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At least 109 records · Page 6

Deep Generative Models that Solve PDEs: Distributed Computing for Training Large Data-Free Models

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been recently reported that successfully solve PDEs, with examples including deep feed forward networks, generative networks, and deep encoder-decoder networks. However, practical adoption of these approaches is limited by the difficulty in training these models, especially to make predictions at large output resolutions (≥1024×1024). Here we report on a software framework for data parallel distributed deep learning that resolves the twin challenges of training these large SciML models - training in reasonable time as well as distributing the storage requirements. Our framework provides several out of the box functionality including (a) loss integrity independent of number of processes, (b) synchronized batch normalization, and (c) distributed higher-order optimization methods. We show excellent scalability of this framework on both cloud as well as HPC clusters, and report on the interplay between bandwidth, network topology and bare metal vs cloud. We deploy this approach to train generative models of sizes hitherto not possible, showing that neural PDE solvers can be viably trained for practical applications. We also demonstrate that distributed higher-order optimization methods are 2-3× faster than stochastic gradient-based methods and provide minimal convergence drift with higher batch-size.

PDEs↗

Controls Status of Fermilab's PIP-II Project

The Fermilab Proton Improvement Project II (PIP-II) is building a new Super Conducting Linear Accelerator (SCL) accelerating protons to 800 MeV for injection into the rest of the FNAL beam complex. Key progress since the last status report given at ICALEPCS includes the adoption of modern DevOps practices with continuous integration and GitOps-based deployments, commissioning of EPICS-based systems at the Cryomodule Test Facility, and integration of a Virtual Accelerator framework for application development ahead of installation. In parallel, web-based applications using Dart and Flutter have matured, providing secure, unified access to both EPICS and legacy ACNET data. Data acquisition and timing systems have also evolved. This paper presents the current state of controls, emphasizing these recent developments and outlining upcoming milestones as PIP-II approaches commissioning of its cryoplant in 2026 and the Warm Front End in 2027.

Crisp, D. B. [Fermilab]↗

Optimization and Experimental Validation of Annular Finned PCM-HX for a Domestic Hot Water Heater Application

The load profile for domestic water heating is time-dependent and can result in high energy demand during peak operating times. Shifting this peak load can have significant environmental and economic impacts. Phase change material (PCM)-based thermal energy storage (TES) is a potentially useful technology for peak load shifting in domestic hot water (DHW) applications thanks to its high latent heat and energy density. In this study, an annular finned-tube PCM-HX design concept was optimized for a load-shifting TES unit to meet the Department of Energy standard for a medium-usage DHW heater using a resistance-capacitance model (RCM) integrated with a Multi-Objective Genetic Algorithm. The optimized design comprised 70 identical annular finned-tube PCM-HX units connected in parallel and utilizing RT62HC as the PCM. A single PCM-HX unit was prototyped and tested in a vertically oriented setup with upward heat transfer fluid (HTF) flow. The hot water supply time was defined based on a cutoff temperature of 51.7°C. The as-designed mass flow rate (1.5 g/s) was tested to assess the performance of the prototyped PCM-HX unit for RCM validation. For the experimental investigation, RTD sensor bundles measured HTF temperature at the PCM-HX inlet and outlet, and a Coriolis flow meter accurately measured the HTF mass flow rate. The simulated discharging power underpredicted the experimental result by about 12%, and the simulated hot water supply time underpredicted the experimental result by approximately 13% for the as-designed mass flow rate (1.5 g/s). The average deviation of the hot water supply temperature between the experimental and RCM results during the complete PCM solidification process was 1.3 K for the as-designed mass flow rate. The overall good agreement between the experimental and RCM results provides confidence that computationally efficient models such as RCM can be utilized for design optimization of PCM-HXs.

