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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

CCN data from TAMU TRACER campaign in the Houston TX region from July to September 2022

During TRACER, the Texas A&M Rapid Onsite Atmospheric Measurements Van (ROAM-V) was deployed to capture airmasses behind (maritime) and ahead (continental) of the passage of the sea-breeze front through Houston. On select sampling days, ROAM-V sampled in the morning/mid-day on the coast and then transited to a second inland site for the afternoon/evening. The suite of instruments deployed on ROAM-V included a Condensation Particle Counter (CPC; GRIMM Model 5.403 CPC), Scanning Mobility Particle Sizer (SMPS; TSI 3750 detector, TSI 3082 classifier, TSI 3088 neutralizer, TSI 3081A Differential Mobility Analyzer), Cloud Condensation Nuclei counter (Droplet Measurement Technologies CCN Counter), micro pulse lidar (Droplet Measurement Technologies Micro Pulse LiDAR (miniMPL)), and a Davis Rotating Uniform size-cut Monitor (DRUM; DRUMAir 4-DRUM). Before sampling at each location, the latitude and longitude were recorded using the GPS on the phone application “My Altitude”. Onboard the ROAM-V, aerosol samples are drawn through a shared isokinetic inlet at a flow rate ranging from 3.5 to 7.0 LPM. A portion of this flow is directed through a cyclone impactor (Brechtel, Inc. Model SCC 0.732) and 0.5 LPM is directed to the CCN. To calculate particle losses, we used a two-step method. First, the measured SMPS size distributions were used to calculate particle loss through the inlet during sampling. Second, the corrected SMPS data was used to calculate the average of the total losses per scan down the CCN line. Then, the correction was applied to the CCN data. This calculation was done separately for each deployment location due to changes in the measured size distributions between locations. Particle loss from diffusion (based on Kesten, 1991 and Gormley, 1949), inertial impaction in 90-degree bends (based on Aerosol Measurement, 2011 and Crane, 1977), and cyclone impactor efficiency (based on Dirgo, 1985) were included in the loss calculation. When the SMPS was not sampling at a location (in the case of an instrument malfunction or operator error), the reported CPC data was corrected with an average of the total losses for the entire campaign at the specified deployment location (e.g., if we needed to correct Galveston data, then the average of all calculated losses at Galveston was taken). These flatline corrections were used for all data on 22/07/13, 22/07/20, 22/07/22, and the data from Galveston on 22/08/09. The supersaturation uncertainty is estimated conservatively at +/- 0.03%, where variation in the inlet temperature, pressure, and calibration technique prevents a more accurate measurement. Confidence in the reported supersaturation measurements is based on a pre-campaign calibration (following the methods from our previous work and Deng, 2014 based on Rose, 2008) in addition to inter-comparisons with the DOE for two days (22/08/18 and 22/09/01) where TAMU was co-located with AMF1. The inter-comparisons show good agreement between our instrument and the DOEs instrument on both days at all supersaturations. After the last inter-comparison on 22/09/01, there was no indication of a malfunction by our instrument through the rest of the campaign. Unfortunately, the instrument was dropped during demobilization. A post-campaign calibration was conducted, which showed a substantial departure from the pre-campaign calibration. The drop may have damaged the instrument’s ability to produce the desired supersaturations. Therefore, we do consider the data after 22/09/01 to be correct, but it should be used with caution. The CCN counter sampled for 3 minutes at each supersaturation setpoint (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2%). At the end of a cycle, the instrument was set to 0.01% supersaturation for 5 minutes. The data is comprised of the last 60 seconds of each supersaturation set point (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2%) to ensure the instrument stabilized and was able to reach thermal equilibrium. We removed the data during the periods where there were operational difficulties, setup, or maintenance. This data was collected for ARM Field Campaign AFC07055 and supported by DOE ASR grant DE-SC0021047. For any further questions, please feel free to contact the instrument PI, Sarah D. Brooks, sbrooks@tamu.edu. Rose et. al. Calibration and Measurement Uncertainties of a Continuous-Flow Cloud Condensation Nuclei Counter (DMT-CCNC): CCN Activation of Ammonium Sulfate and Sodium Chloride Aerosol Particles in Theory and Experiment. Atmos. Chem. Phys., 8, 1153-1179, 2008. Deng et. al. Using Raman Microspectroscopy to Determine Chemical Composition and Mixing State of Airborne Marine Aerosols over the Pacific Ocean. Aerosol Science and Technology, Vol 48, Issue 2, 2014. Kesten et. al. Calibration of a TSI Model 3025 Ultrafine Condensation Particle Counter. Aerosol Science and Technology, 15:2, 107-111, 1991. Gormley et. al. Diffusion from a Stream Flowing through a Cylindrical Tube. Proceedings of the Royal Irish Academy, Vol 52, 163-169, 1948. Aerosol Measurement: Principles, Techniques, and Applications, Third Edition. John Wiley & Sons, Inc, 2011. Crane et. al. Inertial Deposition of Particles in a Bent Pipe. Journal of Aerosol Science, Vol 8, 161-170, 1977. Dirgo et. al. Cyclone Collection Efficiency: Comparison of Experimental Results with Theoretical Predictions. Aerosol Science and Technology, 4:4, 401-415, 1985.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

