Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical Computing”

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 325 records · Page 18

Math modeling and computer mechanization for real time simulation of rotary-wing aircraft

Mathematical modeling and computer mechanization for real time simulation of rotary wing aircraft is discussed. Error analysis in the digital simulation of dynamic systems, such as rotary wing aircraft is described. The method for digital simulation of nonlinearities with discontinuities, such as exist in typical flight control systems and rotor blade hinges, is discussed.

Howe, R. M.↗

Task-oriented machine learning surrogates for tipping points of agent-based models

We present a machine learning framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale approach, for the construction of different types of effective reduced order models from detailed agent-based simulators and the systematic multiscale numerical analysis of their emergent dynamics. The specific tasks of interest here include the detection of tipping points, and the uncertainty quantification of rare events near them. Our illustrative examples are an event-driven, stochastic financial market model describing the mimetic behavior of traders, and a compartmental stochastic epidemic model on an Erdös-Rényi network. We contrast the pros and cons of the different types of surrogate models and the effort involved in learning them. Importantly, the proposed framework reveals that, around the tipping points, the emergent dynamics of both benchmark examples can be effectively described by a one-dimensional stochastic differential equation, thus revealing the intrinsic dimensionality of the normal form of the specific type of the tipping point. This allows a significant reduction in the computational cost of the tasks of interest.

97 MATHEMATICS AND COMPUTING↗

Offline Maximizing Minimally Invasive Proper Orthogonal Decomposition for Reduced-Order Modeling of S n Radiation Transport

Deterministic solutions to the Sn radiation transport equation can be computationally expensive to calculate. Reduced-order modeling enables efficient approximation of the full-order model (FOM) solution. We propose a novel method for constructing reduced-order models (ROMs) of the S n radiation transport equation, offline maximizing minimally invasive (OMMI) proper orthogonal decomposition (POD). POD uses the method of snapshots to create a reduced-order basis for constructing an ROM. Minimally invasive POD leverages the sweep infrastructure existing in deterministic transport codes to create a POD-based ROM, even when infeasible by traditional methods. Offline maximizing minimally invasive proper orthogonal decomposition (OMMI-POD) extends minimally invasive POD by performing sweeps offline, therefore maximizing the potential speedup. OMMI-POD does so by creating a library of reduced systems from a training set. This library of reduced systems is then interpolated to provide a rapid approximate solution of the S n radiation transport equation. The model is evaluated on a set of test problems, achieving a low error with a 466 times speedup over the FOM. Also presented is a study of the effect of sampling method on the performance of OMMI-POD, specifically comparing naive uniform sampling to the more accurate and computationally expensive greedy sampling.

97 MATHEMATICS AND COMPUTING↗

Integrating Energy-Efficient Computing with Computational Research to Accelerate Energy Technology

NREL's computational sciences center hosts the largest high performance computing (HPC) capabilities dedicated to energy research while functioning as a living laboratory for energy-efficient computing. NREL's HPC capabilities support the research needs of the Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE). In ten years of operation, HPC use in EERE-sponsored research has grown by a factor of 30, including work in electricity generation, energy efficiency, transportation, and energy system modeling. This paper analyzes this research portfolio, providing examples of individual use cases. The paper documents NREL's history of operating one of the world's most energy-efficient data centers while examining pathways to reduce economic and environmental impact beyond reduction of Power Usage Efficiency (PUE). This paper concludes by examining the unique opportunities created for accelerating improvements in data center efficiency created by combining an HPC system dedicated to energy research and a research program in energy-efficient computing.