42 ENGINEERING↗

Enabling Modular Autonomous Feedback‐Loops in Materials Science through Hierarchical Experimental Laboratory Automation and Orchestration

Abstract Materials acceleration platforms (MAPs) operate on the paradigm of integrating combinatorial synthesis, high‐throughput characterization, automatic analysis, and machine learning. Within a MAP, one or multiple autonomous feedback loops may aim to optimize materials for certain functional properties or to generate new insights. The scope of a given experiment campaign is defined by the range of experiment and analysis actions that are integrated into the experiment framework. Herein, the authors present a method for integrating many actions within a hierarchical experimental laboratory automation and orchestration (HELAO) framework. They demonstrate the capability of orchestrating distributed research instruments that can incorporate data from experiments, simulations, and databases. HELAO interfaces laboratory hardware and software distributed across several computers and operating systems for executing experiments, data analysis, provenance tracking, and autonomous planning. Parallelization is an effective approach for accelerating knowledge generation provided that multiple instruments can be effectively coordinated, which the authors demonstrate with parallel electrochemistry experiments orchestrated by HELAO. Efficient implementation of autonomous research strategies requires device sharing, asynchronous multithreading, and full integration of data management in experimental orchestration, which to the best of the authors’ knowledge, is demonstrated for the first time herein.

36 MATERIALS SCIENCE↗

Supervised enhancer prediction with epigenetic pattern recognition and targeted validation

Enhancers are important non-coding elements, but they have traditionally been hard to characterize experimentally. The development of massively parallel assays allows the characterization of large numbers of enhancers for the first time. Here, we developed a framework using Drosophila STARR-seq to create shape-matching filters based on meta-profiles of epigenetic features. We integrated these features with supervised machine-learning algorithms to predict enhancers. We further demonstrated that our model could be transferred to predict enhancers in mammals. We comprehensively validated the predictions using a combination of in vivo and in vitro approaches, involving transgenic assays in mice and transduction-based reporter assays in human cell lines (153 enhancers in total). The results confirmed that our model can accurately predict enhancers in different species without re-parameterization. Finally, we examined the transcription factor binding patterns at predicted enhancers versus promoters. Here, we demonstrated that these patterns enable the construction of a secondary model that effectively distinguishes enhancers and promoters.

59 BASIC BIOLOGICAL SCIENCES↗

Rapid in situ diversification rates in Rhamnaceae explain the parallel evolution of high diversity in temperate biomes from global to local scales

Summary The macroevolutionary processes that have shaped biodiversity across the temperate realm remain poorly understood and may have resulted from evolutionary dynamics related to diversification rates, dispersal rates, and colonization times, closely coupled with Cenozoic climate change. We integrated phylogenomic, environmental ordination, and macroevolutionary analyses for the cosmopolitan angiosperm family Rhamnaceae to disentangle the evolutionary processes that have contributed to high species diversity within and across temperate biomes. Our results show independent colonization of environmentally similar but geographically separated temperate regions mainly during the Oligocene, consistent with the global expansion of temperate biomes. High global, regional, and local temperate diversity was the result of high in situ diversification rates, rather than high immigration rates or accumulation time, except for Southern China, which was colonized much earlier than the other regions. The relatively common lineage dispersals out of temperate hotspots highlight strong source‐sink dynamics across the cosmopolitan distribution of Rhamnaceae. The proliferation of temperate environments since the Oligocene may have provided the ecological opportunity for rapid in situ diversification of Rhamnaceae across the temperate realm. Our study illustrates the importance of high in situ diversification rates for the establishment of modern temperate biomes and biodiversity hotspots across spatial scales.

Plant Sciences↗

Increased accuracy of multiphysics simulations through flexible execution, transient algorithms, and modular physics

The MOOSE framework is a foundational capability used by the NEAMS program to create over 15 different simulation tools for advanced nuclear reactors. Due to MOOSE’s broad use, improvements to the framework in support of modeling and simulation goals are critical to the program. Such improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and new capabilities. The work described in this report was conducted in direct support of the simulation tools and has already been deployed. The capabilities were implemented in the same order as they are covered in this report: multiple time integrators in the same input file, initial design of framework Components, an input file Application block, extension of NetGen to 3D geometries in MOOSE, and deployment of executors in the multi-system paradigm. These five additions are fundamental capabilities that will be leveraged by many NEAMS applications.

