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In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...
EPFL2021
Accurately estimating 3D human pose (3D HPE) and joint locations using only 2D keypoints is challenging. The noise in the predictions produced by conventional 2D human pose estimators often impeded the accuracy. In this paper, we present a diffusion-based ...
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...
The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. An error estimate is derived in the ...
Objective: Local pulse wave velocity (PWV) can be estimated from the waterhammer equation and is an essential component of wave separation analysis. However, previous studies have demonstrated inaccuracies in the estimations of local PWV due to the presenc ...
In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...
The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...
EPFL2024
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...
Analysis-suitable T-splines (ASTS) including both extraordinary points and T-junctions are used to solve Kirchhoff-Love shell problems. Extraordinary points are required to represent surfaces with arbitrary topological genus. T-junctions enable local refin ...
We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...
