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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

The Impact of Rise of the Andes and Amazon Landscape Evolution on Diversification of Lowland terra-firme Forest Birds

Since the 19th Century, the unmatched biological diversity of Amazonia has stimulated a diverse set of hypotheses accounting for patterns of species diversity and distribution in mega-diverse tropical environments. Unfortunately, the evidence supporting particular hypotheses to date is at best described as ambiguous, and no generalizations have emerged yet, mostly due to the lack of comprehensive comparative phylogeographic studies with thorough trans-Amazonian sampling of lineages. Here we report on spatial and temporal patterns of diversification estimated from mitochondrial gene trees for 31 lineages of birds associated with upland terra-firme forest, the dominant habitat in modern lowland Amazonia. The results confirm the pervasive role of Amazonian rivers as primary barriers separating sister lineages of birds, and a protracted spatio-temporal pattern of diversification, with a gradual reduction of earlier (1st and 2nd) and older (> 2 mya) splits associated with each lineage in an eastward direction. (The easternmost tributaries of the Amazon, the Xingu and Tocantins Rivers, are not associated with any splits older than > 2 mya). For the suboscine passerines, maximum-likelihood estimates of rates of diversification point to an overall constant rate over the past 5 my (up to a significant downturn at 300,000 y ago). This "younging-eastward" pattern may have an abiotic explanation related to landscape evolution. Triggered by a new pulse of Andean uplift, it has been proposed that modern Amazon basin landscapes may have evolved successively eastward, away from the mountain chain, starting approximately 10 mya. This process was likely based on the deposition of vast fluvial sediment masses, known as megafans, that may have extended progressively and in series eastward from Andean sources. This process plausibly explains the progressive extinction of original Pebas wetland of western-central Amazonia by the present fluvial landsurfaces of a more terra-firme type. The youngest landsurfaces thus lie furthest from the mountains. In this scenario major drainages were also reoriented in wholesale fashion away from a northerly orientation generally towards the east and an Atlantic Ocean outlet. The advance of megafans is best seen by the location of axial rivers such as the Orinoco and Mamore which lie against the cratonic margins furthest from the Andes, at the distal ends of major megafan ramparts. More importantly, other major river courses in western-central Amazonia will have been established at progressively younger dates with distance eastward. If this landscape-sequence scenario is accurate, it parallels the progressive younging of the passerine lineages. The bird DNA data appears to confirm strongly the pervasive role of Amazonian rivers--as primary barriers separating sister lineages of birds, and thus probably as facilitaters of bird speciation. We show for the first time that a general spatio-temporal pattern of diversification for terra-firme lineages in the Amazon is associated with rivers ("younging-eastward"), and furthermore parallels a specific scenario of regional drainage evolution.

Aleixo, Alexandre↗
NASA NTRS1981

Selected stability and control derivatives from the first Space Shuttle entry

Primary stability and control derivative estimates garnered from the first Shuttle entry are reported. The craft was the first vehicle to maneuver over a wide range of hypersonic velocities, yielding data on flight characteristics from previously unexplored regimes. The flight envelope was confined to entry and safe landing, with no additional maneuvers to gain control data. Data for a Mach number range of 25-1.5 and altitudes of 515,000-50,000 ft are provided, and functional ranges of the Shuttle control surfaces and attitude jets are outlined. On-board systems gathered data on aerodynamic coefficient identification, flight condition and Euler angles, and jet chamber pressures. A maximum likelihood estimation program, which contained unknown stability and control derivatives, was used for control; a control input determined the value of the unknown derivatives, and the input and spacecraft response were measured. Longitudinal and lateral directional maneuvers and their derivative estimates are described, noting wind contamination of the sideslip measurements below Mach 3. Further maneuvering and stability tests are projected for subsequent flights.

Iliff, K. W.↗
DOE OSTI2017

First Spectropolarimetric Measurement of a Brown Dwarf Magnetic Field in Molecular Bands

We present the first measurements of the surface magnetic field of a late-M dwarf, LSR J1835+3259, with the help of the full-Stokes spectropolarimetry in the bands of diatomic molecules. Our measurements at different rotational phases of a dwarf yielded one 5 σ and two 3 σ magnetic field detections. The observational data have been obtained with the LRISp polarimeter at the Keck observatory on 2012 August 22 and 23. These data have been compared against synthetic full-Stokes spectra in the bands of the molecules CrH, FeH, and TiO, which have been calculated for a range of the stellar parameters and magnetic field strengths. Making use of χ {sup 2}-minimization and maximum likelihood estimation, we determine the net magnetic field strength B (and not flux Bf ) of LSR J1835+3259 to ∼5 kG with the help of the Paschen–Back effect in the CrH lines. Our measurements at different rotational phases suggest that the dwarf’s surface might be covered with strong small-scale magnetic fields. In addition, recent findings of the dwarf’s hydrogen emission and the Stokes V signal from the lower chromosphere indicate that its surface magnetic field might be changing rapidly giving rise to flare activity, similar to young dMe dwarfs. We substantiate the substellar origin of LSR J1835+3259 by making use of our own data as well as the photometric data from the all-sky surveys 2MASS and WISE .