97 MATHEMATICS AND COMPUTING↗

Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects

We numerically investigate an adaptive version of the parareal algorithm in the context of molecular dynamics. This adaptive variant has been originally introduced in [1]. We focus here on test cases of physical interest where the dynamics of the system is modelled by the Langevin equation and is simulated using the molecular dynamics software LAMMPS. In this work, the parareal algorithm uses a family of machine-learning spectral neighbor analysis potentials (SNAP) as fine, reference, potentials and embedded-atom method potentials (EAM) as coarse potentials. We consider a self-interstitial atom in a tungsten lattice and compute the average residence time of the system in metastable states. Our numerical results demonstrate significant computational gains using the adaptive parareal algorithm in comparison to a sequential integration of the Langevin dynamics. We also identify a large regime of numerical parameters for which statistical accuracy is reached without being a consequence of trajectorial accuracy.

36 MATERIALS SCIENCE↗

Cybersecurity for Grid Connected eXtreme Fast Charging (XFC) Station (CyberX) (Final Scientific/Technical Report)

This report summarizes the activities conducted under the DOE VTO funded project DE- EE0008451, where ABB Inc. (ABB), in collaboration with Idaho National Laboratory (INL), APS Global (APS), and XOS Trucks (XOS) pursued the development of a cyber-resilient extreme fast charging (XFC) management system. This project entitled Cybersecurity for Grid Connected eXtreme Fast Charging (XFC) Station (CyberX) focuses on a resilient architecture for smart charging EV Supply Equipment (EVSE) device control and Coordinated Anomaly Detection System (CADS) features that can be added at the charging site depot level to increase cybersecurity. The project was split into two budget periods focused first on developing the threat model and resilient control concepts and second on testing, improving, and validating those developed resilient control algorithms and features with a focus on key vulnerabilities identified during the threat assessment portion of the project. During the first budget period of the CyberX project, the ABB led team focused on activities to identify, model, and quantitatively prioritize high-impact attack scenarios with potential cyber-physical effects while also modeling and developing concepts for a resilient control system that could securely address integration of DERs and other resources with EV charging. Development of the security focused XFC management system (XMS) was accomplished first by offline simulation using a developed XFC station or depot with 480V input level and simulating measurement inputs to monitoring and control systems in concept development. A representative distribution grid model was developed supporting an EV charging site model with BESS and 6 general EV charging models. These EV charging models allowed multiple configurations of charging level, multiple connected protection and measurement devices, and simulation function to show general compromise of EV, BESS, and protection features based on parallel threat analysis. During the second budget period, the EV site and supporting systems model was developed in more detail and converted from offline model to real-time to real-time with EV charging hardware in the loop (HIL). The resilient control architecture developed as concept in the first part of the project was further tested and validated for integration of local energy resources and XFC charging station site equipment while maintaining cybersecure operating principles. The proposed resilient architecture for smart charging and cybersecurity features consists of two main concepts developed and tested within the project. The first concept is an XFC management system (XMS) consisting of a hardware gateway, software platform, and Supervisory Control and Data Acquisition (SCADA) or Distribution Management System integration components. The second concept is a Coordinated Anomaly Detection System (CADS) which forms a primarily software-related subsystem of the total CyberX solution focused on monitoring system measurements, estimation of measurement states, and predicting current at the utility point of interaction based on machine learning for anomaly detection.

