379 research outputs found

    Stochastic quasi-Newton molecular simulations

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    Article / Letter to editorLeiden Institute of Chemistr

    X-TREAM project: Task 1b - Survey of the state-of-the-art numerical techniques for solving coupled non-linear multi-physics equations

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    Nowadays, the precise modeling of a nuclear reactor core is a challenge. This task involves several aspects, from the computational power needed to perform simulations, to the physics and analysis of the outcome. The need to better understand the physical phenomena is critical in order to quantify and qualify nuclear safety parameters. Currently, substantial research has been done in order to optimize the prediction capabilities of coupled codes. The need to better understand the multi-physics coupling between the neutronics and the thermal-hydraulics is required. In this report, state-of-the art of current methods and numerical techniques used in coupled codes are highlighted. A better understanding of the numerical schemes will allows selecting an appropriate algorithm to be implemented in POLCA-T. POLCA-T is the coupled code developed by Westinghouse that currently uses an explicit approach to couple the neutronics (POLCA7) and thermal-hydraulics (RIGEL). The final objective is to implement the concept of the Jacobian-free Newton-Krylov method, which will be used for solving the nonlinear equations which rise from the coupled solution

    Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VI) HFODD (v2.38j): a new version of the program

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    We describe the new version (v2.38j) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state-dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the D2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected two insignificant errors.Comment: 45 LaTeX pages, 4 figures, submitted to Computer Physics Communication

    New noise-tolerant neural algorithms for future dynamic nonlinear optimization with estimation on hessian matrix inversion

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    Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems

    Riemannian optimization of isometric tensor networks

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    Several tensor networks are built of isometric tensors, i.e. tensors satisfying WW=IW^\dagger W = \mathrm{I}. Prominent examples include matrix product states (MPS) in canonical form, the multiscale entanglement renormalization ansatz (MERA), and quantum circuits in general, such as those needed in state preparation and quantum variational eigensolvers. We show how gradient-based optimization methods on Riemannian manifolds can be used to optimize tensor networks of isometries to represent e.g. ground states of 1D quantum Hamiltonians. We discuss the geometry of Grassmann and Stiefel manifolds, the Riemannian manifolds of isometric tensors, and review how state-of-the-art optimization methods like nonlinear conjugate gradient and quasi-Newton algorithms can be implemented in this context. We apply these methods in the context of infinite MPS and MERA, and show benchmark results in which they outperform the best previously-known optimization methods, which are tailor-made for those specific variational classes. We also provide open-source implementations of our algorithms.Comment: 18 pages + appendices, 3 figures; v3 submission to SciPost; v4 expand preconditioning discussion and add polish, resubmit to SciPos

    Preconditioners for Krylov subspace methods: An overview

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    When simulating a mechanism from science or engineering, or an industrial process, one is frequently required to construct a mathematical model, and then resolve this model numerically. If accurate numerical solutions are necessary or desirable, this can involve solving large-scale systems of equations. One major class of solution methods is that of preconditioned iterative methods, involving preconditioners which are computationally cheap to apply while also capturing information contained in the linear system. In this article, we give a short survey of the field of preconditioning. We introduce a range of preconditioners for partial differential equations, followed by optimization problems, before discussing preconditioners constructed with less standard objectives in mind

    Stochastic quasi-Newton molecular simulations

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    Soft Matter Chemistr
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