We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be used via symmetrization. Different choices of submodular functions give diff...

This work focuses on the approximation of parametric steady Navier–Stokes equations by the reduced basis method. For a particular instance of the parameters under consideration, we are able to solve the underlying partial differential equations, compute an output, and give sharp error bounds. The computations are split into an offline part, where the value of the parameters is not yet identifie...

The photovoltaic (PV) generator exhibits a nonlinear – characteristic and its maximum power (MP) point varies with solar insolation. In this paper, a feedforward MP-point tracking scheme is developed for the coupled-inductor interleaved-boost-converter-fed PV system using a fuzzy controller. The proposed converter has lower switch current stress and improved efficiency over the noncoupled conve...

During the last decades, reduced basis (RB) methods have been developed to a wide methodology for model reduction of problems that are governed by parametrized partial differential equations (P2DEs ). In particular equations of elliptic and parabolic type for linear, low polynomial or monotonic nonlinearities have been treated successfully by RB methods using finite element schemes. Due to the ...

Random errors are omnipresent in sensorimotor tasks due to perceptual and motor noise. The question is, are humans aware of their random errors on an instance-by-instance basis? The appealing answer would be 'no' because it seems intuitive that humans would otherwise immediately correct for the errors online, thereby increasing sensorimotor precision. However, here we show the opposite. Partici...

Reduced basis methods allow efficient model reduction of parametrized partial differential equations. In the current paper, we consider a reduced basis scheme for homogeneous domain decomposition problems. The method is based on iterative Dirichlet-Neumann coupling. We prove convergence of the iterative reduced scheme, derive rigorous a-posteriori error bounds and provide a full offline/online ...

In this work we are considered with parameter optimization of elliptic multiscale problems with macroscopic optimization functionals and microscopic material design parameters. An efficient approximation is obtained by the reduced basis approach. A posteriori error estimates for the reduced forward problem are obtained in the periodic homogenization setting, using the so called two scale weak f...

We present rigorous a posteriori error bounds for the Empirical Interpolation Method (EIM). The essential ingredients are (i) analytical upper bounds for the parametric derivatives of the function to be approximated, (ii) the EIM “Lebesgue constant,” and (iii) information concerning the EIM approximation error at a finite set of points in parameter space. The bound is computed “offline” and is ...