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DOE OSTI2021

Machine Learning Driven Contouring of High-Frequency Four-Dimensional Cardiac Ultrasound Data

Automatic boundary detection of 4D ultrasound (4DUS) cardiac data is a promising yet challenging application at the intersection of machine learning and medicine. Using recently developed murine 4DUS cardiac imaging data, we demonstrate here a set of three machine learning models that predict left ventricular wall kinematics along both the endo- and epi-cardial boundaries. Each model is fundamentally built on three key features: (1) the projection of raw US data to a lower dimensional subspace, (2) a smoothing spline basis across time, and (3) a strategic parameterization of the left ventricular boundaries. Model 1 is constructed such that boundary predictions are based on individual short-axis images, regardless of their relative position in the ventricle. Model 2 simultaneously incorporates parallel short-axis image data into their predictions. Model 3 builds on the multi-slice approach of model 2, but assists predictions with a single ground-truth position at end-diastole. To assess the performance of each model, Monte Carlo cross validation was used to assess the performance of each model on unseen data. For predicting the radial distance of the endocardium, models 1, 2, and 3 yielded average R2 values of 0.41, 0.49, and 0.71, respectively. Monte Carlo simulations of the endocardial wall showed significantly closer predictions when using model 2 versus model 1 at a rate of 48.67%, and using model 3 versus model 2 at a rate of 83.50%. These finding suggest that a machine learning approach where multi-slice data are simultaneously used as input and predictions are aided by a single user input yields the most robust performance. Subsequently, we explore the how metrics of cardiac kinematics compare between ground-truth contours and predicted boundaries. We observed negligible deviations from ground-truth when using predicted boundaries alone, except in the case of early diastolic strain rate, providing confidence for the use of such machine learning models for rapid and reliable assessments of murine cardiac function. To our knowledge, this is the first application of machine learning to murine left ventricular 4DUS data. Future work will be needed to strengthen both model performance and applicability to different cardiac disease models.

4D ultrasound↗

DOE OSTI2022

Generation of Data-Driven Expected Energy Models for Photovoltaic Systems

Although unique expected energy models can be generated for a given photovoltaic (PV) site, a standardized model is also needed to facilitate performance comparisons across fleets. Current standardized expected energy models for PV work well with sparse data, but they have demonstrated significant over-estimations, which impacts accurate diagnoses of field operations and maintenance issues. This research addresses this issue by using machine learning to develop a data-driven expected energy model that can more accurately generate inferences for energy production of PV systems. Irradiance and system capacity information was used from 172 sites across the United States to train a series of models using Lasso linear regression. The trained models generally perform better than the commonly used expected energy model from international standard (IEC 61724-1), with the two highest performing models ranging in model complexity from a third-order polynomial with 10 parameters (Radj2 = 0.994) to a simpler, second-order polynomial with 4 parameters (Radj2=0.993), the latter of which is subject to further evaluation. Subsequently, the trained models provide a more robust basis for identifying potential energy anomalies for operations and maintenance activities as well as informing planning-related financial assessments. We conclude with directions for future research, such as using splines to improve model continuity and better capture systems with low (≤1000 kW DC) capacity.

14 SOLAR ENERGY↗

DOE OSTI2020

Kepler Data Analysis: Non-Gaussian Noise and Fourier Gaussian Process Analysis of Stellar Variability

We develop a statistical analysis model of Kepler stellar flux data in the presence of planet transits, non-Gaussian noise, and stellar variability. We first develop a model for the Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution non-Gaussian. We develop a signal likelihood analysis based on this probability distribution, in which we model the signal as a sum of the star variability and planetary transits. We argue that these components need to be modeled together if optimal signal is to be extracted from the data. For the stellar variability model we develop an optimal Gaussian process analysis using a Fourier-based Wiener filter approach, where the power spectrum is non-parametric and learned from the data. We develop high dimensional optimization of the objective function, where we jointly optimize all the model parameters, including thousands of star variability modes, and planet transit parameters. We apply the method to Kepler-90 data and show that it gives a better match to the stellar variability than the existing methods, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than what the existing methods give, including splines and celerite.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

