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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Feedback-Based Projected-Gradient Method for Real-Time Optimization of Aggregations of Energy Resources

This paper develops an online optimization method to maximize operational objectives of distribution-level distributed energy resources (DERs), while adjusting the aggregate power generated (or consumed) in response to services requested by grid operators. The design of the online algorithm is based on a projected-gradient method, suitably modified to accommodate appropriate measurements from the distribution network and the DERs. By virtue of this approach, the resultant algorithm can cope with inaccuracies in the representation of the AC power flows, it avoids pervasive metering to gather the state of noncontrollable resources, and it naturally lends itself to a distributed implementation. Optimality claims are established in terms of tracking of the solution of a well-posed time-varying convex optimization problem.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Feedback-Based Projected-Gradient Method For Real-Time Optimization of Aggregations of Energy Resources: Preprint

This paper develops an online optimization method to maximize the operational objectives of distribution-level distributed energy resources (DERs) while adjusting the aggregate power generated (or consumed) in response to services requested by grid operators. The design of the online algorithm is based on a projected-gradient method, suitably modified to accommodate appropriate measurements from the distribution network and the DERs. By virtue of this approach, the resultant algorithm can cope with inaccuracies in the representation of the AC power, it avoids pervasive metering to gather the state of noncontrollable resources, and it naturally lends itself to a distributed implementation. Optimality claims are established in terms of tracking of the solution of a well-posed time-varying optimization problem.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

Accelerated iterative beam angle selection in IMRT

Purpose: Iterative methods for beam angle selection (BAS) for intensity-modulated radiation therapy (IMRT) planning sequentially construct a beneficial ensemble of beam directions. In a naïve implementation, the nth beam is selected by adding beam orientations one-by-one from a discrete set of candidates to an existing ensemble of (n − 1) beams. The best beam orientation is identified in a time consuming process by solving the fluence map optimization (FMO) problem for every candidate beam and selecting the beam that yields the largest improvement to the objective function value. This paper evaluates two alternative methods to accelerate iterative BAS based on surrogates for the FMO objective function value. Methods: We suggest to select candidate beams not based on the FMO objective function value after convergence but (1) based on the objective function value after five FMO iterations of a gradient based algorithm and (2) based on a projected gradient of the FMO problem in the first iteration. The performance of the objective function surrogates is evaluated based on the resulting objective function values and dose statistics in a treatment planning study comprising three intracranial, three pancreas, and three prostate cases. Furthermore, iterative BAS is evaluated for an application in which a small number of noncoplanar beams complement a set of coplanar beam orientations. This scenario is of practical interest as noncoplanar setups may require additional attention of the treatment personnel for every couch rotation. Results: Iterative BAS relying on objective function surrogates yields similar results compared to naïve BAS with regard to the objective function values and dose statistics. At the same time, early stopping of the FMO and using the projected gradient during the first iteration enable reductions in computation time by approximately one to two orders of magnitude. With regard to the clinical delivery of noncoplanar IMRT treatments, we could show that optimized beam ensembles using only a few noncoplanar beam orientations often approach the plan quality of fully noncoplanar ensembles. Conclusions: We conclude that iterative BAS in combination with objective function surrogates can be a viable option to implement automated BAS at clinically acceptable computation times.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2023

Distributed-Memory Parallel JointNMF

Joint Nonnegative Matrix Factorization (JointNMF) is a hybrid method for mining information from datasets that contain both feature and connection information. We propose distributed-memory parallelizations of three algorithms for solving the JointNMF problem based on Alternating Nonnegative Least Squares, Projected Gradient Descent, and Projected Gauss-Newton. We extend well-known communication-avoiding algorithms using a single processor grid case to our coupled case on two processor grids. We demonstrate the scalability of the algorithms on up to 960 cores (40 nodes) with 60% parallel efficiency. The more sophisticated Alternating Nonnegative Least Squares (ANLS) and Gauss-Newton variants outperform the first-order gradient descent method in reducing the objective on large-scale problems. We perform a topic modelling task on a large corpus of academic papers that consists of over 37 million paper abstracts and nearly a billion citation relationships, demonstrating the utility and scalability of the methods.

