Orateur
Description
Stabilizing linearized partial differential equations (PDEs) is a fundamental challenge in numerical analysis and control theory. In this talk, we present advanced strategies for enhancing the stability of linearized PDEs. We begin by reminding the concept of linear instability, illustrated through the example of the Klein-Gordon equation. Next, we introduce an optimal stabilization approach, based on the minimization of the Frobenius norm of the discrete linearized operator and its associated second-order eigenvalue problem. Building on this, we explore automatic stabilization using PyTorch, demonstrating how machine learning techniques can adaptively stabilize PDEs. We showcase the effectiveness of these methods through a case study, of the Klein-Gordon and the Korteweg-de Vries equation. Finally, we discuss broader implications, including stabilization at every time step and connections to approximate controllability. This is a joint work with J.P. Chehab and M. Raydan.
