Search NASA⌕ Search

SEARCH · Search NASA

Results for “MATHEMATICS - CALCUS, OPERATIONAL”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 631 records · Page 35

B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD

Here, the Deep Operator Network (DeepONet) is a neural network architecture used to approximate operators, including the solution operator of parametric PDEs. DeepONets have shown remarkable approximation ability. However, the performance of DeepONets deteriorates when the training data is polluted with noise, a scenario that occurs in practice. To handle noisy data, we propose a Bayesian DeepONet based on replica exchange Langevin diffusion (reLD). Replica exchange uses two particles. The first particle trains a DeepONet to exploit the loss landscape and make predictions. The other particle trains a different DeepONet to explore the loss landscape and escape local minima via swapping. Compared to DeepONets trained with state-of-the-art gradient-based algorithms (e.g., Adam), the proposed Bayesian DeepONet greatly improves the training convergence for noisy scenarios and accurately estimates the uncertainty. To further reduce the high computational cost of the reLD training of DeepONets, we propose (1) an accelerated training framework that exploits the DeepONet's architecture to reduce its computational cost up to 25% without compromising performance and (2) a transfer learning strategy that accelerates training DeepONets for PDEs with different parameter values. Finally, we illustrate the effectiveness of the proposed Bayesian DeepONet using four parametric PDE problems.

97 MATHEMATICS AND COMPUTING↗

Assessments of Physiology and Cognition in Hybrid-Reality Environments (APACHE)

NASA is planning to return to the Moon in the mid-2020s as a stepping stone to Mars missions in the 2030s. Spacewalks, or extravehicular activities (EVAs), performed on the Moon and Mars will differ in a variety of ways from those that have been performed in decades past. NASA has identified multiple risks to human health and performance associated with a crewed mission to Mars, especially those associated with exploration EVAs which are expected to be a primary mission activity. Crew may be expected to conduct up to 24 hours of EVA per person per week, where the likelihood of injury and/or mental mistakes are increased compared to ground-based training or current microgravity EVAs and the consequences of which can be catastrophic. Current test environments for exploration EVA research and technology development are large, costly facilities that are limited in their availability or capabilities. Spacesuit testing in a reduced gravity environment such as NASA’s Neutral Buoyancy Laboratory, while a good representation of the crew’s physical workload during exploration EVAs, typically has small datasets and is difficult to integrate physiological sensors or other types of crew performance measures. Meanwhile, scientific field-based testing such as NASA’s Desert Research and Technology Studies offers an operationally relevant environment for exploration EVAs, particularly for cognitive workload, but is also limited by small datasets, lack of a pressurized spacesuit, and obtrusive measures. The limitations of current analogs for exploration EVAs identify a need for a new test environment that can approximate both the physical and cognitive demands associated with exploration EVAs to enable rapid, controlled, and repeatable evaluations of human health and performance risks of exploration missions. In response, the Human Physiology, Performance, Protection, and Operations Laboratory (H-3PO) at NASA Johnson Space Center has developed a hybrid reality exploration EVA analog named the Assessments of Physiology And Cognition in Hybrid-reality Environments (APACHE) to address these limitations using a combination of virtual, physical, and hybrid reality techniques. The APACHE facility resides at NASA Johnson Space Center and serves as a large “sandbox” for EVA research and simulation. At its center is a roughly 15x20ft space surrounded by a 14” tall sandbox partially filled with lunar regolith simulant to emulate the physical feeling of walking on a planetary surface and to allow for simulated geology operations. Nearby, a curved passive treadmill (Skillmill Connect, Technogym, Fairfield, NJ) and an omnidirectional treadmill (Infinadeck, Infinadeck, Rocklin, CA) are included to enable exploration of these large virtual environments while also imposing the physical demands, representative timelines, and cognitive burdens required to navigate and traverse these distances during exploration EVA. A 6DOF motion platform is used to simulate rover operations and supports various human performance evaluations and associated risks. Lastly, APACHE can support two extravehicular (EV) crewmembers working in tandem. A computer workstation is located nearby and also supports an intravehicular (IV) crewmember as part of a full mission simulation. The IV crewmember has direct video and audio communication with the EV crew in VR to provide operational and procedural support. The software used in APACHE was created by the JSC Engineering Directorate, in partnership with Buendea, powered by a custom Unreal Engine 5 (UE5.3, Epic Games) project. APACHE currently utilizes the HTC Vive Pro Eye in a wireless configuration for VR simulations. There are two virtual environments that subjects can explore within APACHE, a Lunar and Martian surface. The virtual Lunar surface was created from LIDAR data of the Lunar South Pole to create roughly 16 sq km of explorable terrain. The virtual Martian surface contains roughly 400 sq km of explorable terrain derived from Mars Reconnaissance Orbiter LIDAR data of the Jezero Crater. The immersion and related cognitive burdens of conducting a planetary EVA is simulated through a series of EVA-relevant tasks performed in the VR environment, using these high-fidelity visual representations. Additionally, APACHE includes biosensor driven informatics, such as real-time heart rate monitoring and/or derived values from model simulations, for active monitoring by the EV crew and added cognitive demand. A “Wizard of Oz” control panel enables test operators to activate contingency events such as simulated spacesuit malfunctions, loss of communications, and/or limited visibility. Embedded performance measures such as accuracy, completeness, and execution time have been developed for various exploration tasks to objectively quantify crew performance during an EVA and compare impacts to performance when different environmental stressors, both physical and cognitive, are added to or removed from the simulation. Additionally, validated cognitive and operational performance measures such as the Digit Symbol Substitution Task have been recreated and embedded in VR for direct and relatively unobtrusive measurement of motor perception. The APACHE environment currently supports multiple research studies at NASA. Examples include the CHAPEA project, a series of simulated year-long missions on Mars by a 4-person crew; and the CO2 Contingency Walk Back Study, an investigation of elevated CO2 exposure on crew performance during a contingency EVA scenario. APACHE also provides a test environment to support the development of the Crew State and Risk Model, which is a collection of individualized, mathematical models of crew physical and cognitive state; and the Personalized EVA Informatics and Decision Support system, an operational tool for flight controllers, and eventually a self-reliant Martian crew, to make biomedically-informed decisions in real-time to optimize the EVA planning and execution with respect to crew health and performance. Some technical challenges associated with developing the APACHE environment, as well as current limitations, include VR limitless natural walking with a hybrid spacesuit simulator, optimizing performance for wireless PC VR streaming while maintaining a high degree of visual fidelity, and the integration of various physiological (metabolic masks) and psychometric (eye tracking) sensors with the VR headset.

