Search NASA⌕ Search

SEARCH · Search NASA

Results for “Stefan Problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

High-order algorithmic developments and optimizations for large-scale GPU-accelerated simulations (Milestone CEED-MS36)

The goal of this milestone was to improve the high-order software ecosystem for CEED-enabled ECP applications by making progress on efficient matrix-free kernels targeting forthcoming ECP architectures. These kernels included matrix-free preconditioning and the development of new set of CEED solver bake-off problems. As part of this milestone, we also released the next version of the CEED software stack, CEED-4.0, reported on results from several application collaborations, and documented the efforts of porting to AMD GPUs for Frontier and other modern architectures, such as Fugaku. The specific tasks addressed in this milestone were: (1) Port and run CEED benchmarks/miniapps on Frontier EA systems; (2) Demonstrate performant libCEED integration in MFEM, Nek and applications; (3) Matrix-free preconditioning of high-order operators; (4) Benchmark problems for fast high-order solvers on GPU platforms; and (5) Public release of CEED-4.0. The artifacts delivered include the next version of the CEED software stack, CEED-4.0, the next libCEED release, libCEED-0.8, and a number of developments integrated within applications to improve their GPU and CPU performance and capabilities. See the CEED website, https://ceed.exascaleproject.org and the CEED GitHub organization, https://github.com/ceed for more details.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantum approximate multi-objective optimization

The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Machine-learning-based inversion of nuclear responses

A microscopic description of the interaction of atomic nuclei with external electroweak probes is required for elucidating aspects of short-range nuclear dynamics and for the correct interpretation of neutrino oscillation experiments. Nuclear quantum Monte Carlo methods infer the nuclear electroweak response functions from their Laplace transforms. Inverting the Laplace transform is a notoriously ill-posed problem; and Bayesian techniques, such as maximum entropy, are typically used to reconstruct the original response functions in the quasielastic region. In this work, we present a physics-informed artificial neural network architecture suitable for approximating the inverse of the Laplace transform. Utilizing simulated, albeit realistic, electromagnetic response functions, we show that this physics-informed artificial neural network outperforms maximum entropy in both the low-energy transfer and the quasielastic regions, thereby allowing for robust calculations of electron scattering and neutrino scattering on nuclei and inclusive muon capture rates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Large-Scale Uncertainty and Error Analysis for Time-dependent Fluid/Structure Interactions in Wind Turbine Applications

The following is the final report covering the entire period of this aforementioned grant, June 1, 2011 - May 31, 2013 for the portion of the effort corresponding to Stanford University (SU). SU has partnered with Sandia National Laboratories (PI: Mike S. Eldred) and Purdue University (PI: Dongbin Xiu) to complete this research project and this final report includes those contributions made by the members of the team at Stanford. Dr. Eldred is continuing his contributions to this project under a no-cost extension and his contributions to the overall effort will be detailed at a later time (once his effort has concluded) on a separate project submitted by Sandia National Laboratories. At Stanford, the team is made up of Profs. Alonso, Iaccarino, and Duraisamy, post-doctoral researcher Vinod Lakshminarayan, and graduate student Santiago Padron. At Sandia National Laboratories, the team includes Michael Eldred, Matt Barone, John Jakeman, and Stefan Domino, and at Purdue University, we have Prof. Dongbin Xiu as our main collaborator. The overall objective of this project was to develop a novel, comprehensive methodology for uncertainty quantification by combining stochastic expansions (nonintrusive polynomial chaos and stochastic collocation), the adjoint approach, and fusion with experimental data to account for aleatory and epistemic uncertainties from random variable, random field, and model form sources. The expected outcomes of this activity were detailed in the proposal and are repeated here to set the stage for the results that we have generated during the time period of execution of this project: 1. The rigorous determination of an error budget comprising numerical errors in physical space and statistical errors in stochastic space and its use for optimal allocation of resources; 2. A considerable increase in efficiency when performing uncertainty quantification with a large number of uncertain variables in complex non-linear multi-physics problems; 3. A solution to the long-time integration problem of spectral chaos approaches; 4. A rigorous methodology to account for aleatory and epistemic uncertainties, to emphasize the most important variables via dimension reduction and dimension-adaptive refinement, and to support fusion with experimental data using Bayesian inference; 5. The application of novel methodologies to time-dependent reliability studies in wind turbine applications including a number of efforts relating to the uncertainty quantification in vertical-axis wind turbine applications. In this report, we summarize all accomplishments in the project (during the time period specified) focusing on advances in UQ algorithms and deployment efforts to the wind turbine application area. Detailed publications in each of these areas have also been completed and are available from the respective conference proceedings and journals as detailed in a later section.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Accelerating $\mathrm{LHC}$ event generation with simplified pilot runs and fast $\mathrm{PDF}$s

