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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.

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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Compressed Sensing with Sparse Corruptions: Fault-Tolerant Sparse Collocation Approximations

The recovery of approximately sparse or compressible coefficients in a polynomial chaos expansion is a common goal in many modern parametric uncertainty quantification (UQ) problems. However, relatively little effort in UQ has been directed toward theoretical and computational strategies for addressing the sparse corruptions problem, where a small number of measurements are highly corrupted. Such a situation has become pertinent today since modern computational frameworks are sufficiently complex with many interdependent components that may introduce hardware and software failures, some of which can be difficult to detect and result in a highly polluted simulation result. In this paper we present a novel compressive sampling--based theoretical analysis for a regularized $\ell^1$ minimization algorithm that aims to recover sparse expansion coefficients in the presence of measurement corruptions. Our recovery results are uniform (the theoretical guarantees hold for all compressible signals and compressible corruptions vectors) and prescribe algorithmic regularization parameters in terms of a user-defined a priori estimate on the ratio of measurements that are believed to be corrupted. We also propose an iteratively reweighted optimization algorithm that automatically refines the value of the regularization parameter and empirically produces superior results. Lastly, our numerical results test our framework on several medium to high dimensional examples of solutions to parameterized differential equations and demonstrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Compressed sensing with sparse corruptions: Fault-tolerant sparse collocation approximations

The recovery of approximately sparse or compressible coefficients in a polynomial chaos expansion is a common goal in many modern parametric uncertainty quantification (UQ) problems. However, relatively little effort in UQ has been directed toward theoretical and computational strategies for addressing the sparse corruptions problem, where a small number of measurements are highly corrupted. Such a situation has become pertinent today since modern computational frameworks are sufficiently complex with many interdependent components that may introduce hardware and software failures, some of which can be difficult to detect and result in a highly polluted simulation result. In this paper we present a novel compressive sampling-based theoretical analysis for a regularized t1 minimization algorithm that aims to recover sparse expansion coefficients in the presence of measurement corruptions. Our recovery results are uniform (the theoretical guarantees hold for all compressible signals and compressible corruptions vectors), and prescribe algorithmic regularization parameters in terms of a user-defined a priori estimate on the ratio of measurements that are believed to be corrupted. We also propose an iteratively reweighted optimization algorithm that automatically refines the value of the regularization parameter, and empirically produces superior results. Our numerical results test our framework on several medium-to-high dimensional examples of solutions to parameterized differential equations, and demonstrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

NONPARAMETRIC EMPIRICAL BAYES ESTIMATION THROUGH DECONVOLUTION IN PROBABILISTIC RISK ANALYSIS

The advent of Markov Chain Monte Carlo (MCMC) simulations and availability of open source software made full hierarchical Bayesian analysis tractable and a popular choice in parameter estimation for Probabilistic Risk Assessment (PRA). However, despite its theoretical attractiveness, the hierarchical Bayesian analysis is not without its problems. Two of the most prominent practical difficulties in applying hierarchical Bayes analysis in practice to analyze source-to-source variability, for example, is its sensitivity to the selection of the first-stage prior and dependence of the rate of convergence on the selection of the first-stage prior. The first-stage prior in hierarchical Bayesian analysis is usually assumed having a parametric form, often conjugate to the likelihood function (aleatory model). To facilitate convergence for hierarchical Bayes models, the first-stage prior is frequently set through empirical Bayes estimate, which can use available historical data to find the parameters of the first-stage prior. The paper discusses a new nonparametric empirical Bayes estimation and compare it to several well-known parametric estimates such as method of moments and maximum likelihood. The new nonparametric technique exploits the prior predictive distribution as integral equation and proceeds to solve it with respect to prior assuming the sampling data distribution and aleatory model are available. The discussion covers topics such as selection of aleatory model for future data, selection of regularization parameter, and density estimation for historical data. For comparison, the paper is using contrived as well as real-world data from utilities. Utilities data represent failure data with Poisson distribution used for aleatory model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Noninvasive liquid level sensing with laser generated ultrasonic waves

This article proposes a noninvasive liquid level sensing technique using laser-generated ultrasound waves for nuclear power plant applications. Liquid level sensors play an important role of managing the coolant system safely and stably in the plant structure. Current sensing techniques are mostly intrusive, performing inside the fluidic structure, which is disadvantageous in terms of the regular maintenance of the plant system. Furthermore, typical intrusive sensors do not perform stably under varying environmental conditions such as temperature and radiation. In this study, sensing units are attached to the outer surface of a liquid vessel to capture guided ultrasound waves in a nonintrusive manner. The signal intensity of the guided wave dissipates when the signal interacts with the internal liquid media. The sensing mechanism is mathematically expressed as an index value to correlate the liquid level with the sensor signal. For the acoustic wave generation, laser-generated ultrasound was adopted instead of using typical contact type transducers. Following the simulation validation of the proposed concept, the performance of the developed sensor was confirmed through experimental results under elevated liquid temperature conditions. Finally, the nonlinear multivariable regression exhibited the best-fit to the datasets measured under the variable liquid level and temperature conditions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Sampling frequency thresholds for the quantum advantage of the quantum approximate optimization algorithm

We compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers Gurobi and MQLib to solve the MaxCut problem on 3-regular graphs. We identify the minimum noiseless sampling frequency and depth p required for a quantum device to outperform classical algorithms. There is potential for quantum advantage on hundreds of qubits and moderate depth with a sampling frequency of 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linear time complexity. In order to match this quality for large graph sizes N, a quantum device must support depth p > 11. Additionally, multi-shot QAOA is not efficient on large graphs, indicating that QAOA p ≤ 11 does not scale with N. These results limit achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The ISTI Rapid Response on Exploring Cloud Computing 2018

The Information Science & Technology Institute (ISTI), with partnering entities at Los Alamos National Laboratory (LANL), regularly organizes and executes Rapid Response efforts in mission-relevant growth areas within information science. This report describes 18 projects conducted at LANL in response to a Rapid Response Familiarization call titled “Exploring Cloud Computing 2018.”

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Formation of Point Shocks for 3D Compressible Euler

We consider the 3D isentropic compressible Euler equations with the ideal gas law. We provide a constructive proof of the formation of the first point shock from smooth initial datum of finite energy, with no vacuum regions, with nontrivial vorticity present at the shock, and under no symmetry assumptions . We prove that for an open set of Sobolev‐class initial data that are a small L ∞ perturbation of a constant state, there exist smooth solutions to the Euler equations which form a generic stable shock in finite time. The blowup time and location can be explicitly computed, and solutions at the blowup time are smooth except for a single point , where they are of cusp‐type with Hölder C 1/3 regularity. Our proof is based on the use of modulated self‐similar variables that are used to enforce a number of constraints on the blowup profile, necessary to establish global existence and asymptotic stability in self‐similar variables. © 2022 Wiley Periodicals LLC.

Mathematics↗
DOE OSTI2018

SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations

We present here the design, convergence analysis and numerical investigations of the nonconforming virtual element method with Streamline Upwind/Petrov–Galerkin (VEM-SUPG) stabilization for the numerical resolution of convection–diffusion–reaction problems in the convective-dominated regime. According to the virtual discretization approach, the bilinear form is split as the sum of a consistency and a stability term. The consistency term is given by substituting the functions of the virtual space and their gradients with their polynomial projection in each term of the bilinear form (including the SUPG stabilization term). Polynomial projections can be computed exactly from the degrees of freedom. The stability term is also built from the degrees of freedom by ensuring the correct scalability properties with respect to the mesh size and the equation coefficients. The nonconforming formulation relaxes the continuity conditions at cell interfaces and a weaker regularity condition is considered involving polynomial moments of the solution jumps at cell interface. Optimal convergence properties of the method are proved in a suitable norm, which includes contribution from the advective stabilization terms. Experimental results confirm the theoretical convergence rates.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Fibonacci Grids

Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.

Swinbank, Richard↗
NASA NTRSDate not supplied

A Preliminary Modeling Study of Biofilm Accumulation in the Water Recovery System

Bacterial biofilms are ubiquitous in wastewater systems on earth and in spacecraft, such as in the International Space Station (ISS) wastewater processing assembly (WPA), where they cause problems in the tank, solenoid valves, and pipelines. Downstream filter applications, tank cycling, and regular biocide water flushing have been used to control biofilm accumulation on board the ISS. Biofilm control is expected to be a challenge for long-term missions with a dormancy period of up to a year, as stagnant water systems are highly susceptible to biofilm growth. Flushing of the system with biocidal water has been proposed to avoid biomass problems for long-term missions. To validate the proposed flush method, a mathematical model, based on the metabolism maintenance rate of bacteria, is being developed to understand the current biofilm accumulation rate in the ISS WPA system and to calculate the biomass production rate under dormancy-like conditions. This method of quantification of biofilm can be applied as a function of nutrient inputs to guide the selection and optimization of biofilm mitigation approaches. The method can also be helpful in understanding, defining, quantifying, visualizing, and simulating the state of the water processing system during operation and after dormancy.

