MATHICSE Technical Report : Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters
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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 ...
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 ...
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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In this paper we investigate how gradient-based algorithms such as gradient descent (GD), (multi-pass) stochastic GD, its persistent variant, and the Langevin algorithm navigate non-convex loss-landscapes and which of them is able to reach the best general ...
This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle ...
Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...
Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...
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 ...
This article presents an enhanced version of our previous work, hybrid nonuniform subdivision (HNUS) surfaces, to achieve optimal convergence rates in isogeometric analysis (IGA). We introduce a parameter lambda (14
Modern machine learning architectures distinguish servers and workers. Typically, a d-dimensional model is hosted by a server and trained by n workers, using a distributed stochastic gradient descent (SGD) optimization scheme. At each SGD step, the goal is ...
Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik2021