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Results for “Stochastic Algorithms”

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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Fluctuating hydrodynamics and the Rayleigh–Plateau instability

The Rayleigh–Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to interfacial energy densities. Consequently, at these scales, thermal fluctuations play a significant role in the dynamics of the instability. These microscopic effects have previously been investigated numerically using particle-based simulations, such as molecular dynamics (MD), and stochastic partial differential equation–based hydrodynamic models, such as stochastic lubrication theory. In this paper, we present an incompressible fluctuating hydrodynamics model with a diffuse-interface formulation for binary fluid mixtures designed for the study of stochastic interfacial phenomena. An efficient numerical algorithm is outlined and validated in numerical simulations of stable equilibrium interfaces. We present results from simulations of the Rayleigh–Plateau instability for long cylinders pinching into droplets for Ohnesorge numbers of Oh = 0.5 and 5.0. Both stochastic and perturbed deterministic simulations are analyzed and ensemble results show significant differences in the temporal evolution of the minimum radius near pinching. Short cylinders, with lengths less than their circumference, were also investigated. As previously observed in MD simulations, we find that thermal fluctuations cause these to pinch in cases where a perturbed cylinder would be stable deterministically. Finally, we show that the fluctuating hydrodynamics model can be applied to study a broader range of surface tension–driven phenomena.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Routing Problem for Unmanned Aerial Vehicle Patrolling Missions - A Progressive Hedging Algorithm

This paper presents a two-stage stochastic program to model a routing problem involving an Unmanned Aerial Vehicle (UAV) in the context of patrolling missions. In particular, given a set of targets and a set of supplemental targets corresponding to each target, the first stage decisions involve finding the sequence in which the vehicle has to visit the set of targets. Upon reaching each target, the UAV collects information and if the operator of the UAV deems that the information collected is not of sufficient fidelity, then the UAV has to visit all the supplemental targets corresponding to that target to collect additional information before proceeding to visit the next target. The problem is solved using a progressive hedging algorithm and extensive computational results corroborating the effectiveness of the proposed model and the solution methodology is presented.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2019

Heterogeneous local dynamics revealed by classification analysis of spatially disaggregated time series data

Time series data provide a crucial window into infectious disease dynamics, yet their utility is often limited by the spatially aggregated form in which they are presented. When working with time series data, violating the implicit assumption of homogeneous dynamics below the scale of spatial aggregation could bias inferences about underlying processes. We tested this assumption in the context of the 2015–2016 Zika epidemic in Colombia, where time series of weekly case reports were available at national, departmental, and municipal scales. First, we performed a descriptive analysis, which showed that the timing of departmental-level epidemic peaks varied by three months and that departmental-level estimates of the time-varying reproduction number, R(t), showed patterns that were distinct from a national-level estimate. Second, we applied a classification algorithm to six features of proportional cumulative incidence curves, which showed that variability in epidemic duration, the length of the epidemic tail, and consistency with a cumulative normal density curve made the greatest contributions to distinguishing groups. Third, we applied this classification algorithm to data simulated with a stochastic transmission model, which showed that group assignments were consistent with simulated differences in the basic reproduction number, R0. This result, along with associations between spatial drivers of transmission and group assignments based on observed data, suggests that the classification algorithm is capable of detecting differences in temporal patterns that are associated with differences in underlying drivers of incidence patterns. Overall, this diversity of temporal patterns at local scales underscores the value of spatially disaggregated time series data.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Randomized Federated Learning Methods for Nonsmooth, Nonconvex, and Hierarchical Optimization (Final Technical Report)

This final technical report summarizes the outcomes of a DOE-funded project on federated scientific machine learning (FL) under nonsmooth, nonconvex, and hierarchical optimization settings. The project develops new mathematical models, algorithms, and theoretical guarantees for decentralized stochastic, bilevel, and minimax optimization problems arising in DOE mission-relevant applications. A unified framework of randomized and zeroth-order federated optimization methods is introduced, providing provable convergence, communication efficiency, and sample-complexity guarantees. The report documents algorithmic design, theoretical analysis, and empirical validation of the proposed federated learning methods. The project also contributes to workforce development through graduate training and dissemination of results via publications and seminars.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Using a derivative-free optimization method for multiple solutions of inverse transport problems

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a mesh adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.

