for CeNi{sub 5}, CeNi{sub 3} and CeSi{sub 2}; while no appreciable solubility was observed for the other binary compounds of the Ce-Ni-Si system. As a prolongation of Rare Earth-Ni-Si system’s isostructural rows, LaNi{sub 7}Si{sub 6} and YNi{sub 6.6}Si{sub 6.1} (GdNi{sub 7}Si{sub 6}-type), ScNi{sub 6}Si{sub 6} (YCo{sub 6}Ge{sub 6}-type), NdNi{sub 6}Si{sub 6} (YNi{sub 6}Si{sub 6}-type), (Tb, Ho){sub 2}Ni{sub 15}Si{sub 2} (Th{sub 2}Zn{sub 17}-type), Nd{sub 2}Ni{sub 2.3}Si{sub 0.7} and Sm{sub 2}Ni{sub 2.2}Si{sub 0.8} (Mo{sub 2}NiB{sub 2}-type), Nd{sub 3}Ni{sub 2.55}Si{sub 1.45} (W{sub 3}CoB{sub 3}-type) and (Tb, Dy){sub 7}Ni{sub 50}Si{sub 19} (Y{sub 7}Ni{sub 49}Si{sub 20}-type) compounds were synthesized and investigated. Magnetic properties of the CeNi{sub 6}Si{sub 6}, CeNi{sub 7}Si{sub 6}, CeNi{sub 8.8}Si{sub 4.2}, Ce{sub 6}Ni{sub 7}Si{sub 4}, CeNi{sub 5}Si, Ce{sub 2}Ni{sub 2.5}Si{sub 0.5}, Nd{sub 2}Ni{sub 2.3}Si{sub 0.7} and Dy{sub 7}Ni{sub 50}Si{sub 19} compounds have also been investigated and are presented here. - Highlights: • Ce-Ni-Si isothermal section was obtained at 870/1070 K. • Twenty one known ternary cerium nickel silicides were confirmed in Ce-Ni-Si. • Five new cerium nickel silicides were detected in Ce-Ni-Si. • Eleven new rare earth nickel silicides were detected in R-Ni-Si. • Magnetic properties of eight rare earth nickel silicides were investigated.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Energy Transduction in Nitrogenase

Nitrogenase is a complicated two-component enzyme system that uses ATP binding and hydrolysis energy to achieve one of the most difficult chemical reactions in nature, the reduction of N2 to NH3. One component of the Mo-based nitrogenase system, Fe protein, delivers electrons one at a time to the second component, the catalytic MoFe protein. This process occurs through a series of synchronized events collectively called the “Fe protein cycle”. Elucidating details of the events associated with this cycle has constituted an important challenge in understanding the nitrogenase mechanism. Electron delivery is a multistep process involving three metal clusters with intra- and interprotein events. It is proposed that the first electron transfer event is a gated intraprotein transfer of one electron from the MoFe protein P-cluster to the FeMo cofactor. Measurement of the effect of osmotic pressure on the rate of this electron transfer process revealed that it is gated by protein conformational changes. This first electron transfer is activated by binding of the Fe protein containing two bound ATP molecules. The mechanism of how this protein-protein association triggers electron transfer remains unknown. The second electron transfer event is proposed to be a rapid interprotein “backfill” with transfer of one electron from the reduced Fe protein 4Fe-4S cluster to the oxidized P-cluster. In this way, electron delivery can be viewed as a case of “deficit spending”. Such a deficit-spending electron transfer process can be envisioned as a way to achieve one-direction electron flow, limiting the potential for back electron flow. Hydrolysis of two ATP molecules associated with the Fe protein occurs after the electron transfer and therefore is not used to directly drive the electron transfer. Rather, ATP hydrolysis is proposed to contribute to relaxation of the “activated” conformational state associated with the ATP form of the complex, with the free energy from ATP hydrolysis being used to pay back energy associated with component protein association and electron transfer. Release of inorganic phosphate (Pi) and protein-protein dissociation follow electron transfer and ATP hydrolysis. The ratelimiting step for the Fe protein cycle is not dissociation of the two proteins, as previously believed, but rather is release of Pi after ATP hydrolysis, which is then followed by rapid protein-protein complex dissociation. Nitrogenase is composed of two catalytic halves that do not function independently but rather exhibit anticooperative nuclear motion in which electron transfer in one-half of the complex partially inhibits electron transfer and ATP hydrolysis in the other half. Calculations indicated the existence of anticooperative interactions across the entire nitrogenase complex, suggesting a mechanism for the control of events on opposite ends of this large complex. The mechanistic necessity for this anticooperative process remains unknown. This Account presents a working model for how all of these processes work together in the nitrogenase “machine” to transduce the energy from ATP binding and hydrolysis to drive N2 reduction.

