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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.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Radial transport modeling of high density deuterium plasmas in proto-MPEX with the B2.5-Eirene code

High density (≥6 × 10 19 m –3 ), low temperature (2–6 eV) helicon discharges in the Prototype Material Plasma Exposure eXperiment (Proto-MPEX) are analyzed with the coupled multifluid plasma, kinetic neutrals code B2.5-Eirene. The interpretative analyses are constrained by data from multiple diagnostics, including Langmuir probes, Mach probes, filterscopes, infrared TV system, Thomson scattering, and baratrons. The objectives of the transport simulations include: investigation of the effects of heating, fueling, and plasma production; pumping, and assumed radial transport models on the calculated density and temperature distributions; plasma flow profiles and power balance. The primary objective in this report is to investigate the effects of the radial transport model in full plasma (the entire length of the plasma column in Proto-MPEX) data-constrained simulations. Results from three assumed forms of the radial transport coefficients are presented, including spatially constant, radially decreasing, and Bohm (D,χ ~T e /|B|). The results from each of the three transport coefficient sets agree qualitatively with the core (near axis) data. With the implicit T e dependence, the Bohm coefficients tend to decrease as functions of radius, although not as strongly as the centrally peaked set. The axial variation in the Bohm coefficients is largely due to the axial structure of the magnetic field. Furthermore, the agreement of the simulations and the diagnostic data with the Bohm set indicates that transport in the plasma column of Proto-MPEX is dominated by Bohm diffusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Incompressible spectral-element method: Derivation of equations

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

Deanna, Russell G.↗
NASA NTRS1997

Aerodynamic Design on Unstructured Grids for Turbulent Flows

An aerodynamic design algorithm for turbulent flows using unstructured grids is described. The current approach uses adjoint (costate) variables for obtaining derivatives of the cost function. The solution of the adjoint equations is obtained using an implicit formulation in which the turbulence model is fully coupled with the flow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with finite-difference gradients and a few example computations are shown. In addition, a user interface is described which significantly reduces the time required for setting up the design problems. Recommendations on directions of further research into the Navier Stokes design process are made.

Anderson, W. Kyle↗
DOE OSTI2020

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

Here we propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Technical Note: Impact of the geometry dependence of the ion chamber detector response function on a convolution-based method to address the volume averaging effect

Purpose: To investigate the geometry dependence of the detector response function (DRF) of three commonly used scanning ionization chambers and its impact on a convolution-based method to address the volume averaging effect (VAE). Methods: A convolution-based approach has been proposed recently to address the ionization chamber VAE. It simulates the VAE in the treatment planning system (TPS) by iteratively convolving the calculated beam profiles with the DRF while optimizing the beam model. Since the convolved and the measured profiles are subject to the same VAE, the calculated profiles match the implicit “real” ones when the optimization converges. Three DRFs (Gaussian, Lorentzian, and parabolic function) were used for three ionization chambers (CC04, CC13, and SNC125c) in this study. Geometry dependent/independent DRFs were obtained by minimizing the difference between the ionization chamber-measured profiles and the diode-measured profiles convolved with the DRFs. These DRFs were used to obtain eighteen beam models for a commercial TPS. Accuracy of the beam models were evaluated by assessing the 20%–80% penumbra width difference (PWD) between the computed and diode-measured beam profiles. Results: The convolution-based approach was found to be effective for all three ionization chambers with significant improvement for all beam models. Up to 17% geometry dependence of the three DRFs was observed for the studied ionization chambers. With geometry dependent DRFs, the PWD was within 0.80 mm for the parabolic function and CC04 combination and within 0.50 mm for other combinations; with geometry independent DRFs, the PWD was within 1.00 mm for all cases. When using the Gaussian function as the DRF, accounting for geometry dependence led to marginal improvement (PWD < 0.20 mm) for CC04; the improvement ranged from 0.38 to 0.65 mm for CC13; for SNC125c, the improvement was slightly above 0.50 mm. Conclusions: Although all three DRFs were found adequate to represent the response of the studied ionization chambers, the Gaussian function was favored due to its superior overall performance. The geometry dependence of the DRFs can be significant for clinical applications involving small fields such as stereotactic radiotherapy.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2011

