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At least 91 records · Page 5

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗

Solar photochemistry using the space shuttle

A continuing source of difficulty in cometary astrophysics is understanding the origin of C2, C3, NH and CO(+) species in comets. An experiment is proposed to investigate these problems by continuously releasing suspected parent gases from the space shuttle and using a dye laser to selectively excite fragments produced as a result of solar photochemical decomposition of the molecules. The backscattered fluorescence is gathered by a telescope, spectrally filtered, and measured as a function of time after the laser pulse.

Jackson, W. M.↗

Quantum space, quantum time, and relativistic quantum mechanics

We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum constraints that lead to emergent features of temporal and spatial translations. Unlike the conventional treatment, we show that Klein-Gordon and Dirac equations in relativistic quantum mechanics can be unified in our paradigm by applying relativistic dispersion relations to eigenvalues rather than treating them as operator-valued equations. With time and space being treated on an equal footing in Hilbert space, we show symmetry transformations to be implemented by unitary basis changes in Hilbert space, giving them a stronger quantum mechanical footing. Global symmetries, such as Lorentz transformations, modify the decomposition of Hilbert space; and local symmetries, such as U(1) gauge symmetry are diagonal in coordinate basis and do not alter the decomposition of Hilbert space. Here, we briefly discuss extensions of this paradigm to quantum field theory and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Application of the Hilbert-Huang Transform to the Search for Gravitational Waves

We present the application of a novel method of time-series analysis, the Hilbert-Huang Transform, to the search for gravitational waves. This algorithm is adaptive and does not impose a basis set on the data, and thus the time-frequency decomposition it provides is not limited by time-frequency uncertainty spreading. Because of its high time-frequency resolution it has important applications to both signal detection and instrumental characterization. Applications to the data analysis of the ground and space based gravitational wave detectors, LIGO and LISA, are described.

Camp, Jordan B.↗

Quantifying Errors in TRMM-Based Multi-Sensor QPE Products Over Land in Preparation for GPM

Determining uncertainties in satellite-based multi-sensor quantitative precipitation estimates over land of fundamental importance to both data producers and hydro climatological applications. ,Evaluating TRMM-era products also lays the groundwork and sets the direction for algorithm and applications development for future missions including GPM. QPE uncertainties result mostly from the interplay of systematic errors and random errors. In this work, we will synthesize our recent results quantifying the error characteristics of satellite-based precipitation estimates. Both systematic errors and total uncertainties have been analyzed for six different TRMM-era precipitation products (3B42, 3B42RT, CMORPH, PERSIANN, NRL and GSMap). For systematic errors, we devised an error decomposition scheme to separate errors in precipitation estimates into three independent components, hit biases, missed precipitation and false precipitation. This decomposition scheme reveals hydroclimatologically-relevant error features and provides a better link to the error sources than conventional analysis, because in the latter these error components tend to cancel one another when aggregated or averaged in space or time. For the random errors, we calculated the measurement spread from the ensemble of these six quasi-independent products, and thus produced a global map of measurement uncertainties. The map yields a global view of the error characteristics and their regional and seasonal variations, reveals many undocumented error features over areas with no validation data available, and provides better guidance to global assimilation of satellite-based precipitation data. Insights gained from these results and how they could help with GPM will be highlighted.

Peters-Lidard, Christa D.↗

Monitoring Phenology as Indicator for Timing of Nutrient Inputs in Northern Gulf Watersheds

