Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Wave functions”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Reinforcement Learning Configuration Interaction

Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. Furthermore, we explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Optimization Stability in Excited-State-Specific Variational Monte Carlo

Here, we investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance.

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

The role of high-order electron correlation effects in a model system for non-valence correlation-bound anions

The diffusion Monte Carlo (DMC), auxiliary field quantum Monte Carlo (AFQMC), and equation-of-motion coupled cluster (EOM-CC) methods are used to calculate the electron binding energy (EBE) of the non-valence anion state of a model (H2O)4 cluster. Two geometries are considered, one at which the anion is unbound and the other at which it is bound in the Hartree–Fock (HF) approximation. It is demonstrated that DMC calculations can recover from the use of a HF trial wave function that has collapsed onto a discretized continuum solution, although larger EBEs are obtained when using a trial wave function for the anion that provides a more realistic description of the charge distribution and, hence, of the nodal surface. For the geometry at which the cluster has a non-valence correlation-bound anion, both the inclusion of triples in the EOM-CC method and the inclusion of supplemental diffuse d functions in the basis set are important. DMC calculations with suitable trial wave functions give EBE values in good agreement with our best estimate EOM-CC result. AFQMC using a trial wave function for the anion with a realistic electron density gives a value of the EBE nearly identical to the EOM-CC result when using the same basis set. For the geometry at which the anion is bound in the HF approximation, the inclusion of triple excitations in the EOM-CC calculations is much less important. The best estimate EOM-CC EBE value is in good agreement with the results of DMC calculations with appropriate trial wave functions.

Upadhyay, Shiv (ORCID:0000000285010501)↗
NASA NTRS1985

Molecular processes in a high temperature shock layer

The development of techniques for the calculation of electron capture widths, electronic wave functions, cross sections and rates needed for the description of the dissociative recombination (DR) of molecular ions with electrons were described. The cross sections and rates were calculated by using harmonic oscillator wave functions for the ion and a delta function approximation for the continuum vibrational wave function in the repulsive dissociative channel. In order to obtain DR cross sections of quantitative accuracy, a computer program which solves the one dimensional nuclear motion wave equation was revised to calculate the cross sections and rates. The program and the new results are described. Included is a discussion of large windows found in the dissociative recombination cross sections from excited ion vibrational levels. These windows have not been previously reported in the literature. The magnitude of the DR cross sections for several dissociative routes are sensitive to the location of the crossing of the neutral and ion potential curves. Studies of the effects of basis set and CI wave function size on vertical excitation energies are described. Preliminary studies on N2 and O2 using large scale wave functions are also reported.

Guberman, S. L.↗
DOE OSTI2021

Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Here, the complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrodinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗
NASA NTRS1961

Absolute Definition of Phase Shift in the Elastic Scattering of a Particle from Compound Systems

The projection of the target wave function on the total wave function of a scattered particle interacting with the target system is used to define an absolute phase shift including any multiples of pi. With this definition of the absolute phase shift, one can prove rigorously in the limit of zero energy for s-wave electrons scattered from atomic hydrogen that the triplet phase shift must approach a nonzero multiple of pi. One can further show that at least one pi of this phase shift is not connected with the existence of a bound state of the H- ion.

Temkin, A.↗
DOE OSTI2020

Annihilation-to-nothing: a quantum gravitational boundary condition for the Schwarzschild black hole

The interior of a static Schwarzschild metric can be written in terms of two functions, similar to some models of anisotropic cosmology. With a suitable choice of canonical variables, we solve the Wheeler-DeWitt equation (WDW) inside the horizon of a Schwarzschild black hole. By imposing classicality near the horizon, and requiring boundedness of the wave function, we get a rather generic solution of the WDW equation, whose steepest-descent solution, i.e., the ridge of the wave function, coincides nicely with the classical trajectory. However, there is an ambiguity in defining the arrow of time which leads to two possible interpretations—(i) if there is only one arrow of time, one can infer that the steepest-descent of the wave function follows the classical trajectory throughout: coming from the event horizon and going all the way down to the singularity, while (ii) if there are two different arrows of time in two separate regimes, it can be inferred that the steepest-descent of the wave function comes inwards from the event horizon in one region while it moves outwards from the singularity in the other region, and there exists an annihilation process of these two parts of the wave function inside the horizon. Additionally, adopting the second interpretation could shed light on the information loss paradox: as time goes on, probabilities for histories that include black holes and singularities decay to zero and eventually only trivial geometries dominate.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

King, H. F.↗
DOE OSTI2023

Improving materials property predictions for graph neural networks with minimal feature engineering *

Graph neural networks (GNNs) have been employed in materials research to predict physical and functional properties, and have achieved superior performance in several application domains over prior machine learning approaches. Recent studies incorporate features of increasing complexity such as Gaussian radial functions, plane wave functions, and angular terms to augment the neural network models, with the expectation that these features are critical for achieving a high performance. Here, we propose a GNN that adopts edge convolution where hidden edge features evolve during training and extensive attention mechanisms, and operates on simple graphs with atoms as nodes and distances between them as edges. As a result, the same model can be used for very different tasks as no other domain-specific features are used. With a model that uses no feature engineering, we achieve performance comparable with state-of-the-art models with elaborate features for formation energy and band gap prediction with standard benchmarks; we achieve even better performance when the dataset size increases. Although some domain-specific datasets still require hand-crafted features to achieve state-of-the-art results, our selected architecture choices greatly reduce the need for elaborate feature engineering and still maintain predictive power in comparison.

