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At least 289 records · Page 16

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Tractable minor-free generalization of planar zero-field Ising models

In this work, we present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive 'gluing' of planar and O(1)-sized components and subsets of at most three vertices into a tree. The polynomial time algorithm of the dynamic programming type for solving exact inference (computing partition function) and exact sampling (generating i.i.d. samples) consists of sequential application of an efficient (for planar) or brute-force (for O(1)-sized) inference and sampling to the components as a black box. To illustrate the utility of the new family of tractable graphical models, we first build a polynomial algorithm for inference and sampling of zero-field Ising models over K 33 -minor-free topologies and over K 5 -minor-free topologies—both of which are extensions of the planar zero-field Ising models—which are neither genus- nor treewidth-bounded. Second, we empirically demonstrate an improvement in the approximation quality of the NP-hard problem of inference over the square-grid Ising model in a node-dependent nonzero 'magnetic' field.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with classical projection-based model reduction techniques. Thus, the proposed approach learns models that are guaranteed to have the well-studied properties of reduced models known from model reduction, without requiring full knowledge of the governing equations and without requiring the operators of the high-dimensional systems. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed pre-asymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. In conclusion, the numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

Vibrations of twisted rotating blades

The literature dealing with vibrations of turbomachinery blades is voluminous, but the vast majority of it treats the blades as beams. In a previous paper a two-dimensional analytical procedure was developed and demonstrated on simple models of blades having camber. The procedure utilizes shallow shell theory along with the classical Ritz method for solving the vibration problem. Displacement functions are taken as algebraic polynomials. In the present paper the method is demonstrated on blade models having camber. Comparisons are first made with results in the literature for nonrotating twisted plates and various disagreements between results are pointed out. A method for depicting mode shape information is demonstrated, permitting one to examine all three components of displacement. Finally, the analytical procedure is demonstrated on rotating twisted blade modes, both without and with camber.

Leissa, A. W.↗

DOE OSTI2026

Jordan–Wigner Transformation for the Description of Strong Correlation in Fermionic Systems

Seniority is a useful way of organizing Hilbert space for strongly correlated systems. The exact zero-seniority wave function, doubly occupied configuration interaction (DOCI), provides accurate results (given the right orbitals) for many strongly correlated electronic systems but has a combinatorial computational cost. In many cases, pair coupled cluster doubles provide a polynomial-cost approximation that closely reproduces the energies of DOCI, but it breaks down in some cases and, as shown herein, it does not provide particularly good density matrices. In this article, we demonstrate that by using the Jordan–Wigner transformation to turn the seniority zero problem back into a Fermionic one, we can provide mean-field variational results of DOCI quality for the Hubbard model and a few small molecular dissociation examples, with polynomial cost, both for the energies and for density matrices, all while being protected from collapse. This success is rooted in the proof we provide, showing that the Hartree–Fock wave function on the Jordan–Wigner-transformed Hamiltonian transforms back to variational coupled cluster doubles in the seniority zero representation, but restricted to have determinant rather than permanent amplitude coefficients, without compromising its overall accuracy.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS2016

Applying Simulated Annealing to Problems in Model-Based Diagnosis

Generating all diagnoses is computationally intractable. Therefore, many of the state-of-the-art approaches are incomplete. Quantum computers may however offer a solution. The first commercially available quantum computer is being used to minimize polynomials that are difficult for classical simulated annealing but easy for quantum annealing. All problems in Model-based Diagnosis (MBD) can be transformed into a polynomial minimization problem, allowing one to apply a quantum algorithm called quantum annealing to solve MBD problems. To better understand the need for this quantum approach, we designed two simulated annealingdiagnostic algorithms tailored to run on a polynomial representation of MBD. These algorithms differ on their policy for random neighborhood variable selection. In addition, enhanced metrics were devised to provide more diagnostic coverage. Finally, these two simulated annealing algorithms were analyzed and empirically evaluated and compared against state-of-the-art probabilistic methods for MBD such as SAFARI using ISCAS-85.