First principles prediction of the Al-Li phase diagram including configurational and vibrational entropic contributions

The whole Al-Li phase diagram is predicted from first principles calculations and statistical mechanics including the effect of configurational and vibrational entropy. The formation enthalpy of different configurations at different temperatures was accurately predicted by means of cluster expansions that were fitted from first principles calculations. The vibrational entropic contribution of each configuration was determined from the bond length vs. bond stiffness relationships for each type of bond and the Gibbs free energy of the different phases was obtained as a function of temperature from Monte Carlo simulations. The predicted phase diagram was in excellent agreement with the currently accepted experimental one in terms of the stable (AlLi, Al 2 Li 3 , AlLi 2 , Al 4 Li 9 ) and metastable (Al 3 Li) phases, of the phase boundaries between them and of the maximum stability temperature of line compounds. In addition, it provided accurate information about the gap between Al 3 Li and AlLi solvus lines. Finally, the influence of the vibrational entropy on the correct prediction of the phase diagram is discussed. Overall, the methodology shows that accurate phase diagrams of alloys of technological interest can be predicted from first principles calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Develop a weather-aware climate model to understand and predict extremes and associated power outages and renewable energy shortages with uncertainty-aware and physics-informed machine learning

Focal Area(s): The focus area is predictive modeling through the use of AI techniques and AI-derived model components with a particular emphasis on extreme weather in Atmospheric Science and power outages and shortages in Energy Science. Science Challenge: Predicting weather extremes (e.g., heavy precipitation, strong wind, and large hailstones), and weather-related power system outages and shortages can mitigate economic losses, save lives, support renewables integration, and improve power system resiliency. However, currently, the poor reliability and large uncertainty associated with the weather extreme prediction in the current climate models make the problem intractable. The key challenges are: (1) physical factors like green-house gases (GHGs), aerosols, and land use and land cover (LULC) can significantly impact extreme storms, but the understanding of these impacts is limited, particularly globally; (2) the convective permitting resolutions needed to model severe convective storms and their impacts are computationally prohibitive with global climate models (GCMs); (3) interactions between weather extremes and power system outages are complex and subject to great uncertainty. Current outage prediction models are short lead (~ 3 days), which do not allow for long-time planning of energy production and distribution. Moreover, we have limited capacity to predict weather events leading to sustained shortages in a renewable-energy-dominated power system. These challenges drive motivation for mechanistic understanding and reliable and efficient predictive modeling of extremes and their impacts from the sub-seasonal to long term projections.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2000

Microgravity Vibration Isolation for the International Space Station

The International Space Station (ISS) is being envisioned as a laboratory for experiments in numerous microgravity (micrograms) science disciplines. Predictions of the ISS acceleration environment indicate that the ambient acceleration levels ill exceed levels that can be tolerated by the science experiments. Hence, microgravity vibration isolation systems are being developed to attenuate the accelerations to acceptable levels. While passive isolation systems are beneficial in certain applications, active isolation systems are required to provide attenuation at low frequencies and to mitigate directly induced payload disturbances. To date, three active isolation systems have been successfully tested in the orbital environment. A fourth system called g-LIMIT is currently being developed for the Microgravity Science Glovebox and is manifested for launch on the UF-1 mission. This paper presents an overview of microgravity vibration isolation technology and the g-LIMIT system in particular.

