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DOE OSTI2022

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1979

Performance optimization of an MHD generator with physical constraints

A technique has been described which optimizes the power out of a Faraday MHD generator operating under a prescribed set of electrical and magnetic constraints. The method does not rely on complicated numerical optimization techniques. Instead the magnetic field and the electrical loading are adjusted at each streamwise location such that the resultant generator design operates at the most limiting of the cited stress levels. The simplicity of the procedure makes it ideal for optimizing generator designs for system analysis studies of power plants. The resultant locally optimum channel designs are, however, not necessarily the global optimum designs. The results of generator performance calculations are presented for an approximately 2000 MWe size plant. The difference between the maximum power generator design and the optimal design which maximizes net MHD power are described. The sensitivity of the generator performance to the various operational parameters are also presented.

Pian, C. C. P.↗

NASA NTRS2016

The Quality Control Algorithms Used in the Process of Creating the NASA Kennedy Space Center Lightning Protection System Towers Meteorological Database

The methodology and the results of the quality control (QC) process of the meteorological data from the Lightning Protection System (LPS) towers located at Kennedy Space Center (KSC) launch complex 39B (LC-39B) are documented in this paper. Meteorological data are used to design a launch vehicle, determine operational constraints, and to apply defined constraints on day-of-launch (DOL). In order to properly accomplish these tasks, a representative climatological database of meteorological records is needed because the database needs to represent the climate the vehicle will encounter. Numerous meteorological measurement towers exist at KSC; however, the engineering tasks need measurements at specific heights, some of which can only be provided by a few towers. Other than the LPS towers, Tower 313 is the only tower that provides observations up to 150 m. This tower is located approximately 3.5 km from LC-39B. In addition, data need to be QC'ed to remove erroneous reports that could pollute the results of an engineering analysis, mislead the development of operational constraints, or provide a false image of the atmosphere at the tower's location.

Orcutt, John M.↗

NASA NTRS1999

Satellite Data Assimilation

Satellite altimetry provides the only routine observation of a dynamic variable of the global ocean. For instance, measurements from the TOPEX/POSEIDON altimeter have provided dramatic basin-wide images of the space-time evolution of sea level associated with the 1997-98 El Nino event. The nature of large-scale ocean circulation is being studied that underlies such sea level changes measured by satellite altimetry. To first approximation, properties of large-scale (order 1000 km and larger) sea level variability is latitudinally dependent. An analysis using a general circulation model shows that sea level changes are largely due to wind-driven baroclinic (depth dependent) circulation in the tropics (within 20 degrees of the equator), but are primarily due to the expansion and contraction of near surface water in temperate latitudes (between 20 deg. and 40 deg.) forced by seasonal heating and cooling. In contrast, wind-driven barotropic (depth independent) circulation dominates sea level variability in high latitudes (40 deg. and higher) characterized by periods that are as short as a few days. The presence of such inhomogeneity and the significance of high-frequency, large-scale sea level changes had not been fully recognized prior to this study, and are summarized in Fukumori et al. Numerical models provide theoretical relationships among properties that can be inverted using observations so as to estimate the entire state of the ocean, including properties that are otherwise difficult to measure remotely. The process is data assimilation. An approximate Kalman filter and smoother have been devised to assimilate three years of TOPEX/POSEIDON sea level data into a global ocean general circulation model. The figure below demonstrates the skill of the assimilation, and shows the altimeter assimilated estimate being in closer agreement than the simulation is with independent in situ measurements of subsur ace temperature and velocity, consistent with formal uncertainty estimates. Results from this study have been summarized and submitted for publication. The study demonstrates the feasibility of global ocean data assimilation and illustrates applications in monitoring and understanding of processes controlling the evolution of the ocean. Additional information is contained in the original.

Fukumori, Ichiro↗

NASA NTRS1979

An efficient algorithm for numerical airfoil optimization

A new optimization algorithm is presented. The method is based on sequential application of a second-order Taylor's series approximation to the airfoil characteristics. Compared to previous methods, design efficiency improvements of more than a factor of 2 are demonstrated. If multiple optimizations are performed, the efficiency improvements are more dramatic due to the ability of the technique to utilize existing data. The method is demonstrated by application to subsonic and transonic airfoil design but is a general optimization technique and is not limited to a particular application or aerodynamic analysis.

Vanderplaats, G. N.↗

NASA NTRS1985

A three-dimensional viscous flow analysis for the helicopter tip vortex generation problem

The tip vortex flow field occurring in the vicinity of the tip region of a a helicopter rotor blade is a very complicated three-dimensional, viscous flow phenomenon. The details of the flow in the tip region can have a major effect in determining the generated rotor noise and can significantly affect the performance and dynamic loading of the rotor blade. The three-dimensional viscous subsonic tip vortex generation processes is investigated by a numerical procedure which allows spatial forward-marching integration, utilizing flow approximations from the velocity-decomposition approach of Briley and McDonald. The approach has been applied to compute the laminar and turbulent tip vortex flows for a constant thickness slab airfoil with a square tip, a constant thickness slab airfoil with a half round tip and a NACA 0012 airfoil with a half round tip. The basic mechanism of the tip vortex generation process as well as the prediction of vortex appearance, strength and secondary flow shown by the calculations are in qualitative agreement with experimental results.

