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All sources NASA NTRS DOE OSTI

DOE OSTI2020

Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness

We report the accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory answers to the problems of approximation and optimization, much less is known about the theory of generalization. Most existing theoretical works for generalization fail to explain the performance of neural networks in practice. To derive a meaningful bound, we study the generalization error of neural networks for classification problems in terms of data distribution and neural network smoothness. We introduce the cover complexity (CC) to measure the difficulty of learning a data set and the inverse of the modulus of continuity to quantify neural network smoothness. A quantitative bound for expected accuracy/error is derived by considering both the CC and neural network smoothness. Although most of the analysis is general and not specific to neural networks, we validate our theoretical assumptions and results numerically for neural networks by several data sets of images. The numerical results confirm that the expected error of trained networks scaled with the square root of the number of classes has a linear relationship with respect to the CC. We also observe a clear consistency between test loss and neural network smoothness during the training process. In addition, we demonstrate empirically that the neural network smoothness decreases when the network size increases whereas the smoothness is insensitive to training dataset size.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2014

A User Guide for Smoothing Air Traffic Radar Data

Matlab software was written to provide smoothing of radar tracking data to simulate ADS-B (Automatic Dependent Surveillance-Broadcast) data in order to test a tactical conflict probe. The probe, called TSAFE (Tactical Separation-Assured Flight Environment), is designed to handle air-traffic conflicts left undetected or unresolved when loss-of-separation is predicted to occur within approximately two minutes. The data stream that is down-linked from an aircraft equipped with an ADS-B system would include accurate GPS-derived position and velocity information at sample rates of 1 Hz. Nation-wide ADS-B equipage (mandated by 2020) should improve surveillance accuracy and TSAFE performance. Currently, position data are provided by Center radar (nominal 12-sec samples) and Terminal radar (nominal 4.8-sec samples). Aircraft ground speed and ground track are estimated using real-time filtering, causing lags up to 60 sec, compromising performance of a tactical resolution tool. Offline smoothing of radar data reduces wild-point errors, provides a sample rate as high as 1 Hz, and yields more accurate and lag-free estimates of ground speed, ground track, and climb rate. Until full ADS-B implementation is available, smoothed radar data should provide reasonable track estimates for testing TSAFE in an ADS-B-like environment. An example illustrates the smoothing of radar data and shows a comparison of smoothed-radar and ADS-B tracking. This document is intended to serve as a guide for using the smoothing software.

Center/Tracon Radar↗

DOE OSTI2023

Smoothing tool design and performance during subaperture glass polishing

During subaperture tool grinding and polishing, overlaps of the tool influence function can result in undesirable mid-spatial frequency (MSF) errors in the form of surface ripples, which are often corrected using a smoothing polishing step. Here, in this study, flat multi-layer smoothing polishing tools are designed and tested to simultaneously (1) reduce or remove MSF errors, (2) minimize surface figure degradation, and (3) maximize the material removal rate. A time-dependent convergence model in which spatial material removal varies with a workpiece-tool height mismatch, combined with a finite element mechanical analysis to determine the interface contact pressure distribution, was developed to evaluate various smoothing tool designs as a function of tool material properties, thicknesses, pad textures, and displacements. An improvement in smoothing tool performance is achieved when the gap pressure constant, $\overline{h}$ (which describes the inverse rate at which the pressure drops with a workpiece-tool height mismatch), is minimized for smaller spatial scale length surface features (namely, MSF errors) and maximized for large spatial scale length features (i.e., surface figure). Five specific smoothing tool designs were experimentally evaluated. A two-layer smoothing tool using a thin, grooved IC1000 polyurethane pad (with a high elastic modulus, E pad =360 MPa ), thicker blue foam (with an intermediate modulus, E foam =5.3 MPa ) underlayer, and an optimized displacement (d t =1 mm ) provided the best overall performance (namely, high MSF error convergence, minimal surface figure degradation, and high material removal rate).

47 OTHER INSTRUMENTATION↗

NASA NTRS1989

An adaptive data-smoothing routine

An adaptive noise reduction algorithm that can be implemented on a microcomputer is developed. Smoothing polynomials are used where the polynomial coefficients are chosen such that the mean-square-error between the noisy and smoothed data is minimized. This approach is equivalent to the implementation of a low-pass finite impulse response filter. The noise reduction depends on the order of the smoothing polynomial. A whiteness test on the error sequence is incorporated to search for the optimal smoothing. Expansion coefficients may be computed via the fast Fourier transform, and the resulting smoothing process is the equivalent of the implementation of an adaptive ideal low-pass filter. Results are obtained for an analytical signal with added white Gaussian noise. The routine may be applied to any smooth signal with additive random noise.