Seefeldt, Lance C.↗

DOE OSTI2023

Toward Machine Learning-Driven Mass Spectrometric Identification of Trichothecenes in the Absence of Standard Reference Materials

While a significant body of work exists on the detection of commonly known trichothecene toxins, biological, environmental, and other transformational processes can generate many under-characterized and unknown modified trichothecenes. Lacking both analytical reference standards and associated mass spectral databases, identification of these modified compounds reflects both a challenge and a critical gap from forensic and public health perspectives. Here we report here the application of machine learning (ML) techniques toward identification of discriminative fragment ions from mass spectrometric data that can be exploited to detect evidence of type A and B trichothecenes. The goal of this work is to establish a new method for the identification of unknown, though structurally similar trichothecenes, by leveraging objective ML techniques. Discriminative fragments derived from a series of gradient-boosted machine learners are then used to develop ML-driven precursor ion scan (PIS) methods on a triple quadrupole mass spectrometer (QQQ) for screening of “unknown unknown” trichothecenes. Specifically, we apply the PIS method to a laboratory-synthesized trichothecene, a first step in demonstrating the power of alternative, machine learning-driven mass spectrometric methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Interpretable machine learning models classify minerals via spectroscopy

Developing methods to identify mineral species confidently and rapidly from Raman spectral analysis is critical to numerous fields. Traditionally, analysis relies on pattern matching the Raman spectrum of an unknown dataset with a supporting library of well-characterized spectral data, which may prove difficult for environmental samples that are poorly crystalline or phase mixtures. Here, we developed interpretable machine learning models that can classify uranium minerals by secondary oxyanion chemistry and other physicochemical properties based solely on Raman spectra. This new ML method produces a mineral profile of physical and chemical properties for an unknown sample and can rapidly classify or identify unknown minerals from Raman data, without the need for an exact pattern match in a spectral library. Training models are validated by 1. Strong correlation of high confidence model regions with published spectroscopic assignments and 2. Correct classification of a mineral not present in training data. Training data are from the Compendium of Uranium Raman and Infrared Experimental Spectra and available crystallographic information files within the open-source Smart Spectral Matching scientific framework. Physically meaningful classifier models can rapidly identify key structural and chemical information about unknown uranium minerals and the overall methodology is broadly applicable for mineral phases.

Machine learning↗

DOE OSTI2015

Assessment of the accuracy of plasma shape reconstruction by the Cauchy condition surface method in JT-60SA

For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichlet and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

Gaussian process model for extrapolation of scattering observables for complex molecules: From benzene to benzonitrile

We consider a problem of extrapolating the collision properties of a large polyatomic molecule A–H to make predictions of the dynamical properties for another molecule related to A–H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A–X. We assume that the effect of the −H →−X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can be used to produce an interval of the observable values which corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C{sub 6}H{sub 5}CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He — C{sub 6}H{sub 6} collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C{sub 6}H{sub 5}CN with He.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Alpert multi-wavelets for functional inverse problems: direct optimization and deep learning