Nutrient over-enrichment defined by the U.S. Environmental Protection Agency as the anthropogenic addition of nutrients, in addition to any natural processes, causing adverse effects or impairments to the beneficial uses of a water body has been identified as one of the most significant environmental problems facing sensitive estuaries and coastal waters. Understanding the timing of nutrient inputs into those waters through remote sensing observables helps define monitoring and mitigation strategies. Remotely sensed data products can trace both forcings and effects of the nutrient system from landscape to estuary. This project is focused on extracting nutrient information from the landscape. The timing of nutrients entering coastal waters from the land boundary is greatly influenced by hydrologic processes, but can also be affected by the timing of nutrient additions across the landscape through natural or anthropogenic means. Non-point source nutrient additions to watersheds are often associated with specific seasonal cycles, such as decomposition of organic materials in fall and winter or addition of fertilizers to crop lands in the spring. These seasonal cycles or phenology may in turn be observed through the use of satellite sensors. Characterization of the phenology of various land cover types may be of particular interest in Gulf of Mexico estuarine systems with relatively short pathways between intensively managed systems and the land/estuarine boundary. The objective of this study is to demonstrate the capability of monitoring phenology of specific classes of land, such as agriculture and managed timberlands, at a refined watershed level. The extraction of phenological information from the Moderate Resolution Imaging Spectroradiometer (MODIS) data record is accomplished using analytical tools developed for NASA at Stennis Space Center: the Time Series Product Tool and the Phenological Parameters Estimation Tool. MODIS reflectance data (product MOD09) were used to compute the Normalized Difference Vegetation Index, which is sensitive to changes in vegetation canopies. The project team is working directly with the Mississippi Department of Environmental Quality to understand end-user requirements for this type of information product. Initial focus areas are identification of time frames for pre-plant fertilizer applications (prior to start of season), side-dress fertilizer applications (during rapid green-up), and periods of plant decomposition (during and after senescence). Prototypical maps of phenological stages related to these time frames have been generated for watersheds in the northern Gulf of Mexico. Where feasible, these maps have been compared to existing in situ nutrient monitoring data, but the in situ data is temporally sparse (monthly frequency or less), which makes interpretation challenging. Future work will include integrating effects of rainfall and seeking couplings with estuarine remote sensing.

Ross, Kenton W.↗

Multi-Scale Temporal Patterns in Stream Biogeochemistry Indicate Linked Permafrost and Ecological Dynamics of Boreal Catchments

Temporal patterns in stream chemistry provide integrated signals describing the hydrological and ecological state of whole catchments. However, stream chemistry integrates multi-scale signals of processes occurring in both the catchment and stream. Deconvoluting these signals could identify mechanisms of solute transport and transformation and provide a basis for monitoring ecosystem change. Here, we applied trend analysis, wavelet decomposition, multivariate autoregressive state-space modeling, and analysis of concentration-discharge relationships to assess temporal patterns in high-frequency (15 min) stream chemistry from permafrost-influenced boreal catchments in Interior Alaska at diel, storm, and seasonal time scales. We compared catchments that varied in spatial extent of permafrost to identify characteristic biogeochemical signals. Catchments with higher spatial extents of permafrost were characterized by increasing nitrate concentration through the thaw season, an abrupt increase in nitrate and fluorescent dissolved organic matter (fDOM) and declining conductivity in late summer, and flushing of nitrate and fDOM during summer rainstorms. In contrast, these patterns were absent, of lower magnitude, or reversed in catchments with lower permafrost extent. Solute dynamics revealed a positive influence of permafrost on fDOM export and the role of shallow, seasonally dynamic flowpaths in delivering solutes from high-permafrost catchments to streams. Lower spatial extent of permafrost resulted in static delivery of nitrate and limited transport of fDOM to streams. Shifts in concentration-discharge relationships and seasonal trends in stream chemistry toward less temporally dynamic patterns might therefore indicate reorganized catchment hydrology and biogeochemistry due to permafrost thaw.

54 ENVIRONMENTAL SCIENCES↗

Theoretically and practically efficient parallel nucleus decomposition

This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves a work complexity matching the best sequential algorithm while also having low depth (parallel running time), which significantly improves upon the only existing parallel nucleus decomposition algorithm (Sariyüce et al. , PVLDB 2018). The key to the theoretical efficiency of our algorithm is a new lemma that bounds the amount of work done when peeling cliques from the graph, combined with the use of a theoretically-efficient parallel algorithms for clique listing and bucketing. We introduce several new practical optimizations, including a new multi-level hash table structure to store information on cliques space-efficiently and a technique for traversing this structure cache-efficiently. On a 30-core machine with two-way hyper-threading on real-world graphs, we achieve up to a 55x speedup over the state-of-the-art parallel nucleus decomposition algorithm by Sariyüce et al. , and up to a 40x self-relative parallel speedup. We are able to efficiently compute larger nucleus decompositions than prior work on several million-scale graphs for the first time.