Human Performance↗

Application of Advanced Metering Infrastructure Data to Advanced Utility System Operations: Cooperative Research and Development, CRADA Number CRD-17-00712 (Final Report)

The primary objective of the proposed project is to evaluate the capabilities of Advanced Metering Infrastructure (AMI) based controls for grid operations. This includes monitoring and control at the secondary transformer level using existing AMI infrastructure. In addition, some of the challenges of using a model-less control will also be identified. The lessons learned will be disseminated to other utilities around the country through peer-reviewed publications with the consent of SDG&E. The scope of the work includes using data from SDG&E's existing AMI infrastructure and working with third party vendors selected by SDG&E. The grid edge monitoring systems and controls provided by the selected vendors will perform grid operations using AMI data. The National Renewable Energy Laboratory (NREL) will perform a software and controller-based evaluation of the grid edge controller, intelligent devices and sensors, at the Energy System Integration Facility (ESIF) laboratory.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A python package for analyzing Resilience of Complex Systems (pyRoCS) v.0.0

SAND2024-01040O PyRoCS software synthesizes mathematical equations from several domains—including information theory, ecology, and engineering sciences—to support resilience analysis for complex systems. Resilience is the ability of the complex system being analyzed to withstand, operate through, and recover from a disruption. The complex system can be a physical system such as an electric grid, an organization such as a company, or even a subfunction of an organization. Existing mathematical equations for resilience analysis are found within multiple domains including information theory, biological sciences, and complex systems. This package synthesizes and refactors equations from these various domains to make them more generalizable for application across different types of complex systems relevant for resilience analysis. Users will be able to apply these equations to characterize different components of complex systems based on available data. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Verzi, Stephen↗