Taylor, Clayborne D.↗

NASA NTRS1992

Comparison of Predictable Smooth Ocular and Combined Eye-Head Tracking Behaviour in Patients with Lesions Affecting the Brainstem and Cerebellum

We compared the ability of eight normal subjects and 15 patients with brainstem or cerebellar disease to follow a moving visual stimulus smoothly with either the eyes alone or with combined eye-head tracking. The visual stimulus was either a laser spot (horizontal and vertical planes) or a large rotating disc (torsional plane), which moved at one sinusoidal frequency for each subject. The visually enhanced Vestibulo-Ocular Reflex (VOR) was also measured in each plane. In the horizontal and vertical planes, we found that if tracking gain (gaze velocity/target velocity) for smooth pursuit was close to 1, the gain of combined eye-hand tracking was similar. If the tracking gain during smooth pursuit was less than about 0.7, combined eye-head tracking was usually superior. Most patients, irrespective of diagnosis, showed combined eye-head tracking that was superior to smooth pursuit; only two patients showed the converse. In the torsional plane, in which optokinetic responses were weak, combined eye-head tracking was much superior, and this was the case in both subjects and patients. We found that a linear model, in which an internal ocular tracking signal cancelled the VOR, could account for our findings in most normal subjects in the horizontal and vertical planes, but not in the torsional plane. The model failed to account for tracking behaviour in most patients in any plane, and suggested that the brain may use additional mechanisms to reduce the internal gain of the VOR during combined eye-head tracking. Our results confirm that certain patients who show impairment of smooth-pursuit eye movements preserve their ability to smoothly track a moving target with combined eye-head tracking.

Grant, Michael P.↗

NASA NTRS1999

Radiative Smoothing in Clouds at Transparent and Absorbing Wavelengths

For absorbing and transparent wavelengths, we discuss the effect of horizontal solar radiative fluxes in clouds on the accuracy of a conventional plane-parallel radiative transfer calculations for a single pixel, known as the Independent Pixel Approximation (IPA). We address the question of correlations between horizontal fluxes, IPA accuracies and radiative smoothing. By smoothing we understand a radiative transfer process whereby radiation does not follow the small-scale fluctuations of cloud structure, producing much smoother radiation fields. The scale eta that characterizes this process is called "radiative smoothing scale." We relate radiative smoothing to the photon's horizontal displacement that characterizes a "spot" of reflected light associated with a point source. We generalize the "spot-size" estimate derived for conservative scattering using the diffusion theory to the case of non-conservative scattering. For reflected light, theoretical results are confirmed with numerical simulations. The radiative smoothing scale eta is a critical value where IPA effectively breaks down; for scales smaller than TI, real radiation field are much smoother than their IPA counterparts for the same cloud structure. In addition to the estimate of il for absorbing wavelengths, we show that: (1) with more absorption, the scale break determined by eta in a log-log plot of wavenumber spectra moves towards smaller scales and (2) the smaller eta the flatter the small-scale slope which means less radiative smoothing, thus more accuracy in the IPA reflection.

Marshak, A.↗

DOE OSTI2025

A Smoothed Augmented Lagrangian Framework for Convex Optimization with Nonsmooth Constraints

Augmented Lagrangian (AL) methods have proven remarkably useful in solving optimization problems with complicated constraints. The last decade has seen the development of overall complexity guarantees for inexact AL variants. Yet, a crucial gap persists in addressing nonsmooth convex constraints. To this end, we present a smoothed augmented Lagrangian (AL) framework where nonsmooth terms are progressively smoothed with a smoothing parameter $\eta _k$ . The resulting AL subproblems are $\eta _k$ -smooth, allowing for leveraging accelerated schemes. By a careful selection of the inexactness level $\epsilon _k$ (for inexact subproblem resolution), the penalty parameter $\rho _k$ , and smoothing parameter $\eta _k$ at epoch k, we derive rate and complexity guarantees of $\tilde{\mathcal {O}}(1/{\varepsilon }^{3/2})$ and $\tilde{\mathcal {O}}(1/{\varepsilon })$ in convex and strongly convex regimes for computing an ${\varepsilon }$ -optimal solution, when $\rho _k$ increases at a geometric rate, a significant improvement over the best available guarantees for AL schemes for convex programs with nonsmooth constraints. Analogous guarantees are developed for settings with $\rho _k = \rho$ as well as $\eta _k = \eta$ . Preliminary numerics on a fused Lasso problem display promise.

