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At least 19 records

Ptychographic phase retrieval by proximal algorithms

We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a simple frame work that allows us to incorporate the effect of noise from a maximum-likelihood (ML) principle. We focus on three particular algorithms, namely proximal minimization, alternating direction method of multiplier and accelerated proximal gradient (APG). We benchmark their performance with numerical simulations, and discuss their optimal conditions for convergence and accuracy. An experimental dataset is used to demonstrate their effectiveness as well, in which case an array of cubic Au nanoparticles with a size of 50 nm is imaged. We show that with the presence of Poisson noise, a dataset with photon counts up to 10 4 at one detector pixel already requires ML-based methods to achieve a stable convergence. Among the three algorithms derived in this work, APG method is reported first time for its application in ptychographic reconstruction and shows superior performance in terms of both accuracy and convergence rate with a noisy dataset.

36 MATERIALS SCIENCE↗

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗

Machine Learning Solutions for a Stable Grid Recovery

Grid operating security studies are typically employed to establish operating boundaries, ensuring secure and stable operation for a range of operation under NERC guidelines. However, if these boundaries are severely violated, existing system security margins will be largely unknown, as would be a secure incremental dispatch path to higher security margins while continuing to serve load. As an alternative to the use of complex optimizations over dynamic conditions, this work employs the use of machine learning to identify a sequence of secure state transitions which place the grid in a higher degree of operating security with greater static and dynamic stability margins. Several reinforcement learning solution methods were developed using deep learning neural networks, including Deep Q-learning, Mu-Zero, and the continuous algorithms Proximal Reinforcement Learning, and Advantage Actor Critic Learning. The work is demonstrated on a power grid with three control dimensions but can be scaled in size and dimensionality, which is the subject of ongoing research.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A proximity‐based image‐processing algorithm for colloid assignment in segmented multiphase flow datasets

Summary Colloidal transport and deposition are of both environmental and engineering importance. Easier access to x‐ray microtomography (XMT) coupled with improved imaging resolution has made XMT a unique and viable tool for visualizing and quantifying these processes. Currently, there is scant information in the literature addressing colloid segmentation and analysis in saturated and unsaturated porous media, in particular related to spatial partitioning of colloids. To support this need, an approach to assign segmented colloidal particles and aggregates to different partitioning classes based on their proximity to different phases is presented here. The method uses different markers for each attachment site (e.g. wetting‐nonwetting phase interfaces). An example XMT dataset from a drainage experiment is used to demonstrate the efficacy of the image processing algorithms. Flow conditions, and fluid and colloid properties, can thus be compared to the behaviour of colloids within the porous medium. This algorithm can help elucidate colloidal deposition mechanisms and the importance of different attachment sites, explore the importance of fluid properties, as well as the arrangement and shape of the colloids.

BRUECK, C. L.↗

Metric Learning to Accelerate Convergence of Operator Splitting Methods

Recent developments in machine learning have led to promising advances in accelerating the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial intelligence and optimal control has led to a variety of proposed strategies for learning to produce fast solutions to optimization problems. For example, recent works have shown that it is possible to accelerate the convergence of optimization algorithms by learning to select their parameters, such as gradient descent stepsizes. This work proposes a new approach, in which the underlying metric spaces of proximal operator splitting algorithms are learned to maximize convergence rate. While prior works in optimization theory have derived optimal metrics in simple cases, no such result exists for many practical problem forms including general Quadratic Programming (QP). This paper shows how differentiable optimization can enable the end-to-end learning of proximal metrics, enhancing the convergence of proximal algorithms for QP problems beyond what is possible based on known theory. Additionally, the results illustrate a strong connection between the learned proximal metrics and active constraints at the optima, leading to an interpretation in which the predicted proximal metrics can be viewed as a form of active set prediction.