Whorton, Mark S.↗
NASA NTRS2008

Close Approach Prediction Analysis of the Earth Science Constellation with the Fengyun-1C Debris

Routine satellite operations for the Earth Science Constellation (ESC) include collision risk assessment between members of the constellation and other orbiting space objects. Each day, close approach predictions are generated by a U.S. Department of Defense Joint Space Operations Center Orbital Safety Analyst using the high accuracy Space Object Catalog maintained by the Air Force's 1" Space Control Squadron. Prediction results and other ancillary data such as state vector information are sent to NASAJGoddard Space Flight Center's (GSFC's) Collision Risk Assessment analysis team for review. Collision analysis is performed and the GSFC team works with the ESC member missions to develop risk reduction strategies as necessary. This paper presents various close approach statistics for the ESC. The ESC missions have been affected by debris from the recent anti-satellite test which destroyed the Chinese Fengyun- 1 C satellite. The paper also presents the percentage of close approach events induced by the Fengyun-1C debris, and presents analysis results which predict the future effects on the ESC caused by this event. Specifically, the Fengyun-1C debris is propagated for twenty years using high-performance computing technology and close approach predictions are generated for the ESC. The percent increase in the total number of conjunction events is considered to be an estimate of the collision risk due to the Fengyun-1C break- UP.

Duncan, Matthew↗
NASA NTRS1984

Numerical Prediction of the President's Day Cyclone

Numerical-diagnostic studies of major anomalous weather events are being conducted in order to investigate the relevant physical processes associated with the events and the role of satellite observing systems in the analysis and prediction of these phenomena. One component of this study is concerned with the numerical prediction of intense coastal and oceanic cyclogenesis. The specific objectives of this research are: (1) to assess the accuracy of Goddard Laboratory for Atmospheric Sciences model predictions of cyclogenesis, (2) to determine the importance of large scale dynamical processes and diabatic heating to the prediction, and (3) to evaluate the sensitivity of the model predictions to the initial conditions. It was shown that diabatic heating resulting from oceanic fluxes significantly contributed to the generation of low level cyclonic vorticity and the intensification and slow rate movement of an upper level ridge over the western Atlantic. As an upper level short-wave trough approached this ridge, diabatic heating associated with the release of latent heat intensified, and the gradient of vorticity, vorticity advection, upper level divergence, and upward vertical motion in advance of the trough were greatly increased, providing strong large-scale forcing for the surface cyclogenesis.

Atlas, R.↗
DOE OSTI2021

Assessing Teleconnections-Induced Predictability of Regional Water Cycle on Seasonal to Decadal Timescales Using Machine Learning Approaches

Focal Area: (3) Insight gleaned from complex data (both observed and simulated) using AI, big data analytics, and other advanced methods, including explainable AI and physics- or knowledge-guided AI. Science Challenge: Predictive understanding of the regional water cycle based on teleconnections of climate modes of variability using AI methods.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

Open-Source Science-Driven Development of the Science Data System (SDS) for Earth System Observatory (ESO) Atmospheric Missions

The NASA Earth System Observatory (ESO) atmospheric missions will provide space-based and suborbital observations of collocated cloud, dynamic, precipitation and aerosol processing leading to improved weather, air quality, and climate predictions. The Science Data System (SDS) will deploy the adaptive processing system (APS) developed within the Cloud to manage the research and operational processing of ESO atmospheric mission orbital and suborbital sensors and curate these data for near real-time and collection reprocessing and transfer them to a NASA Distributed Active Archive Center (DAAC) for long-term storage and distribution. Further, the SDS will follow guidelines provided by NASA Earth Science Data Systems (ESDS) program including standard conventions for data file formats, naming, and metadata to improve data interoperability, interpretability, usability, discovery, provenance, and spatiotemporal representativeness. The SDS follows NASA’s commitment to Open-Source Science (OSS) including the sharing of data, software, and knowledge in an open and timely manner. Each of the SDS system components will be developed with open-source concepts including components of APS itself as well as ESO atmospheric mission algorithms. This presentation describes the framework of the SDS and its integral part in facilitating OSS within the ESO atmospheric missions.

