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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 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events

In thist study, we develop a procedure to utilize error estimates for samples of a surrogate model to compute robust upper and lower bounds on estimates of probabilities of events. We show that these error estimates can also be used in an adaptive algorithm to simultaneously reduce the computational cost and increase the accuracy in estimating probabilities of events using computationally expensive high-fidelity models. Specifically, we introduce the notion of reliability of a sample of a surrogate model, and we prove that utilizing the surrogate model for the reliable samples and the high-fidelity model for the unreliable samples gives precisely the same estimate of the probability of the output event as would be obtained by evaluation of the original model for each sample. The adaptive algorithm uses the additional evaluations of the high-fidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of high-fidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjoint-based approach for estimating the error in samples of a surrogate are provided to demonstrate (1) the robustness of the bounds on the probability of an event, and (2) that the adaptive enhancement algorithm provides a more accurate estimate of the probability of the QoI event than standard response surface approximation methods at a lower computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo

We introduce an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the technique for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. Furthermore, we perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient method for geometry optimization and molecular dynamics within AFQMC.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Robust Containment Queries over Collections of Trimmed NURBS Surfaces via Generalized Winding Numbers

Here, we propose a containment query that is robust to the watertightness of regions bound by trimmed NURBS surfaces, as this property is difficult to guarantee for in-the-wild CAD models. Containment is determined through the generalized winding number (GWN), a mathematical construction that is indifferent to the arrangement of surfaces in the shape. Applying contemporary techniques for the 3D GWN to trimmed NURBS surfaces requires some form of geometric discretization, introducing computational inefficiency to the algorithm and even risking containment misclassifications near the surface. In contrast, our proposed method leverages properties of the 3D solid angle to solve the relevant surface integral using a boundary formulation with rapidly converging adaptive quadrature. Batches of queries are further accelerated by memoizing (i.e., caching and reusing) quadrature node positions and tangents as they are evaluated. We demonstrate that our GWN method is robust to complex trimming geometry in a CAD model, and is accurate up to arbitrary precision at arbitrary distances from the surface. The derived containment query is therefore robust to model non-watertightness while respecting all curved features of the input shape.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Approximate quantum circuit synthesis using block encodings

One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose a novel approximate quantum circuit synthesis technique by relaxing the unitary constraints and interchanging them for ancilla qubits via block encodings. This approach combines smaller block encodings, which are easier to synthesize, into quantum circuits for larger operators. Due to the use of block encodings, our technique is not limited to unitary operators and can be applied for the synthesis of arbitrary operators. Overall, we show that operators which can be approximated by a canonical polyadic expression with a polylogarithmic number of terms can be synthesized with polylogarithmic gate complexity with respect to the matrix dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A two-grid penalty method for American options

In this paper we consider the pricing of American options, governed by a partial differential complementarity problem. The differential problem is first approximated by a semi-linear PDE using two distinct penalty approaches which are well known in computational finance. We then initiate the two-grid algorithm by solving the nonlinear problem on a coarse grid and further the linearized in the interpolated coarse-grid solution problem on a fine grid. By means of the maximum principle the algorithm is shown to be of fourth order convergence rate in space. Numerical experiments verify the presented two-grid approach where we draw some interesting conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Application of Systems Engineering Principles and Techniques in Biological Big Data Analytics: A Review

In the past few decades, we have witnessed tremendous advancements in biology, life sciences and healthcare. These advancements are due in no small part to the big data made available by various high-throughput technologies, the ever-advancing computing power, and the algorithmic advancements in machine learning. Specifically, big data analytics such as statistical and machine learning has become an essential tool in these rapidly developing fields. As a result, the subject has drawn increased attention and many review papers have been published in just the past few years on the subject. Different from all existing reviews, this work focuses on the application of systems, engineering principles and techniques in addressing some of the common challenges in big data analytics for biological, biomedical and healthcare applications. Specifically, this review focuses on the following three key areas in biological big data analytics where systems engineering principles and techniques have been playing important roles: the principle of parsimony in addressing overfitting, the dynamic analysis of biological data, and the role of domain knowledge in biological data analytics.

dynamic analysis↗
DOE OSTI2023

Determining best practices for using genetic algorithms in molecular discovery

Genetic algorithms (GAs) are a powerful tool to search large chemical spaces for inverse molecular design. However, GAs have multiple hyperparameters that have not been thoroughly investigated for chemical space searches. In this tutorial, we examine the general effects of a number of hyperparameters, such as population size, elitism rate, selection method, mutation rate, and convergence criteria, on key GA performance metrics. Here, we show that using a self-termination method with a minimum Spearman’s rank correlation coefficient of 0.8 between generations maintained for 50 consecutive generations along with a population size of 32, a 50% elitism rate, three-way tournament selection, and a 40% mutation rate provides the best balance of finding the overall champion, maintaining good coverage of elite targets, and improving relative speedup for general use in molecular design GAs.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Machine Learning Classical Interatomic Potentials for Molecular Dynamics from First-Principles Training Data

