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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Backpropagation-based learning with local derivative approximation and memory replay in biologically plausible neural systems

When learning, the brain modifies individual synaptic connections to reach a desired behavior. Animal and human brains have been shown to be incredibly capable of learning complex and varied functions across a wide variety of tasks. In recent years, artificial neural networks, inspired by human and animal brains, have shown great capabilities in learning a wide variety of difficult tasks. However, artificial neural networks primarily teach themselves through the use of backpropagation, a learning method which has no clear analogue within the brain. Additionally, Artificial Neural Networks primarily use continuous activation functions, which differ significantly from the spiking neuronal behavior present in the brain. In this paper, we discuss and demonstrate a biologically plausible learning method that approximates backpropagation through two techniques on Spiking Neural Networks. First, we show that the local temporal derivatives that are necessary for backpropagation can be approximately recovered through reconstruction using spike timings. Second, we show that through learning during a sleep phase, inspired by neuroscience research into memory replay, the localized parallel feedback path can learn to approximate the derivative through the forward path weight matrix, thus solving the weight transport problem. Lastly, we demonstrate that the combination of these two methods can approach or exceed the accuracy of backpropagation-based methods for a variety of neuromorphic vision tasks while maintaining biological plausibility.

42 ENGINEERING↗
DOE OSTI2023

Non-adiabatic approximations in time-dependent density functional theory: progress and prospects

Time-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the calculations is limited by the available approximations for the exchange-correlation functional. In particular, it is known that the exact exchange-correlation functional has memory-dependence, but in practise adiabatic approximations are used which ignore this. Here we review the development of non-adiabatic functional approximations, their impact on calculations, and challenges in developing practical and accurate memory-dependent functionals for general purposes.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Relaxation time approximations in PAOFLOW 2.0

Abstract Regardless of its success, the constant relaxation time approximation has limited validity. Temperature and energy dependent effects are important to match experimental trends even in simple situations. We present the implementation of relaxation time approximation models in the calculation of Boltzmann transport in 2.0 and apply those to model band-structures. In addition, using a self-consistent fitting of the model parameters to experimental conductivity data, we provide a flexible tool to extract scattering rates with high accuracy. We illustrate the approximations using simple models and then apply the method to GaAs, Si, $$\hbox {Mg}_3\hbox {Sb}_2$$ Mg 3 Sb 2 , and $$\hbox {CoSb}_3$$ CoSb 3 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Charge transfer rate constants for the carotenoid-porphyrin-C 60 molecular triad dissolved in tetrahydrofuran: The spin-boson model vs the linearized semiclassical approximation

Charge transfer rate constants were calculated for the carotenoid-porphyrin-C 60 (CPC 60 ) molecular triad dissolved in explicit tetrahydrofuran. The calculation was based on mapping the all-atom anharmonic Hamiltonian of this system onto the spin-boson Hamiltonian. The mapping was based on discretizing the spectral density from the time correlation function of the donor–acceptor potential energy gap, as obtained from all-atom molecular dynamics simulations. Different spin-boson Hamiltonians were constructed for each of the possible transitions between the three excited electronic states in two different triad conformations. The rate constants of three possible transitions were calculated via the quantum-mechanically exact Fermi’s golden rule (FGR), as well as a progression of more approximate expressions that lead to the classical Marcus expression. The advantage of the spin-boson approach is that once the mapping is established, the quantum-mechanically exact FGR and the hierarchy of approximations are known in closed form. The classical Marcus charge transfer rate constants obtained with the spin-boson Hamiltonians were found to reproduce those obtained from all-atom simulations with the linearized semiclassical approximation, thereby confirming the equivalence of the two approaches for this system. Furthermore, within the spin-boson Hamiltonian, we also found that the quantum-mechanically exact FGR rate constants were significantly enhanced compared to the classical Marcus theory rate constants for two out of three transitions in one of the two conformations under consideration. The results confirm that mapping to the spin-boson model can yield accurate predictions for charge transfer rate constants in a system as complex as CPC 60 dissolved in tetrahydrofuran.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A windowed mean trajectory approximation for condensed phase dynamics