97 MATHEMATICS AND COMPUTING↗

Preparing angular momentum eigenstates using engineered quantum walks

Coupled angular-momentum eigenstates are widely used in atomic and nuclear physics calculations and are building blocks for spin networks and the Schur transform. To combine two angular momenta J 1 and J 2 , forming eigenstates of their total angular momentum J=J 1 +J 2 , we develop a quantum-walk scheme that does not require inputting O(j 3 ) nonzero Clebsch–Gordan (CG) coefficients classically. In fact, our scheme may be regarded as a unitary method for computing CG coefficients on quantum computers with a typical complexity of O⁡(j) and a worst-case complexity of O⁡(j 3 ). Equivalently, our scheme provides decompositions of the dense CG unitary into sparser unitary operations. Our scheme prepares angular-momentum eigenstates using a sequence of Hamiltonians to move an initial state deterministically to desired final states, which are usually highly entangled states in the computational basis. In contrast with usual quantum walks, whose Hamiltonians are prescribed, we engineer the Hamiltonians in su⁡(2)×su⁡(2), which are inspired by, but different from, Hamiltonians that govern magnetic resonances and dipole interactions. To achieve a deterministic preparation of both ket and bra states, we use projection and destructive interference to double pinch the quantum walks, such that each step is a unit-probability population transfer within a two-level system. We test our state preparation scheme on classical computers, reproducing tables of CG coefficients. Finally, we also implement small test problems on current quantum hardware.

97 MATHEMATICS AND COMPUTING↗

Monitoring installation of partially occluded subassemblies in modular construction factories using BIM, ray tracing, and computer vision

Modular and offsite construction methods are being increasingly adopted due to the advantages they offer in terms of project completion time, quality, and energy-efficiency. Despite these advantages, the current state of monitoring systems in modular construction factories highly relies on labor-intensive, subjective, and error-prone observational methods. A large body of research has aimed to automate the monitoring process using an array of sensors, such as IMUs and RFIDs, during the past two decades. Recently, computer vision-based methods have gained increasing interest as a non-intrusive technology to monitor the process inside modular construction factories. However, partial occlusion challenges have impeded their practical application on a large scale. This challenge is specifically important for monitoring the installation of subassemblies since they can obstruct the view of the monitoring camera, especially those that enable long-term monitoring like closed-circuit television (CCTV) fixed-view surveillance cameras. Here, this paper aims to address this challenge by proposing a novel computer vision-based method to monitor the installation of new subassemblies inside modular factories in highly occluded scenes. The proposed methodology identifies the subassemblies in the CCTV video footage using computer vision, analyzes the occlusions using BIM and ray casting techniques, and estimates the progress of assembly by comparing the BIM model with the detected subassemblies in the video. The proposed methodology was successfully validated on surveillance videos captured from a volumetric modular construction factory in the U.S., achieving 93% accuracy in identifying the installation of subassemblies. The results from this research show that the integration of BIM and computer vision is a promising method for monitoring the installation processes inside modular factories under severe occlusion.

97 MATHEMATICS AND COMPUTING↗

A numerical method for simulating variable density flows in membrane desalination systems

Here, we present a novel method for simulating unsteady, variable density, fluid flows in membrane desalination systems. By assuming the density varies only with concentration and temperature, the scheme decouples the solution of the governing equations into two sequential blocks. The first solves the governing equations for the temperature and concentration fields, which are used to compute all thermophysical properties. The second block solves the conservation of mass and momentum equations for the velocity and pressure. We show that this is computationally more efficient than schemes that iterate over the full coupled equations in one block. We verify that the method achieves second-order spatial-temporal accuracy, and we use the method to investigate buoyancy-driven convection in a desalination process called vacuum membrane distillation. Specifically, we show that with gravity properly oriented, variations in temperature and concentration can trigger a double-diffusive instability that enhances mixing and improves water recovery. We also show that the instability can be strengthened by providing external heating.

97 MATHEMATICS AND COMPUTING↗

Computer simulation of cardiovascular changes during extended duration space flights

The application of mathematical modeling and computer simulation to the study of spaceflight cardiovascular changes is examined using a multicompartment representation model of the entire human cardiovascular system including its control elements. The model simulates the beat-to-beat dynamic responses of the cardiovascular system to orthostatic stresses. Simulation results pertaining to long-term space flight, the combined effect of +G(z) and blood volume loss, and the effect of anti-G suit inflation are discussed, including past results on the original version of the model which has been used in a number of analysis applications at NASA. New results pertain to analysis of cardiovascular changes in extended duration space flights and demonstrate the use of this model in evaluation of physiological factors that contribute to orthostatic intolerance following an exposure to weightlessness, in particular, blood volume loss and changes in the sensitivity of baroreceptors.

