Search NASA⌕ Search

SEARCH · Search NASA

Results for “Differentiability”

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 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Solving differential equations using deep neural networks

Recent work on solving partial differential equations (PDEs) with deep neural networks (DNNs) is presented. The paper reviews and extends some of these methods while carefully analyzing a fundamental feature in numerical PDEs and nonlinear analysis: irregular solutions. First, the Sod shock tube solution to the compressible Euler equations is discussed and analyzed. This analysis includes a comparison of a DNN-based approach with conventional finite element and finite volume methods, and demonstrates that the DNN is competitive in terms of degrees of freedom required for a given accuracy. Further, the DNN-based approach is extended to consider performance improvements and simultaneous parameter space exploration. Next, a shock solution to compressible magnetohydrodynamics (MHD) is solved for, and used in a scenario where experimental data is utilized to enhance a PDE system that is a priori insufficient to validate against the observed/experimental data. This is accomplished by enriching the model PDE system with source terms that are then inferred via supervised training with synthetic experimental data. The resulting DNN framework for PDEs enables straightforward system prototyping and natural integration of large data sets (be they synthetic or experimental), all while simultaneously enabling single-pass exploration of an entire parameter space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Design of Atomically Precise Nanoscale Negative Differential Resistance Devices

Downscaling device dimensions to the nanometer range raises significant challenges to traditional device design, due to potential current leakage across nanoscale dimensions and the need to maintain reproducibility while dealing with atomic–scale components. Here, negative differential resistance (NDR) devices based on atomically precise graphene nanoribbons are investigated. The computational evaluation of the traditional double–barrier resonant–tunneling diode NDR structure uncovers important issues at the atomic scale, concerning the need to minimize the tunneling current between the leads while achieving high peak current. A new device structure consisting of multiple short segments that enables high current by the alignment of electronic levels across the segments while enlarging the tunneling distance between the leads is proposed. The proposed structure can be built with atomic precision using a scanning tunneling microscope (STM) tip during an intermediate stage in the synthesis of an armchair nanoribbon. An experimental evaluation of the band alignment at the interfaces and an STM image of the fabricated active part of the device are also presented. In conclusion, this combined theoretical–experimental approach opens a new avenue for the design of nanoscale devices with atomic precision.

42 ENGINEERING↗
DOE OSTI2022

Prediction of curing kinetics of resorcinol‐added resole phenolic resins using differential scanning calorimetry for the fabrication of carbon/carbon composites

Phenolic resins are commonly used as carbon precursors for the fabrication of carbon/carbon composites due to their high carbon yield and aromatic nature. To decrease curing times, acid catalysts are generally used, but the addition of resorcinol was found to have a similar effect while being incorporated into the resin matrix with no contamination or corrosion issues. In this work, the curing kinetics of pure, 10, 20, and 30 wt% resorcinol-added phenolic resins were investigated through differential scanning calorimetry. Heating rates of 0.5, 1, 2.5, and 5°C min -1 were used with several curing models to predict isothermal curing. Averaged mean absolute error (MAE) for the isoconversional mathematical approaches namely Kissinger–Akahira–Sunose (MAE = 12.9 min), Flynn–Wall–Ozawa (15.8 min), and Vyazovkin (14 min) show that these methods provide the best predictions, attributed to their adoption of an activation energy that depends on the extent of cure (E a (α)). The Kissinger method (MAE = 36 min), which depends only on peak temperature with a constant activation energy assumption, and the data noise sensitive Friedman model (MAE = 1144.7 min) provide the least accurate results. Thermogravimetric analysis revealed that resorcinol decreases the curing times by up to 71% without lowering carbon yield.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Quantifying Uncertainties in Heat Capacity Measurements of Molten Salts Determined Using Differential Scanning Calorimetry

Uncertainty in specific heat capacity values of a molten salt determined by using differential scanning calorimetry (DSC) was assessed based on the precision of replicate measurements of heat flows used in the calculation and effects of corrections that are commonly made to heat flow measurements. The ratio method of determining heat capacity was applied using the results of replicate heat flow measurements made with two empty cells, a sapphire reference material, and three samples of a doped NaCl-UCl 3 salt mixture. Replicate measurements with empty cells were used to quantify the effects of system instabilities and sensitivities on the measured heat flows of sapphire and salt. The combined effects of uncertainties in individual heat flow measurements made with blank cells using this system were quantified to be 2.6 μV based on isothermal holds before and after the scan, with cell placement adding the greatest uncertainty. This value was used as the tolerance for accepting background-corrected heat flows measured with sapphire and salt to calculate the specific heat capacity. The acceptable heat flows measured for sapphire and salt over the temperature range of 540 to 725 °C resulted in calculated specific heat capacity values ranging from 0.53 to 0.91 J g −1 K −1 with an overall average value of 0.70 J g −1 K −1 and an uncertainty of 0.22 J g −1 K −1 at the 99 % confidence level. The combined uncertainty in the specific heat capacity masked detection of any effect of temperature or salt composition that occurred.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Neural lumped parameter differential equations with application in friction-stir processing

Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a “lumped” element representative of the physical scales of the modeled system. For systems where the definition of a lumped element or its associated physics may be unknown, modeling tasks may be restricted to full-fidelity physics simulations. Here, in this work, we consider data-driven modeling tasks with limited point-wise measurements of otherwise continuous systems. We build upon the notion of the Universal Differential Equation (UDE) to construct data-driven models for reducing dynamics to that of a lumped parameter and inferring its properties. The flexibility of UDEs allow for composing various known physical priors suitable for application-specific modeling tasks, including lumped parameter methods. The motivating example for this work is the plunge and dwell stages for friction-stir welding; specifically, (i) mapping power input into the tool to a point-measurement of temperature and (ii) using this learned mapping for process control.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The Hurwitz Product, p-Adic Topology on ℤ, and Fundamental Solution to Linear Differential Equation in the Ring ℤ[[x]]

We study the linear inhomogeneous first order differential equation by′ + f(x) = y in the ring of formal power series with integer coefficients. Using the p-adic topology on the ring of integers, we construct a counterpart of the Hurwitz product of the Euler series and an arbitrary formal power series with integer coefficients. It is shown that the Euler series can be interpreted as the fundamental solution to the equation under consideration. Bibliography: 8 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the Behavior of Solutions of Some Systems of Differential Equations Partially Solved with Respect to the Derivatives in the Presence of a Pole

We study the existence of analytic solutions for some systems of ordinary differential equations partially solvable with respect to the derivatives. We establish sufficient conditions for the existence of analytic solutions of the Cauchy problem in the presence of a pole. An estimate for these solutions is obtained in a certain domain and the problem of the number of solutions is investigated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Oscillation Criterion for Autonomous Differential Equations with Bounded Aftereffect

For autonomous functional-differential equations with delays, we obtain an oscillation criterion, which allows one to reduce the oscillation problem to the calculation of a unique root of a real-valued function determined by the coefficients of the original equation. The criterion is illustrated by examples of equations with concentrated and distributed aftereffect, for which convenient oscillation tests are obtained.

97 MATHEMATICS AND COMPUTING↗