Publication
MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers
Publications associées (98)
Scalable constrained optimization
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 ...
EPFL2024A Combination Technique for Optimal Control Problems Constrained by Random PDEs
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 ...
2024Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures
This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Va ...
New York2023On a Finite-Size Neuronal Population Equation
Tilo Schwalger, Valentin Marc Schmutz, Eva Löcherbach
Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...
SIAM PUBLICATIONS2023Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method
Fabio Nobile, Sundar Subramaniam Ganesh
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...
2022Efficient Meso-Scale Modeling of Alkali-Silica-Reaction Damage in Concrete
The alkali-silica reaction (ASR), also known as concrete cancer, is one of the most prevalent causes of concrete degradation. In this chemical reaction, amorphous silica in the aggregates reacts with alkalis in the pore solution. By absorbing water, hydrop ...
EPFL2022A combination technique for optimal control problems constrained by random PDEs
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 ...
EPFL2022Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation
Gossip algorithms and their accelerated versions have been studied exclusively in discrete time on graphs. In this work, we take a different approach and consider the scaling limit of gossip algorithms in both large graphs and large number of iterations. T ...
OXFORD UNIV PRESS2022Probabilistic 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 ...
EPFL2021Complexity 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 ...
2021