33 ADVANCED PROPULSION SYSTEMS↗

Decoding the protein–ligand interactions using parallel graph neural networks

Abstract Protein–ligand interactions (PLIs) are essential for biochemical functionality and their identification is crucial for estimating biophysical properties for rational therapeutic design. Currently, experimental characterization of these properties is the most accurate method, however, this is very time-consuming and labor-intensive. A number of computational methods have been developed in this context but most of the existing PLI prediction heavily depends on 2D protein sequence data. Here, we present a novel parallel graph neural network (GNN) to integrate knowledge representation and reasoning for PLI prediction to perform deep learning guided by expert knowledge and informed by 3D structural data. We develop two distinct GNN architectures: $$\hbox {GNN}_{\mathrm{F}}$$ GNN F is the base implementation that employs distinct featurization to enhance domain-awareness, while $$\hbox {GNN}_{\mathrm{P}}$$ GNN P is a novel implementation that can predict with no prior knowledge of the intermolecular interactions. The comprehensive evaluation demonstrated that GNN can successfully capture the binary interactions between ligand and protein’s 3D structure with 0.979 test accuracy for $$\hbox {GNN}_{\mathrm{F}}$$ GNN F and 0.958 for $$\hbox {GNN}_{\mathrm{P}}$$ GNN P for predicting activity of a protein–ligand complex. These models are further adapted for regression tasks to predict experimental binding affinities and $$\hbox {pIC}_{\mathrm{50}}$$ pIC 50 crucial for compound’s potency and efficacy. We achieve a Pearson correlation coefficient of 0.66 and 0.65 on experimental affinity and 0.50 and 0.51 on $$\hbox {pIC}_{\mathrm{50}}$$ pIC 50 with $$\hbox {GNN}_{\mathrm{F}}$$ GNN F and $$\hbox {GNN}_{\mathrm{P}}$$ GNN P , respectively, outperforming similar 2D sequence based models. Our method can serve as an interpretable and explainable artificial intelligence (AI) tool for predicted activity, potency, and biophysical properties of lead candidates. To this end, we show the utility of $$\hbox {GNN}_{\mathrm{P}}$$ GNN P on SARS-Cov-2 protein targets by screening a large compound library and comparing the prediction with the experimentally measured data.

59 BASIC BIOLOGICAL SCIENCES↗

Observation of a magneto-Rayleigh-Taylor instability in magnetically collimated plasma jets

We present the direct experimental observation of the formation of a diamagnetic cavity and magneto-Rayleigh-Taylor (MRT) instability in a β ≈ 1 high energy density plasma. Proton radiography is used to measure the two dimensional path-integrated magnetic field in a laser-produced plasma propagating parallel to a preimposed magnetic field. Flutelike structures, associated with the MRT instability, are observed to grow at the surface of the cavity, with a measured wavelength of 1.2 mm and growth time of 4 ns. These measurements are in good agreement with predictions of three dimensional magnetohydrodynamic simulations using the GORGON code. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Toward a Fully Integrated Multiphysics Simulation Framework for Fusion Blanket Design

Fusion is an attractive clean-energy solution, thanks to its various advantages, such as reduced radioactivity, little high-level nuclear waste, ample fuel supplies, and increased safety. However, the harsh operating environment introduced by a complex fusion plasma system makes design and integration of fusion blankets incredibly challenging and time-consuming. This work focuses on developing a fully integrated multiphysics simulation framework based on an advanced open-source platform—the Multiphysics Object-Oriented Simulation Environment (MOOSE)—to alleviate the difficulties in fusion blanket design and integration. MOOSE is a massively parallel finite element/volume multiphysics simulation platform that has been widely adopted within the nuclear fission community. Even though fission and fusion are fundamentally different, they involve similar multiphysics phenomena. A fully integrated open-source multiphysics simulation framework tailored for the fusion blanket design will be implemented by leveraging the well-established multiphysics capabilities in MOOSE. Once successfully developed, this fully integrated framework will rapidly evaluate a blanket design concept and offer insights for subsequent iterations. As the first step, we will mainly aim to integrate neutronics analysis, system thermal hydraulics simulation, and full 3-D heat transfer calculations. The efficacy of the integrated framework will be verified using an innovative solid ceramic blanket design. While the project’s final goal is to enable a fully integrated multiphysics simulation platform for various fusion blanket concepts, here this work, as a preliminary step, will mainly focus on a solid ceramic breeder helium-cooled blanket.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

CaTS: Integration of Geant4 and Opticks

CaTS [6]is an advanced example that is part of Geant4 since version 11.0. It demonstrates the use of Opticks to offload the simulation of optical photons to GPUs. Opticks interfaces with the Geant4 toolkit to collect all the necessary information to generate and trace optical photons, re-implements the optical physics processes to be run on the GPU, and automatically translates the Geant4 geometry into a GPU appropriate format. To trace the photons, Opticks uses NVIDIA OptiX®. In this report, we describe CaTS and the integration of Opticks with Geant4. We demonstrate that the generation and tracing of optical photons represents an ideal application to be offloaded to GPUs, fully utilizing the high degree of available parallelism. In a typical liquid argon TPC simulation, a speedup of several hundred times is observed compared to an equivalent simulation using single threaded Geant4.