Srinivasan, R. Srini↗

Modifying the Asynchronous Jacobi Method for Data Corruption Resilience

Moving scientific computation from high-performance computing (HPC) and cloud computing (CC) environments to devices on the edge, i.e., physically near instruments of interest, has received tremendous interest in recent years. Such edge computing environments can operate on data in situ, offering enticing benefits over data aggregation to HPC and CC facilities that include avoiding costs of transmission, increased data privacy, and real-time data analysis. Because of the inherent unreliability of edge computing environments, new fault-tolerant approaches must be developed before the benefits of edge computing can be realized. Motivated by algorithm-based fault tolerance, a variant of the asynchronous Jacobi (ASJ) method is developed that achieves resilience to data corruption by rejecting solution approximations from neighbor devices according to a bound derived from convergence theory. Numerical results on a two-dimensional Poisson problem show that the new rejection criterion, along with a novel approximation to the shortest path length on which the criterion depends, restores convergence for the ASJ variant in the presence of certain types data corruption. Numerical results are obtained for when the singular values in the analytic bound are approximated. Additional linear systems are also explored, one with a more dense sparsity pattern and one that includes advection. All results indicate that successful resilience to data corruption depends on whether the bound tightens fast enough to reject corrupted data before the iteration evolution deviates significantly from that predicted by the convergence theory defining the bound. This observation generalizes to future work on algorithm-based fault tolerance for other asynchronous algorithms, including upcoming approaches that leverage Krylov subspaces.

97 MATHEMATICS AND COMPUTING↗

Machine learning prediction of enzyme optimum pH

The relationship between pH and enzyme catalytic activity, especially the optimal pH (pH opt ) at which enzymes function, is critical for biotechnological applications. Hence, computational methods to predict pH opt will enhance enzyme discovery and design by facilitating accurate identification of enzymes that function optimally at specific pH levels, and by elucidating sequence-function relationships. Here, in this study, we proposed and evaluated various machine learning methods for predicting pH opt , conducting extensive hyperparameter optimization and training over 11,000 model instances. Our results demonstrate that models utilizing language model embeddings markedly outperform other methods in predicting pHopt. We present EpHod, the best-performing model, to predict pHopt, making it publicly available to researchers. From sequence data, EpHod directly learns structural and biophysical features that relate to pH opt , including proximity of residues to the catalytic centre and the accessibility of solvent molecules. Overall, EpHod presents a promising advancement in pH opt prediction and will potentially speed up the development of enzyme technologies.

97 MATHEMATICS AND COMPUTING↗

Reducing the Energy Consumption of Magnetic Resonance Imaging and Computed Tomography Scanners: Integrating Ecodesign and Sustainable Operations

This review aims to provide valuable insights into how energy consumption in magnetic resonance imaging (MRI) and computed tomography (CT) scanners can be effectively monitored, managed, and reduced, thereby contributing to more sustainable medical imaging practices. Demand for advanced imaging technologies such as MRI and CT scanners continues to increase, and understanding the resultant impact on greenhouse gas emissions requires a thorough evaluation of their energy consumption. Here, this review examines the energy monitoring and consumption characteristics of MRI and CT scanners, highlighting potential approaches for energy savings. An overview of MRI and CT principles, hardware components, and their associated energy consumption is provided. After addressing the technical aspects, the hardware and software requirements essential for accurate energy metering are detailed. Baseline measurements of energy consumption data are then provided as a foundation to understand current usage patterns and identify areas for improvement. Ongoing efforts to reduce energy consumption are categorized into 3 main strategies: operations, scanner design enhancements, and active scanning techniques, including accelerated MRI protocols. Ultimately, we emphasize that achieving sustainability in medical imaging requires collaboration across disciplines. By incorporating eco-friendly design in new imaging equipment, we can reduce the environmental impact, promote sustainability, and set a health care industry standard for a healthier planet.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

a priori uncertainty quantification of reacting turbulence closure models using Bayesian neural networks