Precursor Analysis Report: Ryuk Ransomware Attack on Universal Health Services 2020

The Ryuk Ransomware Attack on Universal Health Services (UHS) 2020 Precursor Analysis Report leverages publicly available information about the 2020 UHS cyber attack and catalogs anomalous observables for each technique employed in the attack. This analysis is based upon the methodology of the Cybersecurity for the Operational Technology Environment (CyOTE) program. UHS manages over 400 hospitals and is one of the largest healthcare providers in the United States with 3.5 million patients each year. On 27 September 2020, UHS suffered a widespread ransomware attack that resulted in a denial of service to critical internet-dependent healthcare systems including workstations, phones, and data centers. Employees resorted to filing patient details with pen and paper, while other facilities had to redirect ambulances and urgent patients to other facilities for adequate care. Adversaries carried out the attack with Ryuk, a ransomware that encrypts data and generates a RyukReadMe.txt ransom note with the ransom fee to decrypt the data, varying from 15 Bitcoin (BTC) to 50 BTC, equivalent to roughly $\$$353,892 to $\$$964,617. UHS did not pay the ransom and was able to recover data through backups, but still reported an impact of $\$$67 million dollars in recovery costs. On 29 October, one month after the attack, UHS made an official statement that their systems had been restored and they were resuming normal operations. Researchers and analysts identified 18 unique techniques (used in a sequence of 19 steps) utilized during the attack with a total of 185 observables using MITRE ATT&CK® for Industrial Control Systems. The CyOTE program assesses observables accompanying techniques used prior to the triggering event to identify opportunities to detect malicious activity. If observables accompanying the attack techniques are perceived and investigated prior to the triggering event, earlier comprehension of malicious activity can take place. Fourteen of the identified techniques used during the UHS cyber attack were precursors to the triggering event. Analysis identified 106 observables associated with these precursor techniques, 82 of which were assessed to have an increased likelihood of being perceived in the 30 days to two hours preceding the triggering event. The response and comprehension time could have been reduced if the observables had been identified earlier. The information gathered in this report contributes to a library of observables tied to a repository of artifacts, data sources, and technique detection references for practitioners and developers to support the comprehension of indicators of attack. Asset owners and operators can use these products if they experience similar observables or to prepare for comparable scenarios.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Vector-Ordering Filter Procedure for Data Reduction

The vector-ordering filter (VOF) technique involves a procedure for sampling a large population of data vectors to select a subset of data vectors that fully characterize the state space of the large population. The VOF technique enables a large reduction of the volume of data that must be handled in the automated monitoring system and method discussed in the two immediately preceding articles. In so doing, the VOF technique enables the development of data-driven mathematical models of a monitored asset from sets of data that would otherwise exceed the memory capacities of conventional engineering computers. Data-driven mathematical models have been shown to offer high fidelity for purposes of control and monitoring of assets. In practice, a collection of asset-operating observations is acquired with the intention that the collection contain observations characteristic of the full dynamic range of operation of the asset. Often, such a collection contains an extremely large number of observations, many of which are redundant. The VOF technique fills the need for a means to extract, from the original collection of observational data, a reduced data matrix that excludes redundant data while maintaining the full statistical character and dynamic range of the original data. The reduced data matrix can then be used as the input data for development of a mathematical model of the monitored asset, or as training data for a neural-network substitute for an explicit mathematical model of the asset. Alternatively, the reduced data matrix can, itself, be used directly as a mathematical model of the monitored asset, as is commonly done in multivariate state-estimation techniques. The original data are collected from the asset over a range of operating states and are put in matrix form. Each column vector in the original data matrix represents the signal values acquired at a particular operational state of the asset. Thus, the number of columns of the original data matrix equals the number of observed states and the number of rows in this matrix equals the number of signals acquired at each observation. In the VOF technique, one extracts the reduced data matrix from the original data matrix through the selection of a representative subset of the column (state) vectors.