42 ENGINEERING↗
DOE OSTI2018

Simple, direct and efficient multi-way spectral clustering

Abstract We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct and requires no initial guess. Furthermore, it scales linearly in the number of nodes of the graph and a randomized variant provides significant computational gains. Provided the subspace spanned by the eigenvectors used for clustering contains a basis that resembles the set of indicator vectors on the clusters, we prove that both our deterministic and randomized algorithms recover a basis close to the indicators in Frobenius norm. We also experimentally demonstrate that the performance of our algorithm tracks recent information theoretic bounds for exact recovery in the stochastic block model. Finally, we explore the performance of our algorithm when applied to a real-world graph.

Damle, Anil↗
DOE OSTI2025

Seasonal Reconfiguration of Electrical Distribution Systems to Mitigate the Impact of Electric Vehicle Charging

Power grids face challenges in their infrastructure related to the integration of electric vehicles (EV). In particular, EV charging stations may induce instability in key system parameters such as substantial voltage drops, active power losses, and transformer overload due to high demand during charging periods. This article presents a seasonal reconfiguration strategy based on the differential evolution (DE) algorithm, aimed at enhancing system performance under highly variable and stochastic load profiles, particularly those driven by EV charging. The DEA algorithm is hybridized with the find-union (FU) algorithm to efficiently ensure network radiality throughout the optimization process. The proposed methodology is validated on a hybrid distribution system composed of the IEEE 33-bus network, a modified IEEE 13-bus system, and a specific 13-bus microgrid. Results have demonstrated that seasonal reconfiguration significantly reduces active power losses and mitigates transformer loading during critical demand hours, thereby quantifiably increasing the system’s performance. As an integral component of the proposed approach, an analysis of CO2 emissions associated with energy losses is included, allowing a contextualized assessment of the environmental benefits of seasonal reconfiguration in various geographical areas.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Pilot Point Optimization of Mining Boundaries for Lateritic Metal Deposits: Finding the Trade-off Between Dilution and Ore Loss

Geological contacts in lateritic metal deposits (footwall topographies) often delineate the orebody boundaries. Spatial variations seen in such contacts are frequently higher than those for the metal grades of the deposit. Therefore, borehole spacing chosen based on the grade variations cannot adequately capture the geological contact variability. Consequently, models created using such boreholes cause high volumetric uncertainties in the actual and targeted ore extraction volumes, which, in turn, lead to high unplanned dilution and ore losses. In this paper, a method to design optimum ore/mining boundaries for lateritic metal deposits is presented. The proposed approach minimizes the dilution/ore losses and comprises two main steps. First, the uncertainty on the orebody boundary is represented using a set of stochastic realizations generated with a multiple-point statistics algorithm. Then, the optimal orebody boundary is determined using an optimization technique inspired by a model calibration method called Pilot Points. The pilot points represent synthetic elevation values, and they are used to construct smooth mining boundaries using the multilevel B-spline technique. The performance of a generated surface is evaluated using the expected sum of losses in each of the stochastic realizations. The simulated annealing algorithm is used to iteratively determine the pilot point values which minimize the expected losses. The results show a significant reduction in the dilution volume as compared to those obtained from the actual mining operation.

58 GEOSCIENCES↗
DOE OSTI2016

Aerodynamic optimization of supersonic compressor cascade using differential evolution on GPU

Differential Evolution (DE) is a powerful stochastic optimization method. Compared to gradient-based algorithms, DE is able to avoid local minima but requires at the same time more function evaluations. In turbomachinery applications, function evaluations are performed with time-consuming CFD simulation, which results in a long, non affordable, design cycle. Modern High Performance Computing systems, especially Graphic Processing Units (GPUs), are able to alleviate this inconvenience by accelerating the design evaluation itself. In this work we present a validated CFD Solver running on GPUs, able to accelerate the design evaluation and thus the entire design process. An achieved speedup of 20x to 30x enabled the DE algorithm to run on a high-end computer instead of a costly large cluster. The GPU-enhanced DE was used to optimize the aerodynamics of a supersonic compressor cascade, achieving an aerodynamic loss minimization of 20%.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Concurrent Monte Carlo transport and fluence optimization with fluence adjusting scalable transport Monte Carlo

