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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Comparison of Tempered and Truncated Fractional Models

Tempered fractional operators are able to model effects that classical partial differential equations cannot quite capture. For example, this includes the super- and subdiffusion effects that are present in hydrology and geophysics models. However, tempered fractional operators are computationally intensive. We analyze a truncated variation of the fractional operators, which are less computationally intensive, in an effort to use them in place of the more complex tempered variation. In particular, we train parameters of the truncated operator using neural networks in order to optimize the difference of the actions of the two operators.

58 GEOSCIENCES↗
DOE OSTI2025

High Purity Germanium Detector Normalization

The presentation summarizes a project completed by our group a couple years ago comparing two detectors and attempting to normalize the results using a mathematical equation and how those results impacted our current operations.

Drumm, Natalie Daphne [Sandia National Laboratorie↗
DOE OSTI2022

The DeepLynx Data Warehouse

Digital Engineering and the development of digital twins necessitate the use of highly sophisticated tools and software. These methodologies and systems bring many benefits but rely on accomplishing challenging goals such as disparate data and systems integration into a single cohesive and holistic system. Idaho National Laboratory has recently released an open-source data warehouse – DeepLynx – to help in the planning, creation, execution, and management of projects in the digital engineering space, with an emphasis on supporting digital twins in an operational space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Finally, our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Auto-encoder↗
DOE OSTI2024

Evaluating Operators in Deep Neural Networks for Improving Performance Portability of SYCL

SYCL is a portable programming model for heterogeneous computing, so it is important to obtain reasonable performance portability of SYCL. Towards the goal of better understanding and improving performance portability of SYCL for machine learning workloads, we have been developing benchmarks for basic operators in deep neural networks (DNNs). These operators could be offloaded to heterogeneous computing devices such as graphics processing units (GPUs) to speed up computation. In this work, we introduce the benchmarks, evaluate the performance of the operators on GPU-based systems, and describe the causes of the performance gap between the SYCL and Compute Unified Device Architecture (CUDA) kernels. We find that the causes are related to the utilization of the texture cache for read-only data, optimization of the memory accesses with strength reduction, shared local memory accesses, and register usage per thread. We hope that the efforts of developing benchmarks for studying performance portability will stimulate discussion and interactions within the community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A new operator-split Compton scattering method

In high-energy-density physics, when the temperatures are high (keV-range) and/or the densities are low, Compton scattering becomes the main energy transfer mechanism between the radiation field and the material. The interaction between the radiation field and the material is non-linear in the radiation field – due to induced processes caused by photons being bosons – and in the material temperature. Many existing codes use a Compton-Fokker-Planck (CFP) approximation – which is inaccurate for high photon energies or material temperatures – or use linear approximations within a time-step. Here, we have implemented a new Compton-heating method called OS-FBC (Operator-Split Full-Boltzmann Compton) that solves the full, nonlinear Compton-heating system with few approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Time managed virtualization for simulating systems of systems

Software is an integral part of almost every non-trivial system. Yet simulation technologies to understand how software affects system performance lag behind what is available to understand physical behavior. This is not surprising. An abstract model of software tells us what it is supposed to do, not what it actually does. In this respect software is very different from a physical system. Kirchhoff’s laws predict the behavior of an electrical circuit with great precision. The mathematics of fluids do an adequate job of anticipating how a wing will perform in flight. Only the software itself, observed in operation, can tell us how it behaves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Probabilistic data fusion and physics-informed machine learning: A new paradigm for modeling under uncertainty, and its application to accelerating the discovery of new materials

In this report we summarize the work conducted by PI Perdikaris and his group under this Early Career project DE–SC0019116 during the period of 09/01/2018 – 08/31/2023. The central aim of the work was to introduce a new paradigm for scientific data analysis that can seamlessly synthesize rigorous mathematical modeling with data of variable fidelity (e.g., measurements at multiple scales/resolutions or predictions of variable fidelity models) and multiple modalities (e.g., images, time–series, or scattered measurements). The setting we are interested in involves complex systems that are partially observed and whose dynamical behavior could be hard to model or totally unknown. The inherent uncertainty associated with this setting necessitates a departure from the classical deterministic realm of modeling and scientific computation, and, consequently, our main building blocks can no longer be crisp deterministic numbers and governing laws, but instead we must operate with probabilistic models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Learning functional priors and posteriors from data and physics

In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Autonomy Loops for Monitoring, Operational Data Analytics, Feedback, and Response in HPC Operations

Many High Performance Computing (HPC) facilities have developed and deployed frameworks in support of continuous monitoring and operational data analytics (MODA) to help improve efficiency and throughput. Because of the complexity and scale of systems and workflows and the need for low-latency response to address dynamic circumstances, automated feedback and response have the potential to be more effective than current human-in-the-loop approaches which are laborious and error prone. Progress has been limited, however, by factors such as the lack of infrastructure and feedback hooks, and successful deployment is often site- and case-specific. In this position paper we report on the outcomes and plans from a recent Dagstuhl Seminar, seeking to carve a path for community progress in the development of autonomous feedback loops for MODA, based on the established formalism of similar (MAPE-K) loops in autonomous computing and self-adaptive systems. By defining and developing such loops for significant cases experienced across HPC sites, we seek to extract commonalities and develop conventions that will facilitate interoperability and interchangeability with system hardware, software, and applications across different sites, and will motivate vendors and others to provide telemetry interfaces and feedback hooks to enable community development and pervasive deployment of MODA autonomy loops.

autonomy loops↗
DOE OSTI2025

Enhancing occupant behavior representation for interoperability between building information modeling and building energy modeling

