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Journal articles on the topic 'Eigenvector Continuation'

Author: Grafiati

Published: 7 December 2024

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1

Drischler, C., M. Quinonez, P. G. Giuliani, A. E. Lovell, and F. M. Nunes. "Toward emulating nuclear reactions using eigenvector continuation." Physics Letters B 823 (December 2021): 136777. http://dx.doi.org/10.1016/j.physletb.2021.136777.

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2

Furnstahl, R. J., A. J. Garcia, P. J. Millican, and Xilin Zhang. "Efficient emulators for scattering using eigenvector continuation." Physics Letters B 809 (October 2020): 135719. http://dx.doi.org/10.1016/j.physletb.2020.135719.

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3

König, S., A. Ekström, K. Hebeler, D. Lee, and A. Schwenk. "Eigenvector continuation as an efficient and accurate emulator for uncertainty quantification." Physics Letters B 810 (November 2020): 135814. http://dx.doi.org/10.1016/j.physletb.2020.135814.

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4

König, S. "Efficient few-body calculations in finite volume." Journal of Physics: Conference Series 2453, no. 1 (March 1, 2023): 012025. http://dx.doi.org/10.1088/1742-6596/2453/1/012025.

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Abstract Simulating quantum systems in a finite volume is a powerful theoretical tool to extract information about them. Real-world properties of the system are encoded in how its discrete energy levels change with the size of the volume. This approach is relevant not only for nuclear physics, where lattice methods for few- and many-nucleon states complement phenomenological shell-model descriptions and ab initio calculations of atomic nuclei based on harmonic oscillator expansions, but also for other fields such as simulations of cold atomic systems. This contribution presents recent progress concerning finite-volume simulations of few-body systems. In particular, it discusses details regarding the efficient numerical implementation of separable interactions and it presents eigenvector continuation as a method for performing robust and efficient volume extrapolations.

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5

Benevieri, Pierluigi, Alessandro Calamai, Massimo Furi, and Maria Patrizia Pera. "Global Persistence of the Unit Eigenvectors of Perturbed Eigenvalue Problems in Hilbert Spaces: The Odd Multiplicity Case." Mathematics 9, no. 5 (March 6, 2021): 561. http://dx.doi.org/10.3390/math9050561.

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We study the persistence of eigenvalues and eigenvectors of perturbed eigenvalue problems in Hilbert spaces. We assume that the unperturbed problem has a nontrivial kernel of odd dimension and we prove a Rabinowitz-type global continuation result. The approach is topological, based on a notion of degree for oriented Fredholm maps of index zero between real differentiable Banach manifolds.

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6

Bi, Size, Xiaoyu Han, Jing Tian, Xiao Liang, Yang Wang, and Tinglei Huang. "Parallelization of Eigenvalue-Based Dimensional Reductions via Homotopy Continuation." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/5815429.

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This paper investigates a homotopy-based method for embedding with hundreds of thousands of data items that yields a parallel algorithm suitable for running on a distributed system. Current eigenvalue-based embedding algorithms attempt to use a sparsification of the distance matrix to approximate a low-dimensional representation when handling large-scale data sets. The main reason of taking approximation is that it is still hindered by the eigendecomposition bottleneck for high-dimensional matrices in the embedding process. In this study, a homotopy continuation algorithm is applied for improving this embedding model by parallelizing the corresponding eigendecomposition. The eigenvalue solution is converted to the operation of ordinary differential equations with initialized values, and all isolated positive eigenvalues and corresponding eigenvectors can be obtained in parallel according to predicting eigenpaths. Experiments on the real data sets show that the homotopy-based approach is potential to be implemented for millions of data sets.

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7

Arief, Ardiaty, and Muhammad Bachtiar Nappu. "Novel Hybrid Modified Modal Analysis and Continuation Power Flow Method for Unity Power Factor DER Placement." Energies 16, no. 4 (February 8, 2023): 1698. http://dx.doi.org/10.3390/en16041698.

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Distributed energy resource (DER) has become an effective attempt in promoting use of renewable energy resources for electricity generation. The core intention of this study is to expand an approach for optimally placing several DER units to attain the most stable performance of the system and the greatest power losses decrease. The recommended technique is established on two analytical methods for analyzing voltage stability: the new modified modal analysis (MMA) and the continuation power flow (CPF) or MMA–CPF methods. The MMA evaluates voltage stability by considering incremental connection relating voltage and active power, which includes the eigenvalue and the related eigenvectors computed from the reduced modified Jacobian matrix. Furthermore, an active participation factor (APF) is computed from the eigenvectors of the reduced modified Jacobian matrix. The CPF method uses a predictor–corrector stepping pattern to reach the solution track and compute the tangent vector sensitivity (TVS). Both APF and TVS indicate each load bus sensitivity in the network. In addition, an objective function regarding losses decrease and eigenvalue is expressed to calculate the best bus position for DER allocation. The proposed MMA–CPF technique has been assessed on a 34-bus RDN and the outcomes demonstrate the effectiveness of the proposed scheme.

