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Penalization and Bayesian numerical methods for multiscale inverse problems

In this thesis we consider inverse problems involving multiscale elliptic partial differential equations. The name multiscale indicates that these models are characterized by the presence of parameters which vary on different spatial scales (macroscopic, m ...

EPFL2019

Convergence Of Variance-Reduced Learning Under Random Reshuffling

Ali H. Sayed, Bicheng Ying, Kun Yuan

Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizers. The existing convergence results assume uniform ...

IEEE2018

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation (PDE) with a random coefficient solved with the stochastic collocation finite element method (SC-FEM). The random diffusion coefficient is assumed to depend in an affine way on independent ...

2018

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

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associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

Efficient Analysis of Confined Guided Modes in Phoxonic Crystal Slabs

Sina Khorasani

Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in studying photonic ...

IEEE Institute of Electrical and Electronics Engineers2017

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Fabio Nobile, Lorenzo Tamellini

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...

2016

Two subtle convex nonlocal approximations of the BV-norm

Hoài-Minh Nguyên

Inspired by the BBM formula and by work of G. Leoni and D. Spector, we analyze the asymptotic behavior of two sequences of convex nonlocal functionals (Psi(n)(u)) and (Phi(n)(u)) which converge formally to the BV-norm of u. We show that pointwise convergen ...

Elsevier2016

Clock-Gating of Streaming Applications for Energy Efficient Implementations on FPGAs

Marco Mattavelli, Endri Bezati, Simone Casale Brunet

This paper investigates the reduction of dynamic power for streaming applications yielded by asynchronous dataflow designs by using clock gating techniques. Streaming applications constitute a very broad class of computing algorithms in areas such as signa ...

2016

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S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

Efficient Analysis of Confined Guided Modes in Phoxonic Crystal Slabs

Sina Khorasani

IEEE Institute of Electrical and Electronics Engineers2017

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Fabio Nobile, Lorenzo Tamellini

2016