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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Large Program Design [Slides]

A slideshow presentation describing how different writing small software coding projects is from writing large software coding projects. It can be OK to just throw together code that is small, single-purpose, and short-lived, but there's more need for good design if the code has to live longer, give highly reliable results, be easy to use, get bigger/cover more physics, cover more application domains. Larger projects also need good code if they are to have more widely-distributed users, have more developers work on it, run larger problems, or run on new architectures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

PDFDataExtractor: A Tool for Reading Scientific Text and Interpreting Metadata from the Typeset Literature in the Portable Document Format

The layout of portable document format (PDF) files is constant to any screen, and the metadata therein are latent, compared to mark-up languages such as HTML and XML. No semantic tags are usually provided, and a PDF file is not designed to be edited or its data interpreted by software. However, data held in PDF files need to be extracted in order to comply with opensource data requirements that are now government-regulated. In the chemical domain, related chemical and property data also need to be found, and their correlations need to be exploited to enable data science in areas such as data-driven materials discovery. Such relationships may be realized using text-mining software such as the “chemistry-aware” natural-language-processing tool, ChemDataExtractor; however, this tool has limited data-extraction capabilities from PDF files. This study presents the PDFDataExtractor tool, which can act as a plug-in to ChemDataExtractor. It outperforms other PDF-extraction tools for the chemical literature by coupling its functionalities to the chemical-named entityrecognition capabilities of ChemDataExtractor. The intrinsic PDF-reading abilities of ChemDataExtractor are much improved. The system features a template-based architecture. This enables semantic information to be extracted from the PDF files of scientific articles in order to reconstruct the logical structure of articles. While other existing PDF-extracting tools focus on quantity mining, this template-based system is more focused on quality mining on different layouts. PDFDataExtractor outputs information in JSON and plain text, including the metadata of a PDF file, such as paper title, authors, affiliation, email, abstract, keywords, journal, year, document object identifier (DOI), reference, and issue number. With a self-created evaluation article set, PDFDataExtractor achieved promising precision for all key assessed metadata areas of the document text.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Innovating the next generation of commercial smart building software

Nearly 30% of commercial building energy use is wasted due to equipment faults and HVAC controls problems. The result is increased emissions, compromised comfort and productivity, and less reliable coordination of building power needs with a clean grid. The energy impact alone represents $17 billion in potential savings. Today’s smart building software provides a robust solution to address these operational deficiencies. Energy management and information systems (EMIS) are saving up to 9% on average, with two-year paybacks. They are being incorporated into energy management processes, commissioning services, and utility programs. As effective as they are, two barriers prevent even deeper benefits; limited personnel to fix problems once they are identified, and the expense and time to manually implement changes in control systems. In partnership with the research community, the EMIS industry is developing new capabilities to overcome these barriers. Moving beyond siloed products for either fault detection and diagnostics, or optimal control, these new capabilities empower users to not only automatically identify faults, but also to push corrective action, and control improvements to their buildings. In this paper, several areas for enhancements are documented: ‘one-time’ correction of faults such as setpoints, schedules, and economizer lockouts; short-term active testing for automated proportional integral derivative (PID) loop tuning and functional testing; and continuous supervisory control for demand flexibility and year-round efficiency. Results are presented from a pair of partner implementations out of a dozen providers integrating these enhancements into their products, including field tests from across the country, and insights into operator acceptance and integration into operations and maintenance practices.