Computer Science↗

Decomposition of Electron Ionization Mass Spectra for Space Application Using a Monte-Carlo approach

Rationale: Quadrupole mass spectrometers equipped with an electron ionization (EI) sources have been widely used in space exploration to investigate the composition of planetary surfaces and atmospheres. However, the complexity of the samples and the minimal calibration for the fragmentation of molecules in the ionization chambers have prevented the deconvolution of the majority of the mass spectra obtained at different targets, thus limiting the determination of the exact composition of the samples analyzed. We propose a Monte‐Carlo approach to solve this issue mathematically. Methods: We decomposed simulated mass spectra of mixtures acquired with unit resolving power mass spectrometers and EI sources into the sum of the single components fragmentation patterns weighted by their relative concentration using interior‐point least‐square fitting. To fit compounds with poorly known fragmentation patterns, we used a Monte‐Carlo method to vary the intensity of individual fragment ions. We then decomposed the spectrum thousands of times to obtain a statistical distribution. Results: By performing the deconvolution on a mixture of seven different molecules with interfering fragmentation patterns (H2O, O2, CH4, Ar, N2, C2H4, and C2H6) we show that this approach retrieves the mixing ratio of the individual components more accurately than regular mass spectra decomposition methods that rely on fragmentation patterns from general databases. It also provides the probability density function for each species's mixing ratio. Conclusions: By removing the solution degeneracy in the decomposition of mass spectra, the method described herein could significantly increase the scientific retrieval from archived space flight mass spectrometry data, where calibration of the ionization source is no longer an option.

Thomas Gautier↗

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗

Open Innovation for a NASA Architecture Library

NASA’s Center of Excellence for Collaborative Innovation (CoECI) uses open innovation, or “crowdsourcing”, to access the global public to find ideas, concepts, designs, or solutions that meet a previously unmet need possibly resulting in significant advances in performance. The Center of Excellence for Collaborative Innovation was launched at the request of the White House Office of Science and Technology Policy. This is both a non-traditional method of innovation and a non-traditional method of outreach to the public to involve them in space technologies and programs. It has been used often for software development and new hardware technology. In this case we applied it to innovate with systems engineering tools for creating space architectures. The challenge was sponsored by NASA Engineering and Safety Center Systems Engineering Technical Fellow as part of a program for NASA’s adoption of MBSE. It was a trial to see if there would be as much participation or quality submissions with this more specialized topic and skill. The challenge sought space architecture representations and decompositions to create a library of modeled parts in a system modeling language (SysML). Mission architects mostly start from scratch to build model elements representing the functional and physical architecture of a system in SysML. There are a few beginning libraries, but these are also local to a program or group. A common library will save system engineers a large amount of time, will allow project stakeholders to recognize common graphics and quickly understand the architecture options. The challenge was promoted internationally, especially through professional organizations and universities with a systems engineering focus. It was open for 4 months, purposefully over the winter holiday break time to allow participants extra time outside of work or school. The challenge was designed so that expertise in space hardware was not necessary but getting to play with models of space architecture could provide motivation to participate. We did not receive as many entries as other broader outreach challenges, but the ones we received were extremely thorough and high quality. Solutions came from individuals and teams, students and professional consultants from the United States and Europe. We learned a few lessons about how to engage with the public and what characteristics of a problem result in good crowdsourcing results. The outreach challenge produced several useful ideas and modeled space elements, and the group will be engaging the winners to learn more about their new approaches.

innovation↗

A general algorithm using finite element method for aerodynamic configurations at low speeds

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

Balasubramanian, R.↗

Program Helps Decompose Complex Design Systems

DeMAID (Design Manager's Aid for Intelligent Decomposition) computer program is knowledge-based software system for ordering sequence of modules and identifying possible multilevel structure for design problems such as large platforms in outer space. Groups modular subsystems on basis of interactions among them. Saves considerable amount of money and time in total design process, particularly in new design problem in which order of modules has not been defined. Originally written for design problems, also applicable to problems containing modules (processes) that take inputs and generate outputs. Available in three machine versions: Macintosh written in Symantec's Think C 3.01, Sun, and SGI IRIS in C language.