Implicit Priors in Galaxy Cluster Mass and Scaling Relation Determinations

Deriving the total masses of galaxy clusters from observations of the intracluster medium (ICM) generally requires some prior information, in addition to the assumptions of hydrostatic equilibrium and spherical symmetry. Often, this information takes the form of particular parametrized functions used to describe the cluster gas density and temperature profiles. In this paper, we investigate the implicit priors on hydrostatic masses that result from this fully parametric approach, and the implications of such priors for scaling relations formed from those masses. We show that the application of such fully parametric models of the ICM naturally imposes a prior on the slopes of the derived scaling relations, favoring the self-similar model, and argue that this prior may be influential in practice. In contrast, this bias does not exist for techniques which adopt an explicit prior on the form of the mass profile but describe the ICM non-parametrically. Constraints on the slope of the cluster mass-temperature relation in the literature show a separation based the approach employed, with the results from fully parametric ICM modeling clustering nearer the self-similar value. Given that a primary goal of scaling relation analyses is to test the self-similar model, the application of methods subject to strong, implicit priors should be avoided. Alternative methods and best practices are discussed.

Mantz, A.↗
DOE OSTI2016

High-order solution methods for grey discrete ordinates thermal radiative transfer

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A high-order discontinuous Galerkin method for fluid–structure interaction with efficient implicit–explicit time stepping

We present a high-order accurate scheme for coupled fluid–structure interaction problems. The fluid is discretized using a discontinuous Galerkin method on unstructured tetrahedral meshes, and the structure uses a high-order volumetric continuous Galerkin finite element method. Standard radial basis functions are used for the mesh deformation. The time integration is performed using a partitioned approach based on implicit–explicit Runge–Kutta methods. The resulting scheme fully decouples the implicit solution procedures for the fluid and the solid parts, which we perform using two separate efficient parallel solvers. We demonstrate up to fifth order accuracy in time on a non-trivial test problem, on which we also show that additional subiterations are not required. We solve a benchmark problem of a cantilever beam in a shedding flow, and show good agreement with other results in the literature. Finally, we solve for the flow around a thin membrane at a high angle of attack in both 2D and 3D, and compare with the results obtained with a rigid plate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Handling Iterative Solvers in an Algorithmic Differentiation Framework Using Implicit Methods

Differentiable programming is a powerful concept as it enables the seemly propagation of gradients through functions, algorithms, and/or whole physics simulations. These gradients are useful for a wide variety of applications, including sensitivity studies and machine learning, but one of particular interest is optimization. Gradient-based optimization, enabled through automatic/algorithmic differentiation (AD), can be used on predictive physical models to efficiently optimize a set of design variables. AD methods are a particularly promising approach to complex physics simulations because they can be shown to scale well with an increasing number of design variables; however, care must be taken when coupling between different models or different states of a single model.

algorithmic differentiation↗
DOE OSTI2014

Multi-center semi-empirical quantum models for carbon under extreme thermodynamic conditions

We report on the development of many-body density functional tight binding (DFTB) models for carbon, which include either explicit or implicit calculation of multi-center terms in the Hamiltonian. Here, we show that all of our methods yield accurate eigenstates and eigenfunctions for both ambient diamond and transitions to molten, metallic states. We then determine a three-body repulsive energy to compute accurate equation of state and structural properties for carbon under these conditions. Our results indicate a straightforward approach by which many-body effects can be included in DFTB, thus extending the method to a wide variety of systems and thermodynamic conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

An enriched finite element model with q-refinement for radiative boundary layers in glass cooling

Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P{sub 1} approximation for the radiation in non-grey semitransparent media. To integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework. A class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls. Using an industrial electromagnetic spectrum, the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h-version finite element method. Furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries. The time integration choice is essential to implement a q-refinement procedure introduced in the current study. The enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment. The performance of the proposed method is analysed for glass annealing in two enclosures where the simplified P{sub 1} approximation solution with the partition of unity method, the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical Rosseland model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Hejre, we introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. Moreover, the effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Development and application of hybrid AIMD/cDFT simulations for atomic-to-mesoscale chemistry