augmented Lagrangian↗

DOE OSTI2025

Surface smoothing for laser powder-bed Ti-6Al-4V by a transient liquid phase

Surface roughness is the primary driver of fatigue for additively manufactured metals. To address surface roughness, this work introduces a new method to smooth features beyond line-of-sight without material removal. The method applies a coating that triggers local surface remelting by activating a eutectic reaction during heat treatment. The associated liquid phase then wets and isothermally solidifies into a smoother surface. For Ti-6Al-4V fabricated with laser powder bed fusion, samples with and without TLP smoothing (using a Cu coating) were characterized with a suite of techniques, including mechanical testing, electron backscatter diffraction, synchrotron X-ray tomography, and fractography. TLP smoothing reduced surface roughness by 80% and amplified compressive residual stress at the surface by about 50%. With statistically equivalent virtual microstructures, crystal plasticity scrutinized the roles of phases, porosity, and surface roughness. Although the tensile strain-to-failure was reduced to 1% strain, the TLP smoothing process increased high-cycle fatigue strength by about 20% compared to control samples, pointing to future opportunities to optimize the new process through various coating compositions and heat treatment schedules. Overall, this work establishes a new paradigm for treating surfaces of materials for smoothness and compressive residual stress.

Additive manufacturing↗

DOE OSTI2021

Endothelial cells control vascular smooth muscle cell cholesterol levels by regulating 24-dehydrocholesterol reductase expression

Highlights: • Suspended endothelial and vascular smooth muscle cells organize to form spherical vascular organoids in hanging drops. • Vascular smooth muscle cells downregulate the expression of metabolism regulating genes in presence of endothelial cells. • Endothelial cells decrease the levels of 24-dehydrocholesterol reductase and cholesterol in vascular smooth muscle cells. • Diminished cholesterol biosynthesis inhibits vascular smooth muscle cell activity. Communication of vascular cells is essential for the control of organotypic functions of blood vessels. In this context, vascular endothelial cells (EC) act as potent regulators of vascular smooth muscle cell (VSMC) functions such as contraction and relaxation. However, the impact of ECs on the gene expression pattern of VSMCs is largely unknown. Here, we investigated changes of the VSMC transcriptome by utilizing 3D human vascular organoids organized as a core of VSMCs enclosed by a monolayer of ECs. Microarray-based analyses indicated that interaction with ECs for 48 h down-regulates expression of genes in VSMCs controlling rate-limiting steps of the cholesterol biosynthesis such as HMGCR, HMGCS1, DHCR24 and DHCR7. Protein analyses revealed a decrease in the abundance of DHCR24 (24-dehydrocholesterol reductase) and lower cholesterol levels in VSMCs co-cultured with ECs. On the functional level, the blockade of the DHCR24 activity impaired adhesion, migration and proliferation of VSMCs. Collectively, these findings indicate that ECs have the capacity to instruct VSMCs to shut down the expression of DHCR24 thereby limiting their cholesterol biosynthesis, which may support their functional steady state.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Extending and Smoothing Two-dimension Equation of State Simulation Data

The Multiphase Equation of State (MEOS) project works to produce high quality equation of state tables which are used in computationally intensive simulations of materials in different conditions. An equation of state table describes the state of matter under certain physical conditions such as pressure, volume, temperature, or internal energy. MEOS uses many different models and combinations thereof to produce accurate tables consisting of continuous smooth data, derivatives, and higher-order derivatives. Accurate and smooth data are important factors in producing precise simulations. This report focuses on improving the electron tables produced from Purgatorio and Thomas-Fermi data. Purgatorio data is extremely accurate but often jagged and discontinuous in the lower temperature and density region. Thomas-Fermi is a model that provides smooth data throughout. Together, this produces an EOS data table that is both accurate and smooth. This report describes the implementation of a new feature that allows users to define more detailed regions in the Purgatorio table to be replaced with Thomas-Fermi. As a result, MEOS can generate a table that is both more smooth and still accurate.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

Recursive algorithms for two-dimensional smoothing using bicubic hermite polynomial

It is noted that in the past, smoothing splines originated from approximation theory have been successfully applied to data filtering and image smoothing problems. Even though the nonrecursive technique of smoothing splines gives an optimal solution, the amount of computation increases rapidly with the size of the two-dimensional data. A derivation is presented here of quarter-plane filtering algorithms that provide smoothed estimates of function values and their derivatives by fitting two-dimensional smoothing splines in a recursive manner. The derivation procedure sheds light on specific problems encountered in two-dimensional filtering problems. What is more, the amount of computation for this recursive processor increases only linearly with the size of the two-dimensional data. Because of certain approximations introduced in its derivation, this recursive processor becomes suboptimal.