King, Ethan [BATTELLE (PACIFIC NW LAB)]↗

A Comparison of Void-finding Algorithms Using Crossing Numbers

We study how well void-finding algorithms identify cosmic void regions and whether we can quantitatively and qualitatively compare the voids they find with dynamical information from the underlying matter distribution. Using the ORIGAMI algorithm to determine the number of dimensions along which dark matter particles have undergone shell crossing (crossing number) in N-body simulations from the AbacusSummit simulation suite, we identify dark matter particles that have undergone no shell crossing as belonging to voids. We then find voids in the corresponding halo distribution using two different void-finding algorithms: VoidFinder and V 2 , a ZOBOV-based algorithm. The resulting void catalogs are compared to the distribution of dark matter particles to examine how their crossing numbers depend on void proximity. While both algorithms' voids have a similar distribution of crossing numbers near their centers, we find that beyond 0.25 times the effective void radius, voids found by VoidFinder exhibit a stronger preference for particles with low crossing numbers than those found by V 2 . We examine two possible methods of mitigating this difference in efficacy between the algorithms. While we are able to partially mitigate the ineffectiveness of V 2 by using the distance from the void edge as a measure of centrality, we conclude that VoidFinder more reliably identifies dynamically distinct regions of low crossing number.

79 ASTRONOMY AND ASTROPHYSICS↗

A safe reinforcement learning algorithm for supervisory control of power plants

Traditional control theory-based methods require tailored engineering for each system and constant fine-tuning. In power plant control, one often needs to obtain a precise representation of the system dynamics and carefully design the control scheme accordingly. Model-free Reinforcement learning (RL) has emerged as a promising solution for control tasks due to its ability to learn from trial-and-error interactions with the environment. It eliminates the need for explicitly modeling the environment’s dynamics, which is potentially inaccurate. However, the direct imposition of state constraints in power plant control raises challenges for standard RL methods. To address this, we propose a chance-constrained RL algorithm based on Proximal Policy Optimization for supervisory control. Our method employs Lagrangian relaxation to convert the constrained optimization problem into an unconstrained objective, where trainable Lagrange multipliers enforce the state constraints. In conclusion, our approach achieves the smallest distance of violation and violation rate in a load-follow maneuver for an advanced Nuclear Power Plant design.

constrained optimization↗

Evaluation of Digital Nautical Chart data for confirmation and expansion of GeoNames data

Here, this work examines how Digital Nautical Chart (DNC) data may contribute to the evolution and refinement of GeoNames data for near-shore features. GeoNames features are point data with one or more possible place names. DNC Earth Cover Text (ECRText) objects are map labels positioned nearby their real word counterpart. ECRText feature map position strikes a compromise between association with real features and cartographic readability. This work explores whether ECRText features can confirm (or expand names for) existing locations or contribute new locations through data conflation. Due to name variations and spatial position, conflating these data are nontrivial. Previous work engaged in a brief examination using the trigram string matching algorithm under coarse proximity constraints, indicating that ECRText could provide additional value to GeoNames. This work builds on that study, by engaging in a deeper examination of spatial proximity and exploring conflation agreement across an ensemble of string matching approaches. The result finds strong ensemble agreement about ECRText features which already exist in GeoNames but mixed results about which features contribute new information, as well as exploring why some of these matching techniques fail. With an eye toward automation, computational efficiency was found not to be a constraint in sustaining updates.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Reinforcement Learning for Intentional Islanding in Resilient Power Transmission Systems

Intentional islanding is the process of identifying and deliberately decomposing the transmission network to form self-sustained islands from an endangered network during disruptions to improve resilience and security. Most existing intentional islanding models are offline resilience decision tools and hence do not provide outage responses in a timely manner. In this paper, a reinforcement learning (RL) based model for intentional islanding is developed, which offers real-time switching control, online deployability, and adaptability to varying system conditions. The intentional islanding process is formulated as a Markov decision process, where the optimal transmission switching policy is learned using the RL approach. The control policy is learned over an environment that encompasses a Power System Simulator for Engineering (PSS/E) model of the transmission network, facilitated by an interface to the standard openAI Gym framework. The proposed RL-based methodology aims to form stable and self-sustainable islands by ensuring voltage stability while reducing the power mismatch in the formed islands. A proximal policy optimization algorithm is designed, which is suitable for controlling the on/off status of the switches with multi-layer perceptron as value and actor networks. The effectiveness of the proposed framework in the self-recovery of the grid by island formation is applied on the modified IEEE 39-bus test network and validated by dynamic simulations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Characterizing and mitigating coherent errors in a trapped ion quantum processor using hidden inverses

