28 feb 2025 -- 09:15   [open in google calendar]

Centro de Giorgi, Sala Conferenze

Abstract.

We introduce some examples of inverse and forward problems, and we consider challenges that may arise and possible solutions. Specifically, we focus on inference for stochastic models and uncertainty propagation for computationally expensive deterministic systems. First, using a maximum likelihood approach, we estimate unknown parameters in stochastic differential equations from observed trajectories. We address challenges like model misspecification, lack of information, and discrete time observations, proposing suitable estimators. Second, we approximate expectations of quantities of interest of expensive models, where Monte Carlo methods are unfeasible. Combining multifidelity approaches with dimensionality reduction techniques, we provide estimators with reduced variance without increasing the cost. The effectiveness of our methods is demonstrated through numerical experiments.