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8

Kosloff, Dan, and David Kessler. "Accurate depth migration by a generalized phase‐shift method." GEOPHYSICS 52, no. 8 (August 1987): 1074–84. http://dx.doi.org/10.1190/1.1442373.

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A new depth migration method derived in the space‐frequency domain is based on a generalized phase‐shift method for the downward continuation of surface data. For a laterally variable velocity structure, the Fourier spatial components are no longer eigenvectors of the wave equation, and therefore a rigorous application of the phase‐shift method would seem to require finding the eigenvectors by a matrix diagonalization at every depth step. However, a recently derived expansion technique enables phase‐shift accuracy to be obtained without resorting to a costly matrix diagonalization. The new technique is applied to the migration of zero‐offset time sections. As with the laterally uniform velocity case, the evanescent components of the solution need to be isolated and eliminated, in this case by the application of a spatially variant high‐cut filter. Tests performed on the new method show that it is more accurate and efficient than standard integration techniques such as the Runge‐Kutta method or the Taylor method.

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9

Leble, Sergey, Sergey Vereshchagin, Nataliya V. Bakhmetieva, and Gennadiy I. Grigoriev. "Study of a Gas Disturbance Mode Content Based on the Measurement of Atmospheric Parameters at the Heights of the Mesosphere and Lower Thermosphere." Atmosphere 12, no. 9 (August 31, 2021): 1123. http://dx.doi.org/10.3390/atmos12091123.

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The main result of this work is the estimation of the entropy mode accompanying a wave disturbance, observed at the atmosphere heights range of 90–120 km. The study is the direct continuation and development of recent results on diagnosis of the acoustic wave with the separation on direction of propagation. The estimation of the entropy mode contribution relies upon the measurements of the three dynamic variables (the temperature, density, and vertical velocity perturbations) of the neutral atmosphere measured by the method of the resonant scattering of radio waves on the artificial periodic irregularities of the ionospheric plasma. The measurement of the atmosphere dynamic parameters was carried out on the SURA heating facility. The mathematical foundation of the mode separation algorithm is based on the dynamic projection operators technique. The operators are constructed via the eigenvectors of the coordinate evolution operator of the transformed system of balance equations of the hydro-thermodynamics.

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10

Wang, Xu, and Peter Schiavone. "Green’s functions for an anisotropic half-space and bimaterial incorporating anisotropic surface elasticity and surface van der Waals forces." Mathematics and Mechanics of Solids 22, no. 3 (August 6, 2016): 557–72. http://dx.doi.org/10.1177/1081286515598826.

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In this paper we derive explicit expressions for the Green’s functions in the case of an anisotropic elastic half-space and bimaterial subjected to a line force and a line dislocation. In contrast to previous studies in this area, our analysis includes the contributions of both anisotropic surface elasticity and surface van der Waals interaction forces. By means of the Stroh sextic formalism, analytical continuation and the state-space approach, the corresponding boundary value problem is reduced to a system of six (for a half-space) or 12 (for a bimaterial) coupled first-order differential equations. By employing the orthogonality relations among the corresponding eigenvectors, the coupled system of differential equations is further decoupled to six (for a half-space) or 12 (for a bimaterial) independent first-order differential equations. The latter is solved analytically using exponential integrals. In addition, we identify four and seven non-zero intrinsic material lengths for a half-space and a bimaterial, respectively, due entirely to the incorporation of the surface elasticity and surface van der Waal forces. We prove that these material lengths can be only either real and positive or complex conjugates with positive real parts.

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11

Yoshida, Sota, and Noritaka Shimizu. "Constructing approximate shell-model wavefunctions by eigenvector continuation." Progress of Theoretical and Experimental Physics, April 13, 2022. http://dx.doi.org/10.1093/ptep/ptac057.