Casillas, Armando↗
DOE OSTI2023

HIPLZ: Enabling performance portability for exascale systems

While heterogeneous computing has emerged as a dominant trend in current and future High-Performance Computing (HPC) systems, it is also widely recognized that this shift has led to increased software complexity due to a proliferation of programming systems for different heterogeneous processors. One such example is the Heterogeneous-Compute Interface for Portability from AMD (HIP ), which is composed of a C Runtime API and C++ Kernel Language. Many HPC applications will likely use HIP on future exascale systems (e.g., Frontier and El Capitan), but HIP currently only targets AMD and NVIDIA processors. This limitation creates challenges for users who would also like to run their applications on exascale systems based on other architectures (e.g., Aurora, which is based on Intel hardware) that are currently not targeted by HIP . In this paper, we introduce the design and implementation of HIPLZ , a compiler and runtime system that uses the Intel Level Zero API to support HIP on Intel GPU architectures. We discuss the design of HIPLZ , derived from HIPCL (an implementation of HIP on top of OpenCL ), and portability issues that occur from using the Level Zero runtime as a backend. We evaluate our implementation by running several performance benchmarks and mini-apps written in HIP on Intel architectures using HIPLZ . Our results show that this approach provides competitive performance relative to Intel's OpenCL implementations on Intel Gen9 and UHD Graphics 770 GPUs, while providing good coverage of features needed by HPC applications. Overall, this approach is a promising demonstration of enabling performance portability for exascale systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Hybrid learning techniques for scientific data reduction with performance guarantees

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Final report- UFL - RAPIDS2: A SciDAC Institute for Computer Science, Data, and Artificial Intelligence

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Towards Automatic and Agile AI/ML Accelerator Design with End-to-End Synthesis

Domain-specific designs offer greater energy efficiency and performance gain than general-purpose processors. For this reason, modern system-on-chips have a significant portion of their silicon area with custom accelerators. However, designing hardware by hand is laborious and time-consuming, given the large design space and the performance, power, and area constraints that are not realized in the software. Moreover, domain-specific algorithms (e.g., machine learning models) are evolving quickly, challenging the accelerator design further. To address these issues, this paper presents SODA Synthesizer, an automated open-source high-level ML framework to Verilog modular compiler targeting AI/ML Application-Specific Integrated Circuits (ASICs) accelerators. SODA tightly couples the Multi- Level Intermediate Representation (MLIR) compiler infrastructure [24] and open-source HLS approaches. Thus, SODA can support various ML frameworks and algorithms and can perform optimizations that combine specialized architecture templates and conventional HLS to generate the hardware modules. In addition, SODA’s closed-loop design space exploration (DSE) engine allows developers to perform end-to-end design space explorations on different metrics and technology nodes.

Zhang, Jeff↗
DOE OSTI2021

Mesoscopic Modeling and Rapid Simulation of Incremental Changes in Epidemic Scenarios on GPUs

In simulation-based studies and analyses of epidemics, a major challenge lies in resolving the conflict between fidelity of models and the speed of their simulation. Another related challenge arises in dealing with the large number of what–if scenarios that need to be explored. Here, we describe new computational methods that together provide an approach to dealing with both challenges. A mesoscopic modeling approach is described that strikes a middle ground between macroscopic models based on coupled differential equations and microscopic models built on fine-grained behaviors at the individual entity level. The mesoscopic approach offers the ability to incorporate complex compositions of multiple layers of dynamics even while retaining the potential for aggregate behaviors at varying levels. It also is an excellent match to the accelerator-based architectures of modern computing platforms in which graphical processing units (GPUs) can be exploited for fast simulation via the parallel execution mode of single instruction multiple thread (SIMT). The challenge of simulating a large number of scenarios is addressed via a method of sharing model state and computation across a tree of what–if scenarios that are localized, incremental changes to a large base simulation. A combination of the mesoscopic modeling approach and the incremental what–if scenario tree evaluation has been implemented in the software on modern GPUs. Synthetic simulation scenarios are presented to demonstrate the computational characteristics of our approach. Results from the experiments with large population data, including USA, UK, and India, illustrate the modeling methodology and computational performance on thousands of synthetically generated what–if scenarios. Execution of our implementation scaled to 8192 GPUs of supercomputing platforms demonstrates the ability to rapidly evaluate what–if scenarios several orders of magnitude faster than the conventional methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation

Here, extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Understanding HPC Benchmark Performance on Intel Broadwell and Cascade Lake Processors