The ever-increasing power of modern super-computers, along with the availability of highly scalable atomistic simulation codes, has begun to revolutionize predictive modeling of materials. In particular, molecular dynamics (MD) has led to breakthrough advances in diverse fields, including tribology, catalysis, sensing, and nanoparticle self-assembly. Furthermore, recent integration of MD simulations with X-ray characterization has demonstrated promise in real-time 3-D characterization of materials on the atomic scale. The popularity of MD is driven by its applicability at disparate length/time scales, ranging from ab initio MD (hundreds of atoms and tens of picoseconds) to all-atom classical MD (millions of atoms over microseconds), and coarse-grained (CG) models (micrometers and tens of microseconds). Nevertheless, a substantial gap persists between AIMD, which is highly accurate but restricted to extremely small sizes, and those based on classical force fields (atomistic and CG) with limited accuracy but access to larger length/time scales. The accuracy and predictive power of classical MD simulations is dictated by the empirical force fields, and their capability to capture the relevant physics. Here, we discuss some of our recent work on the use of machine learning (ML) to combine the accuracy and flexibility of electronic structure calculations with the speed of classical potentials. Our ML framework attempts to bridge the significant gulf that exists between the handful of research groups that develop new interatomic potential models (often requiring several years of effort), and the increasingly large user community from academia and industry that applies these models. Our data-driven approach represents significant departure from the status quo and involves several steps including generation and manipulation of extensive training data sets through electronic structure calculations, defining novel potential functional forms, employing state-of-the-art ML algorithms to formulate highly optimized training procedures, and subsequently developing user-friendly workflow tools integrating these algorithms on high-performance computers (HPCs). Our ML approach shows marked success in developing force fields for a wide range of materials from metals, oxides, nitrides, and heterointerfaces to two-dimensional (2D) materials.

Chan, Henry↗
DOE OSTI2019

Nearly Optimal Lattice Simulation by Product Formulas

We consider simulating an n-qubit Hamiltonian with nearest-neighbor interactions evolving for time t on a quantum computer. We show that this simulation has gate complexity (nt)1+o(1) using product formulas, a straightforward approach that has been demonstrated by several experimental groups. While it is reasonable to expect this complexity—in particular, this was claimed without rigorous justification by Jordan, Lee, and Preskill—we are not aware of a straightforward proof. Furthermore, our approach is based on an analysis of the local error structure of product formulas, as introduced by Descombes and Thalhammer and significantly simplified here. We prove error bounds for canonical product formulas, which include well-known constructions such as the Lie-Trotter-Suzuki formulas. We also develop a local error representation for time-dependent Hamiltonian simulation, and we discuss generalizations to periodic boundary conditions, constant-range interactions, and higher dimensions. Combined with a previous lower bound, our result implies that product formulas can simulate lattice Hamiltonians with nearly optimal gate complexity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

State-of-the-art on research and applications of machine learning in the building life cycle

Fueled by big data, powerful and affordable computing resources, and advanced algorithms, machine learning has been explored and applied to buildings research for the past decades and has demonstrated its potential to enhance building performance. This study systematically surveyed how machine learning has been applied at different stages of building life cycle. By conducting a literature search on the Web of Knowledge platform, we found 9579 papers in this field and selected 153 papers for an in-depth review. The number of published papers is increasing year by year, with a focus on building design, operation, and control. However, no study was found using machine learning in building commissioning. There are successful pilot studies on fault detection and diagnosis of HVAC equipment and systems, load prediction, energy baseline estimate, load shape clustering, occupancy prediction, and learning occupant behaviors and energy use patterns. None of the existing studies were adopted broadly by the building industry, due to common challenges including (1) lack of large scale labeled data to train and validate the model, (2) lack of model transferability, which limits a model trained with one data-rich building to be used in another building with limited data, (3) lack of strong justification of costs and benefits of deploying machine learning, and (4) the performance might not be reliable and robust for the stated goals, as the method might work for some buildings but could not be generalized to others. Finally, findings from the study can inform future machine learning research to improve occupant comfort, energy efficiency, demand flexibility, and resilience of buildings, as well as to inspire young researchers in the field to explore multidisciplinary approaches that integrate building science, computing science, data science, and social science.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Superconducting Hyperdimensional Associative Memory Circuit for Scalable Machine Learning

Here we propose a generalized architecture for the first rapid-single-flux-quantum (RSFQ) associative memory circuit. The circuit employs hyperdimensional computing (HDC), a machine learning (ML) paradigm utilizing vectors with dimensionality in the thousands to represent information. HDC designs have small memory footprints, simple computations, and simple training algorithms compared to superconducting neural network accelerators (SNNAs), making them a better option for scalable SFQ machine learning (ML) solutions. The proposed superconducting HDC (SHDC) circuit uses entirely on-chip RSFQ memory which is tightly integrated with logic, operates at 33.3 GHz, is applicable to general ML tasks, and is manufacturable at practically useful scales given current SFQ fabrication limits. Tailored to a language recognition task, SHDC consists of ~ 2-20 M Josephson junctions (JJs) and consumes up to three times less power than an analogous CMOS HDC circuit while achieving 78-84% higher throughput. SHDC is capable of outperforming the state of the art RSFQ SNNA, SuperNPU, by 48-99% for all benchmark NN architectures tested while occupying up to 90% less area and consuming up to nine times less power. To the best of the authors' knowledge, SHDC is currently the only superconducting ML approach feasible at practically useful scales for real-world ML tasks and capable of online learning.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is #BQP-complete in the worst case. In this work, we introduce QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Asymptotic errors in adiabatic evolution