Quantum computing testbeds exhibit high-fidelity quantum control over small collections of qubits, enabling performance of precise, repeatable operations followed by measurements. Currently, these noisy intermediate-scale devices can support a sufficient number of sequential operations prior to decoherence such that near term algorithms can be performed with proximate accuracy (like chemical accuracy for quantum chemistry problems). While the results of these algorithms are imperfect, these imperfections can help bootstrap quantum computer testbed development. Demonstrations of these algorithms over the past few years, coupled with the idea that imperfect algorithm performance can be caused by several dominant noise sources in the quantum processor, which can be measured and calibrated during algorithm execution or in post-processing, has led to the use of noise mitigation to improve typical computational results. Conversely, benchmark algorithms coupled with noise mitigation can help diagnose the nature of the noise, whether systematic or purely random. Here, we outline the use of coherent noise mitigation techniques as a characterization tool in trapped-ion testbeds. We perform model-fitting of the noisy data to determine the noise source based on realistic physics focused noise models and demonstrate that systematic noise amplification coupled with error mitigation schemes provides useful data for noise model deduction. Further, in order to connect lower level noise model details with application specific performance of near term algorithms, we experimentally construct the loss landscape of a variational algorithm under various injected noise sources coupled with error mitigation techniques. This type of connection enables application-aware hardware codesign, in which the most important noise sources in specific applications, like quantum chemistry, become foci of improvement in subsequent hardware generations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗

Integrated path planning and control through proximal policy optimization for a marine current turbine

This paper presents an integrated path planning and tracking control framework for a marine current turbine (MCT), where the MCT is treated as an energy-harvesting autonomous underwater vehicle (AUV). Considering the ocean (space of action) is continuous, the proposed framework employs two modules to address path planning and path tracking enabled by the proximal policy optimization (PPO) algorithm, which is a policy gradient deep reinforcement learning (RL) method. Further, to enable fully autonomous operation in a stochastic oceanic environment, the proposed path planning seeks a primary objective of maximizing the harvested energy; then, the path tracking module is designed to minimize the tracking error and avoid collisions with static and dynamic obstacles. Using field-collected acoustic Doppler current profiler (ADCP) data, the performance of the proposed framework is evaluated. Comparative studies with baseline algorithms in three different scenarios of path planning, path tracking without an obstacle, and path tracking with collision avoidance verify the effectiveness of our proposed approach.

16 TIDAL AND WAVE POWER↗

A hybrid architecture for volt-var control in active distribution grids

Modern active distribution grids are characterized by the increasing penetration of distributed energy resources (DERs). The proper coordination and scheduling of a large numbers of these small-scale and spatially distributed DERs is necessary, and warrants the use of novel distributed approaches. In this paper, we propose a hybrid volt-var control architecture for the distribution grid, which leverages existing centralized and local approaches to planning, decision making, and control, and augments it with distributed optimization and distributed control for DER management. First, we propose a convex model to describe the power physics of distribution grids of meshed topology and unbalanced structure, based on current injection and McCormick Envelopes. Second, we employ the distributed proximal atomic coordination (PAC) algorithm to coordinate DERs to provide voltage support. We implement volt-var optimization by optimally coordinating DERs including PV smart inverters and demand response. We present results using the IEEE-34 bus network, using real data from a distribution feeder in Hawaii, to model load and PV generation. Different levels of DER penetration and objective functions are simulated. Finally, our results show the need for the coordination of DERs to improve voltage profiles, even in networks with existing voltage control devices. Further, we show the need for flexible reactive power capabilities to achieve desired grid performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Design and optimization of a modular hydrogen-based integrated energy system to maximize revenue via nuclear-renewable sources

Here, this paper demonstrates a novel modular distributed framework that uses optimal energy-dispatching strategies to enable greater flexibility and profitability in nuclear-renewable integrated energy systems (NR-IES). Hydrogen is used as a commodity in this framework since its production can improve grid stability and system operational flexibility, decarbonize heavy industry, and create an additional revenue stream for electricity generators, particularly nuclear power plants with high operational expenses. The proposed solution addresses the challenges associated with merging multiple software and services from various domains by using functional mock-up units (FMU) to co-simulate diverse subsystems designed in various platforms. The tightly coupled integrated energy system (IES) is optimized to maximize revenue by utilizing the deep reinforcement learning (DRL) technique to make smart dispatching decisions based on variable electricity prices and the availability of renewable energy. Proximal policy optimization (PPO) algorithm is used in training and testing the DRL agent. Over a period of 120 days, the proposed hydrogen-based IES framework showed about 10% revenue boost compared to a non-hydrogen generating baseline IES while also providing an easily-adoptable framework which can help to improve the flexibility of future generation nuclear power plants.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