Kim, C. S.↗

NASA NTRS1993

The turbulent thermal boundary layer with an abrupt change from a rough to a smooth wall

The work reported here was motivated by concern over the use of smooth heat flux gages for heat transfer measurements on the otherwise rough turbine blades. Stanton number distributions and boundary layer profiles of mean temperature, mean velocity, and turbulence intensity are reported for a surface with a step change from a rough to a smooth surface. In most cases, the Stanton number immediately downstream of the change in roughness drops below the all-smooth-wall data at the same x-Reynolds number. The alignment of the smooth surface between the bases and crests of the roughness elements is shown to have only a weak effect on the Stanton number distribution. It is concluded that the use of smooth heat flux gages on otherwise rough surfaces can cause large errors. It is recommended that heat transfer data collected in this manner be used with caution.

Taylor, Robert P.↗

NASA NTRS1998

A Novel Four-Node Quadrilateral Smoothing Element for Stress Enhancement and Error Estimation

A four-node, quadrilateral smoothing element is developed based upon a penalized-discrete-least-squares variational formulation. The smoothing methodology recovers C1-continuous stresses, thus enabling effective a posteriori error estimation and automatic adaptive mesh refinement. The element formulation is originated with a five-node macro-element configuration consisting of four triangular anisoparametric smoothing elements in a cross-diagonal pattern. This element pattern enables a convenient closed-form solution for the degrees of freedom of the interior node, resulting from enforcing explicitly a set of natural edge-wise penalty constraints. The degree-of-freedom reduction scheme leads to a very efficient formulation of a four-node quadrilateral smoothing element without any compromise in robustness and accuracy of the smoothing analysis. The application examples include stress recovery and error estimation in adaptive mesh refinement solutions for an elasticity problem and an aerospace structural component.

Tessler, A.↗

NASA NTRS2007

Smooth Phase Interpolated Keying

Smooth phase interpolated keying (SPIK) is an improved method of computing smooth phase-modulation waveforms for radio communication systems that convey digital information. SPIK is applicable to a variety of phase-shift-keying (PSK) modulation schemes, including quaternary PSK (QPSK), octonary PSK (8PSK), and 16PSK. In comparison with a related prior method, SPIK offers advantages of better performance and less complexity of implementation. In a PSK scheme, the underlying information waveform that one seeks to convey consists of discrete rectangular steps, but the spectral width of such a waveform is excessive for practical radio communication. Therefore, the problem is to smooth the step phase waveform in such a manner as to maintain power and bandwidth efficiency without incurring an unacceptably large error rate and without introducing undesired variations in the amplitude of the affected radio signal. Although the ideal constellation of PSK phasor points does not cause amplitude variations, filtering of the modulation waveform (in which, typically, a rectangular pulse is converted to a square-root raised cosine pulse) causes amplitude fluctuations. If a power-efficient nonlinear amplifier is used in the radio communication system, the fluctuating-amplitude signal can undergo significant spectral regrowth, thus compromising the bandwidth efficiency of the system. In the related prior method, one seeks to solve the problem in a procedure that comprises two major steps: phase-value generation and phase interpolation. SPIK follows the two-step approach of the related prior method, but the details of the steps are different. In the phase-value-generation step, the phase values of symbols in the PSK constellation are determined by a phase function that is said to be maximally smooth and that is chosen to minimize the spectral spread of the modulated signal. In this step, the constellation is divided into two groups by assigning, to information symbols, phase values that result in equal numbers of clockwise and counter-clockwise phase rotations for equally likely symbols. The purpose served by assigning phase values in this way is to prevent unnecessary generation of spectral lines and prevent net shifts of the carrier signal. In the phase-interpolation step, the smooth phase values are interpolated over a number, n, of consecutive symbols (including the present symbol) by means of an unconventional spline curve fit.