Building Performance Simulation (BPS) has been adopted as an essential tool for designing, operating, and retrofitting buildings to optimize energy efficiency throughout the building life cycle. The Green Building XML (gbXML) schema facilitates seamless data exchange between Building Information Modeling (BIM) and Building Energy Modeling (BEM) software tools. However, limited occupant behavior (OB) representation in BIM often leads to inconsistent and inaccurate energy simulation in BEM software. This paper presents 154 systematic enhancements to the existing occupant behavior XML (obXML) schema v1.3.4, initially developed for standardizing OB representation for BEM, to address existing limitations and improve interoperability with BIM models. The enhancements encompass improved integration with BIM models through extended building representations and system operations, expanded support for advanced OB models with additional environmental parameters and mathematical capabilities, and implementation of a standardized model documentation framework. To facilitate seamless data transformation between gbXML and obXML schemas, we developed a publicly available gb-obXML Schema Converter. Three case studies demonstrate the enhanced schema’s capabilities: representation of building information using a two-story office building model, documentation of a window operation behavior model, and validation of the schema converter’s functionality. The enhanced obXML schema v1.4 enables sophisticated modeling of occupant-building interactions while maintaining consistency with industry-standard BIM schemas. The standardized documentation framework facilitates reproducibility and knowledge sharing in the OB research community, while the schema converter automates the integration of building information into OB simulation workflows. These enhancements establish a foundation for more accurate building performance simulation by supporting sophisticated representation of occupant behavior within the BIM-to-BEM simulation workflows.

Chung, Jihoon↗
DOE OSTI2022

Hydrogen Blending into Natural Gas Pipeline Infrastructure: Review of the State of Technology

Hydrogen is an energy carrier that could play an important role in reducing emissions associated with difficult-to-decarbonize sectors including peaking and load-following electricity and industrial heating. Blending hydrogen into the natural gas pipelines has been proposed as an approach for achieving near-term emissions reductions and early-market access for hydrogen technologies such as electrolyzers. Numerous challenges and uncertainties complicate this approach to natural gas decarbonization, however, and this review summarizes current research on the material, economic, and operational factors that must be considered for hydrogen blending. First, this review explores previous research regarding the effects of blending hydrogen on gas mixture fluid and thermodynamic properties, pipeline materials and equipment performance within transmission and distribution networks, and supporting facilities such as underground storage and end-use hydrogen separation. We also investigate and summarize studies that developed mathematical models of natural gas pipeline networks with hydrogen blending, and the operational and techno-economic findings of these network studies. Finally, we discuss notable hydrogen blending demonstrations and their key outcomes. Many blending demonstrations internationally have proven that low hydrogen percentage blending is feasible under very specific scenarios with limited end-usage applications on both high-pressure transmission lines and low-pressure distribution lines. This report summarizes findings from literature into key areas of consensus and disagreement. Research gaps and disagreements between the literature are highlighted to provide directions for future hydrogen blending research.

03 NATURAL GAS↗
DOE OSTI2025

Boundary Corrections for Kernel Approximation to Differential Operators

The kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same computational cost as an explicit finite difference scheme but can exhibit order reduction at boundaries. In previous work on periodic domains, order reduction was addressed, yielding high-order accuracy. The issue addressed in this work is the elimination of order reduction of the kernel-based approach for a more general set of boundary conditions. Further, we consider the case of both first and second order operators. To demonstrate the theory, we provide not only the mathematical proofs but also experimental results by applying various boundary conditions to different types of equations. The results agree with the theory, demonstrating a systematic path to high order for kernel-based methods on bounded domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Mixed Precision Fermi-Operator Expansion on Tensor Cores from a Machine Learning Perspective

Here we present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for half-precision floating point operations on Nvidia’s A100 tensor core units. The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem. We demonstrate how this network can be accelerated by optimizing the weight and bias values to substantially reduce the number of layers required for convergence. We also show how this machine learning approach can be used to optimize the coefficients of the recursive Fermi-operator expansion to accurately represent the fractional occupation numbers of the electronic states at finite temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Predictive Models and High-Performance Computing as Tools to Accelerate the Scaling-Up of New Bio-Based Fuels Workshop: Summary Report

This report summarizes the results of a virtual workshop sponsored by the Bioenergy Technologies Office held on June 9–11, 2020. The workshop discussed best practices for utilizing mathematical modeling tools across multiple scales to reduce technology uncertainty and accelerate scaling-up of biorefinery/chemical production equipment and optimize operations.

09 BIOMASS FUELS↗
DOE OSTI2023

Novel Rotated Virtual Synchronous Generator Control for Power-Sharing in Microgrids with Complex Line Impedance

Virtual synchronous generator (VSG) control is based on the fact that the line impedance in a microgrid is highly inductive. This assumption was made due to the emulation of the stator winding of an electrical machine. This concept can affect the controllability of a microgrid with complex line impedance, generating deviations in the chosen operation point. To overcome this issue, additional techniques must be implemented. This paper describes a novel mathematical approach that uses the power line characteristics in a microgrid to rotate the power control reference frame and proposes a new control method called a “Rotated Virtual Synchronous Generator” (RVSG). This RVSG control approach integrates the effect of complex impedance on the microgrid’s operation and adjusts the reference frame accordingly to improve the system’s stability and performance. The use of this proposed mathematical approach in microgrids allows the further emulation of virtual inertia in microgrids that lack inertia. Finally, a comparison between RVSG control and the classical virtual synchronous generator method is carried out to show that it allows the improvement of the transient power response, power quality, stability, and performance, mainly in microgrids with complex line impedance.

42 ENGINEERING↗