Poor computing efficiency of precision event generators for LHC physics has become a bottleneck for Monte-Carlo event simulation campaigns. We provide solutions to this problem by focusing on two major components of general-purpose event generators: The PDF evaluator and the matrix-element generator. For a typical production setup in the ATLAS experiment, we show that the two can consume about 80% of the total runtime. Using NLO simulations of pp→ℓ + ℓ - +jets and pp→$t\bar{t}$+jets as an example, we demonstrate that the computing footprint of LHAPDF and SHERPA can be reduced by factors of order 10, while maintaining the formal accuracy of the event sample. The improved codes are made publicly available.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Sphere-by-Sphere Manufacturing of 3D Microscale Granular Materials

Two of the central challenges in the mechanical design of components in nuclear systems are the dissipation of energy from external shocks and the localization of energy in energetic materials. This research seeks to address these problems by developing a patterned granular microstructure that can be optimized to direct or impede the transfer of energy carried by stress waves. Such structures require the development of a manufacturing technique that can yield perfectly ordered lattices. Two branches of research are detailed here: the development of a sphere-by-sphere additive manufacturing technique, and the development of a framework for modeling the technique in order to guide future improvements. Proof of concept of the method is demonstrated, and recommendations for future work are made.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Quantum Optimization: Potential, Challenges, and the Path Forward

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of algorithmic approaches, often with little linkage. This is further complicated by the fragmented nature of the field of mathematical optimization, where major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions, have devoted communities. With these aspects in mind, this work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory — highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains – finance and sustainability – as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

TAO Users Manual (Rev. 3.15)

The Toolkit for Advanced Optimization (TAO) focuses on the development of algorithms and software for the solution of large-scale optimization problems on high-performance architectures. Areas of interest include unconstrained and bound-constrained optimization, nonlinear least squares problems, optimization problems with partial differential equation constraints, and variational inequalities and complementarity constraints. The development of TAO was motivated by the scattered support for parallel computations and the lack of reuse of external toolkits in current optimization software. Our aim is to produce high-quality optimization software for computing environments ranging from workstations and laptops to massively parallel high-performance architectures. Our design decisions are strongly motivated by the challenges inherent in the use of large-scale distributed memory architectures and the reality of working with large, often poorly structured legacy codes for specific applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The Artificial Scientist: in-Transit Machine Learning of Plasma Simulations

Large-scale simulations or scientific experiments produce petabytes of data per run. This poses massive challenges for I/O and storage when scientific analysis workflows are run manually offline. Unsupervised deep learning-based techniques to extract patterns and non-linear relations from these large amounts of data provide a way to build scientific understanding from raw data, reducing the need for manual pre-selection of analysis steps, but require exascale compute and memory to process the full dataset available. In this paper, we demonstrate a heterogeneous streaming workflow in which plasma simulation data is streamed directly to a Machine Learning (ML) application training a model on the simulation data in-transit, completely circumventing the capacity-constrained filesystem bottleneck. This workflow employs openPMD to provide a high level interface to describe scientific data and also uses ADIOS2, to transfer volumes of data that exceed the capabilities of the filesystem. We employ experience replay to avoid catastrophic forgetting in learning from this non-steady state process in a continual manner and adapt it to improve model convergence while learning in-transit. As a proof-of-concept, we approach the ill-posed inverse problem of predicting particle dynamics from radiation in a particle-incell (PIConGPU) simulation of the Kelvin-Helmholtz instability (KHI). We detail hardware-software co-design challenges as we scale PIConGPU to full Frontier, the Top-1 system as of June 2024 Top500 list.

Kelling, Jeffrey [Helmholtz-Zentrum Dresden Rossen↗
DOE OSTI2024

Stochastic average model methods

We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are computationally expensive and evaluating all summands on every iteration of an optimization method may be undesirable. Here we present the idea of stochastic average model (SAM) methods, inspired by stochastic average gradient methods. SAM methods sample component functions on each iteration of a trust-region method according to a discrete probability distribution on component functions; the distribution is designed to minimize an upper bound on the variance of the resulting stochastic model. We present promising numerical results concerning an implemented variant extending the derivative-free model-based trust-region solver POUNDERS, which we name SAM-POUNDERS.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2016

