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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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Flexible and Modular Simultaneous Modeling of Flow and Reactive Transport in Rivers and Hyporheic Zones

Investigations of coupled multiphysics processes in rivers and hyporheic zones have extensively used numerical models. Most existing models use a sequential, one-way coupling between the surface and subsurface domains. Such one-way coupling potentially introduces error. To overcome this, a fully coupled model, hyporheicFoam, was developed using the open-source computational platform OpenFOAM. It captures the coupled flow and multicomponent reactive transport processes within both surface and subsurface domains and across their interface. The coupling between two domains is implemented by mapping conservative flux boundary conditions at the interface through an iterative algorithm. Reactive transport is enabled by specifying a reaction network. To start, we have implemented reaction kinetics following the double Monod-type model with inhibition. The model capability is illustrated through modeling of both conservative and reactive hyporheic flow and transport through dune bedforms. With the novel coupled model, it is now possible to quantify reactions wherein the reactants and products are constantly exchanging between domains and have feedbacks. hyporheicFoam can simulate large, three-dimensional cases owing to the computational flexibility and power offered by the code structure and parallel design of OpenFOAM.

58 GEOSCIENCES↗
DOE OSTI2022

Improving deep learning performance for predicting large-scale geological ${{CO}_{2}}$ sequestration modeling through feature coarsening

Physics-based reservoir simulation for fluid flow in porous media is a numerical simulation method to predict the temporal-spatial patterns of state variables (e.g. pressure p) in porous media, and usually requires prohibitively high computational expense due to its non-linearity and the large number of degrees of freedom (DoF). This work describes a deep learning (DL) workflow to predict the pressure evolution as fluid flows in large-scale 3-dimensional(3D) heterogeneous porous media. In particular, we develop an efficient feature coarsening technique to extract the most representative information and perform the training and prediction of DL at the coarse scale, and further recover the resolution at the fine scale by spatial interpolation. We validate the DL approach to predict pressure field against physics-based simulation data for a field-scale 3D geologic CO 2 sequestration reservoir model. We evaluate the impact of feature coarsening on DL performance, and observe that the feature coarsening not only decreases the training time by >74% and reduces the memory consumption by >75%, but also maintains temporal error 0.63% on average. Besides, the DL workflow provides predictive efficiency with 1406 times speedup compared to physics-based numerical simulation. The key findings from this research significantly improve the training and prediction efficiency of deep learning model to deal with large-scale heterogeneous reservoir models, and thus it can also be further applied to accelerate workflows of history matching and reservoir optimization for close-loop reservoir management.

58 GEOSCIENCES↗
DOE OSTI2024

Design and evaluation of alphabetic and numeric input methods for virtual reality

In today’s virtual reality (VR), users have various ways to influence their VR experience, including alphanumeric input. While typing characters and numbers is straightforward on desktop computers, it presents challenges and opportunities in head-mounted display VR due to specific interaction methods and a lack of real-world visual stimuli. Addressing these open questions, our work implements and evaluates ten approaches to alphabetic and numeric inputs in VR. Here, we describe the design motivation behind these input methods and evaluate them in a user study with 40 participants divided into groups for alphabetic and numeric keyboards. This comparison investigates each method’s performance and user interactions. Our findings suggest that different input methods significantly impact words per minute and error rates, and that certain keyboard designs may receive better subjective evaluations despite poorer objective performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev–Gauss quadrature

The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev–Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. Here, the method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.

Mathematics↗
DOE OSTI2025

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗
DOE OSTI2020

Multilevel Convergence Analysis of Multigrid-Reduction-in-Time

This study presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time-stepping operator, analyzed directly and bounded in the norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time-stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge--Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge--Kutta schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A combined ensemble-volume average homogenization method for lattice structures with defects under dynamic and static loading

In the study of lattices structures, both experiments and numerical simulations are often conducted with small samples. Using combined ensemble and volume averaging, this work introduces a method to extract a macroscopic constitutive response of a lattice material from numerical simulations performed in periodic domains. The domain size needed to obtain statistically accurate results is investigated. Similar to molecular dynamics, the concept of the virial stress is introduced after homogenized equations are derived using the ensemble averaging method. Under static conditions, the virial stress is shown to agree with the volume averaged solid stress. Using the homogenization method, constitutive relations for this stress can be obtained from systems with uniform strains. Application of such obtained constitutive relations to more general cases results in an error proportional to the square of the ratio between the lattice length scale and the macroscopic length scale. Taking advantage of this property, numerical simulations are performed in systems with a uniform gradient of the average velocity. The volume average method is then used to accelerate convergence when studying lattices with defects. To avoid the artificial numerical time scale from the size of a representative volume element divided by the wave speed, a numerical scheme is developed to enforce a spatially uniform velocity gradient within the computational domain while allowing fluctuations of the velocity or displacement to develop naturally. To account for probability distribution of lattice defects, the stress is calculated as the ensemble-volume averaged value. For dynamic systems, energy dissipation properties are also studied.

