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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 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

On the use of adjoints in the inversion of observed quasi-static deformation

An adjoint-based conjugate gradient algorithm provides an efficient means for imaging sources of deformation within the Earth, such as volume stresses associated with fluid flow in aquifers and reservoirs. For time intervals over which the overburden deforms elastically, one can calculate the gradient elements for a single model update using just two numerical simulations. The first is a forward run that is used to compute the residuals associated with the given iteration. The second simulation is to evaluate the application of the adjoint operator to the residuals. In this adjoint calculation, the residual displacements are applied as sources at the measurement locations, driving the deformation in the simulation. The volume stress on the source grid blocks, in response to the residual displacements, provide the gradient components. We apply this technique to satellite-based interferometric synthetic aperture radar (InSAR) line-of-sight displacements that were observed over an oil reservoir in California’s Central Valley. Furthermore, we find that the adjoint-based gradient estimates, requiring 18 CPU seconds, agree with conventional numerical calculations that take over 3700 CPU seconds to compute. Conjugate gradient algorithms utilizing the conventional approach and adjoint-based gradient computations give roughly the same reductions in misfit and similar final estimates of reservoir volume change.

58 GEOSCIENCES↗
DOE OSTI2023

Real-Time Krylov Theory for Quantum Computing Algorithms

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

When and why PINNs fail to train: A neural tangent kernel perspective

Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial differential equations. However, despite their noticeable empirical success, little is known about how such constrained neural networks behave during their training via gradient descent. More importantly, even less is known about why such models sometimes fail to train at all. Here in this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior of fully-connected neural networks in the infinite width limit during training via gradient descent. Specifically, we derive the NTK of PINNs and prove that, under appropriate conditions, it converges to a deterministic kernel that stays constant during training in the infinite-width limit. This allows us to analyze the training dynamics of PINNs through the lens of their limiting NTK and find a remarkable discrepancy in the convergence rate of the different loss components contributing to the total training error. To address this fundamental pathology, we propose a novel gradient descent algorithm that utilizes the eigenvalues of the NTK to adaptively calibrate the convergence rate of the total training error. Finally, we perform a series of numerical experiments to verify the correctness of our theory and the practical effectiveness of the proposed algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties

Here we introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually denoise images and generate realistic synthetic samples. By learning the reverse of a Markov diffusion process, we design an artificial intelligence to efficiently manipulate the topology of microstructures to generate a massive number of prototypes that exhibit constitutive responses sufficiently close to designated nonlinear constitutive behaviors. To identify the subset of microcstructures with sufficiently precise fine-tuned properties, a convolutional neural network surrogate is trained to replace high-fidelity finite element simulations to filter out prototypes outside the admissible range. Results of this study indicate that the denoising diffusion process is capable of creating microstructures of fine-tuned nonlinear material properties within the latent space of the training data. More importantly, this denoising diffusion algorithm can be easily extended to incorporate additional topological and geometric modifications by introducing high-dimensional structures embedded in the latent space. Numerical experiments are conducted on the open-source mechanical MNIST data set (Lejeune, 2020). Consequently, this algorithm is not only capable of performing inverse design of nonlinear effective media, but also learns the nonlinear structure–property map to quantitatively understand the multiscale interplay among the geometry, topology, and their effective macroscopic properties.

42 ENGINEERING↗
DOE OSTI2020

Economic Dispatch With Distributed Energy Resources: Co-Optimization of Transmission and Distribution Systems

The increasing penetration of distributed energy resources (DERs) in the distribution networks has turned the conventionally passive load buses into active buses that can provide grid services for the transmission system. To take advantage of the DERs in the distribution networks, this letter formulates a transmission-and-distribution (T&D) systems co-optimization problem that achieves economic dispatch at the transmission level and optimal voltage regulation at the distribution level by leveraging large generators and DERs. A primal-dual gradient algorithm is proposed to solve this optimization problem jointly for T&D systems, and a distributed market-based equivalent of the gradient algorithm is used for practical implementation. Finally, the results are corroborated by numerical examples with the IEEE 39-Bus system connected with 7 different distribution networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

A Non-perturbative Approach to Computing Seismic Normal Modes in Rotating Planets

