Venusian Surface Roughness Inversion Using Two Scale Approximation
Magellan was launched on May 4, 1989 on the Shuttle Atlantis in order to achieve global imaging of the Venus surface.
Venus radar mapping surface morphology electrical ↗
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Results for “Approximate inverses”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Inversion of the anomalous diffraction approximation for variable complex index of refraction near unity
The Fymat analytic inversion method for retrieving a particle-area distribution function from anomalous diffraction multispectral extinction data and total area is generalized to the case of a variable complex refractive index m(lambda) near unity depending on spectral wavelength lambda. Inversion tests are presented for a water-haze aerosol model. An upper-phase shift limit of 5 pi/2 retrieved an accurate peak area distribution profile. Analytical corrections using both the total number and area improved the inversion.
Smith, C. B.↗
Multi-frequency progressive refinement for learned inverse scattering
Interpreting scattered acoustic and electromagnetic wave patterns is a computational task that enables remote imaging in a number of important applications, including medical imaging, geophysical exploration, sonar and radar detection, and nondestructive testing of materials. However, accurately and stably recovering an inhomogeneous medium from far-field scattered wave measurements is a computationally difficult problem, due to the nonlinear and non-local nature of the forward scattering process. We design a neural network, called Multi-Frequency Inverse Scattering Network (MFISNet), and a training method to approximate the inverse map from far-field scattered wave measurements at multiple frequencies. We consider three variants of MFISNet, with the strongest performing variant inspired by the recursive linearization method — a commonly used technique for stably inverting scattered wavefield data — that progressively refines the estimate with higher frequency content. MFISNet outperforms past methods in regimes with high-contrast, heterogeneous large objects, and inhomogeneous unknown backgrounds.
97 MATHEMATICS AND COMPUTING↗
Approximation Of Multi-Valued Inverse Functions Using Clustering And Sugeno Fuzzy Inference
Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.
Walden, Maria A.↗
Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem
The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.
Voorhies, Coerte V.↗
A Theoretical and Computational Revisit of Conversions Between Whitham’s F-Function and Equivalent Area
This paper proves mathematically that the integral transforms between Whitham’s F-function and equivalent area are the inverse transforms of each other if and only if the slope of the equivalent area at the origin is zero. This mathematical fact contradicts the accepted unconditional inverse relation between Whitham’s F-function and equivalent area in the sonic boom research literature. Piecewise linear approximations of an F-function and of the second derivative of an equivalent area are used to derive numerical formulas for conversions between Whitham’s F-function and equivalent area. Numerical results are included to show convergence of the numerical conversions as the maximum length of the segments for piecewise linear approximations goes to zero. These numerical conversions are approximately the inverse transforms of each other when the second derivative of an equivalent area is continuous and the slope of the equivalent area at the origin is zero.
Whitham's F-function↗
Learning Optimal Aerodynamic Designs
This project created a framework for efficient, accurate, and scalable deep neural network representations of design optimization problem solutions. The inputs to these DNN representations are the vector of design requirement parameters, the outputs are the optimal design variables, and the goal is to learn the map from inputs to outputs (i.e., inverse design). The team addressed the problem of the optimal shape design of aerodynamic lifting surfaces—in particular aircraft wings—using a Reynolds-Average Navier Stokes model to govern the CFD-based aerodynamic shape optimization. The inverse design map for such problems is very complex and high-dimensional, involving inputs and outputs on the order of 1000s. To approximate this inverse design map, the team developed algorithms to construct parsimonious DNN architectures, which automatically identify low-dimensional manifolds in which design requirements affect optimal shape parameters, and trained these architectures with multifidelity optimization methods. The resulting methodology accurately and automatically designs optimal aerodynamic lifting surfaces with very high accuracy (99%) at interactive speeds, of the order of milliseconds, resulting in factors of one million or more speedup relative to CFD-based design optimization.