The WaZP galaxy cluster sample of the dark energy survey year 1

We present a new (2+1)D galaxy cluster finder based on photometric redshifts called Wavelet Z Photometric (WaZP) applied to DES first year (Y1A1) data. The results are compared to clusters detected by the South Pole Telescope (SPT) survey and the redMaPPer cluster finder, the latter based on the same photometric data. WaZP searches for clusters in wavelet-based density maps of galaxies selected in photometric redshift space without any assumption on the cluster galaxy populations. The comparison to other cluster samples was performed with a matching algorithm based on angular proximity and redshift difference of the clusters. It led to the development of a new approach to match two optical cluster samples, following an iterative approach to minimize incorrect associations. The WaZP cluster finder applied to DES Y1A1 galaxy survey (1511.13 deg^2 up to = 23 mag) led to the detection of 60 547 galaxy clusters with redshifts 0.05 < z < 0.9 and richness N_gals ≥ 5. Considering the overlapping regions and redshift ranges between the DES Y1A1 and SPT cluster surveys, all sz based SPT clusters are recovered by the WaZP sample. The comparison between WaZP and redMaPPer cluster samples showed an excellent overall agreement for clusters with richness N_gals (λ for redMaPPer) greater than 25 (20), with 95 per cent recovery on both directions. Based on the cluster cross-match, we explore the relative fragmentation of the two cluster samples and investigate the possible signatures of unmatched clusters.

79 ASTRONOMY AND ASTROPHYSICS↗

PowerGridworld: A Framework for Multi-Agent Reinforcement Learning in Power Systems: Preprint

We present the PowerGridworld software package to provide users with a light-weight, modular, and customizable framework for creating power systems-focused, multi-agent gym environments that readily integrate with existing training frameworks for reinforcement learning (RL). While many frameworks exist for training multi-agent (MA) RL policies, none exist to rapidly prototype and develop the environments themselves, especially in the context of heterogeneous (composite, multi-device) power systems where power flow solutions are required to define grid-level variables and costs. PowerGridworld is an open-source software package that helps to fill this gap. To highlight PowerGridworld's key features, we present two case studies and demonstrate learning multi-agent RL policies using both OpenAI's MADDPG and RLLib's PPO algorithms where, in both cases, at least some subset of agents incorporate elements of the power flow solution at each time step as part of their reward (negative cost) structures.

MATHEMATICS AND COMPUTING↗

Beyond PID Controllers: PPO with Neuralized PID Policy for Proton Beam Intensity Control in Mu2e

We introduce a novel Proximal Policy Optimization (PPO) algorithm aimed at addressing the challenge of maintaining a uniform proton beam intensity delivery in the Muon to Electron Conversion Experiment (Mu2e) at Fermi National Accelerator Laboratory (Fermilab). Our primary objective is to regulate the spill process to ensure a consistent intensity profile, with the ultimate goal of creating an automated controller capable of providing real-time feedback and calibration of the Spill Regulation System (SRS) parameters on a millisecond timescale. We treat the Mu2e accelerator system as a Markov Decision Process suitable for Reinforcement Learning (RL), utilizing PPO to reduce bias and enhance training stability. A key innovation in our approach is the integration of a neuralized Proportional-Integral-Derivative (PID) controller into the policy function, resulting in a significant improvement in the Spill Duty Factor (SDF) by 13.6%, surpassing the performance of the current PID controller baseline by an additional 1.6%. This paper presents the preliminary offline results based on a differentiable simulator of the Mu2e accelerator. It paves the groundwork for real-time implementations and applications, representing a crucial step towards automated proton beam intensity control for the Mu2e experiment.

43 PARTICLE ACCELERATORS↗