Lin, S. J.↗

DOE OSTI2025

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Estimation of Surface Sensible Heat Flux due to Precipitation over CONUS and Its Impact on Urban Extreme Precipitation Modeling

The surface sensible heat flux induced by precipitation (Q P ) is a consequence of the temperature difference between the surface and the rain droplets. Despite its seemingly negligible nature, Q P is frequently omitted from both meteorological and climatological models. Nevertheless, it is important to acknowledge the numerous occasions in which the instantaneous values of Q P can be significant, particularly during extreme precipitation events. This study undertakes a comprehensive assessment of Q P across the contiguous United States (CONUS) utilizing high-resolution reanalysis, observational data, and numerical modeling to examine the influence of Q P on precipitation and the surface energy budget. The findings indicate that the spatial distribution of Q P climatology is analogous to that of precipitation, with magnitudes ranging from 2 to 3 W m -2 predominantly over the Midwest and Southeast regions. A seasonal analysis of QP reveals that the highest values occurring during the June–August (JJA) period, averaging 3.18 W m -2 . Peak Q P values of approximately 4 W m -2 are observed during JJA over the Great Plains region. We hypothesize that the Q P during an extreme precipitation event would be nonnegligible and have a significant impact on the local weather. To test this conjecture, we perform high-resolution simulations with and without Q P during an extreme precipitation event over the Chicago Metropolitan Area (CMA). The results show that the Q P may be a dominant factor compared to other components of surface heat flux during the zenith of precipitation hours. Also, Q P has the potential to not only diminish precipitation but also alter and reconfigure the remaining surface energy budget components.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1995

Effect of various approximations on predicted progressive failure in plain weave composites

Three-dimensional finite element analysis was used to simulate progressive failure of a plain weave composite subjected to in-plane extension. The loading was parallel to one of the tow directions. The effects of various characteristics of the finite element model on predicted behavior were examined. The predicted behavior was found to be sensitive to quadrature order, mesh refinement, and the material degradation model. Also the sensitivity of the predictions to the tow waviness was studied. The predicted strength decreased considerably with increased waviness. More numerical studies and comparisons with experimental data are needed to establish reliable guidelines for accurate progressive failure prediction.

Whitcomb, John↗

NASA NTRS2004

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗

DOE OSTI2026

Numerical Analysis of Offshore Wind-Farm-Induced Drag Effects on Coastal Upwelling Dynamics

Wind farms extract momentum from the atmospheric flow, generating wind-speed deficits both within the plant, and extending downstream. When located offshore, these deficits modulate air-sea coupling, potentially impacting coastal upwelling in sensitive regions. We investigate impacts of wind farms on coastal upwelling using kilometre-scale, three-way-coupled simulations with the coupled ocean-atmosphere-wave-sediment transport system for the US West Coast. Wind-farm effects are represented by a generalised turbine drag formulation, an idealised, height-dependent body force whose magnitude is systematically varied. This approach isolates the leading-order fluid-dynamical response in a realistic coastal configuration. The atmospheric adjustment exhibits an approximately linear relation between drag force and wind-speed deficit, with wakes that expand downstream and increase in magnitude as drag increases. An empirical orthogonal function analysis of sea-surface-temperature anomalies reveals the emergence of a canonical dipole pattern under strong drag forcing. Subsurface diagnostics show consistent shoaling of the mixed layer and suppressed upward velocities in areas near wind-farm region, accompanied by compensating enhancements of shoaling closer to the coast. These results identify turbine drag as a control parameter in assessing interactions between wind-farm wake and coastal upwelling and provide scaling relationships for understanding offshore wind-farm effects on the coastal circulation dynamics.

16 TIDAL AND WAVE POWER↗

DOE OSTI2021

Identifying Entangled Physics Relationships Through Sparse Matrix Decomposition to Inform Plasma Fusion Design