In this work, a continuous Galerkin method based approach is presented to compute the seismic normal modes of rotating planets. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core using a polynomial filtering eigensolver. The relevant elastic-gravitational system of equations, including the Coriolis force, is subjected to a mixed finite-element method, while self-gravitation is accounted for with the fast multipole method. Our discretization utilizes fully unstructured tetrahedral meshes for both solid and fluid regions. The relevant eigenvalue problem is solved by a combination of several highly parallel and computationally efficient methods. We validate our three-dimensional results in the non-rotating case using analytical results for constant elastic balls, as well as numerical results for an isotropic Earth model from standard “radial” algorithms. We also validate the computations in the rotating case, but only in the slowly-rotating regime where perturbation theory applies, because no other independent algorithms are available in the general case. The algorithm and code are used to compute the point spectra of eigenfrequencies in several Earth and Mars models studying the effects of heterogeneity on a large range of scales.

58 GEOSCIENCES↗
DOE OSTI2022

Quantum algorithm for electronic band structures with local tight-binding orbitals

While the main thrust of quantum computing research in materials science is to accurately measure the classically intractable electron correlation effects due to Coulomb repulsion, designing optimal quantum algorithms for simpler problems with well-understood solutions is a useful tactic to advance our quantum “toolbox”. With this in mind, we consider the quantum calculation of a periodic system’s single-electron band structure over a path through reciprocal space. Previous efforts have used the Variational Quantum Eigensolver algorithm to solve the energy of each band, which involves numerically optimizing the parameters of a variational quantum circuit to minimize a cost function, constructed as the expectation value of a Hamiltonian operator. Traditionally, a unique Hamiltonian operator is constructed for each k-point, so that many cost functions, each with their own parameter space, must be optimized to generate a single band. Similarly, calculating higher bands than the first has traditionally involved modifying the cost function with additional overlap terms to ensure higher-energy eigenstates are orthogonal to those of lower bands. In this paper, we adopt a direct space approach, using a novel hybrid first/second-quantized qubit mapping which allows us to construct a single Hamiltonian, and a single cost-function, suitable for solving the entire electronic band structure. In contrast to previous approaches, the k-point and the band index are selected by additional parameters in our quantum circuit, rather than through modifications to the cost function. The result is a technically and conceptually simpler approach to band structure calculations on a quantum computer. Moreover, we expect that the tools developed herein will motivate new strategies for tackling highly-correlated materials beyond the grasp of classical computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Training neural networks using Metropolis Monte Carlo and an adaptive variant

Abstract We examine the zero-temperature Metropolis Monte Carlo (MC) algorithm as a tool for training a neural network by minimizing a loss function. We find that, as expected on theoretical grounds and shown empirically by other authors, Metropolis MC can train a neural net with an accuracy comparable to that of gradient descent (GD), if not necessarily as quickly. The Metropolis algorithm does not fail automatically when the number of parameters of a neural network is large. It can fail when a neural network’s structure or neuron activations are strongly heterogenous, and we introduce an adaptive Monte Carlo algorithm (aMC) to overcome these limitations. The intrinsic stochasticity and numerical stability of the MC method allow aMC to train deep neural networks and recurrent neural networks in which the gradient is too small or too large to allow training by GD. MC methods offer a complement to gradient-based methods for training neural networks, allowing access to a distinct set of network architectures and principles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The Pristine survey – XVI. The metallicity of 26 stellar streams around the Milky Way detected with the STREAMFINDER in Gaia EDR3

ABSTRACT We use the photometric metallicities provided by the panoramic Pristine survey to study the veracity and derive the metallicities of the numerous stellar streams found by the application of the STREAMFINDER algorithm to the Gaia Early Data Release 3 data. All 26 streams present in Pristine show a clear metallicity distribution function, which provides an independent check of the reality of these structures, supporting the reliability of STREAMFINDER in finding streams and the power of Pristine to measure precise metallicities. We further present six candidate structures with coherent phase-space and metallicity signals that are very likely streams. The majority of studied streams are very metal-poor (14 structures with [Fe/H] < −2.0) and include three systems with [Fe/H] < −2.9 (C-11, C-19, and C-20). These streams could be the closest debris of low-luminosity dwarf galaxies or may have originated from globular clusters of significantly lower metallicity than any known current Milky Way globular cluster. Our study shows that the promise of the Gaia data for Galactic Archeology studies can be substantially strengthened by quality photometric metallicities, allowing us to peer back into the earliest epochs of the formation of our Galaxy and its stellar halo constituents.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Fast Fourier transform evaluation of the Fresnel integral for gravitational-wave lensing