Eswar, Srinivas↗
DOE OSTI2020

Distributed Minimization of the Power Generation Cost in Prosumer-Based Distribution Networks: Preprint

Traditionally, electrical power was generated in big power plants. The cost of producing energy was related to the cost of fuel, e.g., carbon or gas, and by the cost of maintaining the power plants. With the advent of distributed energy resources, power can be produced directly at the edge of the electrical network by a new type of agents: the prosumers. Prosumers are entities that both consume and generate power, e.g., by means of photovoltaic panels. The cost of the power produced by prosumers is no longer related to fuel consumption since energy coming from distributed generators is essentially free. Rather, the cost is related to the remuneration that is due to the prosumers for the services they provide. The proposed control strategy minimizes the active power generation cost in the aforementioned scenario. The control scheme requires that the prosumers measure their voltage and then adjust the amount of injected power, according to a continuous time feedback control law that is indeed a projected gradient descent strategy. Simulations are provided in order to illustrate the algorithm behavior.

distributed control↗
DOE OSTI2023

Protection Against Graph-Based False Data Injection Attacks on Power Systems

Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. By representing power system voltages as smooth graph signals, recent research has focused on developing GSP-based methods for state estimation, attack detection, and topology identification. Included, efficient methods have been developed for detecting false data injection (FDI) attacks, which until now were perceived as non-smooth with respect to the graph Laplacian matrix. Consequently, these methods may not be effective against smooth FDI attacks. In this paper, we propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph total variation (TV) under practical constraints. In addition, we develop a low-complexity algorithm that solves the non-convex GDFI attack optimization problem using ell_1-norm relaxation, the projected gradient descent (PGD) algorithm, and the alternating direction method of multipliers (ADMM). We then propose a protection scheme that identifies the minimal set of measurements necessary to constrain the GFDI output to high graph TV, thereby enabling its detection by existing GSP-based detectors. Our numerical simulations on the IEEE-57 bus test case reveal the potential threat posed by well-designed GSP-based FDI attacks. Moreover, we demonstrate that integrating the proposed protection design with GSP-based detection can lead to significant hardware cost savings compared to previous designs of protection methods against FDI attacks.

Morgenstern, Gal↗
DOE OSTI2025

The Effects of Compounded Model Size Reductions on Adversarial Robustness

Recent advances in Edge AI and Tiny Machine Learning (TinyML) have enabled the deployment of machine learning models on resource-constrained environments. However, deploying these models on edge devices, such as micro-controllers, requires significant model footprint reduction through a variety of techniques such as quantization, pruning, and clustering. While these optimization methods offer considerable advantages, they potentially introduce AI-related security vulnerabilities, particularly concerning model robustness with respect to adversarial AI attacks. Prior research has extensively examined the impact of quantization on adversarial robustness; however, the effects of alternative reduction techniques and their combinations remain understudied. This paper investigates the impact of model size reduction techniques on adversarial robustness, when applied individually and combined. We utilized Fast Gradient Sign Method (FGSM) and Projected Gradient Descent (PGD) attacks to generate adversarial perturbations for both training and testing data, and then evaluated the models' accuracy under adversarial training conditions. Our findings revealed that reduction techniques generally diminished robustness; although, combining techniques was not found to make robustness any worse than when applied individually. Moreover, specific techniques can potentially enhance resistance to small size perturbations. This research provides insights into the trade-offs between model size reduction and security, establishing a foundation for future investigations into improving adversarial training techniques and methodologies for maintaining robustness while preserving memory footprint benefits.

Austria, Phillipe [ORNL] (ORCID:0000000236223973)↗
DOE OSTI2016

Variational projection methods for gradient crystal plasticity using Lie algebras

