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NASA NTRSDate not supplied

Strategies for Automation of Model Tuning in Multifidelity Trajectory Uncertainty Propagation

Multi-model Monte Carlo methods are efficient strategies to perform forward uncertainty quantification studies in entry, descent, and landing (EDL) applications. These multi-model methods are based on the classical Monte Carlo estimator, but fuse predictions from several low-fidelity models to obtain estimators with greater precision given a prescribed computational budget. The effectiveness of these approaches relies on the magnitudes of correlations between the low-fidelity models and the high-fidelity model, as well as the relative computational costs of all models. Identifying and exploiting the best trade-off between correlation and cost, which ultimately depends on the selection of hyperparameters in the low-fidelity models, is a task often performed by hand or simply inspired by the deterministic understanding available for a specific application. This work extends a preliminary effort,

Marten Thompson↗

NASA NTRS2020

Multi Model Monte Carlo with Python (MXMCPy)

Multi Model Monte Carlo with Python (\mxmc {}) is a software package developed as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Motivated by uncertainty propagation problems where classical Monte Carlo (MC) simulation is computationally intractable, various multi-model MC approaches have recently emerged that yield unbiased estimators with significantly reduced variance relative to MC for the same cost. These existing methods include multi-level Monte Carlo (MLMC), multi-fidelity Monte Carlo (MFMC), and approximate control variates (ACV). Given a fixed computational budget and a collection of models with varying cost/accuracy, each method seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. \mxmc {} is a versatile tool that enables convenient access to many existing multi-model MC approaches within one modular and extensible package. With \mxmc {}, users can easily compare existing methods to determine the best choice for their particular problem, while developers have a basis for implementing and sharing new variance reduction approaches. This report introduces the \mxmc {} software, providing a summary of the problem-solving workflow for users as well as a brief overview of the code layout for developers.

Geoffrey F Bomarito↗

NASA NTRS1977

Semiclassical dynamics on multiple electronic surfaces - Three-dimensional treatment of reactive F + H2

The role of electron transitions in collisions is studied for the F + H2 reaction by combining quasi-classical Monte Carlo trajectories with a semiclassical decoupling approximation for the electron transitions. Attention is directed at the reaction of excited state F atoms reacting to form ground state products; the reactants are initiated in either of two spin-orbit states of the atom with the diatom in the ground vibrational state and the lowest four rotational states, at relative translational energies of 0.1, 0.2 and 0.3 eV. Even if the reactants are initiated on the excited state surface, the reactive cross sections (which are classically forbidden) are significant. The major dynamical effects of the excited state reaction are the flow of reactant electronic energy into product internal energy.

Komornicki, A.↗

NASA NTRS1999

Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes

We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.

quantum algorithms numerical integrals↗

NASA NTRS2018

Stochastic Reduced Order Models with Python (SROMPy)

Stochastic Reduced Order Models with Python (SROMPy) is a software package developed to enable user-friendly utilization of the stochastic reduced order model (SROM) approach for uncertainty quantification. A SROM is a low dimensional, discrete approximation to a random quantity that enables efficient and non-intrusive stochastic computations. With SROMPy, a user can easily generate a SROM to approximate a random variable or vector described by several different types of probability distributions using the Python programming language. Once a SROM is constructed, the software can be used to propagate uncertainty through a user-defined computational model to estimate statistics of a given quantity of interest. This report is meant to introduce the SROMPy module and brie y demonstrate its capabilities. A simple example of a spring-mass system with a random input is included to illustrate the practicality of the SROM approach to uncertainty quantification and relative ease of applying it with SROMPy. The example includes a comparison with a solution obtained using classical Monte Carlo simulation, demonstrating the similarities and advantages of using the SROM approach.

Warner, James E.↗

NASA NTRS1978

Monte Carlo simulation of the classical two-dimensional one component plasma

Monte Carlo simulation, lattice dynamics in the harmonic approximation, and solution of the hypernetted chain equation were used to study the classical two-dimensional one component plasma. The system consists of a single species of charged particles immersed in a uniform neutralizing background. The particles interact via a l/r potential, where r is the two dimensional separation. Equations of state were calculated for both the liquid and solid phases. Results of calculation of the thermodynamic functions and one and two particle correlation functions are presented.

Gann, R. C.↗

NASA NTRS1979

Monte Carlo simulation of the classical two-dimensional one-component plasma

A Monte Carlo simulation, lattice dynamics in the harmonic approximation, and solution of the hypernetted chain equation are used to study the classical two-dimensional one-component plasma. A fluid phase is found for a specified dimensionless quantity, and a solid phase for higher values of this quantity. It is reported that the solid phase shows directional long range order, noting that in the solid phase positional long range order is lost as the thermodynamic limit is approached. Finally, the results of calculations of the thermodynamic functions and one- and two-particle correlation functions are presented.

Gann, R. C.↗

NASA NTRS2015

Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations

Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.