97 MATHEMATICS AND COMPUTING↗
Securely Aggregated Coded Matrix Inversion
Coded computing is a method for mitigating straggling workers in a centralized computing network, by using erasure-coding techniques. Federated learning is a decentralized model for training data distributed across client devices. In this work we propose approximating the inverse of an aggregated data matrix, where the data is generated by clients; similar to the federated learning paradigm, while also being resilient to stragglers. To do so, we propose a coded computing method based on gradient coding. We modify this method so that the coordinator does not access the local data at any point; while the clients access the aggregated matrix in order to complete their tasks. Here, the network we consider is not centrally administrated, and the communications which take place are secure against potential eavesdroppers.
97 MATHEMATICS AND COMPUTING↗
Fast matrix algebra for Bayesian model calibration
In Bayesian model calibration, evaluation of the likelihood function usually involves finding the inverse and determinant of a covariance matrix. When Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior, hundreds of thousands of likelihood evaluations may be required. In this paper, we demonstrate that the structure of the covariance matrix can be exploited, leading to substantial time savings in practice. Here, we also derive two simple equations for approximating the inverse of the covariance matrix in this setting, which can be computed in near-quadratic time. The practical implications of these strategies are demonstrated using a simple numerical case study and the "quack" R package. For a covariance matrix with 1000 rows, application of these strategies for a million likelihood evaluations leads to a speedup of roughly 4000 compared to the naive implementation
97 MATHEMATICS AND COMPUTING↗
Neutral to charged kaon yield fluctuations in Pb – Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
We present the first measurement of event-by-event fluctuations in the kaon sector in Pb – Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV with the ALICE detector at the LHC. The robust fluctuation correlator νdyn is used to evaluate the magnitude of fluctuations of the relative yields of neutral and charged kaons, as well as the relative yields of charged kaons, as a function of collision centrality and selected kinematic ranges. While the correlator $ν_{dyn}[K^+, K^–]$ exhibits a scaling approximately in inverse proportion of the charged particle multiplicity, $ν_{dyn}[K^0_S, K^±]$ features a significant deviation from such scaling. Within uncertainties, the value of $ν_{dyn}[K^0_S, K^±]$ is independent of the selected transverse momentum interval, while it exhibits a pseudorapidity dependence. The results are compared with HIJING, AMPT and EPOS–LHC predictions, and are further discussed in the context of the possible production of disoriented chiral condensates in central Pb – Pb collisions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A Study on Particle Trajectory Error in Finite-Element Particle-in-Cell Algorithms
Particle-in-cell (PIC) algorithms are widely used for the simulation of kinetic plasmas. PIC algorithms account for the interaction between charged particles in a plasma and the electromagnetic field in ambient space, including self-field interactions. The objective of this article is to study the error in charged particle trajectories present in finite-element (FE)-based PIC algorithms on unstructured meshes. We study how the trajectory error behaves according to the FE mesh resolution and the matrix solver employed in the FE algorithm. The study is performed by considering a trajectory established by a parabolic electric potential and an axial magnetic force acting on the charged particle. Under a proper choice combination of electric and magnetic field parameters, the 2-D particle trajectories comprise closed orbits. Numerical errors cause small perturbations on the trajectories, with cumulative effects. As a result, the resulting orbital trajectories exhibit distortions including spurious apsidal precession. These distortions provide a clear imprint of the numerical error. Here, we also study the numerical error in a quantitative fashion by computing the distance norm between the trajectories obtained by the exact fields and numerical fields.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Optimizing pollinator conservation and crop yield among perennial bioenergy crops
In order to both combat the decline of biodiversity and produce food, fuel, and fiber for a growing human population, current agricultural landscapes must transition into diversified, multifunctional systems. Perennial cellulosic biofuel crops have potential to meet both of these challenges, acting as multifunctional systems that can enhance biodiversity. What is not well understood, and what we test here, are the tradeoffs among different perennial crops in their performance as biofuels and in biodiversity conservation. Working in an established bioenergy experiment with four native, perennial, cellulosic biofuel crop varieties - ranging from monoculture to diverse restoration planting - we tested the effect of biofuel crop management on flower communities, pollinator communities, and crop yield. The greatest abundance and diversity of pollinators and flowers were in treatments that were successional (unmanaged), followed by restored prairie (seeded mix of native grasses and forbs), switchgrass, and a mix of native grasses. However, biofuel crop yield was approximately the inverse, with native grasses having the highest yield, followed by switchgrass and prairie, then successional treatments. Restored prairie was the optimal biofuel crop when both pollinator conservation and crop yield are valued similarly. We add to mounting evidence that policy is needed to create sustainable markets that value the multifunctionality of perennial biofuel systems in order to achieve greater ecosystem services from agricultural landscapes.