Hardware platforms in high performance computing are constantly getting more complex to handle even when considering multicore CPUs alone. Numerous features and configuration options in the hardware and the software environment that are relevant for performance are not even known to most application users or developers. Microbenchmarks, i.e., simple codes that fathom a particular aspect of the hardware, can help to shed light on such issues, but only if they are well understood and if the results can be reconciled with known facts or performance models. The insight gained from microbenchmarks may then be applied to real applications for performance analysis or optimization. In this paper we investigate two modern Intel x86 server CPU architectures in depth: Broadwell EP and Cascade Lake SP. We highlight relevant hardware configuration settings that can have a decisive impact on code performance and show how to properly measure on-chip and off-chip data transfer bandwidths. The new victim L3 cache of Cascade Lake and its advanced replacement policy receive due attention. Finally we use DGEMM, sparse matrix-vector multiplication, and the HPCG benchmark to make a connection to relevant application scenarios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

High-Fidelity Modeling of a Type-5 Wind Turbine Gearbox (Intern Poster) [Poster]

Type-5 wind turbines are unique in their use of a permanent magnet synchronous generator, as well as their use of a hydraulic torque converter. This architecture presents an opportunity to provide steady and grid-ready energy without the need for a power converter. With infrastructure continuity and reliability being an important topic amongst renewable energies, researchers have been prompted to further investigate the benefits of type-5 turbines’ unique electromechanical configuration on stable electricity generation. Researchers involved in the WindSG project, SG standing for synchronous generator, are aiming to model a type-5 turbine using Real Time Digital Simulation (RTDS) to evaluate its efficacy in the grid. RSCAD, the software run on the RTDS, comes pre-loaded with electrical and electromechanical components to help simulate electrical generation and grid conditions. However, within this repertoire there is a lack of a component to represent a gearbox with high-fidelity. Within RSCAD’s case studies, the gearbox is often represented simply by a gear ratio value. This presented the task of developing a high-fidelity gearbox model in RSCAD for use in the larger RTDS type-5 wind turbine model. This poster describes a method of developing a lumped parameter mathematical model to represent a planetary-parallel-parallel gearbox in RSCAD for use in RTDS.

17 WIND ENERGY↗
DOE OSTI2024

High-Fidelity Modeling of a Type-5 Wind Turbine Gearbox (Intern Technical Presentation) (Poster)

Type-5 wind turbines are unique in their use of a permanent magnet synchronous generator, as well as their use of a hydraulic torque converter. This architecture presents an opportunity to provide steady and grid-ready energy without the need for a power converter. With infrastructure continuity and reliability being an important topic amongst renewable energies, researchers have been prompted to further investigate the benefits of type-5 turbines’ unique electromechanical configuration on stable electricity generation. Researchers involved in the WindSG project, SG standing for synchronous generator, are aiming to model a type-5 turbine using Real Time Digital Simulation (RTDS) to evaluate its efficacy in the grid. RSCAD, the software run on the RTDS, comes pre-loaded with electrical and electromechanical components to help simulate electrical generation and grid conditions. However, within this repertoire there is a lack of a component to represent a gearbox with high-fidelity. Within RSCAD’s case studies, the gearbox is often represented simply by a gear ratio value. This presented the task of developing a high-fidelity gearbox model in RSCAD for use in the larger RTDS type-5 wind turbine model. This presentation describes a method of developing a lumped parameter mathematical model to represent a planetary-parallel-parallel gearbox in RSCAD for use in RTDS.

17 WIND ENERGY↗
DOE OSTI2026

Software Control Program For Transportable Microgrid State-of-charge Balancing And Frequency Stability Controls