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Abstract Shell-model calculations play a key role in elucidating various properties of nuclei. In general, those studies require a huge number of calculations to be repeated for parameter calibration and quantifying uncertainties. To reduce the computational burden, we propose a new workflow of shell-model calculations using a method called eigenvector continuation (EC). It enables us to efficiently approximate the eigenpairs under a given Hamiltonian by previously sampled eigenvectors. We demonstrate the validity of EC as an emulator of the valence shell-model, including first application of EC to electromagnetic transition matrix elements. Furthermore, we propose a new usage of EC: preprocessing, in which we start the Lanczos iterations from the approximate eigenvectors, and demonstrate that this can accelerate subsequent research cycles. With the aid of the EC, the eigenvectors obtained during the parameter optimization are not necessarily to be discarded, even if their eigenvalues are far from the experimental data. Those eigenvectors can become accumulated knowledge.

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12

Sarkar, Avik, and Dean Lee. "Convergence of Eigenvector Continuation." Physical Review Letters 126, no. 3 (January 21, 2021). http://dx.doi.org/10.1103/physrevlett.126.032501.

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13

Yapa, Nuwan, and Sebastian König. "Volume extrapolation via eigenvector continuation." Physical Review C 106, no. 1 (July 18, 2022). http://dx.doi.org/10.1103/physrevc.106.014309.

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14

Frame, Dillon, Rongzheng He, Ilse Ipsen, Daniel Lee, Dean Lee, and Ermal Rrapaj. "Eigenvector Continuation with Subspace Learning." Physical Review Letters 121, no. 3 (July 17, 2018). http://dx.doi.org/10.1103/physrevlett.121.032501.

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15

Sarkar, Avik, and Dean Lee. "Self-learning emulators and eigenvector continuation." Physical Review Research 4, no. 2 (June 15, 2022). http://dx.doi.org/10.1103/physrevresearch.4.023214.

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16

Mejuto-Zaera, Carlos, and Alexander F. Kemper. "Quantum Eigenvector Continuation for Chemistry Applications." Electronic Structure, October 9, 2023. http://dx.doi.org/10.1088/2516-1075/ad018f.

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Abstract A typical task for classical and quantum computing in chemistry is finding a potential energy surface (PES) along a reaction coordinate, which involves solving the quantum chemistry problem for many points along the reaction path. Developing algorithms to accomplish this task on quantum computers has been an active area of development, yet finding all the relevant eigenstates along the reaction coordinate remains a difficult problem, and determining PESs is thus a costly proposal. In this paper, we demonstrate the use of a eigenvector continuation --- a subspace expansion that uses a few eigenstates as a basis --- as a tool for rapidly exploring potential energy surfaces. We apply this to determining the binding PES or torsion PES for several molecules of varying complexity. In all cases, we show that the PES can be captured using relatively few basis states; suggesting that a significant amount of (quantum) computational effort can be saved by making use of already calculated ground states in this manner.

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17

Companys Franzke, M., A. Tichai, K. Hebeler, and A. Schwenk. "Eigenvector continuation for the pairing Hamiltonian." Physical Review C 109, no. 2 (February 13, 2024). http://dx.doi.org/10.1103/physrevc.109.024311.

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18

Demol, P., T. Duguet, A. Ekström, M. Frosini, K. Hebeler, S. König, D. Lee, A. Schwenk, V. Somà, and A. Tichai. "Improved many-body expansions from eigenvector continuation." Physical Review C 101, no. 4 (April 9, 2020). http://dx.doi.org/10.1103/physrevc.101.041302.

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19

Companys Franzke, M., A. Tichai, K. Hebeler, and A. Schwenk. "Excited states from eigenvector continuation: The anharmonic oscillator." Physics Letters B, April 2022, 137101. http://dx.doi.org/10.1016/j.physletb.2022.137101.

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20

Surján, Péter R., and Ágnes Szabados. "Comment on “Improved many-body expansions from eigenvector continuation”." Physical Review C 103, no. 6 (June 28, 2021). http://dx.doi.org/10.1103/physrevc.103.069801.

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21

Yapa, Nuwan, Kévin Fossez, and Sebastian König. "Eigenvector continuation for emulating and extrapolating two-body resonances." Physical Review C 107, no. 6 (June 26, 2023). http://dx.doi.org/10.1103/physrevc.107.064316.

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22

Duguet, Thomas, Andreas Ekström, Richard J. Furnstahl, Sebastian König, and Dean Lee. "Colloquium: Eigenvector continuation and projection-based emulators." Reviews of Modern Physics 96, no. 3 (August 14, 2024). http://dx.doi.org/10.1103/revmodphys.96.031002.

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23

Atalar, Kemal, Yannic Rath, Rachel Crespo-Otero, and George Booth. "Fast and accurate nonadiabatic molecular dynamics enabled through variational interpolation of correlated electron wavefunctions." Faraday Discussions, 2024. http://dx.doi.org/10.1039/d4fd00062e.

