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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An adaptive sampling augmented Lagrangian method for stochastic optimization with deterministic constraints

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is combining the augmented Lagrangian framework with adaptive sampling, resulting in an efficient optimization methodology validated with practical examples. To achieve the presented efficiency, here we consider inexact solutions for the augmented Lagrangian subproblems, and through an adaptive sampling mechanism, we control the variance in the gradient estimates. Furthermore, we analyze the theoretical performance of the proposed scheme by showing equivalence to a gradient descent algorithm on a Moreau envelope function, and we prove sublinear convergence for convex objectives and linear convergence for strongly convex objectives with affine equality constraints. The worst-case sample complexity of the resulting algorithm, for an arbitrary choice of penalty parameter in the augmented Lagrangian function, is $\mathscr{O}$(ϵ -3-δ ) , where ϵ > 0 is the expected error of the solution and δ > 0 is a user-defined parameter. If the penalty parameter is chosen to be $\mathscr{O}$(ϵ -1 ), we demonstrate that the result can be improved to $\mathscr{O}$(ϵ -2 ) , which is competitive with the other methods employed in the literature. Moreover, if the objective function is strongly convex with affine equality constraints, we obtain $\mathscr{O}$(ϵ -1 log(1/ϵ)) complexity. Finally, we empirically verify the performance of our adaptive sampling augmented Lagrangian framework in machine learning optimization and engineering design problems, including topology optimization of a heat sink with environmental uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Assimilating partial observation to enhance feedback control of stochastic dynamical systems

Here, in this paper, we present a novel methodology to tackle feedback optimal control problems in scenarios where the exact state of the controlled process is unknown. It integrates data assimilation techniques and optimal control solvers to manage partial observation of the state process, a common occurrence in practical scenarios. Traditional stochastic optimal control methods assume full state observation, which is often not feasible in real-world fluid dynamics control problems. Our approach underscores the significance of utilizing observational data to inform control policy design. Specifically, we introduce a kernel learning backward stochastic differential equation (SDE) filter to enhance data assimilation efficiency and propose a sample-wise stochastic optimization method within the stochastic maximum principle framework. We demonstrate the efficacy and accuracy of our method in the control of advection-diffusion-reaction flow problem and the Dubins airplane maneuvering problem with model uncertainty.

data driven↗
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 OSTI2021

Distribution System State Estimation With High Penetration of Demand Response Enabled Loads

Demand-side operations incentivize utility customers to take part in various grid services. A demand response enabled load (DREL) is a flexible grid asset that schedules electricity consumption in response to a time-of-use (TOU) energy price. Consequently, its energy profile differs from that of a conventional load that is insensitive to price. This difference may cause new challenges for distribution system state estimation (DSSE). It is well known that DSSE often needs to use pseudo-measurements based on historic load profiles to increase system observability. However, historic profiles of conventional loads are not representative of DREL behaviors. Additionally, the inaccuracy impacts DSSE results and other DSSE-dependent operations. In this paper, we propose an online pseudo-measurement generation approach for DSSE with DRELs. We formulate an optimization model to represent DRELs self-adjusting actions. Sampling-based stochastic optimization techniques are proposed to account for uncertainties in DRELs. A set of representative DREL behavior data corresponding to the samples are used to characterize DREL pseudo-measurements. Case studies with modified IEEE 123-bus test system verify the validity of the proposed work.

24 POWER TRANSMISSION AND DISTRIBUTION↗
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 OSTI2022

Resource distribution under spatiotemporal uncertainty of disease spread: Stochastic versus robust approaches

We consider the problem of optimizing locations of distribution centers (DCs) and plans for distributing resources such as test kits and vaccines, under spatiotemporal uncertainties of disease spread and demand for the resources. We aim to balance the operational cost (including costs of deploying facilities, shipping, and storage) and quality of service (reflected by demand coverage), while ensuring equity and fairness of resource distribution across multiple populations. We compare a sample-based stochastic programming (SP) approach with a distributionally robust optimization (DRO) approach using a moment-based ambiguity set. Numerical studies are conducted on instances of distributing COVID-19 vaccines in the United States and test kits, to compare SP and DRO models with a deterministic formulation using estimated demand and with the current resource distribution plans implemented in the US. We demonstrate the results over distinct phases of the pandemic to estimate the cost and speed of resource distribution depending on scale and coverage, and show the “demand-driven” properties of the SP and DRO solutions. Furthermore, our results further indicate that if the worst-case unmet demand is prioritized, then the DRO approach is preferred despite of its higher overall cost. Nevertheless, the SP approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Three-omega thermal-conductivity measurements with curved heater geometries

The three-omega method, a powerful technique to measure the thermal conductivity of nanometer-thick films and the interfaces between them, has historically employed straight conductive wires to act as both heaters and thermometers. When investigating stochastically prepared samples such as two-dimensional materials and nanomembranes, residue and excess material can make it difficult to fit the required millimeter-long straight wire on the sample surface. There are currently no available criteria for how diverting three-omega heater wires around obstacles affects the validity of the thermal measurement. In this Letter, we quantify the effect of the wire curvature by performing three-omega experiments with a wide range of frequencies using both curved and straight heater geometries on SiO 2 /Si samples. When the heating wire is curved, we find that the measured Si substrate thermal conductivity changes by only 0.2%. Similarly, we find that wire curvature has no significant effect on the determination of the thermal resistance of an ~65 nm SiO 2 layer, even for the sharpest corners considered here, for which the largest measured ratio of the thermal penetration depth of the applied thermal wave to radius of curvature of the heating wire is 4.3. This result provides useful design criteria for three-omega experiments by setting a lower bound for the maximum ratio of the thermal penetration depth to wire radius of curvature.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

