MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition
Graph Chatbot
Chat with Graph Search
Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.
DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.
This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing tech ...
We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of It stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are show ...
This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formal ...
In this paper, we evaluate the performances of state-of-the art higher-order masking schemes for the AES. Doing so, we pay a particular attention to the comparison between specialized solutions introduced exclusively as countermeasures against side-channel ...
In this thesis, we study several stochastic partial differential equations (SPDE’s) in the spatial domain R, driven by multiplicative space-time white noise. We are interested in how rough and unbounded initial data affect the random field solution and the ...
In this work we consider the random discrete L2 projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...
Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of th ...
Randomness is of fundamental importance in various fields, such as cryptography, numerical simulations, or the gaming industry. Quantum physics, which is fundamentally probabilistic, is the best option for a physical random number generator. In this articl ...
The objective of this thesis is to develop reduced models for the numerical solution of optimal control, shape optimization and inverse problems. In all these cases suitable functionals of state variables have to be minimized. State variables are solutions ...