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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗
DOE OSTI2014

Rarefied gas flow in a rectangular enclosure induced by non-isothermal walls

The flow of a rarefied gas in a rectangular enclosure due to the non-isothermal walls with no synergetic contributions from external force fields is investigated. The top and bottom walls are maintained at constant but different temperatures and along the lateral walls a linear temperature profile is assumed. Modeling is based on the direct numerical solution of the Shakhov kinetic equation and the Direct Simulation Monte Carlo (DSMC) method. Solving the problem both deterministically and stochastically allows a systematic comparison and verification of the results as well as the exploitation of the numerical advantages of each approach in the investigation of the involved flow and heat transfer phenomena. The thermally induced flow is simulated in terms of three dimensionless parameters characterizing the problem, namely, the reference Knudsen number, the temperature ratio of the bottom over the top plates, and the enclosure aspect ratio. Their effect on the flow configuration and bulk quantities is thoroughly examined. Along the side walls, the gas flows at small Knudsen numbers from cold-to-hot, while as the Knudsen number is increased the gas flows from hot-to-cold and the thermally induced flow configuration becomes more complex. These flow patterns with the hot-to-cold flow to be extended to the whole length of the non-isothermal side walls may exist even at small temperature differences and then, they are enhanced as the temperature difference between the top and bottom plates is increased. The cavity aspect ratio also influences this flow configuration and the hot-to-cold flow is becoming more dominant as the depth compared to the width of the cavity is increased. To further analyze the flow patterns a novel solution decomposition into ballistic and collision parts is introduced. This is achieved by accordingly modifying the indexing process of the typical DSMC algorithm. The contribution of each part of the solution is separately examined and a physical interpretation of the flow configuration, including the hot-to-cold flow close to the side walls, in the whole range of the Knudsen number is provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Enhancing flexibility for climate change using seasonal energy storage (aquifer thermal energy storage) in distributed energy systems

Long-term energy storage is expected to play a vital role in the deep decarbonization of building energy sectors, while enhancing the flexibility of buildings to withstand future climate variations. However, it is challenging to design distributed multi-energy systems (DMES) while taking into account the uncertainties introduced by climate change, since stochastic optimization of such systems is difficult. The present study introduces a stochastic optimization model to address this bottleneck, taking into account DMES including aquifer thermal energy storage (ATES) as the long-term thermal storage. For the first time, a novel optimization algorithm links ATES with the DMES optimization model with the support of a simplified geotechnical model. Subsequently, a case study was conducted, focusing on a residential district in Chicago where the impact of future climate condition, energy demand, and solar and wind energy potentials were evaluated using Weather Research and Forecasting (WRF) data (up to 2080) and the EnergyPlus model. The study revealed that ATES is an attractive way to improve the renewable energy penetration level and minimize the dependence on fossil fuels with reasonable support from the grid to assist the fluctuations in both demand and generation. Furthermore, ATES notably reduces fuel consumption and dependence while greatly enhancing the flexibility of the energy system to withstand fluctuations in demand and renewable energy generation brought by future climate variations. These qualities will make ATES an important part of distributed energy systems, even though it is not currently the lowest cost alternative due to lack of technology maturity. Furthermore, the design platform introduced in the present study can be used to design DMES enhancing flexibility to accommodate future climate variations.

25 ENERGY STORAGE↗
DOE OSTI2014

A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization

In this paper, we present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Stochastic assessment of distributed generation hosting capacity and energy efficiency in active distribution networks

Active network management (ANM) aims to increase the capacity of variable distributed generation (DG), which can be connected to existing distribution networks. In this study, it is proposed to simultaneously consider the efficient use of energy resources when high shares of DG are procured through the ANM approach. To that end, a multi-period and multiobjective optimisation algorithm, based on the linearised optimal power flow, is formulated. The algorithm seeks to maximise the installed capacity of DG while minimising the energy losses and consumption of voltage-dependent loads. The objectives are optimised considering the coordinated operation of voltage regulators and on-load tap changers, and the management of DG generation curtailment and reactive power compensation from DG. Additionally, the effects of load and generation uncertainties are addressed through a two-stage stochastic programming formulation of the multiobjective problem. The result is a set of non-inferior solutions, which allows exploring the degree of conflict among the objectives. The proposed approach was tested on two IEEE test feeders and the solutions show a significant improvement in the system's energy efficiency with a low impact on the amount of connected DG.