Gravitational waves (GWs) exhibit wave-optics effects when their wavelength is comparable to the scale of the gravitational lens. This may occur in lensing from galactic subhalos in GWs emitted by binary black-hole mergers and is gaining interest as a novel probe of dark matter. Predictions for observables in these cases ultimately rely on evaluating a Fresnel integral that quantifies the effect of lensing on the amplitude of a GW at a given frequency. However, numerical evaluation of this Fresnel integral is tricky, and several algorithms and publicly available codes that implement it have been developed. Here, we show that the dependence of this integral on the lens position can be written as a two-dimensional Fourier transform. Modern FFT techniques then enable rapid evaluation at all-sky positions simultaneously for general lenses without symmetry. Vectorization of FFT routines allows for derivatives with respect to model parameters to be obtained with only incremental additional computational cost. If the lens is axisymmetric, further speedups can be achieved with recently developed techniques for nonuniform fast Hankel transforms. To demonstrate, we make available Fresnel Integral Optimization with Nonuniform Transforms (fiona), an efficient and accurate code that is significantly faster than current methods for dense source grids, reaching 2 orders of magnitude speedups for ∼10 6 GW-emitting points. As part of FIONA , we developed code that provides vectorized nonuniform fast Hankel transforms that may have other uses (e.g., calculation of cosmological two-point correlation functions) beyond those considered here.

dark matter↗
DOE OSTI2026

Rank-Limiting Strategies for Optimizing Tensor-Train Finite-Difference Time-Domain Simulations

We introduce rank-limiting strategies to optimize tensor-train decompositions for three-dimensional finite-difference time-domain simulations using the relationship between the tensors and their specific dimensionality. These include the use of hard caps on the inner ranks of the tensor train decomposition and the use of a group rounding algorithm taking into account all field components simultaneously. Here, several numerical examples are considered to verify the efficacy of the proposed optimization strategies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Joint Planning of EV Fast Charging Stations and Power Distribution Systems With Balanced Traffic Flow Assignment

To tackle the challenges introduced by the fast-growing charging demand of electric vehicles (EVs), the power distribution systems (PDSs) and fast charging stations (FCSs) of EVs should be planned and operated in a more coordinated fashion. However, existing planning approaches generally aim to minimize investment costs in PDSs while ignoring the risk of worsening traffic conditions. To overcome this research gap, this article integrates the interests of traffic networks into PDS and FCS joint planning model to mitigate negative impacts on traffic conditions caused by installing FCSs. First, a novel microscopic method that is different from traditional assignment methods is proposed to simulate the influences of FCSs on traffic flows and EV charging loads. Then, a multiobjective joint planning model is developed to minimize both the planning costs and unbalanced traffic flows. A new bilayer Benders decomposition algorithm is designed to solve the proposed joint planning model. Numerical results on two practical systems in China validate the feasibility of our microscopic method by comparing the simulated results with real data. Compared with existing approaches, it is also demonstrated that the proposed joint planning approach helps to balance traffic flow assignments and relieve traffic congestion.

bilayer expanded Benders decomposition↗
DOE OSTI2024

Distributionally Robust Decentralized Volt-Var Control With Network Reconfiguration

Here, this paper presents a decentralized volt-var optimization (VVO) and network reconfiguration strategy to address the challenges arising from the growing integration of distributed energy resources, particularly photovoltaic (PV) generation units, in active distribution networks. To reconcile control measures with different time resolutions and empower local control centers to handle intermittency locally, the proposed approach leverages a two-stage distributionally robust optimization; decisions on slow-responding control measures and set points that link neighboring subnetworks are made in advance while considering all plausible distributions of uncertain PV outputs. We present a decomposition algorithm with an acceleration scheme for solving the proposed model. Numerical experiments on the IEEE 123 bus distribution system are given to demonstrate its outstanding out-of-sample performance and computational efficiency, which suggests that the proposed method can effectively localize uncertainty via risk-informed proactive timely decisions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Computationally Efficient Decompositions of Oblique Projection Matrices

