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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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Large-scale inverse model analyses employing fast randomized data reduction: INVERSE MODELING WITH DATA REDUCTION

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 10 7 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called “sketching” matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Moreover, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Thus, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Daubechies wavelets for linear scaling density functional theory

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Rational Chebyshev spectral transform for the dynamics of broad-area laser diodes

This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of broad-area laser diodes and amplifiers. This spectral method can be used in combination with the delay algebraic equations approach developed in [1], which substantially reduces the computation time. The theory is presented in such a way that it encompasses the case of the Fourier spectral transform presented in [2] as a particular case. It is also extended to the consideration of index guiding with an arbitrary transverse profile. Because their domain of definition is infinite, the convergence properties of the Chebyshev rational functions allow handling the boundary conditions with higher accuracy than with the previously studied Fourier transform method. As practical examples, we solve the beam propagation problem with and without index guiding: we obtain excellent results and an improvement of the integration time between one and two orders of magnitude as compared with a fully distributed two dimensional model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Parametric matrix models

We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that emulate physical systems. Similar to how physics problems are usually solved, parametric matrix models learn the governing equations that lead to the desired outputs. Parametric matrix models can be efficiently trained from empirical data, and the equations may use algebraic, differential, or integral relations. While originally designed for scientific computing, we prove that parametric matrix models are universal function approximators that can be applied to general machine learning problems. After introducing the underlying theory, we apply parametric matrix models to a series of different challenges that show their performance for a wide range of problems. For all the challenges tested here, parametric matrix models produce accurate results within an efficient and interpretable computational framework that allows for input feature extrapolation.

Computational science↗
DOE OSTI2023

A divergence-free constrained magnetic field interpolation method for scattered data

An interpolation method to evaluate magnetic fields, given its unstructured and scattered magnetic data, is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The coefficients of the expansion are obtained by minimizing a cost function defined as the L2 norm of the difference between the ground truth and the reconstructed magnetic field evaluated on the training data. The divergence-free condition is incorporated as a constraint in the cost function, allowing the method to achieve arbitrarily small errors in the magnetic field divergence. An exponential decay of the approximation error is observed and compared with the less favorable algebraic decay of local splines. Compared to local methods involving computationally expensive search algorithms, the proposed method exhibits a significant reduction of the computational complexity of the field evaluation, while maintaining a small error in the divergence even in the presence of magnetic islands and stochasticity. Finally, applications to the computation of Poincaré sections using data obtained from numerical solutions of the magnetohydrodynamic equations in toroidal geometry are presented and compared with local methods currently in use.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A parallel, distributed memory implementation of the adaptive sampling configuration interaction method

The many-body simulation of quantum systems is an active field of research that involves several different methods targeting various computing platforms. Many methods commonly employed, particularly coupled cluster methods, have been adapted to leverage the latest advances in modern high-performance computing. Selected configuration interaction (sCI) methods have seen extensive usage and development in recent years. However, the development of sCI methods targeting massively parallel resources has been explored only in a few research works. Here, we present a parallel, distributed memory implementation of the adaptive sampling configuration interaction approach (ASCI) for sCI. In particular, we will address the key concerns pertaining to the parallelization of the determinant search and selection, Hamiltonian formation, and the variational eigenvalue calculation for the ASCI method. Load balancing in the search step is achieved through the application of memory-efficient determinant constraints originally developed for the ASCI-PT2 method. The presented benchmarks demonstrate near optimal speedup for ASCI calculations of Cr 2 (24e, 30o) with 10 6 , 10 7 , and 3 × 10 8 variational determinants on up to 16 384 CPUs. Importantly, to the best of the authors’ knowledge, this is the largest variational ASCI calculation to date.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton and quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Weak scaling of the contact distance between two fluctuating interfaces with system size

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ* depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ* scales weakly with system size, i.e., the dependence of ℓ* on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim L→∞ (ℓ*/L) = 0. In particular, for (2+1)-dimensional interfaces ℓ* is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. Overall, this weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable to multilevel MCMC frameworks which build fine-scale random fields in a hierarchical fashion from coarse-scale random fields. Our new hierarchical multilevel method relies on a hierarchical decomposition of the white noise source function in $L^2$ which allows us to form Gaussian random field realizations across multiple levels of discretization in a way that fits into multilevel MCMC algorithmic frameworks. After presenting our main theoretical results and numerical scaling results to showcase the utility of this new hierarchical PDE method for generating Gaussian random field realizations, this method is tested on a four-level MCMC algorithm to explore its feasibility.