Solving the $k$-Sparse Eigenvalue Problem with Reinforcement Learning

We examine the possibility of using a reinforcement learning (RL) algorithm to solve large-scale eigenvalue problems in which the desired the eigenvector can be approximated by a sparse vector with at most k nonzero elements, where k is relatively small compare to the dimension of the matrix to be partially diagonalized. Here, this type of problem arises in applications in which the desired eigenvector exhibits localization properties and in large-scale eigenvalue computations in which the amount of computational resource is limited. When the positions of these nonzero elements can be determined, we can obtain the k-sparse approximation to the original problem by computing eigenvalues of a k × k submatrix extracted from k rows and columns of the original matrix. We review a previously developed greedy algorithm for incrementally probing the positions of the nonzero elements in a k-sparse approximate eigenvector and show that the greedy algorithm can be improved by using an RL method to refine the selection of k rows and columns of the original matrix. We describe how to represent states, actions, rewards and policies in an RL algorithm designed to solve the k-sparse eigenvalue problem and demonstrate the effectiveness of the RL algorithm on two examples originating from quantum many-body physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Evolving Metrics for Resource Adequacy Assessment

Resource adequacy analysis quantifies the likelihood of capacity shortfall on a power system in a probabilistic manner. Using a combination of statistical techniques and power system fundamentals, the analysis typically evaluates hundreds or thousands of stochastic random samples (replications) of varying load, generator outages, variable renewable energy availability, and other aspects of power system uncertainty. In this range of uncertainty, there are - at times - periods where the power system's available resources are insufficient to meet system demand, referred to as a shortfall event. Today's power systems' rapidly evolving generation mix is changing the types of data needed by system planners and regulators, which can often render traditional resource adequacy metrics insufficient for ensuring resource adequacy for tomorrow's grid. In this paper we provide a critical assessment of traditional measures of shortfall risk in power systems, discussing their shortcomings and how they compare to metrics used in other domains. From this analysis we propose four steps forward for improving power system resource adequacy risk metrics in the future.

ENERGY PLANNING, POLICY, AND ECONOMY,POWER TRANSMI↗
DOE OSTI2022

Correlation Calculations for the Russian Pu Metal Fast Experiments

Nuclear criticality experiments are often conducted in campaigns with multiple variations. These experiments reuse the same basic components, like the fuel, moderator, or positioning machines. The components have uncertainties in their geometry and composition that propagate to models of the experiments. Shared components create shared uncertainty between the $k_{eff}$ of benchmarks. The shared uncertainty is commonly quantified with a covariance, or correlation coefficient. These covariances can impact criticality safety and nuclear data validation applications. While benchmark evaluations tabulate an experiment’s uncertainty, they often lack a detailed calculation of correlations between experiments. Even some very commonly used benchmarks, like the Russian Pu Metal Fast (PMF) experiments, have missing correlations. This paper presents our approach to calculate the correlations for five of the Russian PMF experiments. The experiments share hemispherical Pu shells that induce a correlation between modeled $k_{eff}$ values. We estimated the correlations with simplified and detailed models of the experiments through linear-perturbation theory. The correlations between the experiments vary significantly between the detailed vs. simplified models. We also investigate how the correlations affect validation metrics of the experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Beyond Expected Values Evolving Metrics for Resource Adequacy Assessment

Resource adequacy analysis quantifies the likelihood of capacity shortfall on a power system in a probabilistic manner. Using a combination of statistical techniques and power system fundamentals, the analysis typically evaluates hundreds or thousands of stochastic random samples (replications) of varying load, generator outages, variable renewable energy availability, and other aspects of power system uncertainty. In this range of uncertainty, there are - at times - periods where the power system's available resources are insufficient to meet system demand, referred to as a shortfall event. Today's power systems' rapidly evolving generation mix is changing the types of data needed by system planners and regulators, which can often render traditional resource adequacy metrics insufficient for ensuring resource adequacy for tomorrow's grid. In this paper we provide a critical assessment of traditional measures of shortfall risk in power systems, discussing their shortcomings and how they compare to metrics used in other domains. From this analysis we propose four steps forward for improving power system resource adequacy risk metrics in the future.

ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Conditional Point Sampling: A Monte Carlo Method for Radiation Transport in Stochastic Media.

Current methods for stochastic media transport are either computationally expensive or, by nature, approximate. Moreover, none of the well-developed, benchmarked approximate methods can compute the variance caused by the stochastic mixing, a quantity especially important to safety calculations. Therefore, we derive and apply a new conditional probability function (CPF) for use in the recently developed stochastic media transport algorithm Conditional Point Sampling (CoPS), which 1) leverages the full intra-particle memory of CoPS to yield errorless computation of stochastic media outputs in 1D, binary, Markovian-mixed media, and 2) leverages the full inter-particle memory of CoPS and the recently developed Embedded Variance Deconvolution method to yield computation of the variance in transport outputs caused by stochastic material mixing. Numerical results demonstrate errorless stochastic media transport as compared to reference benchmark solutions with the new CPF for this class of stochastic mixing as well as the ability to compute the variance caused by the stochastic mixing via CoPS. Using previously derived, non-errorless CPFs, CoPS is further found to be more accurate than the atomic mix approximation, Chord Length Sampling (CLS), and most of memory-enhanced versions of CLS surveyed. In addition, we study the compounding behavior of CPF error as a function of cohort size (where a cohort is a group of histories that share intra-particle memory) and recommend that small cohorts be used when computing the variance in transport outputs caused by stochastic mixing.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2026

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