DELVE-ing into the Jet: A Thin Stellar Stream on a Retrograde Orbit at 30 kpc

We perform a detailed photometric and astrometric analysis of stars in the Jet stream using data from the first data release of the DECam Local Volume Exploration Survey DR1 and Gaia EDR3. We discover that the stream extends over ∼ 29° on the sky (increasing the known length by 18°), which is comparable to the kinematically cold Phoenix, ATLAS, and GD-1 streams. Using blue horizontal branch stars, we resolve a distance gradient along the Jet stream of 0.2 kpc deg$^{−1}$, with distances ranging from D $_{⊙}$ ∼ 27–34 kpc. We use natural splines to simultaneously fit the stream track, width, and intensity to quantitatively characterize density variations in the Jet stream, including a large gap, and identify substructure off the main track of the stream. Furthermore, we report the first measurement of the proper motion of the Jet stream and find that it is well aligned with the stream track, suggesting the stream has likely not been significantly perturbed perpendicular to the line of sight. Finally, we fit the stream with a dynamical model and find that it is on a retrograde orbit, and is well fit by a gravitational potential including the Milky Way and Large Magellanic Cloud. These results indicate the Jet stream is an excellent candidate for future studies with deeper photometry, astrometry, and spectroscopy to study the potential of the Milky Way and probe perturbations from baryonic and dark matter substructure.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

From the Fire: A Deeper Look at the Phoenix Stream

We use 6 yr of data from the Dark Energy Survey to perform a detailed photometric characterization of the Phoenix stellar stream, a 15° long, thin, dynamically cold, low-metallicity stellar system in the Southern Hemisphere. We use natural splines, a nonparametric modeling technique, to simultaneously fit the stream track, width, and linear density. This updated stream model allows us to improve measurements of the heliocentric distance (17.4 ± 0.1 (stat.) ±0.8 (sys.) kpc) and distance gradient (−0.009 ± 0.006 kpc deg$^{−1}$) of Phoenix, which corresponds to a small change of 0.13 ± 0.09 kpc in heliocentric distance along the length of the stream. We measure linear intensity variations on degree scales, as well as deviations in the stream track on ∼2° scales, suggesting that the stream may have been disturbed during its formation and/or evolution. We recover three peaks and one gap in linear intensity along with fluctuations in the stream track. Compared to other thin streams, the Phoenix stream shows more fluctuations and, consequently, the study of Phoenix offers a unique perspective on gravitational perturbations of stellar streams. We discuss possible sources of perturbations to Phoenix, including baryonic structures in the Galaxy and dark matter subhalos.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Multi-objective optimization of peel and shear strengths in ultrasonic metal welding using machine learning-based response surface methodology

Ultrasonic metal welding (UMW) is a solid-state joining technique with varied industrial applications. Despite of its numerous advantages, UMW has a relative narrow operating window and is sensitive to variations in process conditions. As such, it is imperative to quantitatively characterize the influence of welding parameters on the resulting joint quality. The quantification model can be subsequently used to optimize the parameters. Conventional response surface methodology (RSM) usually employs linear or polynomial models, which may not be able to capture the intricate, nonlinear input-output relationships in UMW. Furthermore, some UMW applications call for simultaneous optimization of multiple quality indices such as peel strength, shear strength, electrical conductivity, and thermal conductivity. To address these challenges, this paper develops a machine learning (ML)-based RSM to model the input-output relationships in UMW and jointly optimize two quality indices, namely, peel and shear strengths. The performance of various ML methods including spline regression, Gaussian process regression (GPR), support vector regression (SVR), and conventional polynomial regression models with different orders is compared. A case study using experimental data shows that GPR with radial basis function (RBF) kernel and SVR with RBF kernel achieve the best prediction accuracy. The obtained response surface models are then used to optimize a compound joint strength indicator that is defined as the average of normalized shear and peel strengths. In addition, the case study reveals different patterns in the response surfaces of shear and peel strengths, which has not been systematically studied in the literature. While developed for the UMW application, the method can be extended to other manufacturing processes.