Oblique projection matrices arise in problems in weighted least squares, signal processing, and optimization. While these matrices can be potentially very large, their low-rank structure can be exploited for efficient computation. Here, we propose fast and scalable algorithms for computing their eigendecomposition and singular value decomposition (SVD). Numerical experiments that compare our proposed approaches to existing methods, including randomized SVD, are presented. In addition, we test their accuracy on linear systems from equality constrained optimization problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Milestone 49 Report: Batched Sparse LA Phase 5 Implementation

Batched sparse linear algebra operations in general, and solvers in particular, have become the major algorithmic development activity and foremost performance engineering effort in the numerical software libraries work on modern hardware with accelerators such as GPUs. Many applications, ECP and non-ECP alike, require simultaneous solutions of many small linear systems of equations that are structurally sparse in one form or another. In order to move towards high hardware utilization levels, it is important to provide these applications with appropriate interface designs to be both functionally efficient and performance portable and give full access to the appropriate batched sparse solvers running on modern hardware accelerators prevalent across DOE supercomputing sites since the inception of ECP. To this end, we present here a summary of recent advances on the interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the corresponding software portable between the major hardware accelerators from AMD, Intel, and NVIDIA, while maintaining the appropriate disclosure levels conforming to the active NDA agreements. The presented interface specifications include a mix of batched band, sparse iterative, and sparse direct solvers with their accompanying functionality that is already required by the application codes or we anticipated to be needed in the near future. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, PETSc, and SuperLU.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Flexible Power Method for Solving Infinite Dimensional Tensor Eigenvalue Problems

We propose a flexible power method for computing the leftmost, i.e., algebraically smallest, eigenvalue of an infinite dimensional tensor eigenvalue problem, $H x = \lambda x$, where the infinite dimensional symmetric matrix $H$ exhibits a translational invariant structure. We assume the smallest eigenvalue of $H$ is simple and apply a power iteration of $e^{-H}$ with the eigenvector represented in a compact way as a translational invariant infinite Tensor Ring (iTR). Hence, the infinite dimensional eigenvector can be represented by a finite number of iTR cores of finite rank. In order to implement this power iteration, we use a small parameter $t$ so that the infinite matrix-vector operation $e^{-Ht}x$ can efficiently be approximated by the Lie product formula, also known as Suzuki--Trotter splitting, and we employ a low rank approximation through a truncated singular value decomposition on the iTR cores in order to keep the cost of subsequent power iterations bounded. We also use an efficient way for computing the iTR Rayleigh quotient and introduce a finite size iTR residual which is used to monitor the convergence of the Rayleigh quotient and to modify the timestep $t$. In this paper, we discuss 2 different implementations of the flexible power algorithm and illustrate the automatic timestep adaption approach for several numerical examples.

Beeumen, Roel Van↗
DOE OSTI2023

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application (“Fragme∩t”), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

Chemistry↗
DOE OSTI2023

Joint optimization of electric bus charging infrastructure, vehicle scheduling, and charging management

High upfront costs of vehicles and charging infrastructure as well as the lack of knowledge related to infrastructure planning and electric bus system operation are major obstacles to the implementation of battery electric buses (BEBs). To tackle the obstacles and promote BEB adoption, a comprehensive optimization framework was developed to address the combined charging infrastructure planning, vehicle scheduling, and charging management problem for BEB systems, with the goal to minimize the total cost of ownership. The problem was formulated as a mixed-integer non-linear problem. A genetic algorithm-based approach was then proposed to solve the problem. Last, three alternative scenarios based on a sub-transit network in Salt Lake City, Utah, were analyzed and compared with the optimal scenario results in the numerical experiments. Our comparison results demonstrate the effectiveness of the proposed model and solution algorithm in determining a cost-efficient planning strategy for BEB systems.

33 ADVANCED PROPULSION SYSTEMS↗