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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An introduction to financial option pricing on a qudit-based quantum computer

The financial sector is anticipated to be one of the first industries to benefit from the increased computational power of quantum computers, in areas such as portfolio optimisation and risk management to financial derivative pricing. Financial mathematics, and derivative pricing in particular, are not areas quantum physicists are traditionally trained in despite the fact that they often have the raw technical skills needed to understand such topics. On the other hand, most quantum algorithms have largely focused on qubits, which are comprised of two discrete states, as the information carriers. However, discrete higher-dimensional qudits, in addition to possibly possessing increased noise robustness and allowing for novel error correction protocols in certain hardware implementations, also have logarithmically greater information storage and processing capacity. In the current NISQ era of quantum computing, a wide array of hardware paradigms are still being studied and any potential advantage a platform offers is worth exploring. Here we introduce the basic concepts behind financial derivatives for the unfamiliar enthusiast as well as outline in great detail the quantum algorithm routines needed to price a European option, the simplest derivative. This is done within the context of a quantum computer comprised of qudits and employing the natural higher-dimensional analogue of a qubit-based pricing algorithm with its various subroutines. From these pieces, one should relatively easily be able to tailor the scheme to more complex, realistic financial derivatives. Finally, the entire stack is numerically simulated with the results demonstrating how the qudit-based scheme's payoff quickly approaches that of both a similarly-resourced classical computer as well as the true payoff, within error, for a modest increase in qudit dimension.

Bornman, Nicholas↗
DOE OSTI2025

Multi-plane moment-of-fluid interface reconstruction in 3D

Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. Here, we present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments. This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess. To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM. Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces. The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values. We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron. Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid. Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.

3D interface reconstruction↗
DOE OSTI2023

Sensitivity of Precipitation Displacement of a Simulated MCS to Changes in Land Surface Conditions

Abstract This study investigates the role of the land surface on the precipitation produced by an elevated mesoscale convective system (MCS) in Iowa between 24–25 June 2015 during the Plains Elevated Convection at Night (PECAN) field campaign. Previous studies have shown a strong effect of low‐level atmospheric moisture on the location of this MCS. A series of semi‐idealized and realistic simulations with irrigation are conducted to understand the effect of moisture perturbations on the MCS precipitation displacement. In general, numerical simulations place the MCS east of the observed location. Adding moisture directly in the low‐level atmosphere in the semi‐idealized experiments reduces this displacement error. However, experiments with perturbed soil moisture result in drying over Iowa induced by moisture flux divergence from cooler low‐level temperatures and higher surface pressure, causing the MCS to move further to the east. The irrigation impact on low‐level moisture is highly dependent on the length of simulation period. Shorter simulations on the order of days generate similar drying over Iowa but the opposite is found for month‐long simulations. Despite the lack of low‐level moistening in the perturbed soil moisture and short‐term irrigation experiments, the sensitivity to low‐level moisture is similar in all runs. More low‐level moisture generates a more convectively unstable environment with less inhibition and a lower level of free convection that leads to more rapid MCS development and a change in MCS location.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Postselection-Free Entanglement Dynamics via Spacetime Duality

The dynamics of entanglement in 'hybrid' non-unitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply postselection on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of non-unitary circuits by taking advantage of spacetime duality. This method maps the purification dynamics of a mixed state under non-unitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code formed by the mixed phase in this class of hybrid dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Evaluation of Oak Ridge National Laboratory Health Physics Research Reactor Operation Data for Critical Benchmark Creation

The Oak Ridge National Laboratory (ORNL) Health Physics Research Reactor (HPRR) was a research reactor designed and built at ORNL in 1961. The critical assembly used a highly enriched uranium and molybdenum alloy as the fuel and could be operated in steady-state or burst modes. The HPRR has recently been the object of an investigation to create a criticality benchmark. Such benchmarks are very important, as they are used primarily to show the accuracy of newly developed modeling codes and to help experimental validation and reactor licensing. The evaluated experiments considered in this paper were carried out between 1974 and 1986 from various HPRR activities such as steady-state subcritical, steady-state critical, and burst prompt super-critical operations of the reactor for dosimetry, irradiation, or training purposes. By using the HPRR experimental logbook information and the as-built drawings of the critical assembly, a highly detailed model of the HPRR was created with SCALE 6.2.4/KENO-VI, and a first version of a critical benchmark of the HPRR was developed following the International Criticality Safety Benchmark Evaluation Project (ICSBEP) guidelines for thorough description and uncertainty/sensitivity quantification. Unfortunately, in most of the evaluated experiments, the obtained difference between calculated and experimental k eff is around 1,000 pcm, corresponding to a relative error of approximately 1%, beyond the quality standards of the ICSBEP recommending a relative error below 0.1%. Moreover, the derived experimental uncertainty is high, around 4% relative, mainly due to the U-Mo fuel density uncertainty, but also from numerous other factors. For these reasons, the creation of a valuable critical benchmark from HPRR operation data is thus far compromised. In this paper, the different steps of the experiments’ evaluation are summarized, and the reasons for the experimental/calculation discrepancies and potential ways to solve them are explored. This paper also aims to remind us always to exercise considerable care when performing experimental work, and to record all the data possible for potential future uses.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Latent Space Simulation for Carbon Capture Design Optimization

