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DOE OSTI2023

AlignOT: An Optimal Transport Based Algorithm for Fast 3D Alignment With Applications to Cryogenic Electron Microscopy Density Maps

Aligning electron density maps from Cryogenic electron microscopy (cryo-EM) is a first key step for studying multiple conformations of a biomolecule. As this step remains costly and challenging, with standard alignment tools being potentially stuck in local minima, we propose here a new procedure, called AlignOT, which relies on the use of computational optimal transport (OT) to align EM maps in 3D space. By embedding a fast estimation of OT maps within a stochastic gradient descent algorithm, our method searches for a rotation that minimizes the Wasserstein distance between two maps, represented as point clouds. Here, we quantify the impact of various parameters on the precision and accuracy of the alignment, and show that AlignOT can outperform the standard local alignment methods, with an increased range of rotation angles leading to proper alignment. We further benchmark AlignOT on various pairs of experimental maps, which account for different types of conformational heterogeneities and geometric properties. As our experiments show good performance, we anticipate that our method can be broadly applied to align 3D EM maps.

3D alignment↗

DOE OSTI2019

A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data are available. In this paper, we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion. We use an alternating direction method to identify new sets of random variables through iterative rotations so the new representation of the uncertainty is sparser. Consequently, we increase both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the previously developed iterative method to enhance the sparsity of Hermite polynomial expansion is a special case of this general framework. Moreover, we use Legendre and Chebyshev polynomial expansions to demonstrate the effectiveness of this method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

Yang, Xiu↗

DOE OSTI2020

PAL Experimental Report Form

We constructed the first simultaneous dark- and bright-field X-ray microscope in this experiment, coupling it to simultaneous measurements of the wide-angle Xray diffraction, and the XFEL pulse intensity and energy spectrum on each shot. This experiment established proof of concept for this new advanced measurement technique and demonstrated DFXM at an XFEL for the first time. Within this complex experiment, we also acquired data that advanced our research goals within materials science and mathematics. These included: A preliminary study of how local effects reduce the X-ray damage threshold in diamond; A preliminary study of how X-ray radiation imparts heat into materials based on irreversible phase transitions that occur in boric acid with increasing temperature (based on hydration); A study of X-ray radiation damage from ultrafast thermal cycling and nonthermal melting in bismuth selenide; We also began developing software to automate alignment of compound refractive lenses (CRLs) using stochastic Nelder-Mead optimization methods. This work will expedite and improve the accuracy of alignments for many future experiments using CRLs.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Scalable Second Order Optimization for Machine Learning

Many machine learning (ML) training tasks are essentially optimization processes that would at first glance appear eminently parallelizable and scalable. However, effective acceleration of these tasks with scalable parallel hardware has proven to be elusive. While standard methods for machine learning, e.g., stochastic gradient descent (SGD) for DNNs, tend to be resource efficient, they appear to be fundamentally sequential in nature.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1983

Identification of helicopter rotor dynamic models

A recursive, extended Kalman-filter approach is applied to the identifiction of rotor damping levels of representative helicopter dynamic systems. The general formulation of the approach is presented in the context of a typically posed stochastic estimation problem, and the method is analytically applied to determining the damping levels of a coupled rotor-body system. The identified damping covergence characteristics are studied for sensitivity to both constant-coefficient and periodic-coefficient measurement models, process-noise covariance levels, and specified initial estimates of the rotor-system damping. A second application of the method to identifying the plant model for a highly damped, isolated flapping blade with a constant-coefficient state model (hover) and a periodic-coefficient state model (forward flight) is also investigated. The parameter-identification capability is evaluated for the effect of periodicity on the plant model coefficients and the influence of different measurement noise levels.