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We build on the concept of eigenvector continuation to develop an efficient multi-state method for the rigorous and smooth interpolation of a small training set of many-body wavefunctions through chemical...

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24

Djärv, T., A. Ekström, C. Forssén, and H. T. Johansson. "Bayesian predictions for A=6 nuclei using eigenvector continuation emulators." Physical Review C 105, no. 1 (January 26, 2022). http://dx.doi.org/10.1103/physrevc.105.014005.

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25

Bai, Dong, and Zhongzhou Ren. "Generalizing the calculable R -matrix theory and eigenvector continuation to the incoming-wave boundary condition." Physical Review C 103, no. 1 (January 25, 2021). http://dx.doi.org/10.1103/physrevc.103.014612.

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26

Luo, Q. Y., X. Zhang, L. H. Chen, and J. M. Yao. "Emulating the generator coordinate method with extended eigenvector continuation for the Lipkin-Meshkov-Glick model." Physical Review C 110, no. 1 (July 2, 2024). http://dx.doi.org/10.1103/physrevc.110.014309.

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27

Bai, Dong. "New extensions of eigenvector continuation R -matrix theory based on analyticity in momentum and angular momentum." Physical Review C 106, no. 2 (August 18, 2022). http://dx.doi.org/10.1103/physrevc.106.024611.

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28

Melendez, Jordan Andrew, Christian Drischler, Richard Furnstahl, Alberto Garcia, and Xilin Zhang. "Model reduction methods for nuclear emulators." Journal of Physics G: Nuclear and Particle Physics, July 25, 2022. http://dx.doi.org/10.1088/1361-6471/ac83dd.

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Abstract The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR methods for the creation of fast & accurate emulators of memory- and compute-intensive nuclear systems, focusing on eigen-emulators and variational emulators. As an example, we describe how "eigenvector continuation'' is a special case of a much more general and well-studied MOR formalism for parameterized systems. We continue with an introduction to the Ritz and Galerkin projection methods that underpin many such emulators, while pointing to the relevant MOR theory and its successful applications along the way. We believe that this will open the door to broader applications in nuclear physics and facilitate communication with practitioners in other fields.

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29

Schrader, Simon Elias, and Simen Kvaal. "Accelerated coupled cluster calculations with Procrustes orbital interpolation." Journal of Chemical Physics, February 27, 2023. http://dx.doi.org/10.1063/5.0141145.

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The coupled cluster method is considered a gold standard in quantum chemistry, reliably giving energies that are exact within chemical accuracy (1.6 mHartree). However, even in the CCSD approximation, where the cluster operator is truncated to include only single and double excitations, the method scales as O(N6) in the number of electrons, and the cluster operator needs to be solved for iteratively, increasing computation time. Inspired by eigenvector continuation, we present here an algorithm making use of Gaussian processes that provides an improved initial guess for the coupled cluster amplitudes. The cluster operator is written as a linear combination of sample cluster operators which are obtained at particular sample geometries. By reusing the cluster operators from previous calculations in that way, it is possible to obtain a start guess for the amplitudes that surpasses both MP2-guesses and "previous geometry"-guesses in terms of the number of necessary iterations. As this improved guess is very close to the exact cluster operator, it can be used directly to calculate the CCSD energy to chemical accuracy, giving approximate CCSD energies scaling as O(N5).

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30

Becker, K. S., K. D. Launey, A. Ekström, and T. Dytrych. "Ab initio symmetry-adapted emulator for studying emergent collectivity and clustering in nuclei." Frontiers in Physics 11 (March 1, 2023). http://dx.doi.org/10.3389/fphy.2023.1064601.

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We discuss emulators from the ab initio symmetry-adapted no-core shell-model framework for studying the formation of alpha clustering and collective properties without effective charges. We present a new type of an emulator, one that utilizes the eigenvector continuation technique but is based on the use of symplectic symmetry considerations. This is achieved by using physically relevant degrees of freedom, namely, the symmetry-adapted basis, which exploits the almost perfect symplectic symmetry in nuclei. Specifically, we study excitation energies, point-proton root-mean-square radii, along with electric quadrupole moments and transitions for 6Li and 12C. We show that the set of parameterizations of the chiral potential used to train the emulators has no significant effect on predictions of dominant nuclear features, such as shape and the associated symplectic symmetry, along with cluster formation, but slightly varies details that affect collective quadrupole moments, asymptotic normalization coefficients, and alpha partial widths up to a factor of two. This makes these types of emulators important for further constraining the nuclear force for high-precision nuclear structure and reaction observables.