Quantum Monte Carlo↗

NASA NTRS2003

Ultraviolet and Visible Emission Mechanisms in Astrophysics

The project involved the study of ultraviolet (UV) and visible emission mechanisms in astrophysical and atmospheric environments. In many situations, the emission is a direct consequence of a charge transferring collision of an ion with a neutral with capture of an electron to an excited state of the product ion. The process is also important in establishing the ionization and thermal balance of an astrophysical plasma. As little of the necessary collision data are available, the main thrust of the project was the calculation of total and state-selective charge transfer cross sections and rate coefficients for a very large number of collision systems. The data was computed using modern explicit techniques including the molecular-orbital close-coupling (MOCC), classical trajectory Monte Carlo (CTMC), and continuum distorted wave (CDW) methods. Estimates were also made in some instances using the multichannel Landau-Zener (MCLZ) and classical over-the-barrier (COB) models. Much of the data which has been computed has been formatted for inclusion in a charge transfer database on the World Wide Web (cfadc.phy.ornl.gov/astro/ps/data/). A considerable amount of data has been generated during the lifetime of the grant. Some of it has not been analyzed, but it will be as soon as possible, the data placed on our website, and papers ultimately written.

Stancil, Phillip C.↗

NASA NTRS1986

The Oort cloud in transition

The evolution of theoretical and empirical models of the Oort cloud (OC) since it was first proposed by Oort in 1950 is traced, and the main features of current models are discussed, in a general review. Consideration is given to work on the classical OC (Monte Carlo simulations of OC evolution, population and mass estimates, and OC perturbation by passing stars and giant molecular clouds), models of a massive inner OC (simulations of planetesimal-swarm evolution in the Uranus-Neptune zone and IRAS observations of circumstellar dust shells), evidence for random and/or periodic comet showers, and the possible role of the Galactic missing mass. The current OC model comprises an almost spherical outer (10,000-100,000-AU) cloud of mass 7-8 earth mass and population (1.4-2.3) x 10 to the 12th, and a flat disklike inner (40-10,000 AU) cloud of mass 100-200 earth mass and population (1-10) x 10 to the 13th.

Weissman, P. R.↗

NASA NTRS2002

Charge Transfer Calculations and Database for Astrophysics

A variety of theoretical approaches, having different but overlapping energy ranges of applicability, are applied to investigate charge transfer processes for collisions of atomic ions with atoms and molecules. The methods include quantal molecular-orbital close-coupling, classical trajectory Monte Carlo, and continuum distorted wave methods. Recent collision systems studied include S(+4) + H, S(+4) + He, N(+7) + He, H2O, CO, and CO2, O(+q)(q = 1 - 8) + H, H2, and S(+q)(q = 1 - 16) + H2. The database effort is concentrating on astrophysically important reactions of atomic ions X(+q)(X=H-Zn, q=1-4, and selected higher charges) with H, He, various metal atoms, H2, and other selected molecular targets. Existing data, much of it produced by us, has been compiled and critically evaluated. Data for many reactions missing in the literature are estimated using the multichannel Landau-Zener approximation. Fits to cross sections and rate coefficients using standard functions are provided as well as tabulations of the raw data. The database is available on the World Wide Web at cfadc.phy.ornl.gov/astro/ps/data.

Wang, J. G.↗

NASA NTRS2019

Characterizing Lunar Polar Volatiles at the Working Scale: Going from Exploration Goals to Mission Requirements

The economic evaluation of natural resources depends on the accuracy of resource distribution estimates. On Earth such estimates are necessary in making decisions about opening new mines or in planning future investment for operating mines or industrial deposits. A frequently discussed lunar resource is water ice, however, we are only at the first stages of understanding its potential as a resource. In particular, we currently do not have a sufficient understanding of the distribution of water or its form at the scales it would be extracted and processed, that is, the “working scale”. Here the “working scale” is defined to be the scales at which sufficient material can be processed to meet some basic demand (for example, 100s of square meters), and the anticipated heterogeneity in the water distribution across those scales (scales <5 - 10s of meters). Several mission concepts have been developed to better understand lunar water, motivated by both scientific and exploration goals. This paper provides an analysis of the number and distribution of observations needed to provide the necessary next steps in lunar water ISRU. We use a combination of Monte Carlo studies and classic geostatistical approaches to go from the exploration goal of “understand the distribution of water” to quantification of specific mission sampling requirements.

Colaprete, A.↗

NASA NTRS1980

Methods for Monte Carlo simulation of the exospheres of the moon and Mercury

A general form of the integral equation of exospheric transport on moon-like bodies is derived in a form that permits arbitrary specification of time varying physical processes affecting atom creation and annihilation, atom-regolith collisions, adsorption and desorption, and nonplanetocentric acceleration. Because these processes usually defy analytic representation, the Monte Carlo method of solution of the transport equation, the only viable alternative, is described in detail, with separate discussions of the methods of specification of physical processes as probabalistic functions. Proof of the validity of the Monte Carlo exosphere simulation method is provided in the form of a comparison of analytic and Monte Carlo solutions to three classical, and analytically tractable, exosphere problems. One of the key phenomena in moonlike exosphere simulations, the distribution of velocities of the atoms leaving a regolith, depends mainly on the nature of collisions of free atoms with rocks. It is shown that on the moon and Mercury, elastic collisions of helium atoms with a Maxwellian distribution of vibrating, bound atoms produce a nearly Maxwellian distribution of helium velocities, despite the absence of speeds in excess of escape in the impinging helium velocity distribution.

