Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Function approximation”

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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Quasi-Stochastic Approximation and Off-Policy Reinforcement Learning: Preprint

The Robbins-Monro stochastic approximation algorithm is a foundation of many algorithmic frameworks for reinforcement learning and often an efficient approach to solving (or approximating the solution to) complex optimal control problems. In many cases, however, practitioners are unable to apply these techniques because of an inherent high variance. This paper aims to provide a general foundation for 'quasi-stochastic approximation,' in which all of the processes under consideration are deterministic, much like quasi-Monte Carlo for variance reduction in simulation. The variance reduction can be substantial, subject to tuning of pertinent parameters in the algorithm. This paper introduces a new coupling argument to establish the optimal rate of convergence provided the gain is sufficiently large. These results are established for linear models and tested also in nonideal settings. A major application of these general results is a new class of reinforcement learning algorithms for deterministic state space models. In this setting, the main contribution is a class of algorithms for approximating the value function for a given policy, using a different policy designed to introduce exploration.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Single field double inflation and primordial black holes

Within the framework of scalar-tensor theories, we study the conditions that allow single field inflation dynamics on small cosmological scales to significantly differ from that of the large scales probed by the observations of cosmic microwave background. The resulting single field double inflation scenario is characterised by two consequent inflation eras, usually separated by a period where the slow-roll approximation fails. At large field values the dynamics of the inflaton is dominated by the interplay between its non-minimal coupling to gravity and the radiative corrections to the inflaton self-coupling. For small field values the potential is, instead, dominated by a polynomial that results in a hilltop inflation. Without relying on the slow-roll approximation, which is invalidated by the appearance of the intermediate stage, we propose a concrete model that matches the current measurements of inflationary observables and employs the freedom granted by the framework on small cosmological scales to give rise to a sizeable population of primordial black holes generated by large curvature fluctuations. We find that these features generally require a potential with a local minimum. We show that the associated primordial black hole mass function is only approximately lognormal.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Accelerated Time-Domain Modeling of Electromagnetic Pulse Excitation of Finite-Length Dissipative Conductors over a Ground Plane via Function Fitting and Recursive Convolution

In this report we overview the fundamental concepts for a pair of techniques which together greatly hasten computational predictions of electromagnetic pulse (EMP) excitation of finite-length dissipative conductors over a ground plane. In a time- domain, transmission line (TL) model implementation, predictions are computationally bottlenecked time-wise, either for late-time predictions (about 100ns-10000ns range) or predictions concerning EMP excitation of long TLs (order of kilometers or more ). This is because the method requires a temporal convolution to account for the losses in the ground. Addressing this to facilitate practical simulation of EMP excitation of TLs, we first apply a technique to extract an (approximate) complex exponential function basis-fit to the ground/Earth's impedance function, followed by incorporating this into a recursion-based convolution acceleration technique. Because the recursion-based method only requires the evaluation of the most recent voltage history data (versus the entire history in a "brute-force" convolution evaluation), we achieve necessary time speed- ups across a variety of TL/Earth geometry/material scenarios. Intentionally Left Blank

36 MATERIALS SCIENCE↗
DOE OSTI2021

Injection data analysis using material balance time for CO 2 storage capacity estimation in deep closed saline aquifers