Summary A computational method is developed for evaluating the plastic strain gradient hardening term within a crystal plasticity formulation. While such gradient terms reproduce the size effects exhibited in experiments, incorporating derivatives of the plastic strain yields a nonlocal constitutive model. Rather than applying mixed methods, we propose an alternative method whereby the plastic deformation gradient is variationally projected from the elemental integration points onto a smoothed nodal field. Crucially, the projection utilizes the mapping between Lie groups and algebras in order to preserve essential physical properties, such as orthogonality of the plastic rotation tensor. Following the projection, the plastic strain field is directly differentiated to yield the Nye tensor. Additionally, an augmentation scheme is introduced within the global Newton iteration loop such that the computed Nye tensor field is fed back into the stress update procedure. Effectively, this method results in a fully implicit evolution of the constitutive model within a traditional displacement‐based formulation. An elemental projection method with explicit time integration of the plastic rotation tensor is compared as a reference. A series of numerical tests are performed for several element types in order to assess the robustness of the method, with emphasis placed upon polycrystalline domains and multi‐axis loading. Copyright © 2016 John Wiley & Sons, Ltd.

Truster, Timothy J.↗
DOE OSTI2023

Nonlinear, real-time optimization for actuator management in tokamaks

Experiments in DIII-D have been carried out to test a novel actuator management approach in tokamaks. Here, the actuator management scheme is posed as a nonlinear-optimization problem in which the actuator commands are calculated in real time according to the changing control priorities, plasma state, and actuator availability. Such optimization problem is solved using the augmented Lagrangian method, combined with a gradient projection method and a conjugate-gradient iteration algorithm. The algorithmic approach followed in this work does not depend on the particular control objectives or actuators considered, which facilitates its integration with other independently-designed control components within a plasma-control system. In addition, the actuator-management algorithm is able to handle the optimization problem in a computationally efficient manner, making it suitable for real-time implementations. Initial DIII-D results in the steady-state high-q min scenario have demonstrated the capabilities of the actuator manager to perform both simultaneous multiple mission and repurposing sharing, which will be required in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

A trust region algorithm for PDE-constrained optimization with bound constraints using reduced order modeling

This paper presents a novel trust region algorithm that relies on proper orthogonal de-composition techniques to construct accurate reduced order models during optimization.The algorithm samples high fidelity snapshots to compute the POD functions that are used to generate reduced order models. The reduced order models are used to replace the computationally intensive high fidelity finite element evaluations during optimization.The proposed algorithm employs a trust region framework to detect loss in predictive ac-curacy in the reduced order model and automatically update the POD functions during optimization. The trust region framework allows the algorithm to use sound mathematical metrics to effectively improve the accuracy and robustness of the reduced order models during optimization. The algorithm also employs a projected gradient algorithm to model bound constraints and compute optimal and feasible controls.This paper also presents an accurate Hessian formulation for topology optimization problems. The proposed trust region framework relies on a quadratic model to update the control. This quadratic model needs reliable second order derivative information to predict the behavior of the objective function within a suitable trust region. If a nonlinear Hessian formulation is used, the computational effort increases due to additional finite element evaluations. The proposed linear Hessian formulation reduces the computational effort and enables the calculation of the second order derivative information without additional finite element model evaluations. Examples in topology optimization are presented to demonstrate the applicability of the proposed algorithm and linear Hessian formulation for large-scale PDE-constrained optimization.

bound constraints↗
DOE OSTI2025

Improved Guarantees for Optimal Nash Equilibrium Seeking and Bilevel Variational Inequalities

We consider a class of hierarchical variational inequality (VI) problems that subsumes VI-constrained optimization and several other problem classes, including the optimal solution selection problem and the optimal Nash equilibrium (NE) seeking problem. Our main contribution is threefold. (i) We consider bilevel VIs with monotone and Lipschitz continuous mappings and devise a single-timescale iteratively regularized extragradient method, named IR-EG 𝚖,𝚖 . We improve the existing iteration complexity results for addressing both bilevel VI and VI-constrained convex optimization problems. (ii) Under the strong monotonicity of the outer-level mapping, we develop a method named IR-EG 𝚜,𝚖 and derive faster guarantees than those in (i). We also study the iteration complexity of this method under a constant regularization parameter. These results appear to be new for both bilevel VIs and VI-constrained optimization. (iii) To our knowledge, complexity guarantees for computing the optimal NE in nonconvex settings do not exist. Motivated by this lacuna, we consider VI-constrained nonconvex optimization problems and devise an inexactly projected gradient method, named IPR-EG, where the projection onto the unknown set of equilibria is performed using IR-EG 𝚜,𝚖 with a prescribed termination criterion and an adaptive regularization parameter. We obtain new complexity guarantees in terms of a residual map and an infeasibility metric for computing a stationary point. Here, we validate the theoretical findings using preliminary numerical experiments for computing the best and the worst NEs.