Molusis, J. A.↗

NASA NTRS1999

External Sources of Water for Mercury's Putative Ice Deposits

Radar images have revealed the possible presence of ice deposits in Mercury's polar regions. Although thermal models indicate that water ice can be stable in permanently shaded regions near Mercury's poles, the ultimate source of the water remains unclear. We use stochastic models and other theoretical methods to investigate the role of external sources in supplying Mercury with the requisite amount of water. By extrapolating the current terrestrial influx of interplanetary dust particles to that at Mercury, we find that continual micrometeoritic bombardment of Mercury over the last 3.5 byr could have resulted in the delivery of (3-60) x 10(exp 16) grams of water ice to the permanently shaded regions at Mercury's poles (equivalent to an average ice thickness of 0.8-20 m). Erosion by micrometeoritic impact on exposed ice deposits could reduce the above value by about a half. For comparison, the current ice deposits on Mercury are believed to be somewhere between approx. 2 and 20 m thick. Using a Monte Carlo model to simulate the impact history of Mercury, we find that asteroids and comets can also deliver an amount of water consistent with the observations. Impacts from Jupiter-family comets over the last 3.5 billion years can supply (0.1-200) x 10(exp 16) grams of water to Mercury's polar regions (corresponding to ice deposits 0.05-60 m thick), Halley-type comets can supply (0.2-20) x 10(exp 16) grams of water to the poles (0.07-7 m of ice), and asteroids can provide (0.4-20) x 10(exp 16) grams of water to the poles (0.1-8 m of ice). Although all these external sources are nominally sufficient to explain the estimated amount of ice currently at Mercury's poles, impacts by a few large comets and/or asteroids seem to provide the best explanation for both the amount and cleanliness of the ice deposits on Mercury. Despite their low population estimates in the inner solar system, Jupiter-family comets are particularly promising candidates for delivering water to Mercury because they have a larger volatile content than asteroids and more favorable orbital and impact characteristics than Halley-type comets.

Moses, Julianne I.↗

NASA NTRS2004

Sensitivity of Simulated Warm Rain Formation to Collision and Coalescence Efficiencies, Breakup, and Turbulence: Comparison of Two Bin-Resolved Numerical Models

Numerical models that resolve cloud particles into discrete mass size distributions on an Eulerian grid provide a uniquely powerful means of studying the closely coupled interaction of aerosols, cloud microphysics, and transport that determine cloud properties and evolution. However, such models require many experimentally derived paramaterizations in order to properly represent the complex interactions of droplets within turbulent flow. Many of these parameterizations remain poorly quantified, and the numerical methods of solving the equations for temporal evolution of the mass size distribution can also vary considerably in terms of efficiency and accuracy. In this work, we compare results from two size-resolved microphysics models that employ various widely-used parameterizations and numerical solution methods for several aspects of stochastic collection.

Fridlind, Ann↗

DOE OSTI2018

On random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability

This paper is devoted to the study of the solvability of random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability. The notions of random fuzzy variables and fuzzy stochastic processes are developed for multivariable functions. The existence and uniqueness of two types of integral solutions generated from Darboux problem for nonlinear wave equations are proved using the successive approximations method and Gronwall’s inequality for stochastic processes. The continuous dependence on the data, the boundedness, and the stability with probability one of integral solutions are established to confirm the well posedness of our model. Some computational examples are presented to illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS2016

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗

NASA NTRS2016

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗

DOE OSTI2015

Numerical Uncertainty Estimation for Stochastic Particle-in-Cell Simulations Applied to Verification and Validation.