A deterministic state-of-charge (SOC) balancing approach software control code is introduced as an integral secondary management to primary control layer of an islanded small microgrid or nanogrid system made up of multiple grid-forming inverter/battery/solar combination systems, where each set of batteries with each inverter are on independent DC buses (i.e. non-paralleled on the DC sides). A DERMS-level control approach, algorithm and automation controller program was developed to improve coordination and enable microgrid asset compliance and SOC balancing, enabling provision of a system-level power stability support architecture, load support, and asset scalability. The architecture is configured to treat each unit or micro/nano-grid as a node in a microgrid network, allowing for autonomous DERMS control regarding load and SOC balancing and power stability. As the network grows with the addition of units, greater coordination efforts may be required. The ideal small network microgrid ranges from 2-10 inverter/battery units before additional control parameters must be considered in the existing architecture. The control approach focuses on a deterministic state-of-charge analysis as the primary level control process followed by a secondary control loop using a forced frequency-watt droop strategy to conform off-the-shelf components into behaving under a leader-follower configuration. Adopting this control scheme has been shown to allow for a balanced, unit-coordinated microgrid network, enabling stable power flow. The deterministic state-of-charge approach is introduced as an integral primary control layer of an islanded small network microgrid. A standard strategy for SOC balancing is implementing a battery management system (BMS) to control SOC on the DC side. An alternative approach is to determine how to coordinate sending and receiving power on the AC side with multiple units. The latter approach assesses all the integrated units in the microgrid network. Once the individual units are identified, further system data is required to calculate each unit's total kWh, provided information about its capability to supply or consume kWh and availability. The secondary control layer in the multi-layered small network microgrid methodology uses the primary layer’s decision to initiate frequency setpoint changes, initializing the SOC balancing. The secondary control layer considers numerous system-dependent variables to enable a charging and discharging profile based on adjustable frequency setpoints. The combined architecture will result in stable, coordinated power flow enhancing an AC microgrid's functionalities.

Myers, KurtS [Idaho National Laboratory (INL), Ida↗
DOE OSTI2023

Orchestration of materials science workflows for heterogeneous resources at large scale

In the era of big data, materials science workflows need to handle large-scale data distribution, storage, and computation. Any of these areas can become a performance bottleneck. We present a framework for analyzing internal material structures (e.g., cracks) to mitigate these bottlenecks. We demonstrate the effectiveness of our framework for a workflow performing synchrotron X-ray computed tomography reconstruction and segmentation of a silica-based structure. Our framework provides a cloud-based, cutting-edge solution to challenges such as growing intermediate and output data and heavy resource demands during image reconstruction and segmentation. Specifically, our framework efficiently manages data storage, scaling up compute resources on the cloud. The multi-layer software structure of our framework includes three layers. A top layer uses Jupyter notebooks and serves as the user interface. A middle layer uses Ansible for resource deployment and managing the execution environment. A low layer is dedicated to resource management and provides resource management and job scheduling on heterogeneous nodes (i.e., GPU and CPU). At the core of this layer, Kubernetes supports resource management, and Dask enables large-scale job scheduling for heterogeneous resources. The broader impact of our work is four-fold: through our framework, we hide the complexity of the cloud’s software stack to the user who otherwise is required to have expertise in cloud technologies; we manage job scheduling efficiently and in a scalable manner; we enable resource elasticity and workflow orchestration at a large scale; and we facilitate moving the study of nonporous structures, which has wide applications in engineering and scientific fields, to the cloud. While we demonstrate the capability of our framework for a specific materials science application, it can be adapted for other applications and domains because of its modular, multi-layer architecture.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Smart connected worker edge platform for smart manufacturing: Part 1—Architecture and platform design

Abstract The challenge of sustainably producing goods and services for healthy living on a healthy planet requires simultaneous consideration of economic, societal, and environmental dimensions in manufacturing. Enabling technology for data driven manufacturing paradigms like Smart Manufacturing (a.k.a. Industry 4.0) serve as the technological backbone from which sustainable approaches to manufacturing can be implemented. Unfortunately, these technologies are typically associated with broader and deeper factory automation that is often too expensive and complex for the small and medium sized manufacturers (SMMs) that comprise the majority of manufacturing business in the USA and for whom their most valuable asset are the people whose jobs automation while replace. This paper describes an edge intelligent platform to integrate internet‐of‐things technologies with computing hardware, software, computational workflows for machine learning, and data ingestion, enabling SMMs to transition into smart manufacturing paradigms by leveraging the intelligence of their people. The platform leverages consumer grade electronics and sensors (affordable and portable), customized software with open source software packages (accessible), and existing communication network infrastructures (scalable). The software systems are implemented via Kubernetes orchestration of Docker containerization to ensure scalability and programmability. The platform is adaptive via computational workflow engines that produce information from data by processing with low‐cost edge computing devices while efficiently accessing resources of cloud servers as needed. The proposed edge platform connects workers to technological resources that provide computational intelligence (i.e., silicon‐based sensing and computation for data collection and contextualization) to enable decision making at the edge of advanced manufacturing.