Estimating the ultimate storage capacity of deep saline aquifers is important to address the formation potential to store the envisioned large volumes of CO 2 . Injection data (i.e. injection rate, bottomhole pressure, and cumulative injected volume of CO 2 ) are routinely recorded during storage operations. These data contain valuable information on the subsurface (e.g. the reservoir pore volume and the formation storage capacity) that can be extracted. In this paper, we present a two-step graphical technique to infer the pore volume and the ultimate storage capacity of closed saline aquifers by analyzing the available injection data. First, the pore volume is inferred through adapting the concept of the material balance time. Material balance time is an approximate superposition time function developed to interpret production data from oil and gas wells operating at variable pressure/rate conditions during the boundary-dominated flow period. Using material balance techniques, the ultimate storage capacity is then estimated through linear extrapolation of the average pressure trend to the maximum allowable pressure the formation can withstand. The average pressure is not available in practice, but is can be obtained from the injection data. Two approaches are presented in this study to calculate the average pressure; namely the rigorous and the approximate approaches. Unlike the rigorous approach, the approximate approach does not require a prior knowledge of some reservoir properties (e.g. relative permeability, absolute permeability, formation porosity and thickness) to calculate the average pressure. To investigate its potential and reliability in analyzing CO 2 injection data, the proposed technique is applied to four synthetic cases representing different well operating conditions. Results indicate that the approximate approach consistently overestimates the actual (simulated) storage capacity as compared to the rigorous approach. The agreement - between the inferred and the simulated reservoir pore volume, and between the analytical and numerical estimates of storage capacity - validates the potential application of the technique to CO 2 storage in closed saline aquifers. The technique is further substantiated through application to a field data set utilized from a commercial-scale geological storage (CGS) project. Finally, field data interpretation shows that the proposed technique can be utilized to identify the degree of hydraulic continuity and reservoir compartmentalization within a target formation by interpreting the corresponding pressure and rate responses.

02 PETROLEUM↗
DOE OSTI2019

Neutrino-Nucleus Cross Section within the Extended Factorization Scheme

The factorization scheme, based on the impulse approximation and the spectral function formalism, has been recently generalized to allow the description of electromagnetic nuclear interactions driven by two-nucleon currents. We have extended this framework to the case of weakly charged and neutral currents, and carried out calculations of the double-differential neutrino-carbon and neutrino-oxygen cross sections using two different models of the target spectral functions. The results, showing a moderate dependence on the input spectral function, confirm that our approach provides a consistent treatment of all reaction mechanisms contributing to the signals detected by accelerator-based neutrino experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations

Physics-informed neural networks (PINNs) based machine learning is an emerging framework for solving nonlinear differential equations. However, due to the implicit regularity of neural network structure, PINNs can only find the flattest solution in most cases by minimizing the loss functions. In this paper, we combine PINNs with the homotopy continuation method, a classical numerical method to compute isolated roots of polynomial systems, and propose a new deep learning framework, named homotopy physics-informed neural networks (HomPINNs), for solving multiple solutions of nonlinear elliptic differential equations. The implementation of an HomPINN is a homotopy process that is composed of the training of a fully connected neural network, named the starting neural network, and training processes of several PINNs with different tracking parameters. The starting neural network is to approximate a starting function constructed by the trivial solutions, while other PINNs are to minimize the loss functions defined by boundary condition and homotopy functions, varying with different tracking parameters. These training processes are regraded as different steps of a homotopy process, and a PINN is initialized by the well-trained neural network of the previous step, while the first starting neural network is initialized using the default initialization method. Finally, several numerical examples are presented to show the efficiency of our proposed HomPINNs, including reaction-diffusion equations with a heart-shaped domain.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Updates to R-matrix Evaluations of Fissile Actinides: 233,235 U, 239 Pu [Slides]

This presentation begins by discussing the importance and significance of cross section fluctuations. It also discusses the motivation and overarching goals which are to establish the highest fidelity nuclear evaluated data. In conclusion, a procedure to accurately model the measured cross section fluctuations for inclusion into evaluated nuclear data files was developed and tested on 239 Pu total cross sections. The procedure consisted of defining population of levels as well as related amplitudes extrapolated from the systematics of the resonance parameters in the resolved resonance region. By using realistic population of extrapolated levels, the fit of measured total cross section produced a continuous S-matrix function S( E ) in Reich-Moore approximation. The S-matrix function averaged over a suitable energy interval was used to obtain averaged cross sections consistent with the measured data. Transmittable formatted files (ENDF, GNDS) with LSSF=1 will consist of File 3 which are smoothed cross sections and File 2 which are average resonance parameters fitted to the energy bins defined in File 3. The capability to store probability tables is a way to show the fluctuating cross sections.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2019