Precision Optical Edges for a Starshade External Occulter

The use of a starshade is one technique to perform high contrast imaging with space-based telescopes. The primary function of a starshade is to suppress light from a target star in order to image its orbiting planets. In order to provide the proper apodization function the edges of the starshade must follow a precise in-plane profile. However of equal importance is the issue of light from our own sun scattering off of the edges and entering the telescope. A method to alleviate this problem is to make the edges extremely sharp (< 1 µmterminal radius) such that the area available for scattering is minimized. The combination of these two requirements, along with the need to integrate the edges into a 30-40 m dia. deployable structure, present a number of significant engineering challenges. Substrate etching techniques are used to obtain both the intended profile as well as the edge sharpness. Current efforts implement an isotropic etching process on thin metal substrates. This paper discusses the progress towards producing a sharp optical edge at the coupon level. Samples have been characterized using scanning electron microscopy as well as a custom testbed to assess their scattered-light performance.

starshade↗
DOE OSTI2016

Bayesian Optimization Under Mixed Constraints with A Slack-Variable Augmented Lagrangian

An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was that expected improvement (EI) evaluations relied on Monte Carlo. Here we introduce an alternative slack variable AL, and show that in this formulation the EI may be evaluated with library routines. The slack variables furthermore facilitate equality as well as inequality constraints, and mixtures thereof. We show our new slack “ALBO” compares favorably to the original. Its superiority over conventional alternatives is reinforced on several mixed constraint examples.

Picheny, Victor↗
NASA NTRS1993

A path-oriented matrix-based knowledge representation system

Experience has shown that designing a good representation is often the key to turning hard problems into simple ones. Most AI (Artificial Intelligence) search/representation techniques are oriented toward an infinite domain of objects and arbitrary relations among them. In reality much of what needs to be represented in AI can be expressed using a finite domain and unary or binary predicates. Well-known vector- and matrix-based representations can efficiently represent finite domains and unary/binary predicates, and allow effective extraction of path information by generalized transitive closure/path matrix computations. In order to avoid space limitations a set of abstract sparse matrix data types was developed along with a set of operations on them. This representation forms the basis of an intelligent information system for representing and manipulating relational data.

Feyock, Stefan↗
DOE OSTI2015

Improving the trust in results of numerical simulations and scientific data analytics

This white paper investigates several key aspects of the trust that a user can give to the results of numerical simulations and scientific data analytics. In this document, the notion of trust is related to the integrity of numerical simulations and data analytics applications. This white paper complements the DOE ASCR report on Cybersecurity for Scientific Computing Integrity by (1) exploring the sources of trust loss; (2) reviewing the definitions of trust in several areas; (3) providing numerous cases of result alteration, some of them leading to catastrophic failures; (4) examining the current notion of trust in numerical simulation and scientific data analytics; (5) providing a gap analysis; and (6) suggesting two important research directions and their respective research topics. To simplify the presentation without loss of generality, we consider that trust in results can be lost (or the results’ integrity impaired) because of any form of corruption happening during the execution of the numerical simulation or the data analytics application. In general, the sources of such corruption are threefold: errors, bugs, and attacks. Current applications are already using techniques to deal with different types of corruption. However, not all potential corruptions are covered by these techniques. We firmly believe that the current level of trust that a user has in the results is at least partially founded on ignorance of this issue or the hope that no undetected corruptions will occur during the execution. This white paper explores the notion of trust and suggests recommendations for developing a more scientifically grounded notion of trust in numerical simulation and scientific data analytics. We first formulate the problem and show that it goes beyond previous questions regarding the quality of results such as V&V, uncertainly quantification, and data assimilation. We then explore the complexity of this difficult problem, and we sketch complementary general approaches to address it. This paper does not focus on the trust that the execution will actually complete. The product of simulation or of data analytic executions is the final element of a potentially long chain of transformations, where each stage has the potential to introduce harmful corruptions. These corruptions may produce results that deviate from the user-expected accuracy without notifying the user of this deviation. There are many potential sources of corruption before and during the execution; consequently, in this white paper we do not focus on the protection of the end result after the execution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Decrease time-to-solution through improved linear-system setup and solve

The goal of the ExaWind project is to enable predictive simulations of wind farms composed of many MW-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines, and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary code in the ExaWind project is Nalu, which is an unstructured-grid solver for the acoustically-incompressible Navier-Stokes equations, and mass continuity is maintained through pressure projection. The model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as re-initialization of matrices and re-computation of preconditioners is required at every time step We describe in this report our efforts to decrease the setup and solution time for the mass-continuity Poisson system with respect to the benchmark timing results reported in FY18 Q1. In particular, we investigate improving and evaluating two types of algebraic multigrid (AMG) preconditioners: Classical Ruge-Stfiben AMG (C-AMG) and smoothed-aggregation AMG (SA-AMG), which are implemented in the Hypre and Trilinos/MueLu software stacks, respectively. Preconditioner performance was optimized through existing capabilities and settings.