Quijano, Darwin Alexis↗
DOE OSTI2026

Adaptive Sampling-Based Bi-Fidelity Stochastic Trust Region Method for Stochastic Derivative-Free Optimization

Bi-fidelity stochastic optimization has gained increasing attention as an efficient approach to reduce computational costs by leveraging a low-fidelity (LF) model to optimize an expensive high-fidelity (HF) objective. In this paper, we propose ASTRO-BFDF, an adaptive sampling trust-region method specifically designed for unconstrained bi-fidelity stochastic derivative-free optimization problems. In ASTRO-BFDF, the LF function serves two purposes: (i) to identify better iterates for the HF function when the optimization process indicates a high correlation between them and (ii) to reduce the variance of the HF function estimates using bi-fidelity Monte Carlo (BFMC). The algorithm dynamically determines sample sizes while adaptively choosing between crude Monte Carlo and BFMC to balance the trade-off between optimization and sampling errors. We prove that the iterates generated by ASTRO-BFDF converge to a first-order stationary point almost surely. Additionally, we demonstrate the effectiveness of the proposed algorithm through numerical experiments on synthetic benchmarks and simulation optimization problems involving discrete event systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fault diagnosis and fault tolerant control for T-S fuzzy stochastic distribution systems subject to sensor and actuator faults

The problem of fault diagnosis (FD) and fault tolerant control (FTC) for a class of Takagi-Sugeno (T-S) fuzzy stochastic distribution control (SDC) systems subject to sensor and actuator faults is discussed in this paper. First, fuzzy logic models are used to approximate the output probability density function (PDF). Next, an adaptive augmented state/fault diagnosis observer is proposed to estimate the system state, sensor and the actuator faults simultaneously. New expected weights based on the sensor fault estimation information and a PI-type fuzzy feedback fault tolerant (FT) controller are designed to compensate the effect of sensor fault and actuator fault simultaneously. When the sensor fault occurs, the expected objective is redesigned to compensate the sensor fault. Meanwhile, the PI controller can compensate the effect of actuator fault, and the output PDF of the system can still track the desired PDF after the fault occurs. Finally, an example of quality distribution control in chemical reaction process is given to confirm the effectiveness of the algorithm.

42 ENGINEERING↗
DOE OSTI2018

Hybrid methods for muon accelerator simulations with ionization cooling

Muon ionization cooling involves passing particles through solid or liquid absorbers. Careful simulations are required to design muon cooling channels. New features have been developed for inclusion in the transfer map code COSY Infinity to follow the distribution of charged particles through matter. To study the passage of muons through material, the transfer map approach alone is not sufficient. The interplay of beam optics and atomic processes must be studied by a hybrid transfer map-Monte-Carlo approach in which transfer map methods describe the deterministic behavior of the particles, and Monte-Carlo methods are used to provide corrections accounting for the stochastic nature of scattering and straggling of particles. The advantage of the new approach is that the vast majority of the dynamics are represented by fast application of the high-order transfer map of an entire element and accumulated stochastic effects. The gains in speed are expected to simplify the optimization of cooling channels which is usually computationally demanding. In conclusion, progress on the development of the required algorithms and their application to modeling muon ionization cooling channels is reported.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Stochastic Gradient-Based Distributed Bayesian Estimation in Cooperative Sensor Networks

Distributed Bayesian inference provides a full quantification of uncertainty offering numerous advantages over point estimates that autonomous sensor networks are able to exploit. However, fully-decentralized Bayesian inference often requires large communication overheads and low network latency, resources that are not typically available in practical applications. In this paper, we propose a decentralized Bayesian inference approach based on stochastic gradient Langevin dynamics, which produces full posterior distributions at each of the nodes with significantly lower communication overhead. We provide analytical results on convergence of the proposed distributed algorithm to the centralized posterior, under typical network constraints. Finally, we also provide extensive simulation results to demonstrate the validity of the proposed approach.

42 ENGINEERING↗
DOE OSTI2024

FuseIM: Fusing Probabilistic Traversals for Influence Maximization on Exascale Systems

Probabilistic breadth-first traversals (BPTs) are used in many network science and graph machine learning applications. In this paper, we are motivated by the application of BPTs in stochastic diffusion-based graph problems such as influence maximization. These applications heavily rely on BPTs to implement a Monte-Carlo sampling step for their approximations. Given the large sampling complexity, stochasticity of the diffusion process, and the inherent irregularity in real-world graph topologies, efficiently parallelizing these BPTs remains significantly challenging. In this paper, we present a new algorithm to fuse massive number of concurrently executing BPTs with random starts on the input graph. Our algorithm is designed to fuse BPTs by combining separate traversals into a unified frontier on distributed multi-GPU systems. To show the general applicability of the fused BPT technique, we have incorporated it into two state-of-the-art influence maximization parallel implementations (gIM and Ripples). Our experiments on up to 4K nodes of the OLCF Frontier supercomputer (32,768 GPUs and 196K CPU cores) show strong scaling behavior, and that fused BPTs can improve the performance of these implementations up to 34x (for gIM) and ~360x (for Ripples).