Partition Density Functionals: Theory and Applications. Final Technical Report

Partition Density Functional Theory is a method to calculate the energy and density of a molecule via self-consistent calculations on isolated fragments. At the start of this project, Partition Density Functional Theory (PDFT) had only been applied to one-dimensional model systems of non-interacting electrons. Its most appealing feature (the reason why PDFT was born in the first place) was that it allowed one to construct an internally-consistent Density Functional Theory (DFT) valid for non-integer electron numbers to be used in the context of Chemical Reactivity Theory. Many formal properties of the quantities entering the theory, such as partition potentials, were unknown when the project started. The connections with other fragment-based electronic structure methods, and especially with embedding theories, were unclear, and the potential of PDFT for fixing problems of approximate exchange-correlation functionals was unanticipated. Supported by grant DE-SC0005031, we made progress in developing, understanding, implementing, and applying PDFT. We discovered its potential for applications in situations where approximate DFT fails, such as when stretching bonds or when calculating the energy of weakly-interacting systems, both cases of importance for energy research applications. We extended PDFT in several directions (spin-densities, current densities, external electric and magnetic fields), and carried out many calculations on diatomic molecules and small clusters to test ideas for approximate non-additive functionals. As a result, we were able to propose physically-motivated fragment-density approximations for both covalent and weak bonds. Because many applications will increasingly benefit from efficient and accurate electronic-structure calculations via density-embedding techniques, the research results enabled by this grant should prove useful for addressing complex problems in a wide variety of fields, from chemistry to molecular biology and materials engineering.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Verification of Anderson superexchange in MnO via magnetic pair distribution function analysis and ab initio theory

Here, we present a temperature-dependent atomic and magnetic pair distribution function (PDF) analysis of neutron total scattering measurements of antiferromagnetic MnO, an archetypal strongly correlated transition-metal oxide. The known antiferromagnetic ground-state structure fits the low-temperature data closely with refined parameters that agree with conventional techniques, confirming the reliability of the newly developed magnetic PDF method. The measurements performed in the paramagnetic phase reveal significant short-range magnetic correlations on a ~1 nm length scale that differ substantially from the low-temperature long-range spin arrangement. Ab initio calculations using a self-interaction-corrected local spin density approximation of density functional theory predict magnetic interactions dominated by Anderson superexchange and reproduce the measured short-range magnetic correlations to a high degree of accuracy. Further calculations simulating an additional contribution from a direct exchange interaction show much worse agreement with the data. Furthermore, the Anderson superexchange model for MnO is thus verified by experimentation and confirmed by ab initio theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Kohn-Sham Solver (KSSOLV) v2.0

KSSOLV is a MATLAB toolbox for solving Kohn-Sham density functional theory based electronic structure eigenvalue problems. It uses an object oriented features of MATLAB to represent atom, molecules, wavefunctions and Hamiltonians and their operations. It is designed to make it easier for users to prototype and test new algorithms for solving the Kohn-Sham problem. KSSOLV2.0 contains significant improvement over the original KSSOLV described in a paper published in ACM Transaction on Mathematical Software (attached). In addition to performing ground state calculation for small molecules, it can also perform geometry optimization for both molecules and solids. It uses standard pseudopotentials and implements local density approximation, generalized gradient approximation and hybrid functionals. Future releases will also include time-dependent DFT and post DFT calculations such as the GW quasi-particle energy calculation and Bethe-Salpeter equation solver for optical absorption.

Yang, Chao↗
DOE OSTI2016

Development of TDLAS for Water Vapor Concentration Measurement during VHTR Steam Ingress

