Inverse problems in PDE with finite measurements

Giovanni S. Alberti (Università di Genova)

Inverse problems arise whenever a physical quantity has to be reconstructed from indirect measurements. Whenever physics plays a crucial role in the description of the inverse problem, the model is based on a partial differential equation. As such, the model is infinite dimensional, so that, in theory, infinitely many measurements are required to recover the unknown. However, in all practical applications, only finite physical measures may be acquired. In this talk, I will discuss methods based on sampling, compressed sensing, and machine learning that allow us to obtain theoretical results for inverse problems in PDE with finite measures.