bilevel optimization↗
DOE OSTI2023

SwitchX : Gmin-Gmax Switching for Energy-efficient and Robust Implementation of Binarized Neural Networks on ReRAM Xbars

Memristive crossbars can efficiently implement Binarized Neural Networks (BNNs) wherein the weights are stored in high-resistance states (HRS) and low-resistance states (LRS) of the synapses. We propose SwitchX mapping of BNN weights onto ReRAM crossbars such that the impact of crossbar non-idealities, that lead to degradation in computational accuracy, are minimized. Essentially, SwitchX maps the binary weights in such a manner that a crossbar instance comprises of more HRS than LRS synapses. We find BNNs mapped onto crossbars with SwitchX to exhibit better robustness against adversarial attacks than the standard crossbar mapped BNNs, the baseline. Finally, we combine SwitchX with state-aware training (that further increases the feasibility of HRS states during weight mapping) to boost the robustness of a BNN on hardware. We find that this approach yields stronger defense against adversarial attacks than adversarial training, a state-of the-art software defense. We perform experiments on a VGG16 BNN with benchmark datasets (CIFAR-10, CIFAR-100 and TinyImagenet) and use Fast Gradient Sign Method (ϵ = 0.05 to 0.3) and Projected Gradient Descent (ϵ = $\frac{2}{255}$ to $\frac{32}{255}$, α = $\frac{2}{255}$) adversarial attacks. We show that SwitchX combined with state-aware training can yield upto ~35% improvements in clean accuracy and ~6–16% in adversarial accuracies against conventional BNNs. Furthermore, an important by-product of SwitchX mapping is increased crossbar power savings, owing to an increased proportion of HRS synapses, which is furthered with state-aware training. We obtain upto ~21–22% savings in crossbar power consumption for state-aware trained BNN mapped via SwitchX on 16 × 16 and 32 × 32 crossbars using the CIFAR-10 and CIFAR-100 datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

DP-TwoLevel: two-stage gradient subspace learning for differentially private federated learning

Federated learning (FL) enables collaborative model training across distributed data sources without sharing raw data, but faces fundamental challenges in communication efficiency and privacy. Differentially private (DP) training mitigates information leakage but introduces noise that degrades model performance, especially in high-dimensional settings. We propose DP-TwoLevel, a hierarchical gradient projection method that improves utility under fixed DP constraints by exploiting low-dimensional structure in model updates. Our approach learns a two-level PCA-based representation of gradients and applies DP noise in a reduced-dimensional subspace, thereby lowering the effective noise magnitude while preserving dominant signal components. We evaluate the method across three datasets (MNIST, Fashion-MNIST, CIFAR-10) and three privacy regimes (ϵ∈0.5, 1.0, 2.0). Across nine experimental settings, DP-TwoLevel consistently outperforms DP-FedAvg, achieving an average accuracy improvement of 9.44%, with larger gains observed in lower ϵ(higher-noise) regimes (up to +22.31%). We further analyze scalability across models ranging from 100K to 1.49M parameters and identify a variance-based success criterion: performance remains strong when the projection preserves more than 75% of gradient variance, degrades in a marginal regime (65–75%), and fails below this threshold. Our results demonstrate that structure-aware dimensionality reduction can significantly improve the privacy–utility tradeoff in FL without modifying formal privacy guarantees. We also provide empirical evidence of scaling limitations for global projections and motivate per-layer extensions for larger models.

Kotevska, Olivera [ORNL] (ORCID:0000000316772243)↗
DOE OSTI2025

On the Sampling-Based Computation of Nash Equilibria Under Uncertainty via the Nikaido–Isoda Function

We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be L 0 -Lipschitz continuous and convex, given rival decisions with convex and closed player-specific feasibility sets. To address this problem, we consider minimizing a suitably defined value function defined using the Nikaido–Isoda function. Such an avenue does not necessitate either monotonicity properties of the concatenated gradient map or potentiality requirements on the game but does require a suitable regularity requirement under which a stationary point is a Nash equilibrium. We design and analyze a sampling-enabled projected-gradient-response method, reliant on inexact resolution of a player-level best-response subproblem. Here, by deriving suitable Lipschitzian guarantees on the value function, we derive both asymptotic guarantees for the sequence of generated iterates as well as rate and complexity guarantees for computing a stationary point by appropriate choices of the sampling rate and inexactness sequence.

