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DOE OSTI2024

Riemannian Optimization Applied to AC Optimal Power Flow: Preprint

The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. They demonstrate that these are viable computational alternatives to interior point methods. This is done by using Julia and the packages PowerModels.jl and Manopt.jl.

manifold optimization↗

DOE OSTI2025

Improved Gas Plume Identification Using Nearest Neighbor Methods for Background Estimation

Longwave infrared (LWIR) hyperspectral imaging (HSI) can be used for many tasks in remote sensing, including detecting and identifying effluent gases by LWIR sensors on airborne platforms. Identification is used after detection to increase confidence in weakly detected plumes, reduce false positives from detection, and distinguish between similar and confounding material signatures. Background estimation is an important step used to reveal the unique spectral characteristics of the detected gas, allowing the identification model to determine what the gas is specifically. The importance of proper background estimation increases when dealing with weak signals, large libraries of gases of interest, and uncommon or heterogeneous backgrounds. In this article, we propose two methods for background estimation: a novel k-nearest segments (KNS) algorithm and the standard k-nearest neighbors (KNN) algorithm. We test our methods and three existing background estimation methods for comparison against global background estimation to determine which performs best at estimating the true background radiance under a plume and for increasing identification confidence using a neural network classification model. We compare the different methods using 640 simulated weak plumes in an urban environment. For identification, our KNS algorithm improves median neural network identification confidence by 53.2%. For background radiance estimation, the KNN algorithm provides a median of 49 times less RMSE than global background estimation. Furthermore, KNN is the easiest method to tune for different plumes, making it an excellent “out of the box” background estimator.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Fair Concurrent Training of Multiple Models in Federated Learning

Federated learning (FL) enables collaborative learning across multiple clients. In most FL work, all clients train a single learning task. However, the recent proliferation of FL applications may increasingly require multiple FL tasks to be trained simultaneously, sharing clients’ computing resources, which we call Multiple-Model Federated Learning (MMFL). Current MMFL algorithms use naïve average-based client-task allocation schemes that often lead to unfair performance when FL tasks have heterogeneous difficulty levels, as the more difficult tasks may need more client participation to train effectively. Furthermore, in the MMFL setting, we face a further challenge that some clients may prefer training specific tasks to others, and may not even be willing to train other tasks, e.g., due to high computational costs, which may exacerbate unfairness in training outcomes across tasks. We address both challenges by firstly designing FedFairMMFL, a difficulty-aware algorithm that dynamically allocates clients to tasks in each training round, based on the tasks’ current performance levels. We provide guarantees on the resulting task fairness and FedFairMMFL’s convergence rate. We then propose novel auction designs that incentivizes clients to train multiple tasks, so as to fairly distribute clients’ training efforts across the tasks, and extend our convergence guarantees to this setting. Here, we finally evaluate our algorithm with multiple sets of learning tasks on real world datasets, showing that our algorithm improves fairness by improving the final model accuracy and convergence speed of the worst performing tasks, while maintaining the average accuracy across tasks.

Federated learning↗

DOE OSTI2026

Computing an Optimal Entanglement Path with Throughput and Fidelity Considerations

Entanglement distribution is a core function of quantum networks essential for operations including teleportation, distributed quantum sensing, and multisite computation. Entanglement throughput and fidelity are two critical performance measures that depend on the quantum transmission along the links and swapping operations at the repeaters along the path. We study the problem of computing a end-to-end entanglement path that satisfies both fidelity and throughput requirements, leveraging qubit buffers at the nodes and considering the sequential swapping order. We show that the general problem of simultaneously satisfying both metrics to be NP-hard, and develop an algorithm to maximize throughput subject to a given fidelity threshold. We introduce the concepts of entanglement probability distribution and path domination and exploit them in the design of our algorithm. Extensive numerical results show that our algorithm can find optimal solutions in networks with thousands of nodes in less than a second. We also describe practical and possible implementation aspects of this algorithm in terms of devices and architecture support.

Xue, Guoliang [Arizona State University]↗

DOE OSTI2025

Tomographic Sparse View Selection Using the View Covariance Loss

Standard computed tomography (CT) reconstruction algorithms such as filtered back projection (FBP) and Feldkamp-Davis-Kress (FDK) require many views for producing high-quality reconstructions, which can slow image acquisition and increase cost in non-destructive evaluation (NDE) applications. Over the past 20 years, a variety of methods have been developed for computing high-quality CT reconstructions from sparse views. However, the problem of how to select the best views for CT reconstruction remains open. In this paper, we present a novel view covariance loss (VCL) function that measures the joint information of a set of views by approximating the normalized mean squared error (NMSE) of the reconstruction. We present fast algorithms for computing the VCL along with an algorithm for selecting a subset of views that approximately minimizes its value. Our experiments on simulated and measured data indicate that for a fixed number of views our proposed view covariance loss selection (VCLS) algorithm results in reconstructions with lower NRMSE, fewer artifacts, and greater accuracy than current alternative approaches.

