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Results for “Stochastic optimization”

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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗
DOE OSTI2026

ExaGO v2

ExaGO is a high-performance computing power systems modeling suite providing models for different power flow analyses. It supports forward AC power flow, multiperiod AC and DC optimal power flow analyses, contingency analysis, as well as stochastic optimal power flow analysis. ExaGO can use HiOp and Ipopt optimization engines. It supports Matpower and PSS/E input file formats. ExaGO v2 includes code from ExaGO 1.6.0.

Peles, Slaven [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2019

Next-Generation Optimization under Uncertainty: Structure-Oriented Algorithms

With the advent of the smart grid, renewable technologies, and carbon emission programs, a key concern is the coordination of national infrastructures such as the electricity, natural gas, and water supply network systems. Anticipating and mitigating uncertainty of weather, demands, and contingencies in a more integrated environment is necessary to maximize resource efficiency and prevent cascading failures that can ultimately lead to catastrophic shortages of supplies. This project developed scalable algorithms for stochastic optimization capable of addressing extreme-scale problems (motivated by challenges in the design and operation of national infrastructures). Specifically, the project developed a new family of algorithms to solve continuous stochastic problems to local and global optimality as well as algorithms to solve mixed-integer convex and nonconvex stochastic programs. We developed supporting local and global convergence theory for these algorithms and implemented the algorithms in open-source software packages that can leverage high-performance computing architectures.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Nonlinear Optimization Methods for Large-Scale Learning

Future advances in large-scale machine learning depend heavily on the availability of new and more powerful nonlinear optimization methods. The goal of this project is to address this challenge by designing new optimization algorithms that can deal with the scale, nonlinearity and stochasticity arising in machine learning models. Our research will provide the theoretical foundations for the new methods, and will involve intensive numerical testing on state-of-the-art machine learning systems. The project is organized into three interrelated projects that constitute a broad research agenda in the area of large-scale stochastic optimization for data science.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Efficient Generalizable Deep Learning

Stochastic optimization is a fundamental field of research for machine learning. Stochastic gradient descent (SGD) and related methods provide a feasible means to train complicated prediction models over large datasets. SGD, however, does not explicitly address the problem of overfitting, which can lead to predictions that perform poorly on new data. This difference between loss performance on unseen testing data verses that of training data defines the generalization gap of a model. We introduce a new computational kernel called Stochastic Hessian Projection (SHP) that uses a maximum likelihood framework to simultaneously estimate gradient noise covariance and local curvature of the loss function. Our analysis illustrates that these quantities affect the evolution of parameter uncertainty and therefore generalizability. We show how these computations allow us to predict the generalization gap without requiring holdout data. Explicitly assessing this metric for generalizability during training may improve machine learning predictions when data is scarce and understanding prediction variability is critical.

42 ENGINEERING↗
DOE OSTI2022

Optimization of Integrated Energy Systems

Integrated energy systems that couple nuclear power plants with additional products including hydrogen, storage, or synthetic fuels provide a more flexible energy source that can be more economical than generating electricity alone. Determining the size and shape of these systems and optimizing their operation is challenging. INL, through the IES program, has developed optimization software to help solve these challenges. Holistic Energy Resource Optimization Network (HERON) is a software tool to optimize the size and capacity of integrated energy systems using stochastic optimization. Optimization of Real-time Capacity Allocation (ORCA) is a software tool under development to perform real-time economic optimization of these systems using economic model predictive control. An overview of these tools and a discussion of their optimization methods will be presented in this talk.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Minimizing Uncertainties Impact in Decision Making with an Applicability Study for Economic Power Dispatch

This report summaries the work performed under the LDRD project on the preliminary study on knowledge automation, where specific focus has been made on the investigation of the impact of uncertainties of human decision making onto the optimization of the process operation. At first the statistics on signals from the Brain-Computing Interface (BCI) is analyzed so as to obtain the uncertainties characterization of human operators during the decision making phase using the electroencephalogram (EEG) signals. This is then followed by the discussions of an architecture that reveals the equivalence between optimization and closed loop feedback control design, where it has been shown that all the optimization problems can be transferred into the control design problem for closed loop systems. This has led to a “closed loop” framework, where the structure of the decision making is shown to be subjected to both process disturbances and controller’s uncertainties. The latter can well represent the uncertainties or randomness occurred during human decision making phase. As a result, a stochastic optimization problem has been formulated and a novel solution has been proposed using probability density function (PDF) shaping for both the cost function and the constraints using stochastic distribution control concept. A sufficient condition has been derived that guarantees the convergence of the optimal solution and discussions have been made for both the total probabilistic solution and chanced constrained optimization which have been well-studied in optimal power flows (OPF) area. A simple case study has been carried out for the economic dispatch of powers for a grid system when there are distributed energy resources (DERs) in the system, and encouraging results have been obtained showing that a significant savings on the generation cost can be expected.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2024