Computational engineering models often contain unknown entities (e.g. parameters, initial and boundary conditions) that require estimation from other measured observable data. Estimating such unknown entities is challenging when they involve spatio-temporal fields because such functional variables often require an infinite-dimensional representation. Here, we address this problem by transforming an unknown functional field using Alpert wavelet bases and truncating the resulting spectrum. Hence the problem reduces to the estimation of few coefficients that can be performed using common optimization methods. We apply this method on a one-dimensional heat transfer problem where we estimate the heat source field varying in both time and space. The observable data is comprised of temperature measured at several thermocouples in the domain. This latter is composed of either copper or stainless steel. The optimization using our method based on wavelets is able to estimate the heat source with an error between 5% and 7%. We analyze the effect of the domain material and number of thermocouples as well as the sensitivity to the initial guess of the heat source. Finally, we estimate the unknown heat source using a different approach based on deep learning techniques where we consider the input and output of a multi-layer perceptron in wavelet form. We find that this deep learning approach is more accurate than the optimization approach with errors below 4%.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Supervised detection of anomalous light curves in massive astronomical catalogs

The development of synoptic sky surveys has led to a massive amount of data for which resources needed for analysis are beyond human capabilities. In order to process this information and to extract all possible knowledge, machine learning techniques become necessary. Here we present a new methodology to automatically discover unknown variable objects in large astronomical catalogs. With the aim of taking full advantage of all information we have about known objects, our method is based on a supervised algorithm. In particular, we train a random forest classifier using known variability classes of objects and obtain votes for each of the objects in the training set. We then model this voting distribution with a Bayesian network and obtain the joint voting distribution among the training objects. Consequently, an unknown object is considered as an outlier insofar it has a low joint probability. By leaving out one of the classes on the training set, we perform a validity test and show that when the random forest classifier attempts to classify unknown light curves (the class left out), it votes with an unusual distribution among the classes. This rare voting is detected by the Bayesian network and expressed as a low joint probability. Our method is suitable for exploring massive data sets given that the training process is performed offline. We tested our algorithm on 20 million light curves from the MACHO catalog and generated a list of anomalous candidates. After analysis, we divided the candidates into two main classes of outliers: artifacts and intrinsic outliers. Artifacts were principally due to air mass variation, seasonal variation, bad calibration, or instrumental errors and were consequently removed from our outlier list and added to the training set. After retraining, we selected about 4000 objects, which we passed to a post-analysis stage by performing a cross-match with all publicly available catalogs. Within these candidates we identified certain known but rare objects such as eclipsing Cepheids, blue variables, cataclysmic variables, and X-ray sources. For some outliers there was no additional information. Among them we identified three unknown variability types and a few individual outliers that will be followed up in order to perform a deeper analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Where’s Swimmy?: Mining unique color features buried in galaxies by deep anomaly detection using Subaru Hyper Suprime-Cam data

Abstract We present the Swimmy (Subaru WIde-field Machine-learning anoMalY) survey program, a deep-learning-based search for unique sources using multicolored (grizy) imaging data from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). This program aims to detect unexpected, novel, and rare populations and phenomena, by utilizing the deep imaging data acquired from the wide-field coverage of the HSC-SSP. This article, as the first paper in the Swimmy series, describes an anomaly detection technique to select unique populations as “outliers” from the data-set. The model was tested with known extreme emission-line galaxies (XELGs) and quasars, which consequently confirmed that the proposed method successfully selected $\sim\!\! 60\%$–$70\%$ of the quasars and $60\%$ of the XELGs without labeled training data. In reference to the spectral information of local galaxies at z = 0.05–0.2 obtained from the Sloan Digital Sky Survey, we investigated the physical properties of the selected anomalies and compared them based on the significance of their outlier values. The results revealed that XELGs constitute notable fractions of the most anomalous galaxies, and certain galaxies manifest unique morphological features. In summary, deep anomaly detection is an effective tool that can search rare objects, and, ultimately, unknown unknowns with large data-sets. Further development of the proposed model and selection process can promote the practical applications required to achieve specific scientific goals.

