Category
Distribution theory
Related publications (682)
Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations
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 ...
EPFL2021Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations
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 ...
EPFL2021A dependence of the cost of fast controls for the heat equation on the support of initial datum
The controllability cost for the heat equation as the control time goes to 0 is well-known of the order for some positive constant , depending on the controlled domain and for all initial datum. In this paper, we prove that the constant $C ...
2021Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters
Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin
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 ...
2021Prediction of the reaction forces of spiral-groove gas journal bearings by artificial neural network regression models
Jürg Alexander Schiffmann, Elia Iseli
This paper presents neural network regression models for predicting the nonlinear static and linearized dynamic reaction forces of spiral grooved gas journal bearings. The partial differential equations (PDEs) are sampled, based on a full factorial and ran ...
2021Substructured Two-grid and Multi-grid Domain Decomposition Methods
Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corr ...
2021On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method
The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...
Springer-Verlag2021Transverse Noise, Decoherence, and Landau Damping in High-Energy Hadron Colliders
High-energy hadron colliders are designed to generate particle collisions within specialized detectors. A higher number of collisions is achieved with high-quality beams of low transverse emittances, meaning a small transverse cross-section, and high inten ...
EPFL2021Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1
We are interested in the well posedness of quasilinear partial differential equations of order two. Motivated by the study of the Einstein equation in relativity theory, there are a number of works dedicated to the local well-posedness issue for the quasil ...
EPFL2021Efficient algorithms for wave problems
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 ...
EPFL2021