Borah, Deva K.↗

NASA NTRS2012

Topographic Rise in the Northern Smooth Plains of Mercury: Characteristics from Messenger Image and Altimetry Data and Candidate Modes of Origin

MESSENGER observations from orbit around Mercury have revealed that a large contiguous area of smooth plains occupies much of the high northern latitudes and covers an area in excess of approx.6% of the surface of the planet [1] (Fig. 1). Smooth surface morphology, embayment relationships, color data, candidate flow fronts, and a population of partly to wholly buried craters provide evidence for the volcanic origin of these plains and their emplacement in a flood lava mode to depths at least locally in excess of 1 km. The age of these plains is similar to that of plains associated with and postdating the Caloris impact basin, confirming that volcanism was a globally extensive process in the post-heavy bombardment history of Mercury [1]. No specific effusive vent structures, constructional volcanic edifices, or lava distributary features (leveed flow fronts or sinuous rilles) have been identified in the contiguous plains, although vent structures and evidence of high-effusion-rate flood eruptions are seen in adjacent areas [1]. Subsequent to the identification and mapping of the extensive north polar smooth plains, data from the Mercury Laser Altimeter (MLA) on MESSENGER revealed the presence of a broad topographic rise in the northern smooth plains that is ~1,000 km across and rises more than 1.5 km above the surrounding smooth plains [2] (Fig. 2). The purpose of this contribution is to characterize the northern plains rise and to outline a range of hypotheses for its origin.

Dickson, James L.↗

NASA NTRS1998

Differential regulation of protease activated receptor-1 and tissue plasminogen activator expression by shear stress in vascular smooth muscle cells

Recent studies have demonstrated that vascular smooth muscle cells are responsive to changes in their local hemodynamic environment. The effects of shear stress on the expression of human protease activated receptor-1 (PAR-1) and tissue plasminogen activator (tPA) mRNA and protein were investigated in human aortic smooth muscle cells (HASMCs). Under conditions of low shear stress (5 dyn/cm2), PAR-1 mRNA expression was increased transiently at 2 hours compared with stationary control values, whereas at high shear stress (25 dyn/cm2), mRNA expression was decreased (to 29% of stationary control; P<0.05) at all examined time points (2 to 24 hours). mRNA half-life studies showed that this response was not due to increased mRNA instability. tPA mRNA expression was decreased (to 10% of stationary control; P<0.05) by low shear stress after 12 hours of exposure and was increased (to 250% of stationary control; P<0.05) after 24 hours at high shear stress. The same trends in PAR-1 mRNA levels were observed in rat smooth muscle cells, indicating that the effects of shear stress on human PAR-1 were not species-specific. Flow cytometry and ELISA techniques using rat smooth muscle cells and HASMCs, respectively, provided evidence that shear stress exerted similar effects on cell surface-associated PAR-1 and tPA protein released into the conditioned media. The decrease in PAR-1 mRNA and protein had functional consequences for HASMCs, such as inhibition of [Ca2+] mobilization in response to thrombin stimulation. These data indicate that human PAR-1 and tPA gene expression are regulated differentially by shear stress, in a pattern consistent with their putative roles in several arterial vascular pathologies.

NASA Discipline Cell Biology↗

DOE OSTI2022

On the Counter‐intuitive Heterogeneous Electron Transfer Barrier Properties of Alkanethiolate Monolayers on Gold: Smooth versus Rough Surfaces

Abstract Alkanethiolate monolayers formed on rough gold surfaces can, somewhat surprisingly, act as stronger barriers to heterogeneous electron transfer than those on smooth gold surfaces. This paper presents a possible explanation for this observation by constructing simple geometric models of a “rough” and “smooth” gold surface to examine how microscopic roughness differences can affect the nucleation/growth of the adlayer and size/density of structural defects. Expectedly, the number of defects predicted for adlayers formed on smooth gold is lower than any of those for rough gold. The counter‐intuitive result is that the sizes of a small portion of the defects in the adlayer on the smooth surface are larger than any of those found on the rough surface. The potential implications of these results are discussed.

Chemistry↗

DOE OSTI2022

Smoothed aggregation for difficult stretched mesh and coefficient variation problems

Abstract Four adaptations of the smoothed aggregation algebraic multigrid (SA‐AMG) method are proposed with an eye toward improving the convergence and robustness of the solver in situations when the discretization matrix contains many weak connections. These weak connections can cause higher than expected levels of fill‐in within the coarse discretization matrices and can also give rise to suboptimal smoothing within the prolongator smoothing phase. These smoothing drawbacks are due to the relatively small size of some diagonal entries within the filtered matrix that one obtains after dropping the weak connections. The new algorithms consider modifications to the Jacobi‐like step that defines the prolongator smoother, modifications to the filtered matrix, and also direct modifications to the resulting grid transfer operators. Numerical results are given illustrating the potential benefits of the proposed adaptations.

Hu, Jonathan J.↗