Systematic veri cation and validation (V&V) is necessary to establish the credibility for high consequence simulations. In this paper, we focus on a radiation-induced plasma experimental validation exercise for simulations which uses both numerical error estimation and input parameter uncertainty quanti cation to provide a direct comparison between Particle-In-Cell (PIC) plasma simulations and experiments. This approach demonstrates how careful validation can uncover missing physics in the simulation. Three di erent validation examples are shown; a vacuum space charge limited cavity, a gas lled space charge limited cavity, and a vacuum non space charge limited cavity. Two of the example are picked to show the importance of error estimation in uncovering inaccuracy/incomplete simulation models. We also report on a newly-developed numerical error estimation approach, StREEQ, which is a notable improvement to past approaches. In the StREEQ approach, a multi- tting scheme based on L 1 , L 2 , and L$\infty$ error norms and alternate weightings is used to propagate uncertainties in the relative importance of outliers and coarse/re ned discretization levels. Bootstrap sampling is used to represent the stochasticity in the response data. The resulting method appears to robustly and conservatively predict the fully-converged response within estimated numerical error bounds for stochastic simulations. The StREEQ approach is demonstrated on two related prototype electron diode problems, and preliminary results are reported for a radiation-induced plasma simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2007

Stochastic Characterization of Flutter using Historical Wind Tunnel Data

Methods for predicting the onset of flutter during an experiment are traditionally applied treating the data as deterministic values. Uncertainty and variation in the data is often glossed over by using best-fit curves to represent the information. This paper applies stochastic treatments to wind tunnel data obtained for the Piezoelectric Aeroelastic Response Tailoring Investigation model. These methods include modal amplitude tracking, modal frequency tracking and several applications of the flutter margin method. The flutter margin method was developed by Zimmerman and Weissenburger, and extended by Poirel, Dunn and Porter to incorporate uncertainty. Much of the current work follows the future work recommendations of Poirel, Dunn and Porter.

Heeg, Jennifer↗

DOE OSTI2015

Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields

A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Bifurcation characteristics and safe basin of MSMA microgripper subjected to stochastic excitation

A kind of magnetic shape memory alloy (MSMA) microgripper is proposed in this paper, and its nonlinear dynamic characteristics are studied when the stochastic perturbation is considered. Nonlinear differential items are introduced to explain the hysteretic phenomena of MSMA, and the constructive relationships among strain, stress, and magnetic field intensity are obtained by the partial least-square regression method. The nonlinear dynamic model of a MSMA microgripper subjected to in-plane stochastic excitation is developed. The stationary probability density function of the system’s response is obtained, the transition sets of the system are determined, and the conditions of stochastic bifurcation are obtained. The homoclinic and heteroclinic orbits of the system are given, and the boundary of the system’s safe basin is obtained by stochastic Melnikov integral method. The numerical and experimental results show that the system’s motion depends on its parameters, and stochastic Hopf bifurcation appears in the variation of the parameters; the area of the safe basin decreases with the increase of the stochastic excitation, and the boundary of the safe basin becomes fractal. The results of this paper are helpful for the application of MSMA microgripper in engineering fields.

36 MATERIALS SCIENCE↗

NASA NTRS1973

Solution of the stochastic control problem in unbounded domains.

Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more efficient than existing methods of solution.

Robinson, P.↗

DOE OSTI2014

Evaluating Kuala Lumpur stock exchange oriented bank performance with stochastic frontiers

Banks play an essential role in the economic development and banks need to be efficient; otherwise, they may create blockage in the process of development in any country. The efficiency of banks in Malaysia is important and should receive greater attention. This study formulated an appropriate stochastic frontier model to investigate the efficiency of banks which are traded on Kuala Lumpur Stock Exchange (KLSE) market during the period 2005–2009. All data were analyzed to obtain the maximum likelihood method to estimate the parameters of stochastic production. Unlike the earlier studies which use balance sheet and income statements data, this study used market data as the input and output variables. It was observed that banks listed in KLSE exhibited a commendable overall efficiency level of 96.2% during 2005–2009 hence suggesting minimal input waste of 3.8%. Among the banks, the COMS (Cimb Group Holdings) bank is found to be highly efficient with a score of 0.9715 and BIMB (Bimb Holdings) bank is noted to have the lowest efficiency with a score of 0.9582. The results also show that Cobb-Douglas stochastic frontier model with truncated normal distributional assumption is preferable than Translog stochastic frontier model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