Bickford, Randall L.↗

Multifidelity deep operator networks for data-driven and physics-informed problems

Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either from experiments or simulations. In this work, we present a composite Deep Operator Network (DeepONet) for learning using two datasets with different levels of fidelity to accurately learn complex operators when sufficient high-fidelity data is not available. Additionally, we demonstrate that the presence of low-fidelity data can improve the predictions of physics-informed learning with DeepONets. We demonstrate the new multi-fidelity training in diverse examples, including modeling of the ice-sheet dynamics of the Humboldt glacier, Greenland, using two different fidelity models and also using the same physical model at two different resolutions.

97 MATHEMATICS AND COMPUTING↗

Deep Learning Experiments for Tropical Cyclone Intensity Forecasts

Reducing tropical cyclone (TC) intensity forecast errors is a challenging task that has interested the operational forecasting and research community for decades. To address this, we developed a deep learning (DL)-based multilayer perceptron (MLP) TC intensity prediction model. The model was trained using the global Statistical Hurricane Intensity Prediction Scheme (SHIPS) predictors to forecast the change in TC maximum wind speed for the Atlantic basin. In the first experiment, a 24-h forecast period was considered. To overcome sample size limitations, we adopted a leave one year out (LOYO) testing scheme, where a model is trained using data from all years except one and then evaluated on the year that is left out. When tested on 2010–18 operational data using the LOYO scheme, the MLP outperformed other statistical–dynamical models by 9%–20%. Additional independent tests in 2019 and 2020 were conducted to simulate real-time operational forecasts, where the MLP model again outperformed the statistical–dynamical models by 5%–22% and achieved comparable results as HWFI. The MLP model also correctly predicted more rapid intensification events than all the four operational TC intensity models compared. In the second experiment, we developed a lightweight MLP for 6-h intensity predictions. When coupled with a synthetic TC track model, the lightweight MLP generated realistic TC intensity distribution in the Atlantic basin. Therefore, the MLP-based approach has the potential to improve operational TC intensity forecasts, and will also be a viable option for generating synthetic TCs for climate studies.

58 GEOSCIENCES↗

Estimating value of information for heliostat washing operations at solar thermal plants

Concentrating solar power (CSP) plants depend on thousands of heliostats whose reflectance declines as dust accumulates. Operators routinely measure reflectance to estimate soiling and, in turn, inform cleaning schedules, but the value of collecting more frequent or more accurate data has not been formally quantified. This study introduces a Monte Carlo discrete event simulation framework that integrates stochastic models of soiling, weather, and measurement error with a dynamic cleaning dispatch policy to estimate annual energy production and operations costs. Applied to two representative central-receiver field configurations, the results show that both the frequency and accuracy of reflectance measurements can meaningfully impact plant performance. In both case studies, reducing measurement intervals yields significant returns, with the energy gains greatly exceeding the cost of more frequent data collection. The simulation framework serves as a decision-support tool for CSP operators, allowing them to input site-specific soiling conditions, measurement accuracy, and survey frequency to evaluate the tradeoffs between data collection cost and energy recovery, and to identify measurement strategies that maximize plant profit.

14 SOLAR ENERGY↗

Projective embedding of dynamical systems: Uniform mean field equations

Herein we study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the original system dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of rank-1 projector operator, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. We prove a variety of results on the relationship between the spectrum of the Jacobian for fixed points in the original and in the embedded system. Direct applications of PEDS can be non-convex optimization and machine learning.

97 MATHEMATICS AND COMPUTING↗

Space Operations Learning Center

The Space Operations Learning Center (SOLC) is a tool that provides an online learning environment where students can learn science, technology, engineering, and mathematics (STEM) through a series of training modules. SOLC is also an effective media for NASA to showcase its contributions to the general public. SOLC is a Web-based environment with a learning platform for students to understand STEM through interactive modules in various engineering topics. SOLC is unique in its approach to develop learning materials to teach schoolaged students the basic concepts of space operations. SOLC utilizes the latest Web and software technologies to present this educational content in a fun and engaging way for all grade levels. SOLC uses animations, streaming video, cartoon characters, audio narration, interactive games and more to deliver educational concepts. The Web portal organizes all of these training modules in an easily accessible way for visitors worldwide. SOLC provides multiple training modules on various topics. At the time of this reporting, seven modules have been developed: Space Communication, Flight Dynamics, Information Processing, Mission Operations, Kids Zone 1, Kids Zone 2, and Save The Forest. For the first four modules, each contains three components: Flight Training, Flight License, and Fly It! Kids Zone 1 and 2 include a number of educational videos and games designed specifically for grades K-6. Save The Forest is a space operations mission with four simulations and activities to complete, optimized for new touch screen technology. The Kids Zone 1 module has recently been ported to Facebook to attract wider audience.