Rogers, James L., Jr.↗

A generative artificial intelligence framework for long-time plasma turbulence simulations

Generative deep learning techniques are employed in a novel framework for the construction of surrogate models capturing the spatiotemporal dynamics of 2D plasma turbulence. The proposed Generative Artificial Intelligence Turbulence (GAIT) framework enables the acceleration of turbulence simulations for long-time transport studies. GAIT leverages a convolutional variational auto-encoder and a recurrent neural network to generate new turbulence data from existing simulations, extending the time horizon of transport studies with minimal computational cost. The application of the GAIT framework to plasma turbulence using the Hasegawa–Wakatani (HW) model is presented, evaluating its performance via various analyses. Very good agreement is found between the GAIT and the HW models in the spatiotemporal Fourier and Proper Orthogonal Decomposition spectra, the flow topology characterized by the Okubo–Weiss parameter, and the time autocorrelation function of turbulent fluctuations. Excellent agreement has also been obtained in the probability distribution function of particle displacements and the effective turbulent diffusivity. In-depth analyses of the latent space of turbulent states, choice of hyperparameters and alternative deep learning models for the time prediction are presented. Our results highlight the potential of Artificial Intelligence-based surrogate models to overcome the computational challenges in turbulence simulation, which can be extended to other situations such as geophysical fluid dynamics.

Artificial intelligence↗

Energy Finite Element Analysis for Computing the High Frequency Vibration of the Aluminum Testbed Cylinder and Correlating the Results to Test Data

The Energy Finite Element Analysis (EFEA) is a finite element based computational method for high frequency vibration and acoustic analysis. The EFEA solves with finite elements governing differential equations for energy variables. These equations are developed from wave equations. Recently, an EFEA method for computing high frequency vibration of structures either in vacuum or in contact with a dense fluid has been presented. The presence of fluid loading has been considered through added mass and radiation damping. The EFEA developments were validated by comparing EFEA results to solutions obtained by very dense conventional finite element models and solutions from classical techniques such as statistical energy analysis (SEA) and the modal decomposition method for bodies of revolution. EFEA results have also been compared favorably with test data for the vibration and the radiated noise generated by a large scale submersible vehicle. The primary variable in EFEA is defined as the time averaged over a period and space averaged over a wavelength energy density. A joint matrix computed from the power transmission coefficients is utilized for coupling the energy density variables across any discontinuities, such as change of plate thickness, plate/stiffener junctions etc. When considering the high frequency vibration of a periodically stiffened plate or cylinder, the flexural wavelength is smaller than the interval length between two periodic stiffeners, therefore the stiffener stiffness can not be smeared by computing an equivalent rigidity for the plate or cylinder. The periodic stiffeners must be regarded as coupling components between periodic units. In this paper, Periodic Structure (PS) theory is utilized for computing the coupling joint matrix and for accounting for the periodicity characteristics.

Vlahopoulos, Nickolas↗

Experiences with the Lanczos method on a parallel computer

A parallel computer implementation of the Lanczos method for the free-vibration analysis of structures is considered, and results for two example problems show substantial time-reduction over the sequential solutions. The major Lanczos calculation tasks are subdivided into subtasks, and parallelism is introduced at the subtask level. A speedup of 7.8 on eight processors was obtained for the decomposition step of the problem involving a 60-m three-longeron space mast, and a speedup of 14.6 on 16 processors was obtained for the decomposition step of the problem involving a blade-stiffened graphite-epoxy panel.

Bostic, Susan W.↗

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