Kim, Yoon G.↗
DOE OSTI2023

Highly-scalable GPU-accelerated compressible reacting flow solver for modeling high-speed flows

Emerging supercomputing systems utilize a combination of central processing units (CPUs) and graphics processing units (GPUs) in an effort to reach exascale capabilities while minimizing the energy footprint of operating such systems. Such heterogeneous machines introduce new challenges for fluids solvers because the hardware architecture and operation of a GPU are fundamentally different from conventional CPUs. In this work, a general approach for efficient implementation of finite-volume based reacting flow solvers on such heterogeneous systems is presented. Three main challenges, namely, data access pattern, thread divergence, and thread safety, are addressed. Since compressible reacting flows require special methods to deal with chemical reactions, hyperbolic and nonlinear convection terms, and the presence of turbulence, specific algorithms that ensure GPU-based efficiency are developed. The approach is demonstrated on the widely available OpenFOAM open source software by modifying core algorithms for GPU accessibility. The scalability of the resulting solver, is demonstrated using practical test cases, including flow through a scramjet engine and the dynamics of a rotating detonation engine. Here, the solver provides near-ideal scaleup on a large number of GPUs (>3000), and extremely efficient use of the GPUs, with throughput nearly a constant even when processing a large number of control volumes.

42 ENGINEERING↗
DOE OSTI2023

CSPlib: A performance portable parallel software toolkit for analyzing complex kinetic mechanisms

Computational singular perturbation (CSP) is a method to analyze dynamical systems. It targets the decoupling of fast and slow dynamics using an alternate linear expansion of the right-hand side of the governing equations based on eigenanalysis of the associated Jacobian matrix. This representation facilitates diagnostic analysis, detection and control of stiffness, and the development of simplified models. For this work, we have implemented CSP in a C++ open-source library CSPlib using the Kokkos parallel programming model to address portability across diverse heterogeneous computing platforms, i.e., multi/many-core CPUs and GPUs. We describe the CSPlib implementation and present its computational performance across different computing platforms using several test problems. Specifically, we test the CSPlib performance for a constant pressure ignition reactor model on different architectures, including IBM Power 9, Intel Xeon Skylake, and NVIDIA V100 GPU. The size of the chemical kinetic mechanism is varied in these tests. As expected, the Jacobian matrix evaluation, the eigensolution of the Jacobian matrix, and matrix inversion are the most expensive computational tasks. When considering the higher throughput characteristic of GPUs, GPUs performs better for small matrices with higher occupancy rate. CPUs gain more advantages from the higher performance of well-tuned and optimized linear algebra libraries such as OpenBLAS.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Bridging Cloud and Edge Computing at NREL Using CONNECT: Cloud Optimized Networking for Next-Gen Edge Computing Technologies [Slides]

CONNECT is an innovative on-premise hardware and software solution that integrates edge and cloud computing infrastructure at NREL. Built on the AWS Greengrass middleware and leveraging the MQTT protocol, CONNECT enables real-time data streaming from IoT devices and gateways to both cloud and local services, empowering researchers to rapidly capture, analyze, and act upon edge-generated data while leveraging cloud capabilities. The platform addresses research infrastructure challenges by providing a pre-approved platform which is already configured with the correct networking and cybersecurity baselines thus eliminating procurement delays and enabling on-demand availability. CONNECT's hybrid architecture efficiently manages burstable workloads, allowing research teams to dynamically scale computational capacity, handle peak data loads, and reduce operational bottlenecks. Advanced capabilities include built-in GPU support for executing machine learning models which enables low-latency inference at the edge from models trained in the cloud. This architecture supports real-time analytics and filtering, providing a mechanism to allow only transmitting and processing high-value data. Cloud-based configuration management permits engineers to manage on-premise systems remotely, optimizing operational efficiency. By bridging edge and cloud computing, CONNECT provides NREL researchers with a flexible, scalable platform that accelerates scientific discovery while maintaining robust security and performance standards.

97 MATHEMATICS AND COMPUTING↗