Optimization of mesh hierarchies in multilevel Monte Carlo samplers
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Machine intelligence greatly impacts almost all domains of our societies. It is profoundly changing the field of mechanical engineering with new technical possibilities and processes. The education of future engineers also needs to adapt in terms of techni ...
Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...
This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...
EPFL2021
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We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...
Many scientific inquiries in natural sciences involve approximating a spherical field –namely a scalar quantity defined over a continuum of directions– from generalised samples of the latter. Typically, a convex optimisation problem is formulated in terms ...
We prove small data modified scattering for the Vlasov-Poisson system in dimension d=3 using a method inspired from dispersive analysis. In particular, we identify a simple asymptotic dynamic related to the scattering mass. ...
We consider the numerical approximation of a risk-averse optimal control problem for an elliptic partial differential equation (PDE) with random coefficients. Specifically, the control function is a deterministic, dis- tributed forcing term that minimizes ...
We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of Optimal Control Problems (OCPs) constrained by random partial differential equ ...
Essentially nonoscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely employed to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well s ...
EPFL2020
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We consider an optimal control problem for an elliptic partial differential equation (PDE) with random coefficients. The control function is a deterministic, distributed forcing term that minimizes an expected quadratic regularized loss functional. We cons ...