Purpose: The future of radiation therapy will require advanced inverse planning solutions to support single-arc, multiple-arc, and “4π” delivery modes, which present unique challenges in finding an optimal treatment plan over a vast search space, while still preserving dosimetric accuracy. The successful clinical implementation of such methods would benefit from Monte Carlo (MC) based dose calculation methods, which can offer improvements in dosimetric accuracy when compared to deterministic methods. The standard method for MC based treatment planning optimization leverages the accuracy of the MC dose calculation and efficiency of well-developed optimization methods, by precalculating the fluence to dose relationship within a patient with MC methods and subsequently optimizing the fluence weights. However, the sequential nature of this implementation is computationally time consuming and memory intensive. Methods to reduce the overhead of the MC precalculation have been explored in the past, demonstrating promising reductions of computational time overhead, but with limited impact on the memory overhead due to the sequential nature of the dose calculation and fluence optimization. The authors propose an entirely new form of “concurrent” Monte Carlo treat plan optimization: a platform which optimizes the fluence during the dose calculation, reduces wasted computation time being spent on beamlets that weakly contribute to the final dose distribution, and requires only a low memory footprint to function. In this initial investigation, the authors explore the key theoretical and practical considerations of optimizing fluence in such a manner. Methods: The authors present a novel derivation and implementation of a gradient descent algorithm that allows for optimization during MC particle transport, based on highly stochastic information generated through particle transport of very few histories. A gradient rescaling and renormalization algorithm, and the concept of momentum from stochastic gradient descent were used to address obstacles unique to performing gradient descent fluence optimization during MC particle transport. The authors have applied their method to two simple geometrical phantoms, and one clinical patient geometry to examine the capability of this platform to generate conformal plans as well as assess its computational scaling and efficiency, respectively. Results: The authors obtain a reduction of at least 50% in total histories transported in their investigation compared to a theoretical unweighted beamlet calculation and subsequent fluence optimization method, and observe a roughly fixed optimization time overhead consisting of ∼10% of the total computation time in all cases. Finally, the authors demonstrate a negligible increase in memory overhead of ∼7–8 MB to allow for optimization of a clinical patient geometry surrounded by 36 beams using their platform. Conclusions: This study demonstrates a fluence optimization approach, which could significantly improve the development of next generation radiation therapy solutions while incurring minimal additional computational overhead.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Performant Optimization Strategies for Multifidelity Stochastic Power Grid Models

This talk goes into the algorithmic work done under the Forest project in order to solve expensive power grid models. We explore multiple fidelities of models that balance accuracy and computational expense. We use bundling strategies and progressive hedging in order to parallelize large stochastic programs.

Alfant, Rachael May [Sandia National Laboratories ↗
DOE OSTI2022

Scalable Energy System Expansion Under Uncertainty Using Multi-Stage Stochastic Optimization

The intermittent nature of power from renewable energy sources poses new challenges for electrical grids. This is due to the variable and uncertain nature of the power output from these resources. These features of renewable generation are becoming more relevant to energy system planning as grids reach higher penetration levels of renewable energy. In this presentation we present approaches for energy system planning based on scalable computational approaches which enable the explicit consideration of operational uncertainties in the planning process. Using multi-stage stochastic programming and the progressive hedging algorithm, we compute energy system expansion decisions on modified versions of the RTS-GMLC test system augmented with large amounts of renewable generation.

MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Reserve Model of Energy Storage in Day-ahead Joint Energy and Reserve Markets: A Stochastic UC Solution

With many favorable advantages including fast response ability in particular, utility-level energy storage systems (ESS) are being integrated into energy and reserve markets to help mitigate uncertain renewable resources and fluctuant demands. This paper discusses a stochastic unit commitment (UC) model to explore capabilities of ESSs in providing valuable grid services by simultaneously joining energy and reserve markets. The proposed reserve model of ESSs presents the following features: (i) two constraints are proposed to formulate ESS’s reserve provision ability in each hour via six operation modes, namely increasing/reducing the level of charge, switching to discharge, increasing/reducing the level of discharge, switching to charge; (ii) as an energy-limited asset, constraints on ESS’s reserve deliverability across multiple hours is introduced to hold enough state of charge (SOC) headroom and floor room, guaranteeing that reserves cleared in individual hours are continuously deliverable over multiple successive hours without violating operation limits. Furthermore, a scenario-based UC model, which addresses uncertainties of renewables and demands, is adopted to evaluate reserves provided by ESSs and generators. To effectively solve the stochastic UC problem, the progressive hedging algorithm with heuristic approaches is discussed. A 6-bus system and a modified IEEE 118-bus system are used to illustrate effectiveness of the proposed approaches.

25 ENERGY STORAGE↗
DOE OSTI2020

GentenMPI: Distributed Memory Sparse Tensor Decomposition

GentenMPl is a toolkit of sparse canonical polyadic (CP) tensor decomposition algorithms that is designed to run effectively on distributed-memory high-performance computers. Its use of distributed-memory parallelism enables it to efficiently decompose tensors that are too large for a single compute node's memory. GentenMPl leverages Sandia's decades-long investment in the Trilinos solver framework for much of its parallel-computation capability. Trilinos contains numerical algorithms and linear algebra classes that have been optimized for parallel simulation of complex physical phenomena. This work applies these tools to the data science problem of sparse tensor decomposition. In this report, we describe the use of Trilinos in GentenMPl, extensions needed for sparse tensor decomposition, and implementations of the CP-ALS (CP via alternating least squares) and GCP-SGD (generalized CP via stochastic gradient descent) sparse tensor decomposition algorithms. We show that GentenMPl can decompose sparse tensors of extreme size, e.g., a 12.6-terabyte tensor on 8192 computer cores. We demonstrate that the Trilinos backbone provides good strong and weak scaling of the tensor decomposition algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Scalable Energy System Expansion Under Uncertainty Using Multi-Stage Stochastic Optimization

The intermittent nature of renewable energy sources poses challenges for electrical grids. This is due to the variable and uncertain nature of the power output from these resources. These features of renewable generation are more relevant to energy system planning as grids reach higher penetration levels of renewable energy. We present approaches for energy system planning based on scalable computational approaches which enable explicit consideration of operational uncertainties in the planning process. Using multi-stage stochastic programming and the progressive hedging algorithm, we compute energy system expansion decisions on modified versions of the RTS-GMLC test system.

electrical↗
DOE OSTI2020

Scalable Transmission Expansion Under Uncertainty Using Three-Stage Stochastic Optimization

The intermittent nature of renewable energy poses new challenges for power grids due to its variable and uncertain power output. These features of renewable generation are becoming more relevant to transmission planning as grids reach higher penetration levels of renewable energy. In this paper we present an approach for transmission planning based on scalable computational approaches which enable the explicit consideration of operational uncertainties in the planning process. Using three-stage stochastic programming and the progressive hedging algorithm, we compute transmission expansion decisions on a modified RTS-GMLC test system. We augment the grid with large amounts of wind generation and consider many operational scenarios subject to wind uncertainty.

multi-stage stochastic optimization↗
DOE OSTI2015

An Assessment of the Impact of Stochastic Day-Ahead SCUC on Economic and Reliability Metrics at Multiple Timescales

This paper incorporates the stochastic day-ahead security-constrained unit commitment (DASCUC) within a multi-timescale, multi-scheduling application with commitment, dispatch, and automatic generation control. The stochastic DASCUC is solved using a progressive hedging algorithm with constrained ordinal optimization to accelerate the individual scenario solution. Sensitivity studies are performed in the RTS-96 system, and the results show how this new scheduling application would impact costs and reliability with a closer representation of timescales of system operations in practice.

24 POWER TRANSMISSION AND DISTRIBUTION↗