Dynamical Approximation and Sensor Placement for the State Estimation of Transport Problems

This talk by Cecilia Pagliantini from the University of Pisa explores the inverse problem of reconstructing unknown functions from finite measurements, specifically when the function is the output of a parametric differential equation with unknown input parameters. Discover how to address inverse problems for wave phenomena in Hamiltonian systems through a method that combines symplectic dynamical low-rank approximation with dynamical placement of sensors to ensure accurate reconstruction. Learn why traditional model order reduction approaches become ineffective for transport problems and how this innovative methodology overcomes these limitations. The presentation, delivered on April 11th, 2025 as part of the DDPS webinar series at Lawrence Livermore National Laboratory, includes joint work with Olga Mula and Federico Vismara from TU/e. Dr. Pagliantini is an Assistant Professor specializing in numerical methods for differential equations, with particular focus on discretizations and model order reduction techniques that preserve geometric structures and physical properties of original models.