Lin, Jingsong [Purdue University]↗

DOE OSTI2025

Accelerating iterative ptychography with an integrated neural network

Electron ptychography is a powerful and versatile tool for high-resolution and dose-efficient imaging. Iterative reconstruction algorithms are powerful but also computationally expensive due to their relative complexity and the many hyperparameters that must be optimised. Gradient descent-based iterative ptychography is a popular method, but it may converge slowly when reconstructing low spatial frequencies. Here, in this work, we present a method for accelerating a gradient descent-based iterative reconstruction algorithm by training a neural network (NN) that is applied in the reconstruction loop. The NN works in Fourier space and selectively boosts low spatial frequencies, thus enabling faster convergence in a manner similar to accelerated gradient descent algorithms. We discuss the difficulties that arise when incorporating a NN into an iterative reconstruction algorithm and show how they can be overcome with iterative training. We apply our method to simulated and experimental data of gold nanoparticles on amorphous carbon and show that we can significantly speed up ptychographic reconstruction of the nanoparticles.

4DSTEM↗

DOE OSTI2026

Simplex‐based model for nanoparticle grain identification in four‐dimensional scanning transmission electron microscopy data

Grain identification in polycrystalline nanoparticles, for example, determining which crystal phases are present at each spatial location, is fundamental to materials characterisation. This is particularly challenging when grains overlap extensively, as commonly occurs in four-dimensional scanning transmission electron microscopy (4D-STEM) datasets. We propose a simplex-based model (SBM) in which each simplex vertex represents the diffraction pattern (DP) of a pure grain, and the simplex edges and interior represent overlapping grains. Our SBM grain identification algorithm operates on the Bragg disk (BD) data matrix distilled from the 4D-STEM data to identify the grain membership at each scan position, together with a BD feature matrix whose columns represent the DPs for each constituent grain, which is important for identifying the crystal structure of each grain. We solve the model using a two-stage algorithm. In Stage 1, we adapt a linear mixing algorithm to estimate an initial BD feature matrix whose columns represent DPs of potentially overlapping grains. Our Stage 2 algorithm incorporates sparsity considerations to transform the initial BD feature matrix so that its columns represent DPs of pure grains. Using simulated datasets with various grain configurations, we demonstrate that SBM recovers both the BD feature matrix and membership maps more accurately than existing methods, even when a grain lacks any pure region and completely overlaps with other grains.

4D-STEM segmentation↗

DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗

DOE OSTI2025

Domain Decomposition for Integer Optimal Control with Total Variation Regularization

Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.

domain decomposition↗

DOE OSTI2025

Analysis of the SiMPL Method for Density-Based Topology Optimization

We present a rigorous convergence analysis of a new method for density-based topology optimization that provides pointwise bound-preserving design updates and faster convergence than other popular first-order topology optimization methods. Due to its strong bound preservation, the method is exceptionally robust, as demonstrated in numerous examples here and in the companion article [D. Kim et al., Struct. Multidiscip. Optim., 68 (2025), 74]. Furthermore, it is easy to implement with clear structure and analytical expressions for the updates. Our analysis covers two versions of the method, characterized by the employed line search strategies. We consider a modified Armijo backtracking line search and a Bregman backtracking line search. For both line search algorithms, our algorithm delivers a strict monotone decrease in the objective function and further intuitive convergence properties, e.g., strong and pointwise convergence of the density variables on the active sets, norm convergence to zero of the increments, convergence of the Lagrange multipliers, and more. In addition, the numerical experiments demonstrate apparent mesh-independent convergence of the algorithm. Here, we refer to the new algorithm as the SiMPL method (pronounced “simple”), which stands for Sigmoidal Mirror descent with a Projected Latent variable.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Fast and Accurate Intersections on a Sphere

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and numerical robustness over the ones traditionally implemented in geoscience software. We then show how algorithms based on the concept of error-free transformations (EFT) can be applied to evaluate this formula within a relative error bound that is on the order of machine precision. Here, we demonstrate that, with a vectorized and parallelized implementation, this enhanced accuracy is achieved with no compute time overhead compared to a direct calculation in hardware floating point, making our algorithm suitable for performance-sensitive applications like regridding of high-resolution climate data. In contrast, evaluating our formula using high-precision data types like quadruple precision and arbitrary precision, or using the robust intersection computation routines from the Computational Geometry Algorithms Library, leads to significant computational overhead, especially since these alternatives inhibit vectorization. More generally, our work demonstrates how EFT techniques can be combined and extended to implement nontrivial geometric calculations with high accuracy and speed.