Tensor decompositions for count data that leverage stochastic and deterministic optimization

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the maximum likelihood estimator (MLE) of the Poisson CPD model. Here, this work presents two new algorithms that extend state-of-the-art local methods for Poisson CPD. Hybrid GCP-CPAPR combines Generalized Canonical Decomposition (GCP) with stochastic optimization and CP Alternating Poisson Regression (CPAPR), a deterministic algorithm, to increase the probability of converging to the MLE over either method used alone. Restarted CPAPR with SVDrop uses a heuristic based on the singular values of the CPD model unfoldings to identify convergence toward optimizers that are not the MLE and restarts within the feasible domain of the optimization problem, thus reducing overall computational cost when using a multi-start strategy. We provide empirical evidence that indicates our approaches outperform existing methods with respect to converging to the Poisson CPD MLE.

CPAPR↗
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 OSTI2024

Efficient Parameterization of Density Functional Tight-Binding for 5 f -Elements: A Th–O Case Study

Density functional tight binding (DFTB) models for f-element species are challenging to parametrize owing to the large number of adjustable parameters. The explicit optimization of the terms entering the semiempirical DFTB Hamiltonian related to f orbitals is crucial to generating a reliable parametrization for f-block elements, because they play import roles in bonding interactions. However, since the number of parameters grows quadratically with the number of orbitals, the computational cost for parameter optimization is much more expensive for the f-elements than for the main group elements. In this work we present a set of efficient approaches for mitigating the hurdle imposed by the large size of the parameter space. A novel group-by-orbital correction functions for two-center bond integrals was developed. With this approach the number of parameters is reduced, and it grows linearly with the number of elements, maintaining the accuracy and the number of parameters, in the case of f elements, by more than 40%. The parameter optimization step was accelerated by means of the mini-batch BFGS method. This method allows parameter optimizations with much larger training sets than other single batch methods. A stochastic optimizer was employed that helped overcome shallow local minima in the objective function. The proposed algorithm was used to parametrize the DFTB Hamiltonian for the Th–O system, which was subsequently applied to the study of ThO 2 nanoparticles. The training set consisted of 6322 unique structures, which is barely feasible with conventional optimization methods. The optimized parameter set, LANL-ThO, displays good agreement with DFT-calculated properties such as energies, forces, and structures for both clusters and bulk ThO 2 . Benefiting from the fewer number of parameters and lower computational costs for objective function evaluations, this new approach shows its potential applications in DFTB parametrization for elements with high angular momentum, which present a challenge to conventional methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Variational design principles for nonequilibrium colloidal assembly

Using large deviation theory and principles of stochastic optimal control, we show that rare molecular dynamics trajectories conditioned on assembling a specific target structure encode a set of interactions and external forces that lead to enhanced stability of that structure. Such a relationship can be formulated into a variational principle, for which we have developed an associated optimization algorithm and have used it to determine optimal forces for targeted self-assembly within nonequilibrium steady-states. We illustrate this perspective on inverse design in a model of colloidal cluster assembly within linear shear flow. We find that colloidal clusters can be assembled with high yield using specific short-range interactions of tunable complexity. Shear decreases the yields of rigid clusters, while small values of shear increase the yields of nonrigid clusters. The enhancement or suppression of the yield due to shear is rationalized with a generalized linear response theory. Furthermore, by studying 21 unique clusters made of six, seven, or eight particles, we uncover basic design principles for targeted assembly out of equilibrium.

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

Stochastic Methods Applied to Power System Operations with Renewable Energy: A Review

Renewable energy resources have been rapidly integrated into power systems in many parts of the world, contributing to a cleaner and more sustainable supply of electricity. Wind and solar resources also introduce new challenges for system operations and planning in terms of economics and reliability because of their variability and uncertainty. Operational strategies based on stochastic optimization have been developed recently to address these challenges. In general terms, these stochastic strategies either embed uncertainties into the scheduling formulations (e.g., the unit commitment [UC] problem) in probabilistic forms or develop more appropriate operating reserve strategies to take advantage of advanced forecasting techniques. Other approaches to address uncertainty are also proposed, where operational feasibility is ensured within an uncertainty set of forecasting intervals. In this report, a comprehensive review is conducted to present the state of the art through Spring 2015 in the area of stochastic methods applied to power system operations with high penetration of renewable energy. Chapters 1 and 2 give a brief introduction and overview of power system and electricity market operations, as well as the impact of renewable energy and how this impact is typically considered in modeling tools. Chapter 3 reviews relevant literature on operating reserves and specifically probabilistic methods to estimate the need for system reserve requirements. Chapter 4 looks at stochastic programming formulations of the UC and economic dispatch (ED) problems, highlighting benefits reported in the literature as well as recent industry developments. Chapter 5 briefly introduces alternative formulations of UC under uncertainty, such as robust, chance-constrained, and interval programming. Finally, in Chapter 6, we conclude with the main observations from our review and important directions for future work.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Optimal mitigation and control over power system dynamics for stochastic grid resilience

Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the western system coordinating council 9-bus test system using synthetic multi-device outage scenarios.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2021

Multiobjective Modular Biorefinery Configuration under Uncertainty

With increasing interest in using biomass as a raw material for fuel, the development of biorefineries is an active area of research. However, increasing market competition, uncertainty, and environmental concerns are a few of the challenges that need to be addressed. In this work, mathematical optimization formulations are proposed to address these challenges simultaneously. A multiobjective deterministic optimization framework is proposed to address economic and environmental objectives. A two-stage stochastic optimization framework is proposed to account for uncertainties in material flow and product yields. To model the environmental objective, an environmental risk metric is proposed. Finally, as modularization is gaining popularity in the process industry due to its ability to save capital cost because of standardization and reduce time to market, a formulation for simultaneously achieving modular process design and biorefinery configuration is proposed. Furthermore, the results demonstrate the efficacy of the proposed approach.

09 BIOMASS FUELS↗
DOE OSTI2016

Data centers as dispatchable loads to harness stranded power

Here, we analyze how traditional data center placement and optimal placement of dispatchable data centers affect power grid efficiency. We use detailed network models, stochastic optimization formulations, and diverse renewable generation scenarios to perform our analysis. Our results reveal that significant spillage and stranded power will persist in power grids as wind power levels are increased. A counter-intuitive finding is that collocating data centers with inflexible loads next to wind farms has limited impacts on renewable portfolio standard (RPS) goals because it provides limited system-level flexibility. Such an approach can, in fact, increase stranded power and fossil-fueled generation. In contrast, optimally placing data centers that are dispatchable provides system-wide flexibility, reduces stranded power, and improves efficiency. In short, optimally placed dispatchable computing loads can enable better scaling to high RPS. In our case study, we find that these dispatchable computing loads are powered to 60-80% of their requested capacity, indicating that there are significant economic incentives provided by stranded power.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

WE-AB-303-06: Combining DAO with MV + KV Optimization to Improve Skin Dose Sparing with Real-Time Fluoroscopy

Purpose: Real-time fluoroscopy may allow for improved patient positioning and tumor tracking, particularly in the treatment of lung tumors. In order to mitigate the effects of the imaging dose, previous studies have demonstrated the effect of including both imaging dose and imaging constraints into the inverse treatment planning object function. That method of combined MV+kV optimization may Result in plans with treatment beams chosen to allow for more gentle imaging beam-on times. Direct-aperture optimization (DAO) is also known to produce treatment plans with fluence maps more conducive to lower beam-on times. Therefore, in this work we demonstrate the feasibility of a combination of DAO and MV+kV optimization for further optimized real-time kV imaging. Methods: Therapeutic and imaging beams were modeled in the EGSnrc Monte Carlo environment, and applied to a patient model for a previously treated lung patient to provide dose influence matrices from DOSXYZnrc. An MV + kV IMRT DAO treatment planning system was developed to compare DAO treatment plans with and without MV+kV optimization. The objective function was optimized using simulated annealing. In order to allow for comparisons between different cases of the stochastically optimized plans, the optimization was repeated twenty times. Results: Across twenty optimizations, combined MV+kV IMRT resulted in an average of 12.8% reduction in peak skin dose. Both non-optimized and MV+kV optimized imaging beams delivered, on average, mean dose of approximately 1 cGy per fraction to the target, with peak doses to target of approximately 6 cGy per fraction. Conclusion: When using DAO, MV+kV optimization is shown to Result in improvements to plan quality in terms of skin dose, when compared to the case of MV optimization with non-optimized kV imaging. The combination of DAO and MV+kV optimization may allow for real-time imaging without excessive imaging dose. Financial support for the work has been provided in part by NIH Grant T32 EB002103, ACS RSG-13-313-01-CCE, and NIH S10 RR021039 and P30 CA14599 grants. The contents of this submission do not necessarily represent the official views of any of the supporting organizations.

60 APPLIED LIFE SCIENCES↗