David M. Giles↗
DOE OSTI2025

Advancing the understanding of coastal disturbances with a network-of-networks approach

Coastal ecosystems are at the nexus of many high priority challenges in environmental sciences, including predicting the influences of compounding disturbances exacerbated by climate change on biogeochemical cycling. Extreme events such as hurricanes, flooding, landslides, and wildfires influence biogeochemical cycling in these systems. However, while research in coastal science is fundamentally transdisciplinary – as drivers of biogeochemical and ecological processes often span scientific and environmental domains – traditional place-based approaches are still often employed to understand coastal ecosystems. In this perspective, we argue that integration among distributed research sites from a macrosystem perspective is crucial to understand how compounding disturbances affect coastal ecosystems. We identify a roadmap for the implementation of an integrated network-of-networks framework that leverages existing research network sites in coastal ecosystems to advance continental-scale process understanding for studying extreme events and global change. We also identify specific ways that existing research efforts can maximize mutual benefit, and where additional infrastructure investments might increase return-on-investment along the coast, using the coastal continental US as a case study.

Myers-Pigg, Allison N. [BATTELLE (PACIFIC NW LAB)]↗
NASA NTRS2024

HPIC: The Habitable Worlds Observatory Preliminary Input Catalog

The Habitable Worlds Observatory Preliminary Input Catalog (HPIC) is a list of ∼13,000 nearby bright stars that will be potential targets for the Habitable Worlds Observatory (HWO) in its search for Earth-sized planets around Sun-like stars. We construct this target list using the TESS and Gaia DR3 catalogs and develop an automated pipeline to compile stellar measurements and derived astrophysical properties for all stars. We benchmark the stellar properties in the HPIC relative to those of the manually curated ExEP HWO Precursor Science Stars list and find that, for the 164 best targets for exo-Earth direct imaging, our stellar properties are consistent. We demonstrate the utility of the HPIC by using it as an input for yield calculations to predict the science output of various mission designs, including those with larger telescope diameters and those focused on other planet types besides Earth analogs, such as Jupiter-mass planets. The breadth and completeness of the HPIC is essential for accurate HWO mission trade studies, and it will be useful for other exoplanet studies and general astrophysics studying the population of bright nearby stars.

Noah W. Tuchow↗
NASA NTRS2018

A Prognostics Framework Development for Swarm Satellite Formations

Prognostics is the science of predicting the failure(s) of a component or a system and understanding how the performance will change in the event of a failure or degradation mechanism. With accurate predictions of possible failures, autonomous mitigative actions can be taken to correct/repair any issues or alert human operators of a failure threshold exceedance requiring condition-based maintenance. Although there is extensive research on failure predictions for a component or a system, there are significantly more opportunities to foray into failure predictions and prognostics for a system of systems such as an airspace consisting of multiple aircraft, a fleet of unmanned aerial vehicles, and a swarm of intelligent satellite systems. Failure prediction and mitigation are particularly important in autonomous systems such as satellite swarm systems that need effective resource management and minimal human interactions. Based on NASA's decadal survey, there is a clear need to prioritize the development of satellite swarm technology for studies of space physics and Earth science. The science community will propose future missions that return in-situ measurements from a 3-D (three-dimensional) volume of space, with relative spacecraft motion and inter-satellite baselines controlled according to the mission objectives. For such multi-spacecraft missions, it is required that ground operations resources do not scale with the number of satellites, thus compromising the swarm or leading to inefficiencies in resource allocation. Swarms of tens or hundreds of small satellites will require autonomy in attitude control, navigation and failure. Although significant research has been conducted in the areas of autonomous formation flying algorithms, less attention has been given to the development of resilient systems robust to failures.The focus of this research paper is the integration of model-based prognostics into the swarm dynamics control and decision-making algorithms. We simulate swarm management strategies for a subsystem failure to demonstrate the importance of failure predictions by comparing two cases: (i) no health information is provided to the system and utilized in the decision-making process and (2) system health information is obtained using prognostics and employed by the control system. One example scenario presented is for the GPS (Global Positioning System) system of an individual satellite to perform off-nominally due to increasing estimated error. In this scenario, the keep-out zone for that satellite would become more conservative, thereby decreasing the risk of collision. This is achieved via tuning the individual artificial repulsive functions assigned to each satellite.This paper is structured as follows. First we provide an overview of current swarm technology development, where we specifically use the term swarm to define multiple satellites flying in formation in similar orbits, with cross-link communication and station-keeping capabilities. Second, we give an introduction to the Swarm Orbital Dynamics Advisor (SODA), a tool that accepts high-level configuration commands and provides the orbital maneuvers required to achieve the prescribed formation configuration. Third, we provide the details of the model-based prognostics algorithm implementation in SODA. Finally, we present different case studies for potential component/subsystem failures and the swarm responses based with and without failure prediction information.