Neff, Reece W.↗
DOE OSTI2020

Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm

Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitch angle scattering. This approach is frequently used in particle based Monte-Carlo simulations of plasma collisions, among others. However, most numerical treatments do not guarantee energy conservation, which may lead to unphysical artifacts such as numerical heating and spectra distortions. We present a novel structure-preserving numerical algorithm for the Langevin equation for pitch angle scattering. Similar to the well-known Boris algorithm, the proposed numerical scheme takes advantage of the structure-preserving properties of the Cayley transform when calculating the velocity-space rotations. The resulting algorithm is explicitly solvable, while preserving the norm of velocities down to machine precision. We demonstrate that the method has the same order of numerical convergence as the traditional stochastic Euler-Maruyama method.

Zhang, Xin↗
DOE OSTI2019

Stochastic Molecular Dynamics

I can not pass up the opportunity to honor Graeme Bird, a true gentleman and a real scholar, if there ever was one. When we first met at a rarefied gas dynamics conference, it was instant mutual admiration. Furthermore, we met rarely thereafter at subsequent rarefied gas meetings since I attended them infrequently as a physicist interested in hydrodynamics, where often even a rarefied gas without deterministic collisions can serve as a simple fluid model but Graeme attended them regularly. In that rst meeting I became aware of DSMC, read Graeme paper and found to my astonishment that the only reference in that paper was to my molecular dynamics work2. Indeed DSMC is computationally faster competitor to molecular dynamics and it is this feature that I would like to emphasize in this brief note. It is for this reason that I entitled this contribution \stochastic molecular dynamics". I once told Graeme that that would have been a more descriptive name to his method than DSMC. DSMC is also a good demonstration that an algorithm developed for an entirely different purposes can also be very useful for other applications.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Computing Nonequilibrium Responses with Score-Shifted Stochastic Differential Equations

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable and general response results rely on path ensemble averaging. Furthermore, these techniques do not apply to perturbations that affect the diffusion tensor in a stochastic system. Here, we introduce an “effective” physical process that represents the diffusion perturbed dynamics and enables accurate calculations of responses to a change in the diffusion. Interestingly, the effective dynamics contain an additional drift involving the instantaneous “score” of the system, and we leverage score matching algorithms to carry out nonequilibrium response calculations on systems for which the exact stationary distribution is unknown.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Adaptive Sparse-Grid Stochastic Collocation Uncertainty Quantification Convergence for Multigroup Diffusion

Advanced methods in uncertainty quantification for numerical models in computational physics continue to gain acceptance in nuclear modeling. Previously, the efficiency of sparse-grid stochastic collocation in comparison with Monte Carlo for uncertainty quantification through convergence studies was demonstrated. An adaptive method for anisotropic sparse grid collocation and its convergence compared to previous efforts is considered. The physical system in consideration is a two-dimensional quarter-core reactor, consisting of 5 materials distributed in 121 regions. The two-group neutron diffusion criticality approximation is solved. Vacuum boundaries are applied on the top and right, and reflecting boundaries on the bottom and left. The material cross sections, neutron multiplication factors, and diffusion coefficients are potential sources of uncertainty. Uniformly-distributed uncertainty within 5% of the reference values is introduced for material properties. The distribution of the uncertain parameters make up the uncertainty space Γ included in R{sup N}, where N is the number of uncertain parameters. The input parameter uncertainties are independently distributed. As expected, the convergence of Monte Carlo on the benchmark as a function of computational solves is nearly linear and lethargic compared to the other methods. The static isotropic index set, in which each input dimension is treated with equal importance, converges much more efficiently than Monte Carlo, but lacks the benefit of emphasizing some dimensions over others. The anisotropic case is most efficient, where first-order sensitivity information was used to determine anisotropic weights for polynomials to use in the polynomial chaos expansion. Interestingly, the adaptive algorithm converges slightly less efficiently than the anisotropic case, while still performing better than the isotropic case. Because the adaptive case has to determine the importance of each input dimension, it occasionally predicts inaccurately and wastes computation solves compared to the more ideal anisotropic case. However, in circumstances when an ideal anisotropy is not understood a priori, the adaptive algorithm may be optimally efficient in representing the original model. Given the potential loss of efficiency when using a poorly-chosen anisotropic weighting, the adaptive algorithm may be an effective choice for initial uncertainty quantification in problems with a low-dimensionality input space. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Controlling the high frequency response of H{sub 2} by ultra-short tailored laser pulses: A time-dependent configuration interaction study

We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H{sub 2} treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a “non-harmonic” response of H{sub 2} to a laser pulse. Specifically, we will show how adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