36 MATERIALS SCIENCE↗
DOE OSTI2020

An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing

The immersed boundary method (IBM) with direct forcing is very popular in the simulation of rigid particulate flows. In the IBM, an interaction force is introduced at the interface between fluid and particle in order to approximate the no-slip boundary condition. The interaction force is calculated through dividing the velocity difference (or error) between fluid and particle at the interface by the time step. Here, a dynamic equation for the velocity difference is derived. Additionally, analyses on the dynamic equation provide a few new findings: (i) The interaction force is the solution of a least-squares error problem, with the direct implication that the Lagrangian marker distribution has no effect on the large scale flow structure once the distribution of Lagrangian markers become saturated along the interface (i.e., each marker remains properly correlated with all its neighbors); (ii) The Lagrangian volume-weight is a relaxation factor to control how fast the velocity error decays to the ideal value of zero; (iii) The optimal choice of the Lagrangian volume-weight is the largest value permissible by a stability condition. A comprehensive convergence analysis with regard to the spatial and temporal resolution is presented for the velocity error and also for the shear-stress and surface pressure. In three simple canonical problems, it is analytically and numerically shown that the IBM results converge to the theoretical solutions obtained with precise imposition of no-slip and no-penetration boundary conditions. It is observed that it is not necessary to match the Lagrangian marker volume-weight to that of the local Eulerian cell volume and in fact this matching leads to lower than optimal computational efficiency. However, it is found that extremely high Eulerian grid resolution and small time step have to be used to obtain high precision simulation results. Especially, the time step should be inversely proportional to the particle Reynolds number for low Reynolds number flows. For high frequency oscillation problems, the grid size needs to be reduced by a factor of the square root of the frequency, and the time step to be reduced by a factor of the frequency. The theoretical findings here can be used to alleviate the technical difficulties in simulating non-spherical particles by not requiring the Lagrangian marker distribution to match the Eulerian grids and also in the implementation of IBM on non-uniform Eulerian grids. The present work also provides simple practical guidance on the choice of temporal and spatial resolution so as to control the simulation error a priori.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Robust trajectory-constrained frequency control for microgrids considering model linearization error

Grid supportive modes integrated within inverter-based resources can improve the frequency response of renewable-rich microgrids. The synthesis of grid supportive modes to guarantee frequency trajectory constraints under a predefined disturbance set is challenging but essential. To tackle this challenge, a numerical optimal control (NOC)-based control synthesis methodology is proposed. Without loss of generality, a wind-diesel fed microgrid is studied, where we aim to design grid supportive functions in the wind turbine. In the control design, linearized models are used, and the linearization-induced errors are quantitatively analyzed by reachability and interval arithmetics and represented in the form of interval uncertainties. Then, the NOC problem can be formulated into a robust mixed-integer linear program. The control structure is strategically configured into two levels to realize online deployment. The proposed control is verified on the modified 33-node microgrid with a full-order three-phase nonlinear model in Simulink. In conclusion, the simulation results show the effectiveness of the proposed control paradigm and the necessity of considering linearization-induced uncertainty.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Mixed precision s –step Lanczos and conjugate gradient algorithms

Compared to the classical Lanczos algorithm, the s-step Lanczos variant has the potential to improve performance by asymptotically decreasing the synchronization cost per iteration. However, this comes at a price; despite being mathematically equivalent, the s-step variant may behave quite differently in finite precision, potentially exhibiting greater loss of accuracy and slower convergence relative to the classical algorithm. It has previously been shown that the errors in the s-step version follow the same structure as the errors in the classical algorithm, but are amplified by a factor depending on the square of the condition number of the O(s)-dimensional Krylov bases computed in each outer loop. As the condition number of these s-step bases grows (in some cases very quickly) with s, this limits the s values that can be chosen and thus can limit the attainable performance. In this work, we show that if a select few computations in s-step Lanczos are performed in double the working precision, the error terms then depend only linearly on the conditioning of the s-step bases. This has the potential for drastically improving the numerical behavior of the algorithm with little impact on per-iteration performance. Our numerical experiments demonstrate the improved numerical behavior possible with the mixed precision approach, and also show that this improved behavior extends to mixed precision s-step CG. Here, we present preliminary performance results on NVIDIA V100 GPUs that show that the overhead of extra precision is minimal if one uses precisions implemented in hardware.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A numerical Poisson solver with improved radial solutions for a self-consistent locally scaled self-interaction correction method