Simulated annealing↗

DOE OSTI2022

Time domain probabilistic seismic risk analysis using ground motion prediction equations of Fourier amplitude spectra

Modeling of Fourier amplitude spectra (FAS) of seismic motions has gained much attention in engineering seismology. In the past few years, several ground motion prediction equations (GMPEs) and inter-frequency correlation structure of FAS have been established. Due to many preferable characteristics of FAS, probabilistic seismic hazard/risk analysis is rapidly changing from ergodic, spectrum acceleration Sa(T 0 )-based approach to non-ergodic, site-specific, FAS-based approach. This paper presents time domain intrusive framework for probabilistic seismic risk analysis using GMPE of FAS. Herein, methodology for time domain stochastic ground motion modeling based on GMPEs of FAS is presented in some detail. The simulated uncertain motions are modeled as a random process and represented by polynomial chaos Karhunen-Loève expansion. The random process excitations are further propagated into the uncertain structural system using Galerkin stochastic finite element method (SFEM). Probabilistic evolution of structural response is solved, and such solution is used to develop seismic risk for any damage state. The presented framework is illustrated through seismic risk analysis of a four-story building subjected to possible earthquakes from two strike slip faults. The influences of the epistemic uncertainties in source stress drop Δσ and site attenuation κ0 on seismic risk are investigated. The need for non-ergodic seismic risk analysis with source-specific and site specific characterizations is emphasized.

58 GEOSCIENCES↗

DOE OSTI2021

Quantum Algorithm for High Energy Physics Simulations

Simulating quantum field theories is a flagship application of quantum computing. However, calculating experimentally relevant high energy scattering amplitudes entirely on a quantum computer is prohibitively difficult. It is well known that such high energy scattering processes can be factored into pieces that can be computed using well established perturbative techniques, and pieces which currently have to be simulated using classical Markov chain algorithms. These classical Markov chain simulation approaches work well to capture many of the salient features, but cannot capture all quantum effects. To exploit quantum resources in the most efficient way, we introduce a new paradigm for quantum algorithms in field theories. This approach uses quantum computers only for those parts of the problem which are not computable using existing techniques. In particular, we develop a polynomial time quantum final state shower that accurately models the effects of intermediate spin states similar to those present in high energy electroweak showers with a global evolution variable. The algorithm is explicitly demonstrated for a simplified quantum field theory on a quantum computer.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Exponential Improvements in the Simulation of Lattice Gauge Theories Using Near-Optimal Techniques

We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2), and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and logical qubit counts for Hamiltonian simulation. We find a reduction of up to 25 orders of magnitude in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories relevant to the standard model. This improvement results from our algorithm having polynomial scaling with the number of colors in the gauge theory, achieved by utilizing oracle constructions relying on the sparsity of physical operators, in contrast to the exponential scaling seen in state-of-the-art Trotter methods, which employ explicit mappings onto Pauli operators. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of simulating fundamental interactions, bringing it in step with resources required for first-principles quantum simulation of chemistry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Calorimetric study of skutterudite (CoAs2.92) and heazlewoodite (Ni3S2)

Abstract Nickel and cobalt arsenides, sulfarsenides, and sulfides occur in many hydrothermal ore deposits, but their thermodynamic properties are not well known, in some cases not known at all. In this work, we determined a full set of thermodynamic properties for heazlewoodite and skutterudite. Both phases were synthesized in evacuated silica tubes at elevated temperatures, and electron microprobe analyses gave their compositions as Ni3S2 and CoAs2.92, respectively. Enthalpies of formation were measured by high-temperature oxide-melt solution calorimetry. The reference phases were pure elements, thus eliminating any systematic errors related to such phases. The enthalpies of formation at T = 298.15 K and P = 105 Pa are –216.0 ± 8.4(2σ) and –88.2 ± 6.1 kJ·mol−1 for Ni3S2 and CoAs2.92, respectively. Entropies were calculated from low-temperature heat capacity (CP) data from relaxation (PPMS) calorimetry and are 133.8 ± 1.6 and 106.4 ± 1.3 J·mol–1·K–1, respectively. The calculated Gibbs free energies of formation are –210.0 ± 8.4 and –79.9 ± 6.2 kJ·mol−1 for Ni3S2 and CoAs2.92, respectively. The PPMS CP data, together with a set of differential scanning calorimetry measurements, were used to derive CP polynomials up to 700 K with the Kieffer model based on previously published frequencies of acoustic and optic modes. Equilibrium constants for selected reactions with an aqueous phase were calculated up to 700 K. Geochemical modeling in these systems, however, should await until more reliable data for other phases from the system Co-Ni-As-S are available.