prognostics↗
NASA NTRS2013

Progress Towards an Interdisciplinary Science of Plant Phenology: Building Predictions Across Space, Time and Species Diversity

Climate change has brought renewed interest in the study of plant phenology - the timing of life history events. Data on shifting phenologies with warming have accumulated rapidly, yet research has been comparatively slow to explain the diversity of phenological responses observed across latitudes, growing seasons and species. Here, we outline recent efforts to synthesize perspectives on plant phenology across the fields of ecology, climate science and evolution. We highlight three major axes that vary among these disciplines: relative focus on abiotic versus biotic drivers of phenology, on plastic versus genetic drivers of intraspecific variation, and on cross-species versus autecological approaches. Recent interdisciplinary efforts, building on data covering diverse species and climate space, have found a greater role of temperature in controlling phenology at higher latitudes and for early-flowering species in temperate systems. These efforts have also made progress in understanding the tremendous diversity of responses across species by incorporating evolutionary relatedness, and linking phenological flexibility to invasions and plant performance. Future research with a focus on data collection in areas outside the temperate mid-latitudes and across species' ranges, alongside better integration of how risk and investment shape plant phenology, offers promise for further progress.

phenology↗
DOE OSTI2021

Identifying precursors of daily to seasonal hydrological extremes over the USA using deep learning techniques and climate model ensembles

Focal Area(s): We focus on two areas of crosscutting interest for DOE: 1) predictability of extreme precipitation and drought in the USA and 2) the integration of climate models with new AI tools, such as convolutional neural networks (CNN) and methods to understand their output (e.g. layer-wise relevance propagation; LRP). This project fits into focus area 3 of this call for white paper using AI to gain insight from complex data, including explainable AI tools. Science Challenge: Predicting hydrological extremes is important due to their impacts on people, agriculture and infrastructure. This prediction is difficult due to the infrequent occurrence of extremes and their complexity. However, extreme events can be related to more predictable conditions in the ocean, such as El Nino, long-term soil moisture or large scale modes of climate variability, such as the North Atlantic Oscillation (NAO).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

B 2 H 6 splitting on catalytic surfaces and role of BH 3 towards hydrogen spillover

A fundamental understanding of the spillover mechanism is an open and challenging problem and plays an important role in catalysis. In particular, bond-exchange spillover mechanism is considered to be effective for reversible storage and release of hydrogen at near ambient conditions. For this, three critical steps are needed: finding the right support (acceptor), the right catalyst to split H 2 , and ensuring that once H 2 is split, the H atoms can migrate on the surface with the help of secondary catalysts and eventually hydrogenate the entire material. In this paper we address these challenges using density functional theory. Here we show that BH 3 , a secondary catalyst, can be produced by symmetrically splitting its stable precursor, B 2 H 6 , on doped metal-free surfaces such as graphene and h-BN as well as on MOF5. In addition, to reduce computational cost, we develop structural descriptor and predictive model equation to effectively screen potential BH 3 binding sites. Symmetrical splitting of B 2 H 6 on different types of materials can address the hydrogen spillover challenge, making efficient storage of hydrogen possible.