Many important chemical processes involve reactivity and dynamics in complex solutions. Gaining a fundamental understanding of these reaction mechanisms is a challenging goal that requires advanced computational and experimental approaches. However, important techniques such as molecular simulation have limitations in terms of scales of time, length, and system complexity. Furthermore, among the currently available solvation models, there are very few designed to describe the interaction between the molecular scale and the mesoscale. To help address this challenge, here, we establish a novel hybrid approach that couples first-principles plane-wave density functional theory with classical density functional theory (cDFT). In this approach, a region of interest described by ab initio molecular dynamics (AIMD) interacts with the surrounding medium described using cDFT to arrive at a self-consistent ground state. cDFT is a robust but efficient mesoscopic approach to accurate thermodynamics of bulk electrolyte solutions over a wide concentration range (up to 2M concentrations). Benchmarking against commonly used continuum models of solvation, such as SMD, as well as experiments, demonstrates that our hybrid AIMD–cDFT method is able to produce reasonable solvation energies for a variety of molecules and ions. With this model, we also examined the solvent effects on a prototype S N 2 reaction of the nucleophilic attack of a chloride ion on methyl chloride in the solution. The resulting reaction pathway profile and the solution phase barrier agree well with experiment, showing that our AIMD/cDFT hybrid approach can provide insight into the specific role of the solvent on the reaction coordinate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

The halo light-cone catalogues of ABACUSSUMMIT

We describe a method for generating halo catalogues on the light-cone using the AbacusSummit suite of N-body simulations. The main application of these catalogues is the construction of realistic mock galaxy catalogues and weak lensing maps on the sky. Our algorithm associates the haloes from a set of coarsely spaced snapshots with their positions at the time of light-cone crossing by matching halo particles to on-the-fly light-cone particles. It then records the halo and particle information into an easily accessible product, which we call the AbacusSummit halo light-cone catalogues. Our recommended use of this product is in the halo mass regime of M halo > 2.1 x 10 11 M ⊙ h -1 for the base resolution simulations, i.e. haloes containing at least 100 particles, where the interpolated halo properties are most reliable. To test the validity of the obtained catalogues, we perform various visual inspections and consistency checks. In particular, we construct galaxy mock catalogues of emission-line galaxies (ELGs) at z ~ 1 by adopting a modified version of the AbacusHOD script, which builds on the standard halo occupation distribution (HOD) method by including various extensions. We find that the multipoles of the autocorrelation function are consistent with the predictions from the full-box snapshot, implicitly validating our algorithm. In addition, we compute and output CMB convergence maps and find that the auto- and cross-power spectrum agrees with the theoretical prediction at the sub-per-cent level.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Beyond the Born-Oppenheimer approximation with quantum Monte Carlo methods

Here, we develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We propose a highly accurate wave function ansatz for electron-ion systems that can involve a combination of both fixed and quantum ions. We explicitly calculate the ground state energies of H 2 , LiH, H 2 O and FHF - using fixed-node quantum Monte Carlo with wave function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our findings to the best theoretical and experimental results available and find excellent agreement.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Compressive Neural Representations of Volumetric Scalar Fields

Here, we present an approach for compressing volumetric scalar fields using implicit neural representations. Our approach represents a scalar field as a learned function, wherein a neural network maps a point in the domain to an output scalar value. By setting the number of weights of the neural network to be smaller than the input size, we achieve compressed representations of scalar fields, thus framing compression as a type of function approximation. Combined with carefully quantizing network weights, we show that this approach yields highly compact representations that outperform state-of-the-art volume compression approaches. The conceptual simplicity of our approach enables a number of benefits, such as support for time-varying scalar fields, optimizing to preserve spatial gradients, and random-access field evaluation. We study the impact of network design choices on compression performance, highlighting how simple network architectures are effective for a broad range of volumes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Domain Aware Deep-learning Algorithms Integrated with Scientific-computing Technologies (DADAIST)

This technical report summarized the contribution of the DADAIST project funded by the Data Model Convergence Initiative via the Laboratory Directed Research and Development (LDRD) investments at Pacific Northwest National Laboratory (PNNL). Specifically, we report the development of the NeuroMANCER (Neural Modules with Adaptive Nonlinear Constraints and Efficient Regularizations), a new open-source Scientific Machine Learning library for formulating and solving parametric constrained optimization problems, physics-informed system identification, and parametric optimal control problems. NeuroMANCER is using differentiable programming to combine modern data-driven models and optimization modeling language into a coherent algorithmic and software framework. NeuroMANCER is a Pytorch-based framework and adopts much of its philosophy focused on research and development, rapid prototyping, and streamlined deployment. Strong emphasis is given to extensibility, interoperability with the PyTorch ecosystem, and quick adaptability to custom domain problems. Neuromancer repository contains a comprehensive library of differentiable modules, including custom activation functions, matrix factorizations, deep learning architectures, neural differential equations, differential equation solvers, implicit layers such as iterative solvers, high-level API for symbolic expressions, API for modeling and control of dynamical systems, and extensive set of tutorial code examples in the form of python scripts and jupyter notebooks.

97 MATHEMATICS AND COMPUTING↗