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2007

Quaternion Averaging

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.

Markley, F. Landis↗
DOE OSTI2017

Orbits for 18 Visual Binaries and Two Double-line Spectroscopic Binaries Observed with HRCAM on the CTIO SOAR 4 m Telescope, Using a New Bayesian Orbit Code Based on Markov Chain Monte Carlo

We present orbital elements and mass sums for 18 visual binary stars of spectral types B to K (five of which are new orbits) with periods ranging from 20 to more than 500 yr. For two double-line spectroscopic binaries with no previous orbits, the individual component masses, using combined astrometric and radial velocity data, have a formal uncertainty of ∼0.1 M{sub ⊙}. Adopting published photometry and trigonometric parallaxes, plus our own measurements, we place these objects on an H-R diagram and discuss their evolutionary status. These objects are part of a survey to characterize the binary population of stars in the Southern Hemisphere using the SOAR 4 m telescope+HRCAM at CTIO. Orbital elements are computed using a newly developed Markov chain Monte Carlo (MCMC) algorithm that delivers maximum-likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate the uncertainty of our derived parameters in a robust way. For spectroscopic binaries, using our approach, it is possible to derive a self-consistent parallax for the system from the combined astrometric and radial velocity data (“orbital parallax”), which compares well with the trigonometric parallaxes. We also present a mathematical formalism that allows a dimensionality reduction of the feature space from seven to three search parameters (or from 10 to seven dimensions—including parallax—in the case of spectroscopic binaries with astrometric data), which makes it possible to explore a smaller number of parameters in each case, improving the computational efficiency of our MCMC code.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1999

How to Estimate Attitude from Vector Observations

In many spacecraft attitude systems, the attitude observations are naturally represented as unit vectors. Typical examples are the unit vectors giving the direction to the sun or a star and the unit vector in the direction of the Earth's magnetic field. In 1965, Grace Wahba, proposed the following problem: Find the orthogonal matrix A with determinant +1 that minimizes the loss function L(A) is identity with 1/2(Sum from i a(sub i) (absolute value of b(sub i - A(r(sub i))(exp 2))) where the set of b(sub i) is a set of unit vectors measured in a spacecraft's body frame, the set of r(sub i) are the corresponding unit vectors in a reference frame, and the set of a(sub i) are non-negative weights. Wahba's problem can be related to Maximum Likelihood Estimation if the weights are chosen to be inverse variances, a(sub i) = sigma((sub -2). Wahba didn't assume this, but it will be convenient to assume it in this paper. Wahba'soptimality condition has provided the basis for many attitude determination algorithms. The purpose of this paper is to give an overview of the most popular and most promising algorithm and to provide accuracy and speed comparisons.

Markley,F. Landis↗
NASA NTRS1994

Applying transfer matrix method to the estimation of the modal characteristics of the NASA Mini-Mass Truss

It is beneficial to use a distributed parameter model for large space structures because the approach minimizes the number of model parameters. Holzer's transfer matrix method provides a useful means to simplify and standardize the procedure for solving the system of partial differential equations. Any large space structures can be broken down into sub-structures with simple elastic and dynamical properties. For each single element, such as beam, tether, or rigid body, we can derive the corresponding transfer matrix. Combining these elements' matrices enables the solution of the global system equations. The characteristics equation can then be formed by satisfying the appropriate boundary conditions. Then natural frequencies and mode shapes can be determined by searching the roots of the characteristic equation at frequencies within the range of interest. This paper applies this methodology, and the maximum likelihood estimation method, to refine the modal characteristics of the NASA Mini-Mast Truss by successively matching the theoretical response to the test data of the truss. The method is being applied to more complex configurations.