Geochemistry & Geophysics↗

NASA NTRS1981

Development of Great Lakes algorithms for the Nimbus-G coastal zone color scanner

A series of experiments in the Great Lakes designed to evaluate the application of the Nimbus G satellite Coastal Zone Color Scanner (CZCS) were conducted. Absorption and scattering measurement data were reduced to obtain a preliminary optical model for the Great Lakes. Available optical models were used in turn to calculate subsurface reflectances for expected concentrations of chlorophyll-a pigment and suspended minerals. Multiple nonlinear regression techniques were used to derive CZCS water quality prediction equations from Great Lakes simulation data. An existing atmospheric model was combined with a water model to provide the necessary simulation data for evaluation of the preliminary CZCS algorithms. A CZCS scanner model was developed which accounts for image distorting scanner and satellite motions. This model was used in turn to generate mapping polynomials that define the transformation from the original image to one configured in a polyconic projection. Four computer programs (FORTRAN IV) for image transformation are presented.

Tanis, F. J.↗

NASA NTRSDate not supplied

COBRA-DDP: Trajectory Generation and Collision Avoidance Augmentations for eVTOL Vehicles

This paper presents a receding horizon model predictive control variation of the combined Bernstein polynomial optimal reciprocal collision avoidance (ORCA) differential dynamic programming (COBRA-DDP) algorithm for AAM vehicles. Collision avoidance in combination with effective trajectory replanning are expected to be core components of AAM vehicles operating within a crowded airspace. This environment necessitates the use of real-time trajectory planning algorithms that are capable of planning around large amounts of stationary and moving obstacles. Previous work on COBRA-DDP demonstrated the capability of the algorithm to produce dynamically feasible trajectories for AAM vehicles and general collision avoidance. This paper improves upon the previous work by increasing the number of stationary and moving obstacles, implementing a variation of COBRA-DDP that lends itself to real-time application. These advancements are demonstrated on a vertical takeoff and landing (VTOL) vehicle simulation with highly nonlinear vehicle dynamics.

COBRA-DDP↗

NASA NTRSDate not supplied

COBRA-DDP: Trajectory Generation and Collision Avoidance Augmentations for eVTOL Vehicles

COBRA-DDP↗

NASA NTRS2023

The Dielectric Constant of Sea Water and Extension to High Salinity

Accurate knowledge of the dielectric constant of sea water is important for remote sensing of surface parameters such as sea surface temperature (SST) and sea surface salinity (SSS). The advent of sensors in space, SMOS [1], Aquarius [2] and SMAP [3] capable of measuring SSS motivated modern measurements [4,5] and modelling [5,6] of the dielectric constant at L-band (1.4 GHz). In the past, the range of salinity included in the data used to create these models has been restricted to values typically encountered in the open ocean (e.g., less than 40 psu). However, there are many smaller water bodies with much higher salinity. Notable examples are the Great Salt Lake in Utah with salinity on the order of 180 psu and Garabogazköl lagoon in Turkmenistan with even higher salinity. Unfortunately, existing models for the dielectric constant can’t necessarily just be extended to higher values of salinity. The problem is that the polynomials in salinity and temperature used to represent the unknown parameters in the models are not constrained outside the range of SSS and SST used to determine their coefficients. While the models for the dielectric constant may be very good within that range, outside that range they can lead to unrealistic behavior. Research is underway to develop a model that represents the dielectric constant well over the ocean and behaves well at high salinity. In preparation for possible wideband remote sensing of salinity [7,8 ,9], the laboratory measurements made at 1.413 GHz [4,5] are being repeated at 0.707 GHz (P-band) and the plan is to include values of high salinity (50, 100, 150 psu).