Environmental sciences↗

DOE OSTI2025

Neutrino interaction vertex reconstruction in DUNE with Pandora deep learning

The Pandora Software Development Kit and algorithm libraries perform reconstruction of neutrino interactions in liquid argon time projection chamber detectors. Pandora is the primary event reconstruction software used at the Deep Underground Neutrino Experiment, which will operate four large-scale liquid argon time projection chambers at the far detector site in South Dakota, producing high-resolution images of charged particles emerging from neutrino interactions. While these high-resolution images provide excellent opportunities for physics, the complex topologies require sophisticated pattern recognition capabilities to interpret signals from the detectors as physically meaningful objects that form the inputs to physics analyses. A critical component is the identification of the neutrino interaction vertex. Subsequent reconstruction algorithms use this location to identify the individual primary particles and ensure they each result in a separate reconstructed particle. A new vertex-finding procedure described in this article integrates a U-ResNet neural network performing hit-level classification into the multi-algorithm approach used by Pandora to identify the neutrino interaction vertex. The machine learning solution is seamlessly integrated into a chain of pattern-recognition algorithms. The technique substantially outperforms the previous BDT-based solution, with a more than 20% increase in the efficiency of sub-1 cm vertex reconstruction across all neutrino flavours.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Shot-noise-induced lower temperature limit of the nonneutral plasma parallel temperature diagnostic

Abstract We develop a new algorithm to estimate the temperature of a nonneutral plasma in a Penning-Malmberg trap. The algorithm analyzes data obtained by slowly lowering a voltage that confines one end of the plasma and collecting escaping charges, and is a maximum likelihood estimator based on a physically-motivated model of the escape protocol presented in (Beck in Measurement of the magnetic and temperature dependence of the electron-electron anisotropic temperature relaxation rate. PhD thesis, 1990). Significantly, our algorithm may be used on single-count data, allowing for improved fits with low numbers of escaping electrons. This is important for low-temperature plasmas such as those used in antihydrogen trapping. We perform a Monte Carlo simulation of our algorithm, and assess its robustness to intrinsic shot noise and external noise. The assumptions in this paper allow for a lower bound for measurable plasma temperatures of approximately $3\,\mathrm{K}$ 3 K for plasmas of length $1\,\mathrm{cm}$ 1 cm , with approximately 100 particle counts needed for an accuracy of $\pm 10 \%$ ± 10 % .

Zhong, Adrianne (ORCID:0000000162618736)↗

DOE OSTI2024

Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding Numbers

Point containment queries for regions bound by watertight geometric surfaces, i.e., closed and without self-intersections, can be evaluated straightforwardly with a number of well-studied algorithms. When this assumption on domain geometry is not met, such methods are either unusable, or prone to misclassifications that can lead to cascading errors in downstream applications. More robust point classification schemes based on generalized winding numbers have been proposed, as they are indifferent to these imperfections. However, existing algorithms are limited to point clouds and collections of linear elements. We extend this methodology to encompass more general curved shapes with an algorithm that evaluates the winding number scalar field over unstructured collections of rational parametric curves. In particular, we evaluate the winding number for each curve independently, making the derived containment query robust to how the curves are arranged. We ensure geometric fidelity in our queries by treating each curve as equivalent to an adaptively constructed polyline that provably has the same generalized winding number at the point of interest. Our algorithm is numerically stable for points that are arbitrarily close to the model, and explicitly treats points that are coincident with curves. We demonstrate the improvements in computational performance granted by this method over conventional techniques as well as the robustness induced by its application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

AI-Batt (Autonomous Identification of Battery Life Models) [SWR 21-36]