Hodges, R. R., Jr.↗

NASA NTRS2008

State of the Art Assessment of Simulation in Advanced Materials Development

Advances in both the underlying theory and in the practical implementation of molecular modeling techniques have increased their value in the advanced materials development process. The objective is to accelerate the maturation of emerging materials by tightly integrating modeling with the other critical processes: synthesis, processing, and characterization. The aims of this report are to summarize the state of the art of existing modeling tools and to highlight a number of areas in which additional development is required. In an effort to maintain focus and limit length, this survey is restricted to classical simulation techniques including molecular dynamics and Monte Carlo simulations.

Wise, Kristopher E.↗

NASA NTRS1976

Linear minimum variance filters applied to carrier tracking

A new approach is taken to the problem of tracking a fixed amplitude signal with a Brownian-motion phase process. Classically, a first-order phase-lock loop (PLL) is used; here, the problem is treated via estimation of the quadrature signal components. In this space, the state dynamics are linear with white multiplicative noise. Therefore, linear minimum-variance filters, which have a particularly simple mechanization, are suggested. The resulting error dynamics are linear at any signal/noise ratio, unlike the classical PLL. During synchronization, and above threshold, this filter with constant gains degrades by 3 per cent in output rms phase error with respect to the classical loop. However, up to 80 per cent of the maximum possible noise improvement is obtained below threshold, where the classical loop is nonoptimum, as demonstrated by a Monte Carlo analysis. Filter mechanizations are presented for both carrier and baseband operation.

Gustafson, D. E.↗

NASA NTRS1978

Semiclassical theory of unimolecular dissociation induced by a laser field

A semiclassical nonperturbative theory of direct photodissociation in a laser field is developed in which photon absorption and dissociation are treated in a unified fashion. This is achieved by visualizing nuclear dynamics as a representative particle moving on electronic-field surfaces. Methods are described for calculating dissociation rates and probabilities by Monte Carlo selection of initial conditions and integration of classical trajectories on these surfaces. This unified theory reduces to the golden rule expression in the weak-field and short-time limits, and predicts nonlinear behavior, i.e., breakdown of the golden rule expression in intense fields. Field strengths above which lowest-order perturbation theory fails to work have been estimated for some systems. Useful physical insights provided by the electronic-field representation have been illustrated. Intense field effects are discussed which are amenable to experimental observation. The semiclassical methods used here are also applicable to multiple-surface dynamics in fieldfree unimolecular and bimolecular reactions.

Yuan, J.-M.↗

NASA NTRS1984

Computer simulation of surface and film processes

All the investigations which were performed employed in one way or another a computer simulation technique based on atomistic level considerations. In general, three types of simulation methods were used for modeling systems with discrete particles that interact via well defined potential functions: molecular dynamics (a general method for solving the classical equations of motion of a model system); Monte Carlo (the use of Markov chain ensemble averaging technique to model equilibrium properties of a system); and molecular statics (provides properties of a system at T = 0 K). The effects of three-body forces on the vibrational frequencies of triatomic cluster were investigated. The multilayer relaxation phenomena for low index planes of an fcc crystal was analyzed also as a function of the three-body interactions. Various surface properties for Si and SiC system were calculated. Results obtained from static simulation calculations for slip formation were presented. The more elaborate molecular dynamics calculations on the propagation of cracks in two-dimensional systems were outlined.

Tiller, W. A.↗

NASA NTRSDate not supplied

A Modern Load Relief Guidance Scheme for Space Launch Vehicles

Launch vehicle load relief algorithms are concerned with realizing a reduction of transient bending moments near maximum dynamic pressure. Traditional approaches to load relief typically use inner-loop acceleration feedback to reduce the wind-induced angle of attack. When implemented in the inner loop, load relief bandwidth is necessarily limited by the achievable stability margins, and when acceleration feedback is employed, by the uncertainty associated with structural modes that couple with the body-mounted accelerometer. The structure of inner loop load relief increases the dimensionality of the flight control gain and filter optimization problem. Most importantly, classical load relief laws do not take advantage of high-rate and high-accuracy GPS-aided inertial velocity data that is readily available from modern strap down IMUs. In this paper, a novel load relief guidance scheme is described that uses direct angle-of-attack feedback in a clever mechanization. The steering commands are determined by examining the wind-perturbed dynamics of a launch vehicle with respect to a gravity turn ascent trajectory. An angle of attack estimate is derived from GPS-aided inertial data and pre-launch range wind measurements, and it is shown that a reduction worst-case rigid-body loads can be realized without requiring air data. The algorithm also includes a high-rate navigation data preprocessing scheme that operates directly on the IMU delta-theta and delta-velocity measurements in order to produce a filtered acceleration estimate at the vehicle center of mass. The outer-loop guidance scheme simplifies the design process for the classical inner-loop autopilot. Algorithm performance is demonstrated using Monte Carlo analysis of a representative liquid booster in a production high fidelity launch vehicle simulation.

NESC↗