Search NASA⌕ Search

SEARCH · Search NASA

Results for “Iterative methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

Convergence Analysis of Fixed Point Chance Constrained Optimal Power Flow Problems

For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not necessarily guaranteed. Here this article analyses the convergence conditions for this fixed point approach, and reports numerical experiments including for large IEEE networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Multigrid Algorithms with Projection and Prolongation over Elements of the Phase Space for K-Eigenvalue Transport Problems

This paper describes new multilevel acceleration methods for solving the multigroup neu- tron transport eigenvalue problems. These multilevel algorithms use different projection and prolongation operators in the phase space. The Nonlinear Diffusion Acceleration (NDA) method with multiple grids in energy is formulated with the prolongation oper- ator based on multiplication iterative correction and linear-in-energy mapping. Another multilevel NDA method uses the projection operator with coarsening in energy between the high-order transport and low-order NDA equations. The third algorithm is formu- lated with the partial-current based CMFD low-order equations and applies projection operators in space and energy. The numerical results are presented.

Cornejo, Luke↗

Simulation of electron Bernstein waves using FullWave with a 2D non-local hot plasma model

Hot plasma wave simulation capability is expanded in the FullWave code by updating the hybrid iterative solver in the code with a semi-implicit time stepping method. The new approach is used to simulate Electron Bernstein Wave (EBW) heating in over-dense spherical tokamak plasmas. The code’s hybrid iterative solver circumvents the prohibitive memory cost of direct methods by combining a time evolution of Maxwell’s equations with frequency-domain relaxation, while the conductivity kernel, calculated via 3D particle tracking, captures the essential non-local wave–particle interactions. One-dimensional EBW simulations verify the algorithm’s accuracy by demonstrating mode conversion from X-mode wave to EBW at the upper hybrid resonance and a strong cyclotron damping near the plasma core. Two-dimensional simulation reproduces the predicted short EBW wavelength and quantitatively matches the hot-plasma dispersion relation. This study demonstrates the fidelity of the hybrid solver for the electron cyclotron frequency range.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow

With the increasing penetration of distributed energy resources, distributed optimization algorithms have attracted significant attention for power systems applications due to their potential for superior scalability, privacy, and robustness to a single point-of-failure. The Alternating Direction Method of Multipliers (ADMM) is a popular distributed optimization algorithm; however, its convergence performance is highly dependent on the selection of penalty parameters, which are usually chosen heuristically. In this work, we use reinforcement learning (RL) to develop an adaptive penalty parameter selection policy for alternating current optimal power flow (ACOPF) problem solved via ADMM with the goal of minimizing the number of iterations until convergence. We train our RL policy using deep Q-learning and show that this policy can result in significantly accelerated convergence (up to a 59% reduction in the number of iterations compared to existing, curvatureinformed penalty parameter selection methods). Furthermore, we show that our RL policy demonstrates promise for generalizability, performing well under unseen loading schemes as well as under unseen losses of lines and generators (up to a 50% reduction in iterations). This work thus provides a proof-of-concept for using RL for parameter selection in ADMM for power systems applications.

alternating current optimal power flow↗

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Towards universal unfolding of detector effects in high-energy physics using denoising diffusion probabilistic models

Correcting for detector effects in experimental data, particularly through unfolding, is critical for enabling precision measurements in high-energy physics. However, traditional unfolding methods face challenges in scalability, flexibility, and dependence on simulations. We introduce a novel approach to multidimensional object-wise unfolding using conditional Denoising Diffusion Probabilistic Models (cDDPM). Our method utilizes the cDDPM for a non-iterative, flexible posterior sampling approach, incorporating distribution moments as conditioning information, which exhibits a strong inductive bias that allows it to generalize to unseen physics processes without explicitly assuming the underlying distribution. Our results highlight the potential of this method as a step towards a "universal" unfolding tool that reduces dependence on truth-level assumptions, while enabling the unfolding of a wide range of measured distributions with improved adaptability and accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem

Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applications. We first train a deep neural operator (DeepONet) to solve wave propagation problems described by the Helmholtz equation in a domain without scatterers but at different wavenumbers and with a complex absorbing boundary condition. We then design two classes of fast meta-solvers by combining DeepONet with either relaxation methods, such as Jacobi and Gauss-Seidel, or with Krylov methods, such as GMRES and BiCGStab, using the trunk basis of DeepONet as a coarse-scale preconditioner. We leverage the spectral bias of neural networks to account for the lower part of the spectrum in the error distribution while the upper part is handled inexpensively using relaxation methods or fine-scale preconditioners. The meta-solvers are then applied to solve scattering problems with different shape of scatterers, at no extra training cost. We first demonstrate that the resulting meta-solvers are shape-agnostic, fast, and robust, whereas the standard standalone solvers may even fail to converge without the DeepONet. We then apply both classes of meta-solvers to scattering from a submarine, a complex three-dimensional problem. We achieve very fast solutions, especially with the DeepONet-Krylov methods, which require orders of magnitude fewer iterations than any of the standalone solvers.

