Search results for " approximation"
showing 10 items of 575 documents
Learning Structures in Earth Observation Data with Gaussian Processes
2020
Gaussian Processes (GPs) has experienced tremendous success in geoscience in general and for bio-geophysical parameter retrieval in the last years. GPs constitute a solid Bayesian framework to formulate many function approximation problems consistently. This paper reviews the main theoretical GP developments in the field. We review new algorithms that respect the signal and noise characteristics, that provide feature rankings automatically, and that allow applicability of associated uncertainty intervals to transport GP models in space and time. All these developments are illustrated in the field of geoscience and remote sensing at a local and global scales through a set of illustrative exa…
Bayesian Unification of Gradient and Bandit-based Learning for Accelerated Global Optimisation
2017
Bandit based optimisation has a remarkable advantage over gradient based approaches due to their global perspective, which eliminates the danger of getting stuck at local optima. However, for continuous optimisation problems or problems with a large number of actions, bandit based approaches can be hindered by slow learning. Gradient based approaches, on the other hand, navigate quickly in high-dimensional continuous spaces through local optimisation, following the gradient in fine grained steps. Yet, apart from being susceptible to local optima, these schemes are less suited for online learning due to their reliance on extensive trial-and-error before the optimum can be identified. In this…
Bayesian Analysis of Population Health Data
2021
The analysis of population-wide datasets can provide insight on the health status of large populations so that public health officials can make data-driven decisions. The analysis of such datasets often requires highly parameterized models with different types of fixed and random effects to account for risk factors, spatial and temporal variations, multilevel effects and other sources on uncertainty. To illustrate the potential of Bayesian hierarchical models, a dataset of about 500,000 inhabitants released by the Polish National Health Fund containing information about ischemic stroke incidence for a 2-year period is analyzed using different types of models. Spatial logistic regression and…
Towards nonlocal density functionals by explicit modelling of the exchange-correlation hole in inhomogeneous systems
2013
We put forward new approach for the development of a non-local density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate xc-energy and an accurate corresponding xc-potential even in difficult near-degeneracy situations such as molecular bond breaking. In particular we demand that: (1) the xc hole properly contains -1 electron, (2) the xc-potential has the asymptotic -1/r behavior outside finite systems and (3) the xc-potential has the correct step structure related to the derivative discontinuities of the xc-energy functional. None of the currently existing functionals satisfies all these re…
Magnetic and electronic properties of double perovskites and estimation of their Curie temperatures byab initiocalculations
2008
First principles electronic structure calculations have been carried out on ordered double perovskites Sr_2B'B"O_6 (for B' = Cr or Fe and B" 4d and 5d transition metal elements) with increasing number of valence electrons at the B-sites, and on Ba_2MnReO_6 as well as Ba_2FeMoO_6. The Curie temperatures are estimated ab initio from the electronic structures obtained with the local spin-density functional approximation, full-potential generalized gradient approximation and/or the LDA+U method (U - Hubbard parameter). Frozen spin-spirals are used to model the excited states needed to evaluate the spherical approximation for the Curie temperatures. In cases, where the induced moments on the oxy…
Fast Solution of 3D Elastodynamic Boundary Element Problems by Hierarchical Matrices
2009
In this paper a fast solver for three-dimensional elastodynamic BEM problems formulated in the Laplace transform domain is presented, implemented and tested. The technique is based on the use of hierarchical matrices for the representation of the collocation matrix for each value of the Laplace parameter of interest and uses a preconditioned GMRES for the solution of the algebraic system of equations. The preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. An original strategy for speeding up the overall analysis is presented and tested. The reported numerical results demonstrate the effectiveness of the technique.
Simultaneous measurement of the muon neutrino charged-current cross section on oxygen and carbon without pions in the final state at T2K
2020
Authors: K. Abe,56 N. Akhlaq,45 R. Akutsu,57 A. Ali,32 C. Alt,11 C. Andreopoulos,54,34 L. Anthony,21 M. Antonova,19 S. Aoki,31 A. Ariga,2 T. Arihara,59 Y. Asada,69 Y. Ashida,32 E. T. Atkin,21 Y. Awataguchi,59 S. Ban,32 M. Barbi,46 G. J. Barker,66 G. Barr,42 D. Barrow,42 M. Batkiewicz-Kwasniak,15 A. Beloshapkin,26 F. Bench,34 V. Berardi,22 L. Berns,58 S. Bhadra,70 S. Bienstock,53 S. Bolognesi,6 T. Bonus,68 B. Bourguille,18 S. B. Boyd,66 A. Bravar,13 D. Bravo Berguño,1 C. Bronner,56 S. Bron,13 A. Bubak,51 M. Buizza Avanzini ,10 T. Campbell,7 S. Cao,16 S. L. Cartwright,50 M. G. Catanesi,22 A. Cervera,19 D. Cherdack,17 N. Chikuma,55 G. Christodoulou,12 M. Cicerchia,24,† J. Coleman,34 G. Collazu…
Quantum-chemical calculation of Born–Oppenheimer breakdown parameters to rotational constants
2010
The paper describes how Born–Oppenheimer breakdown parameters for the rotational constants of diatomic molecules can be determined via quantum-chemical computations. The deviations from the Born–Oppenheimer equilibrium values are accounted for by considering the adiabatic correction to the equilibrium bond distances, the electronic contribution to the rotational constant via the rotational g tensor, and the so-called Dunham correction, which can be computed directly from a polynomial expansion of the potential curve around the equilibrium distance. Calculations for HCl, SiS, and HF demonstrate the accuracy that can be achieved in the theoretical treatment of the considered Born–Oppenheimer …
Analysis and control of a seven mode truncation of the Kolmogorov flow with drag.
2008
The transition from laminar to chaotic motion in a viscous fluid flow is investigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov flow with drag friction. Analytical expressions of the bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynoplds number is increased for fixed values of the drag parameter. An adaptive stabilization of the system trajectories to an equilibrium point or to a periodic orbit is obtained through a model reference approach which makes the control global.
Linear Response Theory with finite-range interactions
2021
International audience; This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle–hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle–hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle–hole interactio…