Search results for "Basis function"
showing 10 items of 103 documents
Learning to Approach a Moving Ball with a Simulated Two-Wheeled Robot
2006
We show how a two-wheeled robot can learn to approach a moving ball using Reinforcement Learning. The robot is controlled by setting the velocities of its two wheels. It has to reach the ball under certain conditions to be able to kick it towards a given target. In order to kick, the ball has to be in front of the robot. The robot also has to reach the ball at a certain angle in relation to the target, because the ball is always kicked in the direction from the center of the robot to the ball. The robot learns which velocity differences should be applied to the wheels: one of the wheels is set to the maximum velocity, the other one according to this difference. We apply a REINFORCE algorith…
Non-parametric spectrum cartography using adaptive radial basis functions
2017
This paper presents a framework for spectrum cartography based on the use of adaptive Gaussian radial basis functions (RBF) centered around a specific number of centroid locations, which are determined, jointly with the other RBF parameters, by the available measurement values at given sensor locations in a specific geographical area. The spectrum map is constructed non-parametrically as no prior knowledge about the transmitters is assumed. The received signal power at each location (over a given bandwidth and time period) is estimated as a weighted contribution from different RBF, in such a way that the both RBF parameters and the weights are jointly optimized using an alternating minimiza…
On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques
2020
Abstract We discuss several approaches involving the reconstruction of discontinuous one-dimensional functions using parameter-dependent multiquadric radial basis function (MQ-RBF) local interpolants combined with weighted essentially non-oscillatory (WENO) techniques, both in the computation of the locally optimized shape parameter and in the combination of RBF interpolants. We examine the accuracy of the proposed reconstruction techniques in smooth regions and their ability to avoid Gibbs phenomena close to discontinuities. In this paper, we propose a true MQ-RBF–WENO method that does not revert to the classical polynomial WENO approximation near discontinuities, as opposed to what was pr…
Exponential convergence andH-c multiquadric collocation method for partial differential equations
2003
The radial basis function (RBF) collocation method uses global shape functions to interpolate and collocatethe approximate solution of PDEs. It is a truly meshless method as compared to some of the so-calledmeshless or element-free finite element methods. For the multiquadric and Gaussian RBFs, there are twoways to make the solution converge—either by refining the mesh size
State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve.
2004
We study the nitrogen binding curve with the density matrix renormalization group (DMRG) and single-reference and multireference coupled cluster (CC) theory. Our DMRG calculations use up to 4000 states and our single-reference CC calculations include up to full connected hextuple excitations. Using the DMRG, we compute an all-electron benchmark nitrogen binding curve, at the polarized, valence double-zeta level (28 basis functions), with an estimated accuracy of 0.03mE_h. We also assess the performance of more approximate DMRG and CC theories across the nitrogen curve. We provide an analysis of the relative strengths and merits of the DMRG and CC theory under different correlation condition…
Classification and retrieval on macroinvertebrate image databases
2011
Aquatic ecosystems are continuously threatened by a growing number of human induced changes. Macroinvertebrate biomonitoring is particularly efficient in pinpointing the cause-effect structure between slow and subtle changes and their detrimental consequences in aquatic ecosystems. The greatest obstacle to implementing efficient biomonitoring is currently the cost-intensive human expert taxonomic identification of samples. While there is evidence that automated recognition techniques can match human taxa identification accuracy at greatly reduced costs, so far the development of automated identification techniques for aquatic organisms has been minimal. In this paper, we focus on advancing …
DLPNO-MP2 second derivatives for the computation of polarizabilities and NMR shieldings
2021
We present a derivation and efficient implementation of the formally complete analytic second derivatives for the domain-based local pair natural orbital second order Møller–Plesset perturbation theory (MP2) method, applicable to electric or magnetic field-response properties but not yet to harmonic frequencies. We also discuss the occurrence and avoidance of numerical instability issues related to singular linear equation systems and near linear dependences in the projected atomic orbital domains. A series of benchmark calculations on medium-sized systems is performed to assess the effect of the local approximation on calculated nuclear magnetic resonance shieldings and the static dipole …
Eulerian models of the rotating flexible wheelset for high frequency railway dynamics
2019
Abstract In this paper three formulations based on an Eulerian approach are presented to obtain the dynamic response of an elastic solid of revolution, which rotates around its main axis at constant angular velocity. The formulations are especially suitable for the study of the interaction of a solid with a non-rotating structure, such as occurs in the coupled dynamics of a railway wheelset with the track. With respect to previous publications that may adopt similar hypotheses, this paper proposes more compact formulations and eliminates certain numerical problems associated with the presence of second-order derivatives with respect to the spatial coordinates. Three different models are dev…
Parallel Calculation of CCSD and CCSD(T) Analytic First and Second Derivatives.
2007
In this paper we present a parallel adaptation of a highly efficient coupled-cluster algorithm for calculating coupled-cluster singles and doubles (CCSD) and coupled-cluster singles and doubles augmented by a perturbative treatment of triple excitations (CCSD(T)) energies, gradients, and, for the first time, analytic second derivatives. A minimal-effort strategy is outlined that leads to an amplitude-replicated, communication-minimized implementation by parallelizing the time-determining steps for CCSD and CCSD(T). The resulting algorithm is aimed at affordable cluster architectures consisting of compute nodes with sufficient memory and local disk space and that are connected by standard co…
Improved Algorithms for the Modeling of Vibrational Polyads of Polyatomic Molecules: Application toT,O, andC3Molecules
1997
Abstract Improved algorithms for the construction of rovibrational operators of polyatomic molecules are presented. Vibrationally diagonal and off-diagonal terms are obtained by a specific coupling scheme of creation and annihilation elementary operators. Recursive procedures are used to generate all possible terms and associated basis functions as well as to calculate matrix elements and commutators. Explicit formulations are given forTd,Oh, andC3vmolecules.