Abstract The universal applicability of density functional approximations is limited by self-interaction error made by these functionals. Recently, a novel one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities was proposed. The locally scaled SIC (LSIC) method is exact for the one-electron densities, and unlike the well-known Perdew–Zunger SIC (PZSIC) method recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to PZSIC method as a special case when isoorbital indicator is set to the unity. Here, we present a numerical scheme that we have adopted to evaluate the Coulomb potential of the electron density scaled by the iso-orbital indicator required for the self-consistent LSIC calculations. After analyzing the behavior of the finite difference method (FDM) and the green function solution to the radial part of the Poisson equation, we adopt a hybrid approach that uses the FDM for the Coulomb potential due to the monopole and the GF for all higher-order terms. The performance of the resultant hybrid method is assessed using a variety of systems. The results show improved accuracy than earlier numerical schemes. We also find that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Anderson acceleration with approximate calculations: Applications to scientific computing

Here we provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least-squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed-point iterations arising from the Richardson's scheme to solve linear systems with open-source benchmark matrices with various preconditioners and (ii) non-linear deterministic fixed-point iterations arising from non-linear time-dependent Boltzmann equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Coupling Approaches with Non-matching Grids for Classical Linear Elasticity and Bond-based Peridynamic Models in 1D

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal grids usually require a finer resolution than local grids. In that case, it is often convenient to resort to interpolation operators so that models can exchange information in the overlap regions when nodes from the two grids do not coincide. This paper studies three existing coupling approaches, namely 1) a method that enforces matching displacements in an overlap region, 2) a variant that enforces a constraint on the stresses instead, and 3) a method that considers a variable horizon in the vicinity of the interfaces. Further, the effect of the interpolation order and of the grid ratio on the performance of the three coupling methods with non-matching grids is carefully studied on one-dimensional examples using polynomial manufactured solutions. The numerical results show that the degree of the interpolants should be chosen with care to avoid introducing additional modeling errors, or simply minimize these errors, in the coupling approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A numerical extension of the spatially-filtered Euler equations for contact discontinuities

Solving the spatially-filtered Euler equations with a kinetic energy-preserving centered discretization is an efficient framework for simulating shock-dominated flows. Here, the present work describes a numerical treatment of the spatially-filtered Euler equations to minimize oscillations when simulating contact discontinuities. To counteract dispersive errors inherent to centered schemes, a WENO-like correction term is applied to the enthalpy transport in the energy equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Accelerating gradient descent and Adam via fractional gradients

Here we propose a class of novel fractional-order optimization algorithms. We define a fractional-order gradient via the Caputo fractional derivatives that generalizes integer-order gradient. We refer it to as the Caputo fractional-based gradient, and develop an efficient implementation to compute it. A general class of fractional-order optimization methods is then obtained by replacing integer-order gradients with the Caputo fractional-based gradients. To give concrete algorithms, we consider gradient descent (GD) and Adam, and extend them to the Caputo fractional GD (CfGD) and the Caputo fractional Adam (CfAdam). We demonstrate the superiority of CfGD and CfAdam on several large scale optimization problems that arise from scientific machine learning applications, such as ill-conditioned least squares problem on real-world data and the training of neural networks involving non-convex objective functions. Numerical examples show that both CfGD and CfAdam result in acceleration over GD and Adam, respectively. We also derive error bounds of CfGD for quadratic functions, which further indicate that CfGD could mitigate the dependence on the condition number in the rate of convergence and results in significant acceleration over GD.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Statistical and systematic uncertainties in extracting the source properties of neutron star-black hole binaries with gravitational waves

Gravitational waves emitted by neutron star black hole mergers encode key properties of neutron stars - such as their size, maximum mass and spins - and black holes. However, the presence of matter and the high mass ratio makes generating long and accurate waveforms from these systems hard to do with numerical relativity, and not much is known about systematic uncertainties due to waveform modeling. In this work, we simulate gravitational waves from neutron star black hole mergers by hybridizing numerical relativity waveforms produced with the SpEC code with a recent numerical relativity surrogate NRHybSur3dq8Tidal. These signals are analyzed using a range of available waveform families, and statistical and systematic errors are reported. We find that at a network signal-to-noise ratio (SNR) of 30, statistical uncertainties are usually larger than systematic offsets, while at an SNR of 70 the two become comparable. The individual black hole and neutron star masses, as well as the mass ratios, are typically measured very precisely, though not always accurately at high SNR. At a SNR of 30 the neutron star tidal deformability can only be bound from above, while for louder sources it can be measured and constrained away from zero. All neutron stars in our simulations are non-spinning, but in no case we can constrain the neutron star spin to be smaller than ~0.4 (90% credible interval). Waveform families whose late inspiral has been tuned specifically for neutron star black hole signals typically yield the most accurate characterization of the source parameters. Their measurements are in tension with those obtained using waveform families tuned against binary neutron stars, even for mass ratios that could be relevant for both binary neutron stars and neutron star black holes mergers.

79 ASTRONOMY AND ASTROPHYSICS↗