D.M. Le Vine↗

DOE OSTI2024

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2006

An improved method for precise automatic co-registration of moderate and high-resolution spacecraft imagery

Improvements to the automated co-registration and change detection software package, AFIDS (Automatic Fusion of Image Data System) has recently completed development for and validation by NGA/GIAT. The improvements involve the integration of the AFIDS ultra-fine gridding technique for horizontal displacement compensation with the recently evolved use of Rational Polynomial Functions/ Coefficients (RPFs/RPCs) for image raster pixel position to Latitude/Longitude indexing. Mapping and orthorectification (correction for elevation effects) of satellite imagery defies exact projective solutions because the data are not obtained from a single point (like a camera), but as a continuous process from the orbital path. Standard image processing techniques can apply approximate solutions, but advances in the state-of-the-art had to be made for precision change-detection and time-series applications where relief offsets become a controlling factor. The earlier AFIDS procedure required the availability of a camera model and knowledge of the satellite platform ephemeredes. The recent design advances connect the spacecraft sensor Rational Polynomial Function, a deductively developed model, with the AFIDS ultrafine grid, an inductively developed representation of the relationship raster pixel position to latitude /longitude. As a result, RPCs can be updated by AFIDS, a situation often necessary due to the accuracy limits of spacecraft navigation systems. An example of precision change detection will be presented from Quickbird.

co-registration↗

DOE OSTI2022

Analytic error analysis of cross section interpolation methods in nodal diffusion codes - I : Theory

This paper discusses two cross section interpolation methods commonly found in popular nodal codes; the partial derivatives and multiple tables models. The motivation for choosing a model, and thus a case matrix structure, is a trade off between accuracy and computational cost. Due to decades of experience, there are default structures that are sufficient for current light water reactor analysis. However, this is not necessarily the case for advanced reactor designs. Therefore, it is advantageous to understand the sources of error in cross section interpolation models so that the quality of a case matrix may be improved. A mathematical framework for these models is presented in this work that provides a more rigorous connection between the nuclear engineering field's cross section interpolation methods and the broader mathematical field of function approximation. The two cross section models examined in this paper were found to utilize Lagrange interpolation and are a subset of Lagrange tensor products. Classical results of Lagrange polynomial error analysis were then applied to the partial derivative and multiple tables models to derive expressions for the total point-wise error. The analytical results classify the total error into two parts: the model form error and interpolation error. Finally, based on our observations, a better foundation for improving the quality of a case matrix is proposed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Peridynamics and surrogate modeling of pressure-driven well stimulation

In this work we use the peridynamics theory of solid mechanics to simulate fracture in an annular rock domain subject to an in-situ stress and create surrogate models that predict the area of the resulting cracks. Peridynamics is a non-local formulation of continuum mechanics that naturally accommodates material discontinuities. Furthermore, unlike other fracture modeling techniques there is no need to provide information about the crack path. We utilize the peridynamics code Peridigm and take a two-stage approach to fracture modeling. First an implicit solve is performed to compute the in-situ stress state. We then execute an explicit solve where a pressure loading designed to emulate fluid-driven hydraulic fracture is applied at the borehole and transmitted to the pre-stressed rock. We present results from polynomial and single and multi-level Gaussian process surrogate models constructed from a sampling study of the peridynamics model. The surrogates predict crack area given a measure of the in-situ stress anisotropy and rise time and amplitude of the pressure loading. These surrogates take a minuscule fraction of peridynamics model's running time to evaluate and are a step towards enabling advanced optimization and uncertainty quantification workflows that require many model evaluations.

42 ENGINEERING↗

NASA NTRSDate not supplied

Cryogenic Extension of NASA Species Polynomials Using Hydrogen and Oxygen at Stoichiometry

The Helmholtz free energy for a mixture has been used in many chemistry and combustion studies for mixtures. An approach is described where polynomial fits intended for a thermally perfect ideal gases can be modified and implemented into a Helmholtz free energy model, such as those used by NIST in their REFPROP program. However, the limitation of the polynomial fits must be respected and should only used in a valid temperature interval where the flow field can be treated as a thermally perfect ideal gas when these species are present. This approach can allow a CFD simulation to have cryogenic regions of a flow field where high fidelity cryogenic species models are needed and allows for the use of species in other areas at higher temperatures where combustion species do not have such a model available or is not needed. Presented in the paper are CFD 1D detonation wave and species mass fraction simulation results which have cryogenic upstream conditions of Hydrogen and Oxygen at stoichiometry.

Combustion↗