97 MATHEMATICS AND COMPUTING↗

Probability of Initiation in Neutron Transport

We discuss the numerical solution of the nonlinear integro-differential equation for the probability of a divergent neutron chain in a stationary system (i.e., the probability of initiation (POI)). We follow the development described in Bell’s classic paper on the stochastic theory of neutron transport. As noted by Bell, the linearized form of this equation resembles the linear adjoint neutron transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed-point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.

42 ENGINEERING↗

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗

Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers

In this article, we discuss some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are reviewed. After briefly discussing some of the standard symmetries relevant for many-particle systems, we discuss the advantage of encoding some symmetries directly in quantum ansätze, especially to reduce the quantum register size. It is, however, well-known that the use of symmetry-breaking states can also be a unique way to incorporate specific internal correlations when a spontaneous symmetry breaking occurs. These aspects are discussed in the quantum computing context. Ultimately, an accurate description of quantum systems can be achieved only when the initially broken symmetries are properly restored. We review several methods explored previously to perform symmetry restoration on a quantum computer, for instance, the ones based on symmetry filtering by quantum phase estimation and by an iterative independent set of Hadamard tests. We propose novel methods that pave the new directions to perform symmetry restoration, like those based on the purification of the state employing the linear combination of unitaries (LCU) approach.

97 MATHEMATICS AND COMPUTING↗

Proton radiography inversions with source extraction and comparison to mesh methods

In this article, proton radiography is a central diagnostic technique for measuring electromagnetic (EM) fields in high-energy-density, laser-produced plasmas. In this technique, protons traverse the plasma where they accumulate small EM deflections which lead to variations in the proton fluence pattern on a detector. Path-integrated EM fields can then be extracted from the fluence image through an inversion process. In this work, experiments of laser-driven foils were conducted on the OMEGA laser and magnetic field reconstructions were performed using both “fluence-based” techniques and high-fidelity “mesh-based” methods. We implement nonzero boundary conditions into the inversion and show their importance by comparing against mesh measurements. Good agreement between the methods is found only when nonzero boundary conditions are used. We also introduce an approach to determine the unperturbed proton source profile, which is a required input in fluence reconstruction algorithms. In this approach, a fluence inversion is embedded inside of a mesh region, which provides overconstrained magnetic boundary conditions. A source profile is then iteratively optimized to satisfy the boundary information. This method substantially enhances the accuracy in recovering EM fields. Lastly, we propose a scheme to quantify uncertainty in the final inversion that is introduced through errors in the source retrieval.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Efficient shallow Ritz method for 1D diffusion problems

This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is $\mathcal{O}$(n). Starting with the non-linear parameters as a uniform partition of the interval, numerical experiments show that the dBN is capable of efficiently moving mesh points to nearly optimal locations. In conclusion, to improve the efficiency of the dBN further, we propose an adaptive damped block Newton (AdBN) method by combining the dBN with the adaptive neuron enhancement (ANE) method [28].

Diffusion problems↗

AdS/CFT unitarity at higher loops: high-energy string scattering

What is the space of weakly-coupled, gravitational theories which contain massive, higher-spin particles? This class of theories is highly constrained and it is conjectured their ultraviolet completion must be string theory. We provide more evidence for this conjecture by studying the Regge limit in large N, 4d CFTs with single-trace operators of unbounded spin. We show that in the Regge limit, these theories have bulk scattering amplitudes which are consistent with the string theory prediction to all orders in 1/N for large, but finite, coupling. In the language of Regge theory, we show Pomeron exchange naturally exponentiates in the 1/N expansion. To do this, we solve the bootstrap equations at tree-level and then use the Lorentzian inversion formula to find the one-loop correlator in the Regge limit. This is a unitarity method for AdS/CFT which can be repeated iteratively to make all orders statements. We also explain under what conditions the tree-level result exponentiates in the 1/N expansion at arbitrary coupling. Finally, we comment on further inelastic effects and show they give subleading contributions at large coupling. As a consistency check, we recover results from bulk Einstein gravity in the limit where all higher-spin particles decouple.