Nikaido-Isoda function↗
DOE OSTI2020

MimicGAN: Robust Projection onto Image Manifolds with Corruption Mimicking

In the past few years, Generative Adversarial Networks (GANs) have dramatically advanced our ability to represent and parameterize high-dimensional, non-linear image manifolds. As a result, they have been widely adopted across a variety of applications, ranging from challenging inverse problems like image completion, to problems such as anomaly detection and adversarial defense. A recurring theme in many of these applications is the notion of projecting an image observation onto the manifold that is inferred by the generator. In this context, Projected Gradient Descent (PGD) has been the most popular approach, which essentially optimizes for a latent vector that minimizes the discrepancy between a generated image and the given observation. However, PGD is a brittle optimization technique that fails to identify the right projection (or latent vector) when the observation is corrupted, or perturbed even by a small amount. Such corruptions are common in the real world, for example images in the wild come with unknown crops, rotations, missing pixels, or other kinds of non-linear distributional shifts which break current encoding methods, rendering downstream applications unusable. To address this, we propose corruption mimicking—a new robust projection technique, that utilizes a surrogate network to approximate the unknown corruption directly at test time, without the need for additional supervision or data augmentation. The proposed method is significantly more robust than PGD and other competing methods under a wide variety of corruptions, thereby enabling a more effective use of GANs in real-world applications. Finally, more importantly, we show that our approach produces state-of-the-art performance in several GAN-based applications—anomaly detection, domain adaptation, and adversarial defense, that benefit from an accurate projection.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Constructing the Pareto front for multi-objective Markov chains handling a strong Pareto policy approach

In this paper, we present a multi-objective solution of the Pareto front for a certain class of discrete-time ergodic controllable Markov chains. For solving the problem, we transform the original multi-objective problem into an equivalent nonlinear programming problem implementing the Lagrange principle. We then propose to adopt the Tikhonov’s regularization method to ensure the convergence of the cost functions to a unique point into the Pareto front. We show that Pareto policies are characterized as optimal policies. One of the fundamental problems related to the construction of the Pareto front is the existence and characterization of both, Pareto and strong Pareto policies. By introducing the Tikhonov’s regularizator, we ensure the existence of strong Pareto policies. This paper proposes a real solution to this problem. We formulate the original problem considering several constraints: (a) we employ the c-variable method for the introduction of linear constraints over the nonlinear problem and (b) restrict the cost functions, allowing points in the Pareto front to have a small distance from one another. The constraints imposed by the c-variable method make the problem computationally tractable and the restriction imposed by the small distance change ensures the continuation of the Pareto front. The resulting equation in this nonlinear system is an optimization problem for which the necessary and efficient condition of a minimum is solved using the projected gradient method. Moreover, we also prove the convergence conditions and compute the estimate rate of convergence of variables corresponding to the Lagrange principle and the Tikhonov’s regularization, respectively. We provide all the details needed to implement the proposed method in an efficient way. The usefulness of the method is successfully demonstrated by a numerical example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On convergent finite difference schemes for variational–PDE-based image processing

We study an adaptive anisotropic Huber functional-based image restoration scheme. Using a combination of L2–L1 regularization functions, an adaptive Huber functional-based energy minimization model provides denoising with edge preservation in noisy digital images. We study a convergent finite difference scheme based on continuous piecewise linear functions and use a variable splitting scheme, namely the Split Bregman (In: Goldstein and Osher, SIAM J Imaging Sci 2(2):323–343, 2009) algorithm, to obtain the discrete minimizer. Experimental results are given in image denoising and comparison with additive operator splitting, dual fixed point, and projected gradient schemes illustrates that the best convergence rates are obtained for our algorithm.

97 MATHEMATICS AND COMPUTING↗