42 ENGINEERING↗

DOE OSTI2023

Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations

In this study, we present a data-driven approach for approximating entropy-based closures of moment systems from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the spacetime discretization of the moment system or specific problem configurations such as initial and boundary conditions. With convex and C 2 approximations, this data-driven closure inherits several structural properties from entropy-based closures, such as entropy dissipation, hyperbolicity, and H-Theorem. We construct convex approximations to the Maxwell–Boltzmann entropy using convex splines and neural networks, test them on the plane source benchmark problem for linear transport in slab geometry, and compare the results to the standard, entropy-based systems which solve a convex optimization problem to find the closure. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than that required by the optimization routine.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Numerical integrators for Lagrangian oceanography

Abstract. A common task in Lagrangian oceanography is to calculate a large number of drifter trajectories from a velocity field precalculated with an ocean model. Mathematically, this is simply numerical integration of an ordinary differential equation (ODE), for which a wide range of different methods exist. However, the discrete nature of the modelled ocean currents requires interpolation of the velocity field in both space and time, and the choice of interpolation scheme has implications for the accuracy and efficiency of the different numerical ODE methods. We investigate trajectory calculation in modelled ocean currents with 800 m, 4 km, and 20 km horizontal resolution, in combination with linear, cubic and quintic spline interpolation. We use fixed-step Runge–Kutta integrators of orders 1–4, as well as three variable-step Runge–Kutta methods (Bogacki–Shampine 3(2), Dormand–Prince 5(4) and 8(7)). Additionally, we design and test modified special-purpose variants of the three variable-step integrators, which are better able to handle discontinuous derivatives in an interpolated velocity field. Our results show that the optimal choice of ODE integrator depends on the resolution of the ocean model, the degree of interpolation, and the desired accuracy. For cubic interpolation, the commonly used Dormand–Prince 5(4) is rarely the most efficient choice. We find that in many cases, our special-purpose integrators can improve accuracy by many orders of magnitude over their standard counterparts, with no increase in computational effort. Equivalently, the special-purpose integrators can provide the same accuracy as standard methods at a reduced computational cost. The best results are seen for coarser resolutions (4 and 20 km), thus the special-purpose integrators are particularly advantageous for research using regional to global ocean models to compute large numbers of trajectories. Our results are also applicable to trajectory computations on data from atmospheric models.

58 GEOSCIENCES↗

NASA NTRS1965

Indexing device ensures proper mating of electrical connectors

Indexing splines with modified standard male and female connectors eliminates the possibility of incorrect mating. Large stock quantities of differently indexed connectors are unnecessary since connectors from a single stock can be indexed as desired at installation time.

Jenkins, L. M.↗

NASA NTRS1972

Computer programs for plotting curves with various dashed-line sequences

Two FORTRAN-callable subprograms have been written to draw a smooth curve through a set of input points as a solid line or as a general sequence of long and short dashes. Subroutine LINSEQ draws conventional curves whereas subroutine CONSEQ draws smooth closed curves (contours). The subprograms are based on an approximate calculation of the arc length along the curve and spline interpolation along the arc length. Options are provided for smoothing of the input data and for offsetting the plotted curve from the input data points. The method of calculation of the arc length and the generation of the line sequence are described.Usage descriptions of the main subprograms, sample calling programs illustrating the various features of the subprograms, and sample plots are given. The subroutines should be readily adaptable to almost any computer-driven incremental plotter.

Desmarais, R. N.↗

NASA NTRS1972

FORTRAN program for generating a two-dimensional orthogonal mesh between two arbitrary boundaries

A FORTRAN 4 program is presented which computes and plots coordinates for a two-dimensional orthogonal mesh in the region between the walls of a flow channel. The program is designed for a channel containing a body about which flow passes and which spans the channel from one wall to the other. However, the condition that the channel contain an immersed body can be easily removed from the program. Input to the program consists of spline points of the channel walls and the body geometry. Output includes printed and plotted coordinates of the generated orthogonal mesh and angles of the mesh with the horizontal plane.

Mcnally, W. D.↗

NASA NTRS1972

On the calculation of panel flutter boundaries.

Methods are described for the complete automation of flutter boundary calculations when the aerodynamic forces are derived from linear three-dimensional unsteady potential flow theory. The usual process of visual curve fairing in the mass ratio versus structural damping plane is replaced by numerical procedures for ordering the eigenvalues in such a way that the n-th eigenvalue is always associated with the same flutter boundary. The mass ratio versus structural damping curves are interpolated via parametric cubic spline functions to produce the desired plots in the stiffness-parameter/mass-ratio plane. The entire process is accomplished in a single computer run.