Angie M Diaz↗
DOE OSTI2018

Compact video content representation for video coding using low multi-linear tensor rank approximation with dynamic core tensor order

Tensor is a multi-way representation of an entity that is widely used in many applications of mathematics and physics. The wide range of tensor algebra operations attract the researchers of graphical and vision field to identify unique methods for various applications such as segmentation, compression, indexing and so on. In this paper, low multi-linear rank approximation of a tensor is used for decomposition so as to perform compression on a video that is represented as a 4D tensor. Thus, the encoder has blocks for (1) multilinear rank approximation method so as to aid decomposition, (2) sparsity removal of residual data to reduce the required memory storage to a small level, (3) quantization on the sparse less residual data and (4) LZ77 dictionary coding for the video. The decoder uses a tensor reconstruction block along with residual error correction block that reduces loss/error in the reconstructed video. The size of core tensor is an important factor in rank approximation. It is identified at run time depending on the video contents. This size is determined adaptively using Tikhonov’s regularization method. The best value of core tensor size is identified with the corner of L-curve which preserves the video contents from heavy loss/error. Experimental results of the proposed work on comparison with H.264/AVC compression method indicate that the proposed method achieves up to 10% improvement in compression ratio with the least amount of loss and a maximum signal to noise ratio of 0.14. The proposed system gives better compression ratio than H.265 for videos with more number of frames without compromising quality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Simultaneous Sensing Error Recovery and Tomographic Inversion Using an Optimization-Based Approach

Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental conditions, which are often beyond the capabilities of the state-of-the-art reconstruction techniques such as regularizations. Because they can lead to reduced spatial resolution and even misinterpretation of the underlying sample structures, these errors present a fundamental obstacle to full realization of the capabilities of next-generation physical imaging. In this work, we develop efficient and explicit recovery schemes of the most common experimental error: movement of the center of rotation during the experiment. We formulate new physical models to capture the experimental setup, and we devise new mathematical optimization formulations for reliable inversion of complex samples. We demonstrate and validate the efficacy of our approach on synthetic data under known perturbations of the center of rotation.

Nonlinear optimization↗
DOE OSTI2023

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

CUDA Enabled Graph Subset Examiner

Finding Godsil-McKay switching sets in graphs is one way to demonstrate that a specific graph is not determined by its spectrum--the eigenvalues of its adjacency matrix. An important area of active research in pure mathematics is determining which graphs are determined by their spectra, i.e. when the spectrum of the adjacency matrix uniquely determines the underlying graph. We are interested in exploring the spectra of graphs in the Johnson scheme and specifically seek to determine which of these graphs are determined by their spectra. Given a graph G, a Godsil-McKay switching set is an induced subgraph H on 2k vertices with the following properties: I) H is regular, ii) every vertex in G/H is adjacent to either 0, k, or 2k vertices of H, and iii) at least one vertex in G/H is adjacent to k vertices in H. The software package examines each subset of a user specified size to determine whether or not it satisfies those 3 conditions. The software makes use of the massive parallel processing power of CUDA enabled GPUs. It also exploits the vertex transitivity of graphs in the Johnson scheme by reasoning that if G has a Godsil-McKay switching set, then it has a switching set which includes vertex 1. While the code (in its current state) is tuned to this specific problem, the method of examining each induced subgraph of G can be easily re-written to check for any user specified conditions on the subgraphs and can therefore be used much more broadly.

Johnston, JeremyT.↗
DOE OSTI2022

Posterior Regularized Bayesian Neural Network

Traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs(BNNs) could help measure the confidence level by using distributions in NNs modeling. Besides, knowledge is commonly available and could improve the performance of BNNs if it can be properly incorporated. In this work, we propose a novel Posterior-Regularized BNN(PR-BNN) model by incorporating soft and hard constraints as a posterior regularization term. We also propose an augmented Lagrangian method and stochastic optimization algorithm for efficient updating via Monte Carlo sampling. The simulations and case studies for solar PV plants have shown the performance improvement of the proposed model over traditional BNNs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

CUDA Enabled Graph Subset Examiner

Finding Godsil-McKay switching sets in graphs is one way to demonstrate that a specific graph is not determined by its spectrum--the eigenvalues of its adjacency matrix. An important area of active research in pure mathematics is determining which graphs are determined by their spectra, i.e. when the spectrum of the adjacency matrix uniquely determines the underlying graph. We are interested in exploring the spectra of graphs in the Johnson scheme and specifically seek to determine which of these graphs are determined by their spectra. Given a graph G, a Godsil-McKay switching set is an induced subgraph H on 2k vertices with the following properties: I) H is regular, ii) every vertex in G/H is adjacent to either 0, k, or 2k vertices of H, and iii) at least one vertex in G/H is adjacent to k vertices in H. The software package examines each subset of a user specified size to determine whether or not it satisfies those 3 conditions. The software makes use of the massive parallel processing power of CUDA enabled GPUs. It also exploits the vertex transitivity of graphs in the Johnson scheme by reasoning that if G has a Godsil-McKay switching set, then it has a switching set which includes vertex 1. While the code (in its current state) is tuned to this specific problem, the method of examining each induced subgraph of G can be easily re-written to check for any user specified conditions on the subgraphs and can therefore be used much more broadly.

Johnston, Jeremy T.↗
DOE OSTI2021

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