42 ENGINEERING↗
DOE OSTI2021

Short-range correlation physics at low renormalization group resolution

Recent experiments have succeeded in isolating processes for which short-range correlation (SRC) physics is dominant and well accounted for by SRC phenomenology. But an alternative and compelling picture emerges from renormalization group (RG) evolution to low RG resolution. At high RG resolution, SRCs are identified as components in the nuclear wave function with relative pair momenta greater than the Fermi momentum. Scale separation results in wave-function factorization that can be exploited with phenomenologies such as the generalized contact formalism or the low-order correlation operator approximation. Evolution to lower resolution shifts SRC physics from nuclear structure to the reaction operators without changing the measured observables. We show how the features of SRC phenomenology manifested at high RG resolution are cleanly identified at low RG resolution using simple two-body operators and local-density approximations with uncorrelated wave functions, all of which can be systematically generalized. We verify that the experimental consequences to date follow directly at low resolution from well-established properties of nucleon-nucleon interactions such as the tensor force. Thus the RG reconciles the contrasting pictures of the same experiment and shows how to get correct results using wave functions without SRC components. Finally, our demonstration has implications for the analysis of knockout reactions for which SRC physics is not cleanly isolated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1980

Electron-impact excitation of Li II in the distorted-wave approximation

The 1(1)S yields 2(3)P electron-impact-excitation cross section for Li II is calculated in the distorted-wave approximation. Two forms of the distorted-wave method are examined; in the first form both the initial and final wave functions are distorted, while in the second form only the initial wave function is distorted. In both forms a partial-wave expansion of the scattered amplitude is made, and exchange is incorporated in a consistent manner. The effects of including more than one configuration in the target-state wave function are also examined. For incident energies greater than 90 eV, distorted-wave calculations agree moderately well with recent experimental and theoretical results.

Pindzola, M. S.↗
NASA NTRS1989

A numerically exact full wave packet approach to molecule-surface scattering

A numerically exact spectral method for solving the time-dependent Schroedinger equation in spherical coordinates is described. The angular dependence of the wave function is represented on a two-dimensional grid of evenly spaced points. The fast Fourier transform algorithm is used to transform between the angle space representation of the wave function and its conjugate representation in momentum space. The time propagation of the wave function is evaluated using an expansion of the time evolution operator as a series of Chebyshev polynomials. Calculations performed for a model system representing H2 scattering from a rectangular corrugated surface yield transition probabilities that are in excellent agreement with those obtained using the close-coupling wave packet (CCWP) method. However, the new method is found to require substantially more computation time than the CCWP method because of the large number of grid points needed to represent the angular dependence of the wave function and the variation in the number of terms required in the Chebyshev representation of the time evolution operator.

Mowrey, R. C.↗
NASA NTRS1992

Resolution properties of the Fourier method for discontinuous waves

In this paper we discuss the wave-resolution properties of the Fourier approximations of a wave function with discontinuities. It is well known that a minimum of two points per wave is needed to resolve a periodic wave function using Fourier expansions. For Chebyshev approximations of a wave function, a minimum of pi points per wave is needed. Here we obtain an estimate for the minimum number of points per wave to resolve a discontinuous wave based on its Fourier coefficients. In our recent work on overcoming the Gibbs phenomenon, we have shown that the Fourier coefficients of a discontinuous function contain enough information to reconstruct with exponential accuracy the coefficient of a rapidly converging Gegenbauer expansion. We therefore study the resolution properties of a Gegenbauer expansion where both the number of terms and the order increase.

Gottlieb, David↗
NASA NTRS1993

Quantum wormholes and harmonic oscillators

The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.

Garay, Luis J.↗
DOE OSTI2025

Control-Affine Schrödinger Bridge and Generalized Bohm Potential

From a stochastic control perspective, the Schrödinger bridge is a density-valued continuous curve parameterized by time that connects a given pair of initial and terminal probability densities via minimum effort controlled Brownian motion. The control-affine Schrödinger bridge extends this idea to a generic control-affine Itô diffusion, possibly with an additive state cost. Here, in this letter, we recast the necessary conditions of optimality for the control-affine Schrödinger bridge problem as a two point boundary value problem for a quantum mechanical Schrödinger PDE with complex potential. This complex-valued potential is a generalization of the real-valued Bohm potential in quantum mechanics. Our derived potential is akin to the optical potential in nuclear physics where the real part of the potential encodes elastic scattering (transmission of wave function), and the imaginary part encodes inelastic scattering (absorption of wave function). The key takeaway is that the process noise that drives the evolution of probability densities induces an absorbing medium in the evolution of wave function. These results make new connections between control theory and non-equilibrium statistical mechanics through the lens of quantum mechanics.

Markov processes↗