Astronomy & Astrophysics↗

DOE OSTI2015

Constraints on the off-shell Higgs boson signal strength in the high-mass ZZ and WW final states with the ATLAS detector

The measurements of the ZZ and WW final states in the mass range above the $2m_Z$ and $2m_W$ thresholds provide a unique opportunity to measure the off-shell coupling strength of the Higgs boson. This paper presents constraints on the off-shell Higgs boson event yields normalised to the Standard Model prediction (signal strength) in the $ZZ \rightarrow 4\ell $, $ZZ\rightarrow 2\ell 2\nu $ and $WW\rightarrow e\nu \mu \nu $ final states. The result is based on pp collision data collected by the ATLAS experiment at the LHC, corresponding to an integrated luminosity of 20.3 fb$^{-1}$ at a collision energy of $\sqrt{s}=8$ TeV. Using the $CL_s$ method, the observed 95 $\%$ confidence level (CL) upper limit on the off-shell signal strength is in the range 5.1–8.6, with an expected range of 6.7–11.0. In each case the range is determined by varying the unknown $gg\rightarrow ZZ$ and $gg\rightarrow WW$ background K-factor from higher-order quantum chromodynamics corrections between half and twice the value of the known signal K-factor. Assuming the relevant Higgs boson couplings are independent of the energy scale of the Higgs boson production, a combination with the on-shell measurements yields an observed (expected) 95 $\%$ CL upper limit on $\Gamma _H/\Gamma _H^{\mathrm {SM}}$ in the range 4.5–7.5 (6.5–11.2) using the same variations of the background K-factor. Assuming that the unknown $gg\rightarrow VV$ background K-factor is equal to the signal K-factor, this translates into an observed (expected) 95 $\%$ CL upper limit on the Higgs boson total width of 22.7 (33.0) MeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Extending the predictive power of perturbative QCD using the principle of maximum conformality and the Bayesian analysis

In addition to the evaluation of high-order loop contributions, the precision and predictive power of perturbative QCD (pQCD) predictions depends on two important issues: (1) how to achieve a reliable, convergent fixed-order series, and (2) how to reliably estimate the contributions of unknown higher-order terms. The recursive use of renormalization group equation, together with the Principle of Maximum Conformality (PMC), eliminates the renormalization scheme-and-scale ambiguities of the conventional pQCD series. The result is a conformal, scale-invariant series of finite order which also satisfies all of the principles of the renormalization group. In this paper we propose a novel Bayesian-based approach to estimate the size of the unknown higher order contributions based on an optimized analysis of probability distributions. We show that by using the PMC conformal series, in combination with the Bayesian analysis, one can consistently achieve high degree of reliability estimates for the unknown high order terms. Thus the predictive power of pQCD can be greatly improved. We illustrate this procedure for two pQCD observables: R e+e– and R τ , which are each known up to four loops in pQCD. Numerical analyses confirm that by using the scale-independent and more convergent PMC conformal series, one can achieve reliable Bayesian probability estimates for the unknown higher-order contributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

ShiftNMFk 1.2

The ShiftNMFk1.2 code, or as we call it, GreenNMFk, represents a hybrid algorithm combining unsupervised adaptive machine learning and Green's function inverse method. GreenNMFk allows an efficient and high performance de-mixing and feature extraction of a multitude of nonnegative signals that change their shape propagating through the medium. The signals are mixed and recorded by a network of uncorrelated sensors. The code couples Non-negative Matrix Factorization (NMF) and inverse-analysis Green's functions method. GreenNMF synergistically performs decomposition of the recorded mixtures, finds the number of the unknown sources and uses the Green's function of the governing partial differential equation to identify the unknown sources and their charecteristics. GreenNMF can be applied directly to any problem controlled by a known partial-differential parabolic equation where mixtures of an unknown number of sources are measured at multiple locations. Full GreenNMFk method is a subject LANL U.S. Patent application S133364.000 August, 2017. The ShiftNMFk 1.2 version here is a toy version of this method that can work with a limited number of unknown sources (4 or less).