Lui, Ben↗

Aspects of job scheduling

A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Communications Complex, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germane to scheduling are presented.

Phillips, K.↗

STABCAR: A program for finding characteristic root systems having transcendental stability matrices

STABCAR can be used to determine the characteristic roots of flexible, actively controlled aircraft, including the effects of unsteady aerodynamics. A modal formulation and a transfer-matrix representation of the control system are employed. Operable in either a batch or an interactive mode, STABCAR can provide graphical or tabular output of the variation of the roots with velocity, density, altitude, dynamic pressure or feedback gains. Herein the mathematical model, program structure, input requirements, output capabilities, and a series of sample cases are detailed. STABCAR was written for use on CDC CYBER 175 equipment; modification would be required for operation on other machines.

Adams, W. M., Jr.↗

On relaxations of the max k -cut problem formulations

Here, a tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max k-cut problem is a fundamental combinatorial optimization problem with multiple notorious mixed integer optimization formulations. In this paper, we explore four existing mixed integer optimization formulations of the max k-cut problem. Specifically, we show that the continuous relaxation of a binary quadratic optimization formulation of the problem is: (i) stronger than the continuous relaxation of two mixed integer linear optimization formulations and (ii) at least as strong as the continuous relaxation of a mixed integer semidefinite optimization formulation. We also conduct a set of experiments on multiple sets of instances of the max k-cut problem using state-of-the-art solvers that empirically confirm the theoretical results in item (i). Furthermore, these numerical results illustrate the advances in the efficiency of global non-convex quadratic optimization solvers and more general mixed integer nonlinear optimization solvers. As a result, these solvers provide a promising option to solve combinatorial optimization problems. Our codes and data are available on GitHub.

97 MATHEMATICS AND COMPUTING↗

Federated benchmarking of medical artificial intelligence with MedPerf

Medical artificial intelligence (AI) has tremendous potential to advance healthcare by supporting and contributing to the evidence-based practice of medicine, personalizing patient treatment, reducing costs, and improving both healthcare provider and patient experience. Unlocking this potential requires systematic, quantitative evaluation of the performance of medical AI models on large-scale, heterogeneous data capturing diverse patient populations. Here, to meet this need, we introduce MedPerf, an open platform for benchmarking AI models in the medical domain. MedPerf focuses on enabling federated evaluation of AI models, by securely distributing them to different facilities, such as healthcare organizations. This process of bringing the model to the data empowers each facility to assess and verify the performance of AI models in an efficient and human-supervised process, while prioritizing privacy. We describe the current challenges healthcare and AI communities face, the need for an open platform, the design philosophy of MedPerf, its current implementation status and real-world deployment, our roadmap and, importantly, the use of MedPerf with multiple international institutions within cloud-based technology and on-premises scenarios. Finally, we welcome new contributions by researchers and organizations to further strengthen MedPerf as an open benchmarking platform.

60 APPLIED LIFE SCIENCES↗

Supporting Resource Adequacy via the ReEDS-India Model [Slides]

ReEDS-India is an open-access tool for mid- and long-term capacity expansion modeling that finds the mix of generation, transmission, and storage technologies that meet the anticipated requirements of the electric sector at least cost.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Method of calculating gas dynamics and heat transfer in single stage refrigeration units

A generalized mathematical model of gas-dynamic and heat transfer processes in single-stage regenerative installations operating in Stirling, MacMahon, Gifford-MacMahon, and pulsating tube cycles is proposed. A numerical method os solving initial equations on a digital computer is given. This makes it possible to calculate the change in the thermodynamic parameters in the working cycle in different machine components, as well as the dependence of cold productivity on the temperature level in the steady regime.

Zhitomirskiy, I. S.↗