We propose a trajectory-based quasi-classical method for approximating dynamics in condensed phase systems. Building upon the previously developed optimized mean trajectory approximation that has been used to compute linear and nonlinear spectra, we borrow some ideas from filtering trajectory methods to obtain a novel semiclassical method for the dynamical propagation of density matrices. This new approximation is tested rigorously against standard multistate electronic models, spin-boson models, and models of the Fenna–Matthews–Olson complex. For dissipative systems, the current method is significantly better or as good as many other semiclassical methods available, especially at low temperatures and for off-diagonal density matrix elements, whereas for scattering models, the current method bears similar limitations as mean-field propagation schemes. All results are tested against the numerically exact hierarchical equations of motion method. In conclusion, the new method shows excellent agreement across various parameter regimes with numerically exact results, highlighting the robustness and accuracy of our approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Exact sum rules with approximate ground states

Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One alternative is through transition sum rules, in particular the non-energy-weighted and energy-weighted sum rules, which can be computed as expectation values of operators. We investigate by computing sum rules for a variety of nuclei, comparing the numerically exact full configuration-interaction shell model, as a reference, to Hartree-Fock, projected Hartree-Fock, and the nucleon pair approximation. Furthermore, these approximations yield reasonable agreement, which we explain by prior work on the systematics of transition moments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

We present a simple analytic approximation for the covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction two-point correlation functions. This cross-covariance is essential for joint analyses that combine full-shape clustering information with baryon acoustic oscillation (BAO) measurements, as commonly performed in modern spectroscopic surveys. Our model builds on the disconnected contribution to the covariance and accounts for the damping of correlations due to the BAO reconstruction process. We validate our analytic prescription against numerical simulations from the Dark Energy Spectroscopic Instrument (DESI), testing both idealized cubic geometries and realistic survey configurations including complex footprints and fiber assignment effects. Despite neglecting survey window functions in the analytic calculation, we find excellent agreement with simulation-based covariances and demonstrate that cosmological parameter constraints are virtually unchanged when using our approximation. Our results show that the pre-post cross-covariance is sufficiently small that even approximate treatments are adequate for cosmological inference, opening a pathway toward fully analytic covariance matrices for next-generation galaxy surveys.

baryon acoustic oscillations↗
DOE OSTI2020

Validity of the static-exchange approximation for inner-shell photoionization of polyatomic molecules

The simple single-channel static-exchange approximation completely ignores correlation between the continuum and molecular ion electrons. In molecular systems with symmetry equivalent atoms, the single-channel approximation can seriously fail in core ionization when using delocalized orbitals to represent the core hole states. We present cross sections and molecular frame photoelectron angular distributions with both localized and delocalized core orbitals in CF 4 F (1 s ) ionization. We show that only a full coupled-channel calculation can recover an accurate description of the physics of inner-shell photoionization when using delocalized orbitals, whereas nearly the same result can be obtained from independent single-channel static-exchange calculations when localized core orbitals are used. A grid-based variational method described here makes such single-channel calculations possible on larger systems without local-exchange approximations. Illustrative calculations on the core ionization of SF 6 are presented to illustrate the power of the grid-based method.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Loschmidt-echo approach to error estimation in Krylov-subspace approximation

The Krylov subspace method is a traditional approach to approximate quantum evolution, allowing us to treat systems with large Hilbert spaces. Despite its popularity, current bounds typically overestimate the error, which translates into more expensive simulation routines. Here, in this paper, we tackle this problem by realizing that the error can be understood as a Loschmidt echo in a one-dimensional (1D) noninteracting tight-binding Hamiltonian. We show that the different time regimes of the approximation can be understood using simple physical ideas. More importantly, we obtain computationally cheap error bounds that describe with high precision the actual error in the approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Modeling noise in global Mølmer-Sørensen interactions applied to quantum approximate optimization