Shen, Ji-Yao↗
DOE OSTI2020

Remote Radiation Sensing Using Aerial and Ground Platforms

Remote sensing of ionizing radiation has a significant role in waste management, nuclear material management and nonproliferation, and radiation safety. Robotic platforms can surpass the number of tasks that are achieved by humans. With this technique, the operator's radiation exposure can be decreased. Remote sensing allows for the evaluation and monitoring of radiological contamination. Gamma-ray and neutron sensors were integrated onto the robotic platforms. This approach allows for the radiation sensor data to be dynamically tracked and mapped thus enabling further analysis of the radiation flux in temporal and spatial domains. The goal is to complete scheduled tasks while the robot is being irradiated. To achieve this, electronic components must be shielded and radiation hardened. CZT Detector: Cadmium Zinc Telluride (CZT) detector technology has been a promising solution for gamma-ray and x-ray measurements. Detector data is transferred to the Odroid minicomputer that controls and powers the module via the USB. Robot Operating System (ROS) was utilized for data acquisition and data fusion. The Mariscotti method was employed for the spectrum analysis. A function was programmed in ROS for the automatic identification of photopeaks. CLYC Detector: A Cs{sub 2}LiYCl{sub 6}:Ce{sup 3+} (CLYC) detector was used for simultaneous medium-resolution gamma-ray measurements and neutron counting. A 2.54 cm diameter photomultiplier tube (PMT) was equipped with a high voltage supply and a miniature digitizer. Gamma-ray excitation: fast core-to-valence luminescence (CVL) with 1 ns decay constant, and prompt Ce{sup 3+} emission with 50 ns decay constant. Neutron excitation: slow cerium self-trapped excitation (Ce{sup 3+} STE), 1000 ns decay constant. Radiation Source Localization: Maximum Likelihood Estimation (MLE) and gradient-based methods were used to locate the position of a radiation source based on measured radiation intensities. Multi-Particle Transport Code FLUKA: Estimation of radiation damage of the electronic components is important in order to optimize the robot's operational time while it is irradiated. Displacement per atom (DPA) represents the radiation damage in materials exposed to the ionizing radiation. Various shielding layers of different thickness t were analyzed (< 5% statistical error). The model of the controller of the UAS was designed in FLUKA. Conclusion: CZT and CLYC detectors were integrated onto the robotic platforms. Radiation source localization and contour mapping using robotic platforms were studied. Functions for data analysis and fusion were developed in ROS. FLUKA code was utilized to analyze DPA values. Layers of low-density and high-density materials were used to shield the UAS electronics.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1972

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Grove, R. D.↗
NASA NTRS1990

Application of a novel multi-stage signal parameter estimator to high dynamic GPS receivers

The performance of a novel multistage estimator when applied to the estimation of the position, velocity, and acceleration of high dynamic Global Positioning System (GPS) receivers is discussed. For the present application, a two-stage specialization of the more general estimation scheme is considered, wherein the first-stage algorithm is selected to be a modified least-squares algorithm operating upon the differential signal model and referred to as differential least-squares (DLS) and the second stage is simply an extended Kalman filter (EKF). In terms of the threshold on received carrier power-to-noise power spectral density ratio (CNR), when compared to the single-stage EKF algorithm, the DLS-EKF algorithm is about 1.5-2.0 dB better in terms of threshold and outperforms the crossproduct AFC (automatic frequency control) loop by 2-5 dB. For the case when data modulation is present, the proposed scheme provides an improvement of about 6 dB in terms of CNR compared to an earlier approximate MLE (maximum likelihood estimation) scheme. There are also very significant improvements in terms of other performance measures.

Kumar, R.↗
DOE OSTI2021

Orbits and Masses of Binaries from Speckle Interferometry at SOAR

We present results from Speckle inteferometric observations of 15 visual binaries and one double-line spectroscopic binary, carried out with the HRCam Speckle camera of the SOAR 4.1 m telescope. These systems were observed as a part of an on-going survey to characterize the binary population in the solar vicinity, out to a distance of 250 pc. We obtained orbital elements and mass sums for our sample of visual binaries. The orbits were computed using a Markov Chain Monte Carlo algorithm that delivers maximum likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate their uncertainty. Their periods cover a range from 5 yr to more than 500 yr; and their spectral types go from early A to mid M, implying total system masses from slightly more than 4M{sub ⊙} down to 0.2M {sub ⊙}. They are located at distances between approximately 12 and 200 pc, mostly at low Galactic latitude. For the double-line spectroscopic binary YSC8, we present the first combined astrometric/radial-velocity orbit resulting from a self-consistent fit, leading to individual component masses of 0.897 ± 0.027 M {sub ⊙} and 0.857 ± 0.026 M {sub ⊙}; and an orbital parallax of 26.61 ± 0.29 mas, which compares very well with the Gaia DR2 trigonometric parallax (26.55 ± 0.27 mas). In combination with published photometry and trigonometric parallaxes, we place our objects on an H-R diagram and discuss their evolutionary status. We also present a thorough analysis of the precision and consistency of the photometry available for them.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1985

