970,166 research outputs found
Separable Dual Space Gaussian Pseudo-potentials
We present pseudo-potential coefficients for the first two rows of the
periodic table. The pseudo potential is of a novel analytic form, that gives
optimal efficiency in numerical calculations using plane waves as basis set. At
most 7 coefficients are necessary to specify its analytic form. It is separable
and has optimal decay properties in both real and Fourier space. Because of
this property, the application of the nonlocal part of the pseudo-potential to
a wave-function can be done in an efficient way on a grid in real space. Real
space integration is much faster for large systems than ordinary multiplication
in Fourier space since it shows only quadratic scaling with respect to the size
of the system. We systematically verify the high accuracy of these
pseudo-potentials by extensive atomic and molecular test calculations.Comment: 16 pages, 4 postscript figure
Multi-objective discrete particle swarm optimisation algorithm for integrated assembly sequence planning and assembly line balancing
In assembly optimisation, assembly sequence planning and assembly line balancing have been extensively studied because both activities are directly linked with assembly efficiency that influences the final assembly costs. Both activities are categorised as NP-hard and usually performed separately. Assembly sequence planning and assembly line balancing optimisation presents a good opportunity to be integrated, considering the benefits such as larger search space that leads to better solution quality, reduces error rate in planning and speeds up time-to-market for a product. In order to optimise an integrated assembly sequence planning and assembly line balancing, this work proposes a multi-objective discrete particle swarm optimisation algorithm that used discrete procedures to update its position and velocity in finding Pareto optimal solution. A computational experiment with 51 test problems at different difficulty levels was used to test the multi-objective discrete particle swarm optimisation performance compared with the existing algorithms. A statistical test of the algorithm performance indicates that the proposed multi-objective discrete particle swarm optimisation algorithm presents significant improvement in terms of the quality of the solution set towards the Pareto optimal set
Deep Learning Applied to the Asteroseismic Modeling of Stars with Coherent Oscillation Modes
We develop a novel method based on machine learning principles to achieve
optimal initiation of CPU-intensive computations for forward asteroseismic
modeling in a multi-D parameter space. A deep neural network is trained on a
precomputed asteroseismology grid containing about 62 million coherent
oscillation-mode frequencies derived from stellar evolution models. These
models are representative of the core-hydrogen burning stage of
intermediate-mass and high-mass stars. The evolution models constitute a 6D
parameter space and their predicted low-degree pressure- and gravity-mode
oscillations are scanned, using a genetic algorithm. A software pipeline is
created to find the best fitting stellar parameters for a given set of observed
oscillation frequencies. The proposed method finds the optimal regions in the
6D parameters space in less than a minute, hence providing the optimal starting
point for further and more detailed forward asteroseismic modeling in a
high-dimensional context. We test and apply the method to seven pulsating stars
that were previously modeled asteroseismically by classical grid-based forward
modeling based on a statistic and obtain good agreement with past
results. Our deep learning methodology opens up the application of
asteroseismic modeling in +6D parameter space for thousands of stars pulsating
in coherent modes with long lifetimes observed by the space telescope
and to be discovered with the TESS and PLATO space missions, while applications
so far were done star-by-star for only a handful of cases. Our method is open
source and can be used by anyone freely.Comment: Accepted for publication in PASP Speciale Volume on Machine Learnin
Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices
Petrov-Galerkin formulations with optimal test functions allow for the
stabilization of finite element simulations. In particular, given a discrete
trial space, the optimal test space induces a numerical scheme delivering the
best approximation in terms of a problem-dependent energy norm. This ideal
approach has two shortcomings: first, we need to explicitly know the set of
optimal test functions; and second, the optimal test functions may have large
supports inducing expensive dense linear systems. Nevertheless, parametric
families of PDEs are an example where it is worth investing some (offline)
computational effort to obtain stabilized linear systems that can be solved
efficiently, for a given set of parameters, in an online stage. Therefore, as a
remedy for the first shortcoming, we explicitly compute (offline) a function
mapping any PDE-parameter, to the matrix of coefficients of optimal test
functions (in a basis expansion) associated with that PDE-parameter. Next, as a
remedy for the second shortcoming, we use the low-rank approximation to
hierarchically compress the (non-square) matrix of coefficients of optimal test
functions. In order to accelerate this process, we train a neural network to
learn a critical bottleneck of the compression algorithm (for a given set of
PDE-parameters). When solving online the resulting (compressed) Petrov-Galerkin
formulation, we employ a GMRES iterative solver with inexpensive matrix-vector
multiplications thanks to the low-rank features of the compressed matrix. We
perform experiments showing that the full online procedure as fast as the
original (unstable) Galerkin approach. In other words, we get the stabilization
with hierarchical matrices and neural networks practically for free. We
illustrate our findings by means of 2D Eriksson-Johnson and Hemholtz model
problems.Comment: 28 pages, 16 figures, 4 tables, 6 algorithm
Reduction of Real Power Loss by Improved Evolutionary Algorithm
This paper presents an Improved Evolutionary Algorithm (IEA), to solve optimal reactive power dispatch problem. In IEA objective space is disintegrated into a set of sub objective spaces by a set of route vectors. In the evolutionary procedure, each sub objective space has a solution. In such a way, the diversity of achieved solutions can be upheld. In addition, if a solution is conquered by other solutions, the solution can produce more newfangled solutions than those solutions, which makes the solution of each sub objective space converge to the optimal solutions as far as conceivable. The planned IEA has been tested in standard IEEE 30, 118 bus test systems and simulation results show clearly the improved performance of the planned algorithm in declining the real power loss. Keywords: Evolutionary Algorithm, genetic operators, optimal reactive power, Transmission loss
A Homotopy-Based Method for Optimization of Hybrid High-Low Thrust Trajectories
Space missions require increasingly more efficient trajectories to provide payload transport and mission goals by means of lowest fuel consumption, a strategic mission design key-point. Recent works demonstrated that the combined (or hybrid) use of chemical and electrical propulsion can give important advantages in terms of fuel consumption, without losing the ability to reach other mission objectives: as an example the Hohmann Spiral Transfer, applied in the case of a transfer to GEO orbit, demonstrated a fuel mass saving between 5-10% of the spacecraft wet mass, whilst satisfying a pre-set boundary constraint for the time of flight. Nevertheless, methods specifically developed for optimizing space trajectories considering the use of hybrid high-low thrust propulsion systems have not been extensively developed, basically because of the intrinsic complexity in the solution of optimal problem equations with existent numerical methods. The study undertaken and presented in this paper develops a numerical strategy for the optimization of hybrid high-low thrust space trajectories. An indirect optimization method has been developed, which makes use of a homotopic approach for numerical convergence improvement. The adoption of a homotopic approach provides a relaxation to the optimal problem, transforming it into a simplest problem to solve in which the optimal problem presents smoother equations and the shooting function acquires an increased convergence radius: the original optimal problem is then reached through a homotopy parameter continuation. Moreover, the use of homotopy can make possible to include a high thrust impulse (treated as velocity discontinuity) to the low thrust optimal control obtained from the indirect method. The impulse magnitude, location and direction are obtained following from a numerical continuation in order to minimize the problem cost function. The initial study carried out in this paper is finally correlated with particular test cases, in order to validate the work developed and to start investigating in which cases the effectiveness of hybrid-thrust propulsion subsists
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