Many-qubit Mølmer-Sørensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parametrizes these errors from simple experimental measurements, without free parameters. Herein, we validate the model in comparison with experiments that implement sequences of MS interactions on two 171 Yb + ions. The model shows reasonable agreement after several MS interactions as quantified by the reduced chi-squared statistic $χ^{2}_{red}$≈2. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are 91% and 83% of the optimal theoretical values. Our model predicts $0.93^{+0.03}_{-0.02}$ and $0.95^{+0.04}_{-0.03}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations, the model achieves approximation ratios that are 99% of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Success and breakdown of the T-matrix approximation for phonon-disorder scattering

Here, we examine the validity of the widely used T-matrix approximation for treating phonon-disorder scattering by implementing an unfolding algorithm that allows simulation of disorder up to tens of millions of atoms. The T-matrix approximation breaks down for low-energy flexure phonons that play an important role in thermal transport in two-dimensional materials. Furthermore, insights are developed into the success of the T-matrix approximation in describing maximally mass disordered systems. To achieve this, the phonon unfolding formalism is generalized to describe mass disorder and strongly nonperturbative features of the spectrum are connected to the Boltzmann quasiparticle picture.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Formation energy puzzle in intermetallic alloys: Random phase approximation fails to predict accurate formation energies

We performed density functional calculations to estimate the formation energies of intermetallic alloys. We used two semilocal approximations, the generalized gradient approximation (GGA) by Perdew-Burke- Ernzerhof (PBE) and the strongly constrained and appropriately normed (SCAN) meta-GGA. In addition, we utilized two nonlocal DFT functionals, the hybrid HSE06, and the state-of-the-art random phase approximation (RPA). The nonlocal functionals such as HSE06 and RPA yield accurate formation energies of binary alloys with completely-filled d-band metals, where semilocal functionals underperform. The accuracy at the nonlocal functionals is greatly reduced when a partially-filled d-band metal is present in an alloy, while PBE-GGA outperforms in these cases. We show that the accurate prediction of formation energies by any DFT method depends on its ability to predict the accurate electronic properties, e.g., valence d-band contribution to the density of states (DOS). The SCAN meta-GGA often corrects the PBE-DOS, however, it does not provide accurate formation energies compared to PBE. This is assumed to be due to the lack of proper error cancellation that should be expected due to the similar bulk nature of both alloys and their constituents, which may improve with the modification of meta-GGA ingredients. RPA yields too negative formation energies of alloys with partially-filled d-band metals. RPA results can be corrected by restoring the exchange-correlation kernel, thereby improving the short-range electron-electron correlation in metallic densities.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Twisted bilayer graphene. I. Matrix elements, approximations, perturbation theory, and a k · p two-band model

We investigate the twisted bilayer graphene (TBG) model of Bistritzer and MacDonald (BM) [Bistritzer and MacDonald, Proc. Natl. Acad. Sci. 108, 12233 (2011)] to obtain an analytic understanding of its energetics and wave functions needed for many-body calculations. We provide an approximation scheme for the wave functions of the BM model, which first elucidates why the BM K M -point centered original calculation containing only four plane waves provides a good analytical value for the first magic angle (θ M ≈ 1°). The approximation scheme also elucidates why most of the many-body matrix elements in the Coulomb Hamiltonian projected to the active bands can be neglected. By applying our approximation scheme at the first magic angle to a Γ M -point centered model of six plane waves, we analytically understand the reason for the small Γ M -point gap between the active and passive bands in the isotropic limit w 0 = w 1 . Furthermore, we analytically calculate the group velocities of the passive bands in the isotropic limit, and show that they are almost doubly degenerate, even away from the Γ M point, where no symmetry forces them to be. Furthermore, moving away from the Γ M and K M points, we provide an explicit analytical perturbative understanding as to why the TBG bands are flat at the first magic angle, despite the first magic angle is defined by only requiring a vanishing K M -point Dirac velocity. We derive analytically a connected “magic manifold” w 1 = $2\sqrt{1 + w^{2}_{0}}$ $-\sqrt{2 + 3w^2_0}$, on which the bands remain extremely flat as w 0 is tuned between the isotropic (w 0 = w 1 ) and chiral (w 0 = 0) limits. We analytically show why going away from the isotropic limit by making w 0 less (but not larger) than w 1 increases the Γ M -point gap between the active and the passive bands. Finally, by perturbation theory, we provide an analytic Γ M point k ∙ p two-band model that reproduces the TBG band structure and eigenstates within a certain w 0 , w 1 parameter range. Further refinement of this model are discussed, which suggest a possible faithful representation of the TBG bands by a two-band Γ M point k ∙ p model in the full w 0 , w 1 parameter range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Dynamical vertex approximation for many-electron systems with spontaneously broken SU(2) symmetry