The adiabatic theorem in quantum mechanics implies that if a system is in a discrete eigenstate of a Hamiltonian and the Hamiltonian evolves in time arbitrarily slowly, the system will remain in the corresponding eigenstate of the evolved Hamiltonian. Understanding corrections to the adiabatic result that arise when the evolution of the Hamiltonian is slow—but not arbitrarily slow—has become increasingly important, especially since adiabatic evolution has been proposed as a method of state preparation in quantum computing. Here, this paper identifies two regimes, an adiabatic regime in which corrections are generically small and can depend on details of the evolution throughout the path, and a hyperadiabatic regime in which the error is given by a form similar to an asymptotic expansion in the inverse of the evolution time with the coefficients depending principally on the behavior at the endpoints. However, the error in this hyperadiabatic regime is neither given by a true asymptotic series nor solely dependent on the endpoints: the coefficients combine the contributions from both endpoints, with relative phase factors that depend on the average spectral gaps along the trajectory, multiplied by the evolution time. The central result of this paper is to identify a quantity, referred to as the typical error, which is obtained by appropriately averaging the error over evolution times that are small compared to the evolution time itself. This typical error is characterized by an asymptotic series and depends solely on the endpoints of the evolution, remaining independent of the details of the intermediate evolution.

adiabatic approximation↗
DOE OSTI2024

Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

We introduce a safe extremum-seeking (Safe ES) algorithm which achieves the minimization of an unknown objective function while ensuring that an unknown, yet measured, control barrier function (CBF) remains above an arbitrarily small negative value for all time. In other words, “practical safety” is maintained during the entire period of convergence to the constrained extremum. Our design is based on quadratic program (QP) CBF style filters for safety, which is applied in an average and estimated sense. Using nonsmooth analysis tools, we guarantee semiglobal practical asymptotic (SPA) stability of the global constrained optimum, practical convergence to the safe set if starting in a condition violating the CBF, and practical safety for all time—semiglobally—if starting in safe set. The safety result of the paper is analogous with modern notions of SPA stability, guaranteeing that, for any small violation of safety, there exist design coefficients which guarantee that such a small violation is not exceeded. The paper outlines a set of sufficient conditions on the barrier and objective functions, and by way of a Lyapunov argument, we demonstrate that nonconvex constrained optimization problems can be solved. We present these results in the setting of a static map and a dynamical system. A simulation example illustrates the results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach

Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up new ways for simulating complex dynamics of e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Scaling Limits and Generic Bounds for Exploration Processes

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. I. Explicit Methods

We develop a general algorithm for the analysis the spectral stability of generalized multistage Runge–Kutta methods of various orders of accuracy as applied to the numerical integration with respect to time of an initial-boundary-value problem for the second-order parabolic equation. The expression for the function of spectral stability is obtained in two alternative forms: on the basis of matrix relations and in the determinant form. We study specific realizations of various generalized explicit Runge–Kutta methods and their spectral stability. It is shown that all explicit generalized Runge–Kutta methods possess the property of conditional spectral stability and the property of conditional monotonicity of the numerical solution in time whose violation leads to the appearance of false oscillations of the approximate solution. The stability function for these methods is polynomial. It is shown that the application of two-stage generalized explicit Runge–Kutta methods leads to the appearance of predictor-corrector-type schemes. In the case of nonstationary one-dimensional heat-conduction problem, on the basis of a one-stage generalized Runge–Kutta method, we obtain the classical two-layer conditionally stable explicit finite-difference scheme on a four-point template. It is demonstrated that the five-stage generalized Runge–Kutta–Merson method is characterized by the weakest condition of spectral stability as compared with all investigated explicit generalized Runge–Kutta methods.

42 ENGINEERING↗
DOE OSTI2018

A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs

This paper considers the linear weighted complementarity problem (denoted by LWCP) introduced by Potra (SIAM J Optim 22:1634–1654, 2012). Based on two weighted smoothing functions, we propose a new nonmonotone smoothing algorithm for solving the LWCP and establish its global and local quadratic convergence without the strict complementarity assumption. Compared to existing nonmonotone smoothing algorithms, the proposed algorithm solves the linear system only approximately which can save the computation work when one solves large-scale LWCPs. Moreover, the nonmonotone line search technique adopted in this paper includes the usual monotone line search and some existing nonmonotone line searches as special cases. Numerical results show that our algorithm is considerably efficient for solving large-scale LWCPs.

97 MATHEMATICS AND COMPUTING↗