Very-high-temperature reactors (VHTR) utilize a graphite-moderated, helium-cooled design that provides higher efficiencies and a low-carbon source of process heat (>700 deg. C) for many industrial applications. Safety concerns have led to extensive accident condition investigations. Steam generator heat-exchanger tube rupture accidents (SGTR) can lead to increased reactor core steam density, which causes neutron slowing-down and chemical corrosion of the graphite fuel elements and structural columns. It is important to be able to computationally model the propagation of steam throughout the lower plenum and nuclear reactor core, but experimental data is needed to validate such models. The primary objective of this project is to instrument a scaled down experiment of a VHTR designed by Ohio State University (OSU), with tunable diode laser absorption spectroscopy (TDLAS) diagnostics to measure steam concentration changes and map how water vapor propagates through the test facility's lower plenum and core. The basic principle of absorption spectroscopy is based on a molecular species ability to absorb photons of specific energies. A collimated laser beam of known energy is passed through a test section containing a sample gas. When a transition of the absorbing gas species resonates with the laser frequency, a certain amount of energy will be absorbed based on the rovibrational characteristics of the molecule. The intensity of the transmitted laser light can be measured by a detector after exiting the test section. The Beer-Lambert Law of absorbance is used to recover this information relating beam attenuation to the system dimensions, gas composition, pressure, and temperature. The line-strength is a function of temperature alone and relates the fraction of molecules in a given rovibrational state through the partition function. The partition function describes the statistical properties of a system in thermodynamic equilibrium where the states obey a Boltzmann distribution. Thus, the number density of molecules in a particular state can be determined from the total internal partition function at a particular temperature. The lineshape function of a given absorption transition is derived from the physical interaction between the absorbing species and is dependent on temperature and pressure. Random thermal motion of absorbing molecules result in broadening of the linewidth, called Doppler broadening, which follows a Gaussian distribution. Molecular collisions result in broadening and shifting of the linewidth, called pressure broadening, which follows a Lorentzian distribution. The overall lineshape results in a Voigt profile, which is a convolution of the Gaussian and Lorentzian distributions. The Voigt profile does not have a simple analytical form and is most often calculated numerically or approximated by complex functions. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

First-Principles-Based Machine Learning Models for Phase Behavior and Transport Properties of CO 2

In this work, we construct distinct first-principles-based machine-learning models of CO 2 , reproducing the potential energy surface of the PBE-D3, BLYP-D3, SCAN and SCAN-rvv10 approximations of density functional theory. Here we employ the Deep Potential methodology to develop the models and consequently achieve a significant computational efficiency over ab initio molecular dynamics (AIMD) that allows for larger system sizes and time scales to be explored. Although our models are trained only with liquid phase configurations, they are able to simulate a stable interfacial system and predict vapor-liquid equilibrium properties, in good agreement with results from the literature. Because of the computational efficiency of the models, we are also able to obtain transport properties, such as viscosity and diffusion coefficients. We find that the SCAN-based model presents a temperature shift in the position of the critical point, while the SCAN-rvv10-based model shows improvement but still exhibits a temperature shift that remains approximately constant for all properties investigated in this work. We find that the BLYP-D3-based model generally performs better for liquid phase and vapor-liquid equilibrium properties, but the PBE-D3-based model is better suited for predicting transport properties.

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

Spectral-density estimation with the Gaussian integral transform

The spectral-density operator $\hat{ρ}(ω) = δ(ω–\hat{H})$ plays a central role in linear response theory as its expectation value, the dynamical response function, can be used to compute scattering cross sections. In this work, we describe a near optimal quantum algorithm providing an approximation to the spectral density with energy resolution $\Delta$ and error $\epsilon$ using $O(\sqrt{\text{log}_2 (1/ε)[\text{log}_2 (1 / Δ) + \text{log}_2 (1/ε)]/ Δ)}$ operations. This is achieved without using expensive approximations to the time-evolution operator, but instead exploiting qubitization to implement an approximate Gaussian integral transform of the spectral density. Finally, we also describe appropriate error metrics to assess the quality of the spectral function approximations more generally.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Controlling dynamical thermal transport of biased bilayer graphene by impurity atoms

We address the dynamical thermal conductivity of biased bilayer graphene doped with acceptor impurity atoms for AA-stacking in the context of tight binding model Hamiltonian. The effect of scattering by dilute charged impurities is discussed in terms of the self-consistent Born approximation. Green’s function approach has been exploited to find the behavior of thermal conductivity of bilayer graphene within the linear response theory. We have found the frequency dependence of thermal conductivity for different values of concentration and scattering strength of dopant impurity. Also the dependence of thermal conductivity on the impurity concentration and bias voltage has been investigated in details.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2016

Theoretical and experimental study of the dynamic response of absorber-based, micro-scale, oscillatory probes for contact sensing applications