Alexandrov, BoianS.↗

DOE OSTI2024

Enabling Ultralow Volume Analysis with a High-Resolution Ion Mobility Mass Spectrometry Platform

Of all the molecules thought to exist in the universe, it is estimated that researchers only know the chemical structures of 5% of them. Identifying the chemical structures of the remaining 95% has proven extremely challenging because many molecules exhibit low abundance, are contained in small volumes (e.g., <10 nL), do not readily ionize, exhibit similar structures to other molecules, etc. No single analytical technique exists to definitively identify the structure of an unknown molecule, and thus multiple different molecular measurements are typically made (i.e., multi-modal approach). Ion mobility (IMS) and mass spectrometry (MS) are two key tools that researchers use to determine the chemical structures of unknown molecules, and recently high-resolution and ultrahigh resolution IMS-MS instruments have provided greater confidence than ever before. However, HR-IMS-MS instruments typically exhibit low ion utilization efficiency, meaning they require large amounts of sample for an analysis (e.g., >10 µL). Unfortunately, this limitation prohibits the analysis of small volume samples where many unknown molecules exist. Described herein are the efforts made to enable the analysis of ultralow volumes with an HR-IMS-MS platform. A new scanning technique, termed a ‘stuttered traveling wave scan’, was developed as a replacement for the dual-gated scanning technique and works by halting the traveling waves after allowing ions to separate and then repeatedly restarting and stopping the traveling waves to incrementally move ions from the SLIM to the Orbitrap. Ions were stored inside the SLIM while the TWs were stopped, allowing the Orbitrap to perform high-resolution mass analysis. When the Orbitrap was ready, the TWs were restarted for short periods of time (<10 ms) to move ions from the SLIM to the Orbitrap. It was discovered that lower TW amplitudes and speeds than used during IMS separation were required to produce IMS peaks with the highest signal intensities and best resolving powers. The stuttered TW scan was found to produce similar resolutions and signal intensities compared to the dual-gated scanning technique. A new IMS design possessing an intersecting ‘tee’ with a reversible traveling wave was also developed to improve ion utilization efficiency during cyclic operation, which is necessary when only a single IMS spectrum can be acquired, such as when analyzing ultralow volume samples. The new capabilities described in this report lay the groundwork for acquiring HR-IMS-MS spectra of ultralow volume biological samples, such as single cells, where HR-IMS-MS can help elucidate the structures of unknown compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1974

Adjustment technique without explicit formation of normal equations /conjugate gradient method/

For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).

Saxena, N. K.↗

NASA NTRS1985

Improved mapping of radio sources from VLBI data by least-square fit

A method is described for producing improved mapping of radio sources from Very Long Base Interferometry (VLBI) data. The method described is more direct than existing Fourier methods, is often more accurate, and runs at least as fast. The visibility data is modeled here, as in existing methods, as a function of the unknown brightness distribution and the unknown antenna gains and phases. These unknowns are chosen so that the resulting function values are as near as possible to the observed values. If researchers use the radio mapping source deviation to measure the closeness of this fit to the observed values, they are led to the problem of minimizing a certain function of all the unknown parameters. This minimization problem cannot be solved directly, but it can be attacked by iterative methods which we show converge automatically to the minimum with no user intervention. The resulting brightness distribution will furnish the best fit to the data among all brightness distributions of given resolution.

Rodemich, E. R.↗

NASA NTRS1992

Kinematic equations for control of the redundant eight-degree-of-freedom advanced research manipulator 2

The forward position and velocity kinematics for the redundant eight-degree-of-freedom Advanced Research Manipulator 2 (ARM2) are presented. Inverse position and velocity kinematic solutions are also presented. The approach in this paper is to specify two of the unknowns and solve for the remaining six unknowns. Two unknowns can be specified with two restrictions. First, the elbow joint angle and rate cannot be specified because they are known from the end-effector position and velocity. Second, one unknown must be specified from the four-jointed wrist, and the second from joints that translate the wrist, elbow joint excluded. There are eight solutions to the inverse position problem. The inverse velocity solution is unique, assuming the Jacobian matrix is not singular. A discussion of singularities is based on specifying two joint rates and analyzing the reduced Jacobian matrix. When this matrix is singular, the generalized inverse may be used as an alternate solution. Computer simulations were developed to verify the equations. Examples demonstrate agreement between forward and inverse solutions.

Williams, Robert L., II↗

NASA NTRS1993

Control of Complex Dynamic Systems by Neural Networks

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations.

Spall, James C.↗