Figure 1 - uploaded by Xavier Bay
Content may be subject to copyright.
Source publication
http://afst.cedram.org/afst-bin/fitem?id=AFST_2012_6_21_3_439_0
Similar publications
The singularities of V-notches in the material whose modulus of elasticity varying as a power function of the r −coordinate are investigated. The eigen-equations are derived by substituting the asymptotic expansions of displacement fields around a notch vertex into the elasticity equilibrium equations. The radial boundary conditions are also presen...
There are many alternatives for treating the problem of a solid moving completely inside a fluid. One of them is using the fluid equations strictly in the space occupied by the fluid, and adjusting the mesh in each temporal step. If the displacements are limited a node-movement strategy without topology changes may be used to keep low the computati...
![Computed errors versus αs\documentclass[12pt]{minimal}...](publication/357695718/figure/fig5/AS:11431281104396098@1670035962682/Computed-errors-versus-asdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
A meshfree weak-form method based on combining a radial point interpolation method (RPIM) and modified Dirichlet-to-Neumann (MDtN) boundary condition is proposed for use in analyzing underwater acoustic radiation. To apply a meshfree weak-form method to exterior acoustic radiation prediction, an unbounded problem domain is truncated by an artificia...
![The partition of Ω for k=3 and l=2 where Ω=[0,1]2](publication/353108940/figure/fig1/AS:11431281177629979@1690561769239/The-partition-of-O-for-k3-and-l2-where-O0-12_Q320.jpg)
In this article, Richardson extrapolation technique is employed to investigate the local ultraconvergence properties of Lagrange finite element method using piecewise polynomials of degrees () for the second order elliptic problem with inhomogeneous boundary. A sequence of special graded partition are proposed and a new interpolation operator is in...
In a series of papers published since 2017 the author introduced a simple alternative of the $n$-simplex type, to enhance the accuracy of approximations of second-order boundary value problems subject to Dirichlet boundary conditions, posed on smooth curved domains. This technique is based upon trial functions consisting of piecewise polynomials de...
Citations
... Adding virtual derivative observations on the boundary like in Siivola et al. (2018) is hardly feasible in high dimension, as derivative information is only analytically enforceable at finitely many collocation points in GPs (and indeed scales cubically in the same). An infinite version could possibly be entertained via spectral methods, e.g., based on Gauthier and Bay (2012). In such a case, the use of a trust-region (TR) can limit the size of the search space drastically, which has been shown to be quite beneficial in high-dimension (Regis, 2016;Eriksson et al., 2019;Diouane et al., 2021;Zhou et al., 2021;Daulton et al., 2021), perhaps at the cost of a less global search (possibly compensated for with restarts or parallel TR). ...
Extending the efficiency of Bayesian optimization (BO) to larger number of parameters has received a lot of attention over the years. Even more so has Gaussian process regression modeling in such contexts, on which most BO methods are based. A variety of structural assumptions have been tested to tame high dimension, ranging from variable selection and additive decomposition to low dimensional embeddings and beyond. Most of these approaches in turn require modifications of the acquisition function optimization strategy as well. Here we review the defining assumptions, and discuss the benefits and drawbacks of these approaches in practice.
Bayesian Optimization, the application of Bayesian function approximation to finding optima of expensive functions, has exploded in popularity in recent years. In particular, much attention has been paid to improving its efficiency on problems with many parameters to optimize. This attention has trickled down to the workhorse of high dimensional BO, high dimensional Gaussian process regression, which is also of independent interest. The great flexibility that the Gaussian process prior implies is a boon when modeling complicated, low dimensional surfaces but simply says too little when dimension grows too large. A variety of structural model assumptions have been tested to tame high dimensions, from variable selection and additive decomposition to low dimensional embeddings and beyond. Most of these approaches in turn require modifications of the acquisition function optimization strategy as well. Here we review the defining structural model assumptions and discuss the benefits and drawbacks of these approaches in practice.