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31

Svensson, Isak, Andreas Ekström, and Christian Forssén. "Inference of the low-energy constants in Δ -full chiral effective field theory including a correlated truncation error." Physical Review C 109, no. 6 (June 18, 2024). http://dx.doi.org/10.1103/physrevc.109.064003.

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We sample the posterior probability distributions of the low-energy constants (LECs) in Δ-full chiral effective field theory (χEFT) up to third order. We use eigenvector continuation for fast and accurate emulation of the likelihood and Hamiltonian Monte Carlo to draw effectively independent samples from the posteriors. Our Bayesian inference is conditioned on the Granada database of neutron-proton (np) cross sections and polarizations. We use priors grounded in χEFT assumptions and a Roy-Steiner analysis of pion-nucleon scattering data. We model correlated EFT truncation errors using a two-feature Gaussian process, and find correlation lengths for np scattering energies and angles in the ranges 45–83 MeV and 24–39 degrees, respectively. These correlations yield a nondiagonal covariance matrix and reduce the number of independent scattering data with factors of 8 and 4 at the second and third chiral orders, respectively. The relatively small difference between the second- and third-order predictions in Δ-full χEFT suppresses the marginal variance of the truncation error and the effects of its correlation structure. Our results are particularly important for analyzing the predictive capabilities in nuclear theory. Published by the American Physical Society 2024

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32

Benevieri, Pierluigi, Alessandro Calamai, Massimo Furi, and Maria Patrizia Pera. "Global continuation in Euclidean spaces of the perturbed unit eigenvectors corresponding to a simple eigenvalue." Topological Methods in Nonlinear Analysis, March 7, 2020, 1. http://dx.doi.org/10.12775/tmna.2019.093.

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33

Haller, George, Bálint Kaszás, Aihui Liu, and Joar Axås. "Nonlinear model reduction to fractional and mixed-mode spectral submanifolds." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 6 (June 1, 2023). http://dx.doi.org/10.1063/5.0143936.

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A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace E of a dynamical system linearized at a fixed point. Passing from the full nonlinear dynamics to the flow on an attracting primary SSM provides a mathematically precise reduction of the full system dynamics to a very low-dimensional, smooth model in polynomial form. A limitation of this model reduction approach has been, however, that the spectral subspace yielding the SSM must be spanned by eigenvectors of the same stability type. A further limitation has been that in some problems, the nonlinear behavior of interest may be far away from the smoothest nonlinear continuation of the invariant subspace E. Here, we remove both of these limitations by constructing a significantly extended class of SSMs that also contains invariant manifolds with mixed internal stability types and of lower smoothness class arising from fractional powers in their parametrization. We show on examples how fractional and mixed-mode SSMs extend the power of data-driven SSM reduction to transitions in shear flows, dynamic buckling of beams, and periodically forced nonlinear oscillatory systems. More generally, our results reveal the general function library that should be used beyond integer-powered polynomials in fitting nonlinear reduced-order models to data.

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34

Hegde, Shreyas S., Jonathan Inge, and Robert Kielb. "Effect of System Mode and Structural Damping Perturbation On the Mistuned Forced Response and Aerodynamic Damping of Embedded Compressor Rotors." Journal of Engineering for Gas Turbines and Power, September 29, 2022. http://dx.doi.org/10.1115/1.4055832.

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Abstract This paper is a continuation of previous papers by the authors that focuses on predicting the mistuned embedded rotor blade forced response. The compressor under consideration is a part of a 3.5stage rig located at Purdue University. Previously, the current authors have discussed the impact of sideband travelling wave forcing functions on the mistuned response and pinned down the reason for a constant underprediction in the amplification factor. This prompted further research to determine the sensitivity of the response to a known change in the system mode. In the first section of the current paper, the authors perturb the system modes frequencies in a probabilistic manner and compute the influence of the system mode on the mistuning amplification factor. The second part of this study involves determining the impact of a perturbation in the structural damping on the mistuned response. Finally, a brief investigation of system eigenvalues and eigenvectors is conducted to understand the impact of mistuning on aerodynamic damping suppression. The key conclusions from this paper are: 1) The mistuned forced response was highly sensitive to the system mode input. 2) Since the aerodynamic damping dominates in the case study, a change in the structural damping parameter has minimal effect on the mistuning amplification factor. 3) The results of the flutter analysis show that a perturbation in the system mode frequency stabilizes the system much faster than a perturbation in the structural damping .

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