Gaspers, P. A., Jr.↗

NASA NTRS1972

Inviscid surface streamlines and heat transfer on shuttle-type configurations.

A method is developed which calculates laminar, transitional, and turbulent heating rates on arbitrary blunt-nosed three-dimensional bodies at angle of attack in hypersonic flow. The geometry of the body may be specified analytically, or generated from a doubly cubic spline fit to coordinate points. Inviscid surface streamlines are calculated from Euler's equation using a prescribed pressure distribution. Laminar and turbulent heating rates are determined along a streamline by applying the axisymmetric analog to solutions of the axisymmetric boundary-layer equations. The location of the transition region may be specified optionally by geometric location, momentum thickness Reynolds number, or integrated unit Reynolds number along a streamline. Transitional heating rates are then calculated as a weighted average of the local laminar and turbulent values. Either ideal gas or equilibrium air properties may be used.

Dejarnette, F. R.↗

NASA NTRS1972

Quantitative simultaneous multi-element microprobe analysis using combined wavelength and energy dispersive systems

A combined WDS-EDS system obviates the severe X-ray peak overlap problems encountered with Na, Mg, Al and Si common to pure EDS systems. By application of easily measured empirical correction factors for pulse pile-up and peak overlaps which are normally observed in the analysis of silicate minerals, the accuracy of analysis is comparable with that expected for WDS electron microprobe analyses. The continuum backgrounds are subtracted for the spectra by a spline fitting technique based on integrated intensities between the peaks. The preprocessed data are then reduced to chemical analyses by existing data reduction programs.

Walter, L. S.↗

NASA NTRS1971

ADMAP (automatic data manipulation program)

Instructions are presented on the use of ADMAP, (automatic data manipulation program) an aerospace data manipulation computer program. The program was developed to aid in processing, reducing, plotting, and publishing electric propulsion trajectory data generated by the low thrust optimization program, HILTOP. The program has the option of generating SC4020 electric plots, and therefore requires the SC4020 routines to be available at excution time (even if not used). Several general routines are present, including a cubic spline interpolation routine, electric plotter dash line drawing routine, and single parameter and double parameter sorting routines. Many routines are tailored for the manipulation and plotting of electric propulsion data, including an automatic scale selection routine, an automatic curve labelling routine, and an automatic graph titling routine. Data are accepted from either punched cards or magnetic tape.

Mann, F. I.↗

NASA NTRS1973

Resolution improvement of remote sensing data.

Discussion of the theory of a technique for image restoration in the reconstruction of a spatial input scene mapped by a line scanner. Special attention is given to the application of this technique in reducing the data telemetered from the Infrared Scanning Radiometer of the Apollo 17 spacecraft. The technique is based on the theory of splines and uses the results of optimal approximation studies by Colomb (1959), Sard (1967), and Anselone (1968). A recursive algorithm is also developed to improve the reconstruction. The study treats a one-dimensional case, but the treatment can be readily extended to multi-dimensional situations.

Caprihan, A.↗

NASA NTRS1973

Subgrid resolution of flow and force fields.

By means of spline fitting, both while converting a Lagrangian distribution of field sources onto an Eulerian grid, and while interpolating the field from its Eulerian grid to the Lagrangian positions of the responding elements, one achieves effective resolution down to about one-eight of a grid mesh unit. One also avoids discontinuities and noise due to cell boundary crossings.

Buneman, O.↗

NASA NTRS1973

An automated procedure for computing flutter eigenvalues.

A new, fast and economical automated procedure for implementing the traditional V-g method of flutter solution is described. The procedure requires as input the generalized aerodynamic forces for a range of reduced frequencies obtained from an aerodynamic program. These aerodynamic forces are interpolated with respect to reduced frequency using a newly developed, partially tabulated cubic spline that is both fast in execution and economical in storage. The flutter solution is then obtained using an eigenvalue routine that has been developed to take advantage of the parametric nature of the V-g type of solution. Furthermore, the routine takes care of the fundamental and troublesome problem of properly sorting the output eigenvalues. By solving the root-sorting problem, the interpolation for flutter crossings and automatic plotting are accomplished efficiently. The computational techniques used in this new program are described and some sample results are given.

Desmarais, R. N.↗