Probabilistic Constraints have become one of the most popular tools to deal with uncertain inequality constraints in engineering problems. When a decision has to be taken prior to observing uncertain parameters affecting the constraint, then it is very natural to define a decision as feasible whenever the uncertain constraint is satisfied with high probabilty. Due to the absence of explicit...
This talk is concerned with inverse problems in imaging from
a Bayesian point of view, i.e. we want to sample from the posterior distribution given noisy measurement. We tackle the problem by studying gradient flows of particles in high dimensions. More precisely, we analyze Wasserstein gradient flows of maximum mean discrepancies defined with respect to different kernels,
including...
Parameters in mathematical models for physical processes are often impossible to determine fully or accurately, and are hence subject to uncertainty. By modelling the input parameters as stochastic processes, it is possible to quantify the uncertainty in the model outputs. In this talk, we employ the multilevel Monte Carlo (MLMC) method to compute expected values of quantities of interest...
The total variation has been successful as a regularizer for inverse problems in imaging, thanks to its ability to preserve discontinuities (edges) and its relative simplicity (convexity). Even if largely outdated by deep learning based method, it still can be useful in some regimes (low noise, large scale images). This talk is about the preservation of edges in total-variation based...
Estimation of tail probabilities in systems that involve uncertain
parameters or white noise forcing is important when these unlikely
events have severe consequences. Examples of such events are
hurricanes, energy grid blackouts or failure of engineered
systems. After explaining the challenges of estimating rare event
probabilities, I will make a connection between extreme...
Despite its importance in applications, there are not many references dealing with the analysis of bilinear control problems governed by elliptic partial differential equations.
In this talk, we will deal with an optimal control problem where the control acts in a multiplicative way. We will investigate both the case in which the control is the reaction coefficient (distributed) and the...
There is a large literature on opinion formation models; in many of them the dynamics are driven by binary interactions between individuals that are modulated by an underlying (social) network structure. In this talk I will discuss different mathematical modeling approaches in this setting, and how we can derive partial differential equation models in suitable scaling limits. Furthermore I...
Semi-supervised learning (SSL) is the problem of finding missing labels from a partially labelled data set. The heuristic one uses is that “similar feature vectors should have similar labels”. The notion of similarity between feature vectors explored in this talk comes from a graph-based geometry where an edge is placed between feature vectors that are closer than some connectivity radius. A...