We report a sustainable burn platform through inertial confinement fusion (ICF) has been an ongoing challenge for over 50 years. Mitigating engineering limitations and improving the current design involves an understanding of the complex coupling of physical processes. While sophisticated simulation codes are used to model ICF implosions, these tools contain necessary numerical approximation but miss physical processes that limit predictive capability. Identification of relationships between controllable design inputs to ICF experiments and measurable outcomes (e.g., neutron yield, neutron velocity, areal density) from performed experiments can help guide the future design of experiments and development of simulation codes, to potentially improve the accuracy of the computational models used to simulate ICF experiments. We use sparse matrix decomposition methods to identify clusters of a few related design variables. Sparse principal component analysis (SPCA) identifies groupings that are related to the physical origin of the variables (laser, hohlraum, and capsule). A variable importance analysis finds that in addition to variables highly correlated with neutron yield, such as picket power and laser energy, variables that represent a dramatic change of the ICF design, such as number of pulse steps, are also very important. The obtained sparse components are then used to train a random forest (RF) regression surrogate for predicting total yield. The RF performance on the training and testing data compares with the performance of the RF trained using all the design variables considered. This work is intended to inform design changes in future ICF experiments by augmenting the expert intuition and simulation results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Scaled Vecchia Approximation for Fast Computer-Model Emulation

Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia’s ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction, and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Classification of Ultrasonic Weld Quality using Acoustic Signatures Acquired During Manufacture

Ultrasonic welding is a process is based on generating a solid-state bond between two metals by applying moderate pressure and high intensity sound waves (20-70 kHz frequencies) at their interface. During the solid-state process numerous material, surface, instrument, and environmental factors contribute to bond formation, strength, and durability. The inherent difficulty of measuring and controlling each of these factors has, to date, made predicting bond quality elusive. In this work, a Sonics model MWB20 ultrasonic spot welder with integral base, was used to produce a variety of welds of different metal foils under varying weld conditions. Acoustic measurements were recorded throughout the measurement process. Subsequent analysis of the signals using metrics that approximate the energy dispersed during the weld proved to successfully predict weld quality. Two metrics based on normalized energy differential and Renyi entropy were developed into Python and C++ scripts for direct analysis of weld acoustic data.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Spindown of Pulsars Interacting with Companion Winds: The Impact of Magnetospheric Compression

Pulsars in binary systems with strong companion winds can have the magnetopause separating their magnetosphere from the wind located well within their light cylinder. This bow-like enclosure effectively creates a waveguide that confines the pulsar's electromagnetic fields and can significantly alter its spindown. In this paper, we study the spindown of compressed pulsar magnetospheres in such systems. We parameterize the confinement as the ratio between the equatorial position of the magnetopause (or standoff distance) R m and the pulsar's light cylinder R LC . Using particle-in-cell simulations, we quantify the pulsar spindown for a range of compressions, R m /R LC = 1/3–1, and inclination angles, χ = 0°...90°, between magnetic and rotation axes. Our strongly confined models (R m /R LC = 1/3) show two distinct limits. For χ = 0°, the spindown of a compressed pulsar magnetosphere is enhanced by approximately a factor of three compared to an isolated pulsar due to the increased number of open magnetic field lines. Conversely, for χ = 90°, the compressed pulsar spins down at less than 40% of the rate of an isolated reference pulsar due to the mismatch between the pulsar wind stripe wavelength and the waveguide size. We apply our analysis to the 2.77 s oblique rotator (χ = 60°) in the double-pulsar system PSR J0737-3039. With the numerically derived spindown estimate, we constrain its surface magnetic field to B* ≈ (7.3 ± 0.2) × 10 11 G. We discuss the time modulation of its period derivative, the effects of compression on its braking index, and implications for the radio eclipse in PSR J0737-3039.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1973

Viscous effects in rapidly rotating stars with application to white-dwarf models. I, II.

A general approximate numerical technique is proposed for constructing evolutionary sequences of rapidly rotating axisymmetric barytropic equilibrium configurations, with allowance for angular momentum transfer by a nonconstant isotropic viscosity. The principal physical assumption involved is the constancy of the angular momentum per unit mass on cylinders about the axis of rotation. Rapidly rotating nonmagnetic white-dwarf models with a zero-temperature degenerate-electron equation of state are considered as a particular application. The viscosity used in the analysis is that of the degenerate electrons.

Durisen, R. H.↗

NASA NTRS1987

Near-symmetric instability for general Prandtl number

An analysis of the stability of a simple baroclinic flow to perturbations whose horizontal wave vector lies in and near the vertical plane containing the density gradient has been performed. The Ekman number (E) and 'azimuthal' wavenumber (alpha) were both assumed much less than 1, and expansions about these quantities were performed for the eigenmodes and Richardson number (R). Agreement with the previous analysis of Busse and Chen (1981) that the correction to the critical R was O(alpha) for Prandtl number (P) away from unity was obtained. An expression for the correction to the critical R for arbitrary P, and an approximate expression for P = 1 were obtained as new results. The correction for P = 1 has the same sign as that for P less than 1, and is O(alpha E exp 2/3). This result compares well with the numerical results of Miller and Antar (1986) for small E.

Reynolds, Nathaniel D.↗

NASA NTRS1992

Modal element method for scattering of sound by absorbing bodies

The modal element method for acoustic scattering from 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

Baumeister, Kenneth J.↗