Post-flight BET products for the 2nd discovery entry, STS-19 (51-A)

The post-flight products for the second Discovery flight, STS-19 (51-A), are summarized. The inertial best estimate trajectory (BET), BT19D19/UN=169750N, was developed using spacecraft dynamic measurements from Inertial Measurement Unit 2 (IMU2) in conjunction with the best tracking coverage available for any of the earlier Shuttle entries. As a consequence of the latter, an anchor epoch was selected which conforms to an initial altitude of greater than a million feet. The Extended BET, ST19BET/UN=274885C, incorporated the previously mentioned inertial reconstructed state information and the Langley Atmospheric Information Retrieval System (LAIRS) atmosphere, ST19MET/UN=712662N, with some minor exceptions. Primary and back-up AEROBET reels are NK0165 and NK0201, respectively. This product was only developed over the lowermost 360 kft altitude range due to atmosphere problems but this relates to altitudes well above meaningful signal in the IMUs. Summary results generated from the AEROBET for this flight are presented with meaningful configuration and statistical comparisons from the previous thirteen flights. Modified maximum likelihood estimation (MMLE) files were generated based on IMU2 and the Rate Gyro Assembly/Accelerometer Assembly (RGA/AA), respectively. Appendices attached define spacecraft and physical constants utilized, show plots of the final tracking data residuals from the post-flight fit, list relevant parameters from the BET at a two second spacing, and retain for archival purpose all relevant input and output tapes and files generated.

Kelly, G. M.↗
DOE OSTI2019

Systematic analysis on spectral statistics of odd-A nuclei

Level statistics for given spin and parity below 10 MeV within A≤71, 71≤A≤151, and 151≤A≤221 mass regions are systematically analyzed. We have taken 5316 level spacings from 266 odd-A nuclei in the light mass region, 6897 level spacings from 478 ones in the medium mass region, and 2768 level spacings from 143 ones in the heavy mass region for the statistics. In the analysis, the chaoticity parameter in the Berry–Robnik distribution is determined based on the method of maximum likelihood estimation. The results show a mass number A-dependence in the level statistics. The larger the mass number, the relatively stronger in chaoticity. In addition, with the level statistics in using data sequences classified according to the order of magnitude of half-lives, it is shown that the level energies to be more chaotic for longer lived light and heavy mass odd-A nuclei, and intermediate between regular and chaotic in medium mass odd-A nuclei. The level statistical analysis in concerning E2 transition strengths of E2 or mixed E2+M1 transitions in odd-A nuclei is also made, which shows chaos in level energies likely occurring in those with weaker E2 transition strengths. Therefore, it can be concluded that odd-A nuclei are, more often than not, chaotic. Chaos is likely emergent in level energies of stable light mass nuclei with weaker E2 transition strengths, while it is definitely emergent in level energies of heavy mass nuclei, and even stronger in comparatively stable ones and those with weaker E2 transition strengths.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1995

Multiparameter linear least-squares fitting to Poisson data one count at a time

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Wheaton, Wm. A.↗
DOE OSTI2021

Flexible nonstationary spatiotemporal modeling of high-frequency monitoring data

Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of nonstationarity in space and time and demonstrate that this method provides a natural and tractable way to incorporate complex behaviors into a covariance model. Further, we use this method with fully time-domain computations to obtain bona fide maximum likelihood estimators—as opposed to using Whittle-type likelihood approximations, for example—that can still be computed conveniently. Additionally, we apply this method to very high-frequency Doppler LIDAR vertical wind velocity measurements, demonstrating that the model can expressively capture the extreme nonstationarity of dynamics above and below the atmospheric boundary layer and, more importantly, the interaction of the process dynamics across it.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

A second‐generation virtual‐pinhole PET device for enhancing contrast recovery and improving lesion detectability of a whole‐body PET/CT scanner