Wenzel, Hans↗

7.2 kV Three-Port SiC Single-Stage Current-Source Solid-State Transformer With 90 kV Lightning Protection

This article proposes a multiport modular single-stage current-source solid-state transformer (SST) for applications like photovoltaic, energy storage integration, electric vehicle fast charging, data center, etc. The 7.2 kV 50 kVA current-source SST consists of five input-series output-parallel modules, each based on 3.3 kV SiC reverse-blocking MOSFET-plus-diode modules. The proposed SST has some unique features. First, compared to the voltage-source or matrix converter-based SSTs, the current-source SST has a unique advantage of single-stage isolated AC/DC or AC/AC conversion with an inductive DC link, but no medium-voltage (MV) AC experiments have been reported. This article for the first time demonstrates MV AC current-source SST up to 7.5 kV peak. Second, the multiport SST has a buffer port for active power decoupling (APD) or energy storage integration. The double-line-frequency power ripple from single-phase AC grid normally results in a large capacitor size in MV SSTs. The APD scheme is proposed in MV applications for the first time to enable a reduced DC link and the electrolytic capacitor-less SST with high reliability. Third, as a direct grid-connected converter without line-frequency transformer, insulation and protection are critical. A medium-frequency transformer design passes 55 kV basic-insulation level (BIL) and 60 kV high potential dielectrics withstand test with only 0.09% leakage inductance. Importantly, a lightning protection scheme is presented to protect the SST itself from 90 kV BIL impulse. Fourth, the proposed current-source SST topology is a modular soft-switching solid-state transformer (M-S4T) with full-range zero-voltage switching and controlled dv/dt for low electromagnetic interference. Furthermore, these concepts are verified in a three-port M-S4T prototype with forced oil cooling under single-module, stacked-module, steady-state, and dynamic operations.

14 SOLAR ENERGY↗

Implementing machine learning methods on QICK hardware for qubit readout & control

Quantum readout and control is a fundamental aspect of quantum computing that requires accurate measurement of qubit states. Errors emerge in all stages, from initialization to readout, and identifying errors in post-processing necessitates resource-intensive statistical analysis. In our work, we use a lightweight fully-connected neural network (NN) to classify states of a transmon system with no prior processing. Our NN accelerator yields higher fidelities (92%) than the classical matched filter method (84%). By exploiting the natural parallelism of NNs and their placement near the source of data on field-programmable gate arrays (FPGAs), we can achieve ultra-low latency on the Quantum Instrumentation Control Kit (QICK). Integrating machine learning methods on QICK opens several pathways for efficient real-time processing of quantum circuits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Computer Science Research Needs for Parallel Discrete Event Simulation (PDES)