08 HYDROGEN↗
DOE OSTI2021

Machine learning-enabled prediction of chemical durability of A 2 B 2 O 7 pyrochlore and fluorite

Pyrochlore-structure type and its derivative in a general formula A 2 B 2 O 7 (A = rare earth elements and actinides; B = Ti, Sn, Zr, Hf, Pb, Si, etc.) display excellent structural flexibility and rich crystal chemistry as promising nuclear waste form materials capable of immobilizing actinides and fission products. It is essential to understand these materials’ chemical durability and element release of radionuclides in order to evaluate their performance in near-field environment. However, it is a formidable grand technological challenge to experimentally perform durability testing across hundreds of thousands of possibilities resulting from their extreme compositional complexities due to cation substitutions at both A and B-sites. In this work, we demonstrate a machine learning approach to determine the key materials parameters and structural characteristics governing the leaching behaviors from a small set of selected compositions as model systems, enabling a science-based prediction of their chemical durability that can be extended to a wide range of chemical compositions. The combination of four key structural characteristics and materials parameters, including ionic radius size difference , ionic potential difference , electronegativity difference , and lattice parameter , creates features an optimized prediction of the chemical durability. Two machine learning models, linear regression and Kernel ridge regression models, are trained on the randomly-split training dataset derived from the experimentally-determined elemental release rates, and subsequently tested on the testing dataset. The predicted leaching rates from both machine learning models show an excellent agreement with the experimental data, demonstrating the feasibility of rapidly evaluating the material properties of new compositions. These results highlight the immense potential of synergizing informatics through machine learning-based models and well-controlled experiments of selected model systems to accelerate materials design and discovery with optimized compositions and performance of promising materials for effective nuclear waste management.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Growth Strategy of a Hybrid Yb3Rh4Sn13/LaRuSn3 Structure Type: Integrating Thermal Analysis, In Situ Diffraction, and Geometric Descriptors

Remeika phases form a versatile family of cage like intermetallics built from transition metal–centered trigonal prisms linked into three dimensional frameworks that generate two characteristic voids: a large [AX₁₂] cuboctahedral cage hosting the rare earth ion and an [XX′₁₂] icosahedral cage accommodating the tetrel atom. In this work, we present a tool driven approach for targeted solid state synthesis of Remeika phases, integrating differential scanning calorimetry, in situ neutron diffraction, and a geometric tolerance factor that quantifies rare earth size compatibility within these polyhedral cages. When combined with arc melting and metallic flux crystal growth, this framework enables prediction, verification, and isolation of specific Remeika phases. Applying this strategy, we obtain single crystals of the predicted pseudo-perovskite Fe based Remeika compound Yb0.9FeGe3.1. More broadly, this perspective highlights how coupling real time structural probes with simple geometric descriptors provides a general pathway for designing synthesis conditions and accessing potentially metastable structure types in complex intermetallic systems.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Machine learning-driven predictive resource management in complex science workflows

Here, the collaborative efforts of large communities in science experiments, often comprising thousands of global members, reflect a monumental commitment to exploration and discovery. Recently, advanced and complex data processing has gained increasing importance in science experiments. Data processing workflows typically consist of multiple intricate steps, and the precise specification of resource requirements is crucial for each step to allocate optimal resources for effective processing. Estimating resource requirements in advance is challenging due to a wide range of analysis scenarios, varying skill levels among community members, and the continuously increasing spectrum of computing options. One practical approach to mitigate these challenges involves initially processing a subset of each step to measure precise resource utilization from actual processing profiles before completing the entire step. While this two-staged approach enables processing on optimal resources for most of the workflow, it has drawbacks such as initial inaccuracies leading to potential failures and suboptimal resource usage, along with overhead from waiting for initial processing completion, which is critical for fast-turnaround analyses. In this context, our study introduces a novel pipeline of machine learning models within a comprehensive workflow management system, the Production and Distributed Analysis (PanDA) system. These models employ advanced machine learning techniques to predict key resource requirements, overcoming challenges posed by limited upfront knowledge of characteristics at each step. Accurate forecasts of resource requirements enable informed and proactive decision-making in workflow management, enhancing the efficiency of handling diverse, complex workflows across heterogeneous resources.

97 MATHEMATICS AND COMPUTING↗