The CO2 capture efficiency in solvent-based carbon capture systems (CCSs) critically depends on the gas-solvent interfacial area (IA), making maximization of IA a foundational challenge in CCS design. While the IA associated with a particular CCS design can be estimated via a computational fluid dynamics (CFD) simulation, using CFD to derive the IAs associated with numerous CCS designs is prohibitively costly. However, previous works such as Deep Fluids (Kim et al., 2019) show that large simulation speed-ups and low error are achievable by replacing CFD simulators with neural-network (NN) surrogates that mimic the CFD simulation process. This raises the possibility for a fast, accurate replacement for a CFD simulator, and thus computationally feasible IA-based CCS-design optimization. As such, here, we explore whether an existing NN-surrogate approach (and variants we develop) can successfully be applied to our complex carbon-capture CFD simulations, with the ultimate goal of obtaining a fast and accurate simulator for our CCS-design application. Our experiments build on the Deep Fluids approach and find that resulting surrogates can produce large speed ups (4000x) while maintaining IA relative errors as low as 4% on unseen CCS configurations (interpolating between configurations seen during training). Thus, despite less faithfulness to the underlying physics of the problem, NN surrogates may be a promising tool for our CCS design optimization problem. Notably, though, the Deep Fluids approach has limitations for our application (such as model non-transferability to CCS-packing changes), which we discuss. We conclude with potential directions for future work that may, like innovations we introduced here (e.g., transformer-based dynamics prediction), improve performance on our complicated dataset of CCS CFD simulations.

AI Surrogate Simulation, Carbon Capture, design op↗
NASA NTRS1972

Effects of interplanetary magnetic field on the propagation of flare-generated interplanetary shock waves.

The effects of an interplanetary magnetic field on the propagation of flare-generated interplanetary shock waves are investigated with an approximate analytical method. It is found that the interplanetary magnetic field is relatively unimportant for strong shocks as far as the shock speed and transit time are concerned. It has more significant effects for weak shocks. However, in all the situations examined, the error committed if the magnetic field is neglected is no more than 10%. It is suggested that a model without a magnetic field gives sufficiently accurate numerical results for the propagation of flare-generated shocks.

Tam, C. K. W.↗
NASA NTRS1981

Time elements in rectangular coordinates

In a paper by the second author (Nacozy, 1981), various time elements are presented for use with the Sundman time transformation. In that paper, the time elements are given in terms of Keplerian orbital elements. We give here the corresponding time elements in terms of rectangular coordinates. Extensive references are given in the previous paper and will be omitted here. We present additional numerical experiments comparing the use of time elements and time transformations together with the use of time transformations alone. The results indicate a reduction in computational error when time elements are used.

Kwok, J. H.↗
NASA NTRS1981

The NASTRAN theoretical manual

Designed to accommodate additions and modifications, this commentary on NASTRAN describes the problem solving capabilities of the program in a narrative fashion and presents developments of the analytical and numerical procedures that underlie the program. Seventeen major sections and numerous subsections cover; the organizational aspects of the program, utility matrix routines, static structural analysis, heat transfer, dynamic structural analysis, computer graphics, special structural modeling techniques, error analysis, interaction between structures and fluids, and aeroelastic analysis.

Source record↗
NASA NTRS1984

Holographic interferometry - Errors caused by thermal gradients in holographic plates

Thermal effects as sources of errors in holographic interferometry are illustrated on an example of reflection holography patterns obtained on graphite-epoxy specimens exposed before and after compressive loading. The numerical interpretation of the obtained holograms indicated some peculiar unexpected thickness changes in the specimen. In addition, some patterns showed random occurrence of zones of low and zero contrast. These discrepancies occurred usually in the first of the two exposures and were traced to thermal warping and thermal relaxation patterns caused by small temperature gradients that resulted from heat transfer to the photographic plates during their installation. Suggested precautions to minimize thermal effects include using thick holographic plates (photographic plates attached to glass plates) and insulated gloves during handling and allowing time to establish thermal equilibrium before the exposure.

Post, D.↗
NASA NTRS1990

Spectral Analysis Of Linear, Shift-Invariant Interpolants

Method of analysis provides quantitative measure of reconstruction and interpolation performances of linear, shift-invariant interpolants. Criterion of performance based upon mean-square error of difference between sampled and reconstructed functions. Applicable to reconstruction algorithms used in processing of signals and images and to types of interpolants used in numerical analysis, computer-aided design, and computer graphics.