Purpose We have developed a second‐generation virtual‐pinhole (VP) positron emission tomography (PET) device that can position a flat‐panel PET detector around a patient's body using a robotic arm to enhance the contrast recovery coefficient (CRC) and detectability of lesions in any region‐of‐interest using a whole‐body PET/computed tomography (CT) scanner. Methods We constructed a flat‐panel VP‐PET device using 32 high‐resolution detectors, each containing a 4 4 MPPC array and 16 16 LYSO crystals of 1.0 1.0 3.0 mm 3 each. The flat‐panel detectors can be positioned around a patient's body anywhere in the imaging field‐of‐view (FOV) of a Siemens Biograph 40 PET/CT scanner by a robotic arm. New hardware, firmware and software have been developed to support the additional detector signals without compromising a scanner's native functions. We stepped a 22 Na point source across the axial FOV of the scanner to measure the sensitivity profile of the VP‐PET device. We also recorded the coincidence events measured by the scanner detectors and by the VP‐PET detectors when imaging phantoms of different sizes. To assess the improvement in the CRC of small lesions, we imaged an elliptical torso phantom measuring 316 228 162 mm 3 that contains spherical tumors with diameters ranging from 3.3 to 11.4 mm with and without the VP‐PET device. Images were reconstructed using a list mode Maximum‐Likelihood Estimation‐Maximization algorithm implemented on multiple graphics processing units (GPUs) to support the unconventional geometries enabled by a VP‐PET system. The mean and standard deviation of the CRC were calculated for tumors of different sizes. Monte Carlo simulation was also conducted to image clusters of lesions in a torso phantom using a PET/CT scanner alone or the same scanner equipped with VP‐PET devices. Receiver operating characteristic (ROC) curves were analyzed for three system configurations to evaluate the improvement in lesion detectability by the VP‐PET device over the native PET/CT scanner. Results The repeatability in positioning the flat‐panel detectors using a robotic arm is better than 0.15 mm in all three directions. Experimental results show that the average CRC of 3.3, 4.3, and 6.0 mm diameter tumors was 0.82%, 2.90%, and 5.25%, respectively, when measured by the native scanner. The corresponding CRC was 2.73%, 6.21% and 10.13% when imaged by the VP‐PET insert device with the flat‐panel detector under the torso phantom. These values may be further improved to 4.31%, 9.65% and 18.01% by a future dual‐panel VP‐PET insert device if DOI detectors are employed to triple its detector efficiency. Monte Carlo simulation results show that the tumor detectability can be improved by a VP‐PET device that has a single flat‐panel detector. The improvement is greater if the VP‐PET device employs a dual‐panel design. Conclusions We have developed a prototype flat‐panel VP‐PET device and integrated it with a clinical PET/CT scanner. It significantly enhances the contrast of lesions, especially for those that are borderline detectable by the native scanner, within regions‐of‐interest specified by users. Simulation demonstrated the enhancement in lesion detectability with the VP‐PET device. This technology may become a cost‐effective solution for organ‐specific imaging tasks.

Jiang, Jianyong↗
DOE OSTI2022

Learning generative neural networks with physics knowledge

Deep generative neural networks have enabled modeling complex distributions, but incorporating physics knowledge into the neural networks is still challenging and is at the core of current physics-based machine learning research. To this end, we propose a physics generative neural network (PhysGNN), a new class of generative neural networks for learning unknown distributions in a physical system described by partial differential equations (PDE). PhysGNN couples PDE systems with generative neural networks. It is a fully differentiable model that allows back-propagation of gradients through both numerical PDE solvers and generative neural networks, and is trained by minimizing the discrete Wasserstein distance between generated and observed probability distributions of the PDE outputs using the stochastic gradient descent method. Moreover, PhysGNN does not require adversarial training like standard generative neural networks, which offers better stability than adversarial training. We show that PhysGNN can learn complex distributions in stochastic inverse problems, where conventional methods such as maximum likelihood estimation and momentum matching methods may be inapplicable when little knowledge is known about the form of unknown distributions or the physical model is too complex. Furthermore, our method allows physics-based generative neural network training for learning complex distributions in the context of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Latent map Gaussian processes for mixed variable metamodeling

Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. Here we introduce latent map Gaussian processes (LMGPs) that inherit the attractive properties of GPs and are also applicable to mixed data which have both quantitative and qualitative inputs. The core idea behind LMGPs is to learn a continuous, low-dimensional latent space or manifold which encodes all qualitative inputs. To learn this manifold, we first assign a unique prior vector representation to each combination of qualitative inputs. We then use a low-rank linear map to project these priors on a manifold that characterizes the posterior representations. As the posteriors are quantitative, they can be directly used in any standard correlation function such as the Gaussian or Matern. Hence, the optimal map and the corresponding manifold, along with other hyperparameters of the correlation function, can be systematically learned via maximum likelihood estimation. Through a wide range of analytic and real-world examples, we demonstrate the advantages of LMGPs over state-of-the-art methods in terms of accuracy and versatility. In particular, we show that LMGPs can handle variable-length inputs, have an explainable neural network interpretation, and provide insights into how qualitative inputs affect the response or interact with each other. We also employ LMGPs in Bayesian optimization and illustrate that they can discover optimal compound compositions more efficiently than conventional methods that convert compositions to qualitative variables via manual featurization.

42 ENGINEERING↗