Autonomous Identification of Battery Life Models (AI-Batt) AI-Batt is a MATLAB code base for developing lifetime models for batteries from accelerated aging data. The code base provides many functions for processing, visualizing, and modeling battery aging data, making the data processing, exploration, and modeling workflow substantially faster. These tools are tailored for working with battery aging data sets, which usually consist of many separate time-series for each cell, with many test conditions and possible replicates at each condition, which makes it difficult to simply process or visualize the data set. Complex modeling tasks, such as cross-validation, sensitivity analysis, and uncertainty quantification have been implemented to enable thorough statistical investigation of model predictions. Additionally, several machine-learning algorithms are implemented to autonomously identify suitable models via symbolic regression. Data processing functions automatically cast data from the struct data type, which is commonly used to store experimental data, but is not an acceptable input for most algorithms, to the table data type, which can be easily used as input to any optimization algorithm. Also, the data can be separated into time-invariant and time-variant data tables, which is helpful for exploring the data set as well as developing separate models for time-variant and time-invariant aging mechanisms. For example, in aging tests with constant temperature, temperature is a time-invariant experimental condition. Visualization tools enable plotting of data, model fits, and model simulations possible with single-line function calls, empowering data exploration of complex data sets with both time-varying and time-invariant trends. Plots can be automatically generated for the whole data set, or separated by data group (groups of test replicates) or individual data series. Data points or data series can be automatically colored by the value of a variable with a variety of color maps, and model predictions can also be colored by the value of a fit statistic. Comparisons between data sets and the predictions/simulations of different models on the same data set can be easily plotted as well. Distributions of parameter values from bootstrap resampling can be plotted to visualize the reliability of parameter estimation, or determine any correlations between parameters. Modeling tools handle the complex task of creating and parsing symbolic equations for modeling battery lifetime. Equations are parsed to grab relevant data variables, parameter values, or specified sub-models for input into optimization, evaluation, or simulation functions. Models can be optimized locally (one set of parameters for each data series), bi-level (some parameters shared across the data set), or globally (single set of parameters for all data). Functions implementing symbolic regression algorithms help users to discover effective model equations, even in poorly sampled, high-dimensional data.

Smith, Kandler [National Renewable Energy Lab. (NR↗

DOE OSTI2024

Continuous thermostat setpoint monitoring and correction (Thermostat setpoint correction) v1.0

The Continuous Thermostat Setpoint Monitoring and Correction software is a set of fault detection and correction algorithms that can be implemented in thermostats with two-way OpenAPIs. It is written in the Python language. The algorithms aim to detect the most common and impactful efficiency problems associated with thermostat setpoints - overly aggressive heating or cooling setpoints, incorrect schedules/setbacks, and overly narrow deadbands. These algorithms can automatically detect faults, and implement associated corrective actions to bring the system back to a state of efficient operation. The algorithms can run remotely in the cloud, and directly implemented by connected thermostat manufacturers, or by third party service providers. The software enables a lightweight cost-effective energy management strategy for HVAC systems. The solution is specially viable for small and medium sized commercial buildings, where a full scale building automation system and fault detection and diagnostic tools are often unavailable.

Granderson, Jessica↗

DOE OSTI2026

Finite deformation implementation of a mixed-mode single-integral type cohesive zone with reorienting surfaces of separation

To model material ductile failure and crack propagation, cohesive zone elements can be embedded along potential fracture paths in a finite element simulation. When damage criteria are met, elements in the mesh decohere, simulating the formation and propagation of a crack. In this paper, we present a novel computational algorithm based on finite deformation theory, essential to modeling crack initiation and growth in solids undergoing large deformations. This new algorithm was formulated within a Lagrangian frame of reference to extend previous cohesive zone algorithms to include modeling crack growth in finite deformation contexts. The local coordinate system, necessary for defining an embedded cohesive zone, is constructed based upon the current configuration and is updated within the nonlinear iteration process, thereby resulting in the convergence of the solution for a growing crack in a large deformation quasi-static setting. The model’s accuracy was demonstrated by comparing finite element model simulation results with the analytic case of a constant surface separation, as shown in the verification examples. The power and efficacy of the algorithm to capture large deformations during crack growth were then demonstrated with a double cantilever beam example case. It indicates that the model can be applied to a variety of physical circumstances for predicting crack initiation and growth with delamination and fracture.

42 ENGINEERING↗

DOE OSTI2024

Enhanced material identification via momentum-integrated muon scattering tomography

Cosmic ray muons, originating from interactions in the upper atmosphere, possess high energy and unique penetrative capabilities suitable for non-traditional radiographic inspection. This study explores their application in various fields such as nuclear fuel cask monitoring, nuclear reactor imaging, and archaeology, leveraging the principle of multiple Coulomb scattering for imaging dense materials. While muon scattering tomography has shown promise, accurately measuring muon momentum remains challenging. This research introduces the Momentum Integrated Point-of-Closest Approach (mPoCA) algorithm, integrating muon momentum data into the traditional Point-of-Closest Approach (PoCA) framework. Utilizing the Cherenkov muon spectrometer, renowned for precise muon momentum estimation, the mPoCA algorithm offers a novel imaging approach. Simulations conducted with GEANT4 evaluate the mPoCA algorithm’s performance against the standard PoCA method, demonstrating superior image resolution and enhanced material identification capabilities, particularly in distinguishing materials like uranium and lead. These findings underscore the potential of the mPoCA algorithm for advancing muon scattering tomography applications.

36 MATERIALS SCIENCE↗