1/N Expansion↗

Tuning successive linear programming to solve AC optimal power flow problem for large networks

Successive linear programming (SLP) is a practical approach for solving large-scale nonlinear optimization problems. Alternating current optimal power flow (ACOPF) is no exception, particularly the large size of real-world networks. However, in order to achieve tractability, it is essential to tune the SLP algorithm presented in the literature. This paper presents a modified SLP algorithm to solve the ACOPF problem, specified by the U.S. Department of Energy’s (DOE) Grid Optimization (GO) Competition Challenge 1, within strict time limits. The algorithm first finds a near-optimal solution for the relaxed problem (i.e., Stage 1). Then, it finds a feasible solution in the proximity of the near-optimal solution (i.e., Stage 2 and Stage 3). The numerical experiments on test cases ranging from 500-bus to 30,000-bus systems show that the algorithm is tractable. Here the results show that our proposed algorithm is tractable and can solve more than 80% of test cases faster than the well-known Interior Point Method while significantly reduce the number of iterations required to solve ACOPF. The number of iterations is considered an important factor in the examination of tractability which can drastically reduce the computational time required within each iteration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Elevated temperature mechanical properties of Inconel 617 surface oxide using nanoindentation

Inconel 617 is a principal candidate material for helium gas cooled very-high-temperature reactors with outlet temperatures of 700–950 °C. Recent findings showed that this alloy develops unique surface oxide layers especially at high temperature (HT) helium environment with distinctive wear, friction and contact properties. This study investigates the elevated temperature mechanical properties of Inconel 617 top surface layers aged in HT helium environment. Nanoindentation technique is used to obtain load-displacement graphs of the alloy top surface oxide in temperatures ranging from 25 °C up to 600 °C. In addition, using finite element analysis along with an iterative regression technique, a semi-numerical method is developed to further measure and quantify the material parameters and, in particular, time-independent and creep characteristics of the oxide. Although Young's modulus of the oxide is found to be relatively close to the bulk for the tested temperatures, the yield strength and hardness, in comparison to the bulk material, increase significantly as the material is oxidized after aging. The oxide exhibits significant softening as the temperature increases to 600 °C. Unlike the bulk material, diffusion through the grains is found to be the dominant creep mechanism for the oxide. Considerable difference between the mechanical properties of the oxide and the bulk material shows the need for accurate measurements of near surface mechanical properties, if reliable predictive contact and tribological models are sought at elevated temperatures.

36 MATERIALS SCIENCE↗

Development of Nontargeted Workflow of Occupational Exposure by Infrared Ion Spectroscopy and Silicone Wristbands’ Passive Sampling

Monitoring chemical exposure has well-established protocols and procedures for occupational health and industrial hygiene across various career fields and in a variety of occupational and environmental conditions. Iterative analytical development has led to validated methods to provide employers and employees with safe working conditions in terms of industrial hygiene. These validated methods are commonly supported by commercial laboratories. Here, this workflow is explicitly a targeted approach in which sampling media, sample preparation, chemical separation, quantitative target detection, and post processing are well established. This workflow also relies on commercially available chemical surrogates, isotopically labeled internal standards, and certified/standard reference materials from reputable vendors. An untargeted workflow lacks many key ingredients of validated analytical methods to include the known chemical target.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Robust design of semi-automated clustering models for 4D-STEM datasets

Materials discovery and design require characterizing material structures at the nanometer and sub-nanometer scale. Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM) resolves the crystal structure of materials, but many 4D-STEM data analysis pipelines are not suited for the identification of anomalous and unexpected structures. This work introduces improvements to the iterative Non-Negative Matrix Factorization (NMF) method by implementing consensus clustering for ensemble learning. We evaluate the performance of models during parameter tuning and find that consensus clustering improves performance in all cases and is able to recover specific grains missed by the best performing model in the ensemble. The methods introduced in this work can be applied broadly to materials characterization datasets to aid in the design of new materials.

Bruefach, Alexandra (ORCID:0000000209323477)↗

Iterative self-organizing SCEne-LEvel sampling (ISOSCELES) for large-scale building extraction

Convolutional neural networks (CNN) provide state-of-the-art performance in many computer vision tasks, including those related to remote-sensing image analysis. Successfully training a CNN to generalize well to unseen data, however, requires training on samples that represent the full distribution of variation of both the target classes and their surrounding contexts. With remote sensing data, acquiring a sufficiently representative training set is a challenge due to both the inherent multi-modal variability of satellite or aerial imagery and the general high cost of labeling data. To address this challenge, we have developed ISOSCELES, an Iterative Self-Organizing SCEne LEvel Sampling method for hierarchical sampling of large image sets. Using affinity propagation, ISOSCELES automates the selection of highly representative training images. Compared to random sampling or using available reference data, the distribution of the training is principally data driven, reducing the chance of oversampling uninformative areas or undersampling informative ones. In comparison to manual sample selection by an analyst, ISOSCELES exploits descriptive features, spectral and/or textural, and eliminates human bias in sample selection. Using a hierarchical sampling approach, ISOSCELES can obtain a training set that reflects both between-scene variability, such as in viewing angle and time of day, and within-scene variability at the level of individual training samples. We verify the method by demonstrating its superiority to stratified random sampling in the challenging task of adapting a pre-trained model to a new image and spatial domain for country-scale building extraction. Using a pair of hand-labeled training sets comprising 1,987 sample image chips, a total of 496,000,000 individually labeled pixels, we show, across three distinct model architectures, an increase in accuracy, as measured by F1-score, of 2.2–4.2%.

42 ENGINEERING↗