Historically, scientific computing efforts have demonstrated the clear need for, and effective use of, supercomputing with traditional time-stepped simulations. Nevertheless, there are several areas in the mission spaces of the U.S. Department of Energy and other agencies waiting to tap advanced computing research using a different, discrete event style of modeling, simulation, and analysis. These span a wide spectrum of applications including energy grid resilience, urban planning and policy, transportation science, building technologies, emergency response and planning, environmental impact analysis, computational epidemiology, Internet communications, cyber security, and cyber-physical systems, to name only a few. Even within traditional scientific applications, the role of discrete event modes of execution is increasing in the form of new event-based mathematical solvers such as quantized state integration methods and discrete-continuous hybrid system solvers. Co-design of advanced supercomputing hardware systems is another area that exploits discrete event simulation at its core for effective analyses. Complex systems, entity behaviors and interconnections play a significant role in all these applications, which are mapped to large-scale models with discrete event formulations. To make advancements in all the aforementioned scientific areas, many technical aspects need to be more thoroughly studied and deeply understood in parallel discrete event simulation (PDES). The unique dynamics inherent in a discrete event modeling approach, by their very nature, intersect and influence the entire stack of the computing system, including (a) the unique nature of the instruction sets exercised in PDES workloads without a predominance of high-precision floating point operations, (b) virtual time-constrained multi-threaded execution of many logical processes per processor, (c) extremely variable and difficult to predict network traffic characteristics, (d) interfaces and inter-dependencies with machine learning and artificial intelligence codes at higher software layers, and (e) highly challenging load balancing needs, especially in effectively accounting for accelerated/extremely heterogeneous computing in current and future high-performance computing systems. Efficient and accurate parallel execution of PDES workloads is also dominated by challenges in dealing with their asynchronous concurrency fundamentally present at the model level. Conservative synchronization, optimistic/speculative synchronization, and their hybrid schemes open new questions in fundamental computer science with respect to reversibility of computation and prediction (lookahead) of behaviors inherent within model codes. On the implementation front, there are relatively few scalable, general-purpose parallel discrete event simulators in the world, and even fewer have been studied on emerging hardware platforms. To enable scientific advances using PDES, the research needs in computer science must also be pursued and met in the intersection of the algorithmic and hardware-aware aspects of scalable PDES engines. This report is aimed at capturing a computer science-oriented view of this important area of research in PDES, presenting a sample of important applications with their inherent discrete event technology elements. Needs are outlined in core areas of parallel discrete event research as well as cross-cutting directions in computer science research that positively impact scientific advancements across several important application areas. A selection of priority research opportunities in advanced computing for PDES is identified to serve as reference for key research topics and their order of importance for scientific advancements.

97 MATHEMATICS AND COMPUTING↗

Model-based, in-situ, non-destructive qualification and certification of parts made by autonomous additive manufacturing

To address the significant productivity challenges associated with the qualification and certification (Q&C) tasks of additively manufactured (AM) parts, which have traditionally relied on rigorous post‐build inspection and testing, we propose an integrated framework that combines model‐based qualification and certification (MBQ&C) with autonomous additive manufacturing (AAM). MBQ&C employs high‐fidelity predictive models, developed within the Integrated Computational Materials Engineering (ICME) paradigm, to simulate process–structure–property–performance relationships for assessing a part’s fitness for use. Since predictive models are commonly machine learning (ML)-based or reduced-order surrogates of validated physics models, they run efficiently, enabling timely inference. In parallel, the self-driving AAM utilises ML-based adaptive, closed‐loop control strategies to avoid, mitigate, or repair defects and anomalies during fabrication, thereby increasing the likelihood of producing acceptable parts. A key feature of the combined AAM-MBQ&C framework is that predictive models explicitly incorporate defects or anomalies that persist after the build, using instance-specific data captured via in-situ sensing. This customisation enables a build‐specific assessment of fitness for use, rather than relying on nominal or generic parameters. Such individualised evaluation provides a robust basis for Q&C-related acceptance decisions relating to each build. Additionally, the rapid solution capabilities of ML or reduced-order models enable the determination of a part’s suitability for service shortly after build completion. As the framework matures, it has the potential to substantially reduce reliance on conventional point‐design approaches—such as time‐consuming post‐build computed tomography scanning and costly destructive testing. Thus, the AAM-MBQ&C framework represents a transformative, scalable strategy for quality assurance of AM components, as parts produced within a stable, validated, and certified envelope can be certified with reduced testing. Key benefits include: (1) significant gains in Q&C productivity through efficient, model-centric assessment; (2) performance-based classification of defects into critical and non-critical categories; (3) the ability to predict potential deviations in the performance of parts affected by real-time, adaptive process control interventions relative to those produced under a certified process, and (4) the enabling of virtual Q&C for service environments that are difficult, hazardous, or impractical to access or reproduce experimentally. Collectively, these capabilities strengthen the business case for AM, particularly for high‐consequence and mission‐critical applications. Finally, although this work focuses on powder-based AM, the proposed techniques could be extended to AM processes employing alternative feedstock forms.

Gunasegaram, Dayalan↗

Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation

With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. Here, the selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases.

97 MATHEMATICS AND COMPUTING↗