Lansing, Donald L.↗
NASA NTRS1990

Estimation and filtering for high-precision GPS positioning applications

Estimation of GPS satellite orbits and other parameters for high-accuracy geodetic and tracking applications is carried out with a multi-satellite batch sequential pseudo-epoch state process noise filter. Both square-root information filtering and UD factorized covariance filtering and smoothing formulations are implemented in the software to enhance numerical stability. The filtering algorithms have been arranged to take advantage of sparse matrices and other characteristics of the GPS measurement scenarios. The filter includes unique error evaluation capabilities to assess effects from mismodeling. Process noise plays a key role in the orbit determination for stochastic behavior of transmitter/receiver clocks, atmospheric-induced delay fluctuations, and unmodeled spacecraft accelerations. Present GPS orbit accuracy is better than 1 m, with ground baselines determined simultaneously to relative accuracy of 1.5 parts in 10 to the 8th over several thousand km distance.

Lichten, Stephen M.↗
NASA NTRS1992

Analysis of crustal structure of Venus utilizing residual Line-of-Sight (LOS) gravity acceleration and surface topography data. A trial of global modeling of Venus gravity field using harmonic spline method

To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.

Fang, Ming↗
NASA NTRS1994

Gain weighted eigenspace assignment

This report presents the development of the gain weighted eigenspace assignment methodology. This provides a designer with a systematic methodology for trading off eigenvector placement versus gain magnitudes, while still maintaining desired closed-loop eigenvalue locations. This is accomplished by forming a cost function composed of a scalar measure of error between desired and achievable eigenvectors and a scalar measure of gain magnitude, determining analytical expressions for the gradients, and solving for the optimal solution by numerical iteration. For this development the scalar measure of gain magnitude is chosen to be a weighted sum of the squares of all the individual elements of the feedback gain matrix. An example is presented to demonstrate the method. In this example, solutions yielding achievable eigenvectors close to the desired eigenvectors are obtained with significant reductions in gain magnitude compared to a solution obtained using a previously developed eigenspace (eigenstructure) assignment method.

Davidson, John B.↗
NASA NTRS1994

Accuracy enhancements for overset grids using a defect correction approach

A defect-correction approach is investigated as a means of enhancing the accuracy of flow computations on overset grids. Typically, overset-grid techniques process and pass information only at grid boundaries. In the current approach, error corrections at all overlapped interior points are injected between grids by using a defect-correction scheme. In some cases this is found to enhance the overall accuracy of the overset-grid method. Locally refined overset grids can be used to provide an efficient solution-adaptation method. The defect correction can also be ultilized as an error-correction technique for a coarse grid by evaluating the residual using a fine base grid, but solving the implicit equations only on the coarse grid. Numerical examples include an accuracy and dissipation study of an unsteady decaying vortex flow, the flow over a NACA 0012 airfoil, and the flow over a mulit-element high-lift airfoil.

Rogers, Stuart E.↗
NASA NTRS1995

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗
NASA NTRS1998

A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

Lewis, Robert Michael↗
NASA NTRS2007

Methods for Characterizing Fine Particulate Matter Using Satellite Remote-Sensing Data and Ground Observations: Potential Use for Environmental Public Health Surveillance

This study describes and demonstrates different techniques for surfacing daily environmental / hazards data of particulate matter with aerodynamic diameter less than or equal to 2.5 micrometers (PM2.5) for the purpose of integrating respiratory health and environmental data for the Centers for Disease Control and Prevention (CDC s) pilot study of Health and Environment Linked for Information Exchange (HELIX)-Atlanta. It described a methodology for estimating ground-level continuous PM2.5 concentrations using B-Spline and inverse distance weighting (IDW) surfacing techniques and leveraging National Aeronautics and Space Administration (NASA) Moderate Resolution Imaging Spectrometer (MODIS) data to complement The Environmental Protection Agency (EPA) ground observation data. The study used measurements of ambient PM2.5 from the EPA database for the year 2003 as well as PM2.5 estimates derived from NASA s satellite data. Hazard data have been processed to derive the surrogate exposure PM2.5 estimates. The paper has shown that merging MODIS remote sensing data with surface observations of PM2.5 not only provides a more complete daily representation of PM2.5 than either data set alone would allow, but it also reduces the errors in the PM2.5 estimated surfaces. The results of this paper have shown that the daily IDW PM2.5 surfaces had smaller errors, with respect to observations, than those of the B-Spline surfaces in the year studied. However the IDW mean annual composite surface had more numerical artifacts, which could be due to the interpolating nature of the IDW that assumes that the maxima and minima can occur only at the observation points. Finally, the methods discussed in this paper improve temporal and spatial resolutions and establish a foundation for environmental public health linkage and association studies for which determining the concentrations of an environmental hazard such as PM2.5 with good accuracy levels is critical.

Al-Hamdan, Mohammad Z.↗