From the 1 of 16 linked papers with an AI index.
16 papers
Analytic inverse problems with finitely many random measurements
Giovanni S. Alberti, Damiano Poletti, Simone Sanna +1
While infinite-dimensional inverse problems are traditionally analyzed assuming continuous data, practical applications rely on finitely many discrete measurements. Recent determin…
PIKS: Universal Physics-Informed Kernel Methods
Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria +1
The paper proposes Physics-Informed Kernel Methods (PIKS), a kernel-based approach that incorporates linear differential constraints into learning, proving universal consistency an…
MAD: Manifold Attracted Diffusion
Dennis Elbrächter, Giovanni S. Alberti, Matteo Santacesaria
Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy ve…
Stochastic Generalized Sampling
Luca Finotti, Matteo Santacesaria
Reconstructing an infinite-dimensional signal from a finite set of measurements is a fundamental problem in approximation theory and signal processing. While the generalized sampli…
Diffusion Graph Posterior Sampling for Nonlinear Inverse Problems with Application to Electrical Impedance Tomography
Giovanni S. Alberti, Damiana Lazzaro, Serena Morigi +2
Deep generative models have emerged as state-of-the-art for solving inverse problems, but applying them to inverse problems for PDEs, like electrical impedance tomography (EIT) rem…
Inverse problems for quasi-linear elliptic systems modeling electrolysers
Giovanni S. Alberti, Wadim Gerner, Matteo Santacesaria
We investigate the electrochemical processes within an electrolyser cell, which are modelled by a coupled system of second-order quasi-linear elliptic PDEs. In this context, we stu…