While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulations (DNS) create opportunities to leverage data-driven modeling techniques. Albeit flexible, data-driven models still depend on the dataset and the functional form of the model chosen. Increased adoption of such models requires reliable uncertainty estimates both in the data-informed and out-of-distribution regimes. Here, in this work, we employ Bayesian neural networks (BNNs) to capture both epistemic and aleatoric uncertainties in a reacting flow model. In particular, we model the filtered progress variable scalar dissipation rate which plays a key role in the dynamics of turbulent premixed flames. We demonstrate that BNN models can provide unique insights about the structure of uncertainty of the data-driven closure models. We also propose a method for the incorporation of out-of-distribution information in a BNN, which can be used for out-of-distribution query detection. The efficacy of the model is demonstrated by a priori evaluation on a dataset consisting of a variety of flame conditions and fuels.

97 MATHEMATICS AND COMPUTING↗

Cluster-Graph Fingerprinting: A Framework for Quantitative Analysis of Machine-Learned Interatomic Model Training and Simulation Data

Machine-learned interatomic models represent a significant advancement in simulation methods, extending the predictive ability of first-principles methods to previously inaccessible length and time scales. However, the data-driven nature of these models can lead to difficult-to-detect errors that can compromise prediction accuracy. To address this challenge, we introduce a novel fingerprinting approach based on the Chebyshev Interaction Model for Efficient Simulation (ChIMES) ML-IAM graph-based descriptor. Our strategy enables efficient and statistically rigorous analysis of system configurations used in ML-IAM training and those generated by their application, e.g., in molecular dynamics simulations. We demonstrate that these fingerprints can effectively assess novelty of a configuration relative to an existing data set and determine dissimilarity among individual configurations, which are two key tasks in workflows for active learning-based ML-IAM training, data set curation, and on-the-fly uncertainty quantification.

36 MATERIALS SCIENCE↗

Learning robust parameter inference and density reconstruction in flyer plate impact experiments

Estimating physical parameters or material properties from experimental observations is a common objective in many areas of physics and material science. In many experiments, especially in shock physics, radiography is the primary means of observing the system of interest. However, radiography does not provide direct access to key state variables, such as density, which prevents the application of traditional parameter estimation approaches. Here we focus on flyer plate impact experiments on porous materials, and resolving the underlying parameterized equation of state (EoS) and crush porosity model parameters given radiographic observation(s). We use machine learning as a tool to demonstrate with high confidence that using only high impact velocity data does not provide sufficient information to accurately infer both EoS and crush model parameters, even with fully resolved density fields or a dynamic sequence of images. We thus propose an observable data set consisting of low and high impact velocity experiments/simulations that capture different regimes of compaction and shock propagation, and proceed to introduce a generative machine learning approach which produces a posterior distribution of physical parameters directly from radiographs. We demonstrate the effectiveness of the approach in estimating parameters from simulated flyer plate impact experiments, and show that the obtained estimates of EoS and crush model parameters can then be used in hydrodynamic simulations to obtain accurate and physically admissible density reconstructions. Finally, we examine the robustness of the approach to model mismatches, and find that the learned approach can provide useful parameter estimates in the presence of out-of-distribution radiographic noise and previously unseen physics, thereby promoting a potential breakthrough in estimating material properties from experimental radiographic images.

97 MATHEMATICS AND COMPUTING↗

Requirements Framework for Cyber-Informed Engineering

The existing requirements frameworks or models cater to the existing practices. However, they fall short in directly using them for Cyber informed engineering. Therefore, this paper develops and presents a comprehensive framework that can be used for Cyber informed Engineering during the requirements phase. We describe the existing requirements process and models, then develop a requirements framework for cyber informed engineering.

97 MATHEMATICS AND COMPUTING↗