We generalize the formalism of the dynamical vertex approximation (DΓA)—a diagrammatic extension of the dynamical mean-field theory (DMFT)—to treat magnetically ordered phases. To this aim, we start by concisely illustrating the many-electron formalism for performing ladder resummations of Feynman diagrams in systems with broken SU(2) symmetry associated to ferromagnetic (FM) or antiferromagnetic (AF) order. We then analyze the algorithmic simplifications introduced by taking the local approximation of the two-particle irreducible vertex functions in the Bethe-Salpeter equations, which defines the ladder implementation of DΓA for magnetic systems. The relation of this assumption with the DMFT limit of large coordination-number/high dimensions is explicitly discussed. As a last step, we derive the expression for the ladder DΓA self-energy in the FM- and AF-ordered phases of the Hubbard model. The physics emerging in the AF-ordered case is explicitly illustrated by means of approximated calculations based on a static mean-field input for DΓA equations. The results obtained capture fundamental aspects of both metallic and insulating ground states of two-dimensional antiferromagnets, providing a reliable compass for future, more extensive applications of our approach. Furthermore, possible routes to further develop diagrammatic-based treatments of magnetic phases in correlated electron systems are briefly outlined in the Conclusions.

2-dimensional systems↗
DOE OSTI2022

Generalized quasiharmonic approximation via space group irreducible derivatives

The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature-dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. In this work we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second-order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate our approach by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (ThO 2 ) using density functional theory with three exchange-correlation functionals. The QHA results are compared to our measurements of the elastic constant tensor using time-domain Brillouin scattering and inelastic neutron scattering. Our irreducible derivative approach simplifies the implementation of the generalized QHA, which will facilitate reproducible, data-driven applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Power Flow Geometry and Approximation

Here, the power flow equations are important in numerous power systems problems of practical interest which consider alternating current power flow (ACPF) physics. Perhaps the most well studied being the alternating current optimal power flow problem (ACOPF), seeking to optimize the operation of an electric power system. Due to their non-linearity, problems which include the power flow equations are typically challenging, particularly in optimization. Interestingly, the set of solutions to the power flow equations forms a smooth manifold. As a result, differential geometry can be used to describe and analyze this set of equations. This approach has proven effective in several engineering applications (e.g., solving ACOPF and analyzing the solution space boundary). Central to the success of this approach is an understanding of the power flow manifold's geometry. In this work, we develop the geometric and topological properties of this manifold using concepts from differential geometry. After demonstrating the convenience of this manifold's representation as a function's graph, computational methods are emphasized: we develop retractions, error bounds for linear approximation, and formulas for evaluating the Riemannian metric (including associated objects such as geodesics and the curvature tensor). Scalar curvature and the second fundamental form play a new role in quantifying the quality of linear approximations, like the popular direct current approximation. All functions are implemented in Julia and available in an online repository. Proofs are included for completeness.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Fast increased fidelity samplers for approximate Bayesian Gaussian process regression

Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H-matrix approximations that scales at O(n log 2 n). We show that this approximation’s Kullback-Leibler divergence to the true posterior can be made arbitrarily small. Though multidimensional GPs could be used with our algorithm, d-dimensional surfaces are modeled as tensor products of univariate GPs to minimize the cost of matrix construction and maximize computational efficiency. We illustrate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and non-synthetic data sets

97 MATHEMATICS AND COMPUTING↗