17 WIND ENERGY↗
DOE OSTI2018

Simulation tools for atom probe tomography: A path for diagnosis and treatment of image degradation

The ideal picture of a near-perfect 3D microscope often presented regarding Atom Probe Tomography faces several issues. These issues degrade the metrological performance of the instrument and find their roots in the phenomena acting at the atomic to the mesoscopic level in the vicinity of the surface of a field emitter. From the field evaporation process at the atomic scale, to the macroscopic scale of the instrument, the path to model the imaging process and to develop more accurate and reliable reconstruction algorithms is not a single lane road. This paper focused on the numerical methods used to understand, treat, and potentially heal imaging issues commonly affecting the data in atom probe experiments. A lot of room for improvement exists in solving accuracy problems observed in complex materials by means of purely electrostatic models describing the image formation in a classical approach. Looking at the sample at the atomic scale, the phenomena perturbing the imaging process are subtle. An examination of atomic scale modifications of the sample surface in the presence of a high surface electric field is therefore mandatory. Atomic scale molecular dynamic models integrating the influence of the high surface electric are being developed with this aim. It is also demonstrated that the complex behavior of atoms and molecules in high fields, and consequences on collected data, can be understood through the use of accurate ab-initio models modified to include the impact of the extreme surface electric field.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2019

Spatial and temporal variation in river corridor exchange across a 5th-order mountain stream network

Although most field and modeling studies of river corridor exchange have been conducted at scales ranging from tens to hundreds of meters, results of these studies are used to predict their ecological and hydrological influences at the scale of river networks. Further complicating prediction, exchanges are expected to vary with hydrologic forcing and the local geomorphic setting. While we desire predictive power, we lack a complete spatiotemporal relationship relating discharge to the variation in geologic setting and hydrologic forcing that is expected across a river basin. Indeed, the conceptual model of Wondzell (2011) predicts systematic variation in river corridor exchange as a function of (1) variation in baseflow over time at a fixed location, (2) variation in discharge with location in the river network, and (3) local geomorphic setting. To test this conceptual model we conducted more than 60 solute tracer studies including a synoptic campaign in the 5th-order river network of the H. J. Andrews Experimental Forest (Oregon, USA) and replicate-in-time experiments in four watersheds. We interpret the data using a series of metrics describing river corridor exchange and solute transport, testing for consistent direction and magnitude of relationships relating these metrics to discharge and local geomorphic setting. We confirmed systematic decrease in river corridor exchange space through the river networks, from headwaters to the larger main stem. However, we did not find systematic variation with changes in discharge through time or with local geomorphic setting. While interpretation of our results is complicated by problems with the analytical methods, the results are sufficiently robust for us to conclude that space-for-time and time-for-space substitutions are not appropriate in our study system. Finally, we suggest two strategies that will improve the interpretability of tracer test results and help the hyporheic community develop robust datasets that will enable comparisons across multiple sites and/or discharge conditions.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2000

Intensive HST, RXTE, and ASCA Monitoring of NGC 3516: Evidence against Thermal Reprocessing

During 1998 April 1316, the bright, strongly variable Seyfert 1 galaxy NGC 3516 was monitored almost continuously with HST for 10.3 hr at ultraviolet wavelengths and 2.8 days at optical wavelengths, and simultaneous RXTE and ASCA monitoring covered the same period. The X-ray fluxes were strongly variable with the soft (0.5-2 keV) X-rays showing stronger variations (approx. 65% peak to peak) than the hard (2-10 keV) X-rays (approx. 50% peak to peak). The optical continuum showed much smaller but still highly significant variations: a slow approx. 2.5% rise followed by a faster approx. 3.5% decline. The short ultraviolet observation did not show significant variability. The soft and hard X-ray light curves were strongly correlated, with no evidence for a significant interband lag. Likewise, the optical continuum bands (3590 and 5510 A) were also strongly correlated, with no measurable lag, to 3(sigma) limits of approx. less than 0.15 day. However, the optical and X-ray light curves showed very different behavior, and no significant correlation or simple relationship could be found. These results appear difficult to reconcile with previous reports of correlations between X-ray and optical variations and of measurable lags within the optical band for some other Seyfert 1 galaxies. These results also present serious problems for "reprocessing" models in which the X-ray source heats a stratified accretion disk, which then reemits in the optical/ultraviolet : the synchronous variations within the optical would suggest that the emitting region is approx. less than 0.3 It-day across, while the lack of correlation between X-ray and optical variations would indicate, in the context of this model, that any reprocessing region must be approx. greater than 1 It-day in size. It may be possible to resolve this conflict by invoking anisotropic emission or special geometry, but the most natural explanation appears to be that the bulk of the optical luminosity is generated by some mechanism other than reprocessing.

Edelson, Rick↗