09 BIOMASS FUELS↗
Convergence Analysis of the Alternating Anderson–Picard Method for Nonlinear Fixed-Point Problems
Anderson acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson–Picard (AAP) method. Furthermore, despite introducing more “slow” Picard iterations, this method has been shown to be efficient and even more robust in both linear and nonlinear cases. However, there is a lack of theoretical analysis for AAP in the nonlinear case. In this paper, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that uses GMRES to solve a multisecant linear system at each iteration. From this perspective, we show that AAP “converges” to the Newton-GMRES method. Specifically, as the residual approaches zero, the multisecant matrix, the approximate Jacobian inverse, the search direction, and the optimization gain of AAP converge to their counterparts in the Newton-GMRES method. These connections provide insights for analyzing the asymptotic convergence properties of AAP. Consequently, we show that AAP is locally 𝑞-linear convergent and provide an upper bound for the convergence factor of AAP. To validate the theoretical results, numerical examples are provided.
Anderson acceleration↗
A systematic experimental investigation of significant parameters affecting model tire hydroplaning
The results of a comprehensive parametric study of model and small pneumatic tires operating on a wet surface are presented. Hydroplaning inception (spin down) and rolling restoration (spin up) are discussed. Conclusions indicate that hydroplaning inception occurs at a speed significantly higher than the rolling restoration speed. Hydroplaning speed increases considerably with tread depth, surface roughness and tire inflation pressure of footprint pressure, and only moderately with increased load. Water film thickness affects spin down speed only slightly. Spin down speed varies inversely as approximately the one-sixth power of film thickness. Empirical equations relating tire inflation pressure, normal load, tire diameter and water film thickness have been generated for various tire tread and surface configurations.
Wray, G. A.↗
Saturn's rings - Particle size distributions for thin layer model
A model incorporating limited interaction between the incident energy and particles in the ring is considered which appears to be consistent with the multiple scattering process in Saturn's rings. The model allows for the small physical thickness of the rings and can be used to relate Voyager 1 observations of 3.6- and 13-cm wavelength microwave scatter from the rings to the ring particle size distribution function for particles with radii ranging from 0.001 to 20 m. This limited-scatter model yields solutions for particle size distribution functions for eight regions in the rings, which exhibit approximately inverse-cubic power-law behavior.
Zebker, H. A.↗
A methodology for designing robust multivariable nonlinear feedback control systems
This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.
Grunberg, D. B.↗
Digital restoration of multichannel images
The Wiener solution of a multichannel restoration scheme is presented. Using matrix diagonalization and block-Toeplitz to block-circulant approximation, the inversion of the multichannel, linear space-invariant imaging system becomes feasible by utilizing a fast iterative matrix inversion procedure. The restoration uses both the within-channel (spatial) and between-channel (spectral) correlation; hence, the restored result is a better estimate than that produced by independent channel restoration. Simulations are also presented.
Galatsanos, Nikolas P.↗
Polynomial Transformations For Discrete-Time Linear Systems
Transformations based on polynomial matrices of finite degree developed for use in computing functions for compensation, inversion, and approximation of discrete-time, multivariable, linear systems. Method derived from z-transform transfer-function form of matrices. Applicable to cascade-compensation problems in design of control systems.
Baram, Yoram↗