This paper presents two models for predicting the frequency response of micro-scale oscillatory probes. These probes are manufactured by attaching a thin fiber to the free end of one tine of a quartz tuning fork oscillator. In these studies, the attached fibers were either 75 μm diameter tungsten or 7 μm diameter carbon with lengths ranging from around 1 to 15 mm. The oscillators used in these studies were commercial 32.7 kHz quartz tuning forks. The first theoretical model considers lateral vibration of two beams serially connected and provides a characteristic equation from which the roots (eigenvalues) are extracted to determine the natural frequencies of the probe. A second, lumped model approximation is used to derive an approximate frequency response function for prediction of tine displacements as a function of a modal force excitation corresponding to the first mode of the tine in the absence of a fiber. These models are used to evaluate the effect of changes in both length and diameter of the attached fibers. Theoretical values of the natural frequencies of different modes show an asymptotic relationship with the length and a linear relationship with the diameter of the attached fiber. Similar results are observed from experiment, one with a tungsten probe having an initial fiber length of 14.11 mm incrementally etched down to 0.83 mm, and another tungsten probe of length 8.16 mm incrementally etched in diameter, in both cases using chronocoulometry to determine incremental volumetric material removal. The lumped model is used to provide a frequency response again reveals poles and zeros that are consistent with experimental measurements. Finite element analysis shows mode shapes similar to experimental microscope observations of the resonating carbon probes. This model provides a means of interpreting measured responses in terms of the relative motion of the tine and attached fibers. Of particular relevance is that, when a “zero” is observed in the response of the tine, one mode of the fiber is matched to the tine frequency and is acting as an absorber. This represents an optimal condition for contact sensing and for transferring energy to the fiber for fluid mixing, touch sensing, and surface modification applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Gaussian kernel density functions for compositional quantification in atom probe tomography

Highlights: • A methodology for compositional quantification from atom probe tomography is proposed. • A probability density function p(x) given discrete data points is constructed. • Each atom approximated by a Gaussian function with a particular smoothing parameter. • Density Kernel functions are used to find the optimum smoothing parameter. • The method is validated by using simulated data of semiconductor materials. - Abstract: Atom probe tomography (APT) has the ability to identify the nature and position of single atoms in a material with an almost 3D atomic resolution. However, the quantification of the material composition requires an appropriate treatment of the discrete APT data. When the amount of atoms selected to quantify the composition is relatively small, the spatial resolution is enhanced but the statistical error worsens. Conversely, the increase in the number of atoms considered reduces the spatial resolution, but improving the statistics. We have developed a methodology to reach an optimum equilibrium between the positional and the statistical error in an unsupervised form using Gaussian Kernel density functions. The validity of the method has been tested using APT simulated data of semiconductor materials. It has been proved that the chemical quantification in these materials requires the appropriate selection of the smoothing parameter, obtained without user intervention. In addition, the results have been compared to the usual techniques for composition measurement from APT data (voxelization and proximity histograms), showing better precision for high spatial resolution. This work supplies a data driven methodology based in Gaussian Kernel density functions for the accurate quantification of the composition from APT data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Alternative CNDOL Fockians for fast and accurate description of molecular exciton properties

CNDOL is an a priori, approximate Fockian for molecular wave functions. In this study, we employ several modes of singly excited configuration interaction (CIS) to model molecular excitation properties by using four combinations of the one electron operator terms. Those options are compared to the experimental and theoretical data for a carefully selected set of molecules. The resulting excitons are represented by CIS wave functions that encompass all valence electrons in the system for each excited state energy. The Coulomb–exchange term associated to the calculated excitation energies is rationalized to evaluate theoretical exciton binding energies. This property is shown to be useful for discriminating the charge donation ability of molecular and supermolecular systems. Multielectronic 3D maps of exciton formal charges are showcased, demonstrating the applicability of these approximate wave functions for modeling properties of large molecules and clusters at nanoscales. This modeling proves useful in designing molecular photovoltaic devices. Our methodology holds potential applications in systematic evaluations of such systems and the development of fundamental artificial intelligence databases for predicting related properties.

Chemistry↗