algebraic multigrid↗
DOE OSTI2021

Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning

Various modeling techniques are used to predict the capacity fade of Li-ion batteries. Algebraic reduced-order models, which are inherently interpretable and computationally fast, are ideal for use in battery controllers, technoeconomic models, and multi-objective optimizations. For Li-ion batteries with graphite anodes, solid-electrolyte-interphase (SEI) growth on the graphite surface dominates fade. This fade is often modeled using physically informed equations, such as square-root of time for predicting solvent-diffusion limited SEI growth, and Arrhenius and Tafel-like equations predicting the temperature and state-of-charge rate dependencies. In some cases, completely empirical relationships are proposed. However, statistical validation is rarely conducted to evaluate model optimality, and only a handful of possible models are usually investigated. This article demonstrates a novel procedure for automatically identifying reduced-order degradation models from millions of algorithmically generated equations via bi-level optimization and symbolic regression. Identified models are statistically validated using cross-validation, sensitivity analysis, and uncertainty quantification via bootstrapping. On a LiFePO 4 /Graphite cell calendar aging data set, automatically identified models utilizing square-root, power law, stretched exponential, and sigmoidal functions result in greater accuracy and lower uncertainty than models identified by human experts, and demonstrate that previously known physical relationships can be empirically "rediscovered" using machine learning.

25 ENERGY STORAGE↗
DOE OSTI2021

Asynchronous Iterative Solvers for Extreme-Scale Computing

The Asynchronous Iterative Solvers for Extreme-Scale Computing (AsyncIS) project aims to explore more efficient numerical algorithms by decreasing their overhead. AsyncIS does this by replacing the outer Krylov subspace solver with an asynchronous optimized Schwarz method, thereby removing the global synchronization and bulk synchronous operations typically used in numerical codes. AsyncIS—a U.S. Department of Energy (DOE)-funded collaboration between Georgia Tech, the University of Tennessee, Knoxville, Temple University, and Sandia National Laboratories—also focuses on the development and optimization of asynchronous preconditioners (i.e., preconditioners that are generated and/or applied in an asynchronous fashion). The novel preconditioning algorithms that provide fine-grained parallelism enable preconditioned Krylov solvers to run efficiently on large-scale distributed systems and manycore accelerators like GPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

EnergyPlus Interior Radiant Heat Exchange Runtime Performance Improvements

EnergyPlus is the flagship whole-building energy simulation program developed by the US Department of Energy. This paper describes the various approaches to improve the performance of the interior radiant heat exchange algorithm. Vectorization, optimized Basic Linear Algebra Subprograms (BLAS) library, multithreading, and Graphical Processing Unit (GPU) computation are all investigated. The approach with the best performance, while maintaining drop-in compatibility with existing EnergyPlus code, is the optimized BLAS library. However, GPU computing has the potential to reduce simulation time by orders of magnitude with major refactoring to EnergyPlus.

Adams, Mark↗
DOE OSTI2020

Computing Hypergraph Homology in Chapel

In this paper, we discuss our experience in implementing homology computation, in particular Betti number calculation in Chapel hypergraph Library (CHGL). Given a dataset represented as a hypergraph, a Betti number for a particular dimension $k$ indicates how many $k$-dimensional `voids' are present in the dataset. Computing Betti number involves various array-centric and linear algebra operations. We demonstrate that implementing these operations in Chapel is both concise and intuitive. In addition, we show that Chapel provides language constructs for implementing parallel and distributed execution of the linear algebra kernels with minimal effort. Syntactically, Chapel provides succinctness of Python, while delivering comparable and better performance than C++-based and Julia-based packages for calculating Betti numbers respectively.

hypergraph, topological data analysis↗
DOE OSTI2019

A parallel-in-time algorithm for variable step multistep methods

This paper presents a multigrid reduction in time (MGRIT) algorithm for achieving time parallelism using multistep backward difference formula (BDF) methods on variably-spaced temporal grids. This MGRIT approach transforms the linear multistep methods into single step methods applied to groups of time steps. Stability considerations are addressed through lowering of the order on coarse grids. The methods are presented for fixed and variable time step formulations. Furthermore, numerical results show moderate speedups for the heat equation as well as two IEEE power grid test problems characterized by nonlinear differential algebraic equations (DAE) of index 1. The performance of MGRIT with BDF is compared to MGRIT with Runge-Kutta for both the fixed and variable step methods of the same order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function $f_{NTU}$(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. Here, the new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Efficient and Robust Dynamic Simulation of Power Systems With Holomorphic Embedding

Dynamic simulation is vitally important in power system analysis, but traditional approaches based on numerical integration over small time steps are time-consuming. Also, the Newton-Raphson method suffers from difficulty in convergence when solving nonlinear algebraic equations. In this paper, we propose a novel dynamic simulation approach based on holomorphic embedding. By obtaining a high-order approximation of system dynamics, it achieves a much larger time step and thus enhances the computational efficiency significantly. In addition, the new approach avoids non-convergence issues in solving algebraic equations, which improves robustness. The approach includes flexible modeling of synchronous generators and controllers, and we propose a method for modeling generator coordinate transformations. The approach is tested on the IEEE 39-bus, 10-generator system and a Polish 2383-bus, 327-generator system. The results demonstrate promising computational efficiency and satisfactory numerical robustness for the analysis of large-scale power systems.

42 ENGINEERING↗
DOE OSTI2020

Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction

In this paper, we continue our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. Furthermore, we consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. In conclusion, we present numerical studies illustrating the optimization-based formulations and comparing them with AFC

97 MATHEMATICS AND COMPUTING↗