Description
Chair: Benedetta Morini
In this contribution I propose a new problem in low-rank matrix factorization, that is the Nonlinear Matrix Decomposition (NMD): given a sparse nonnegative matrix~$X$, find a low-rank matrix $\Theta$ such that $X \approx f(\Theta)$, where $f$ is element-wise nonlinear. I will focus on the so-called ReLU-NMD, where $f(\cdot) = \max(0, \cdot)$, the rectified unit (ReLU) non-linear...
Optimal control problems with PDEs as constraints arise very often in scientific and industrial applications. Due to the difficulties arising in their numerical solution, researchers have put a great effort into devising robust solvers for this class of problems. An example of a highly challenging problem attracting significant attention is the distributed control of incompressible viscous...
Photometric stereo is a computer vision technique for reconstructing the shape of a three-dimensional object starting from digital images. Several assumptions are required but they are rarely verified in experimental datasets. Specifically, the object under observation should behave as a Lambertian reflector, with light sources positioned at an infinite distance, along known directions. In...
In archaeology it is a common task to extract incisions or glyphs from a surface. This procedure is usually done manually and, therefore, it is prone to errors and it can be extremely time consuming. In this talk we present a variational model to automatically extract these incisions from a smooth surface.
We model this problem in the following way. Let $\mathbf{x}\in\mathbb{R}^n$ be a...
Neural Operators such as DeepONets have been recently introduced to approximate nonlinear operators with a focus on solution operators of PDEs. However, their implementation requires the use of deep neural networks whose training is performed in a high-dimensional space of parameters and hyperparameters. This, coupled with the need for significant computational resources, creates challenges...
We address two inverse source problems when determining a space-dependent source term and a time-dependent coefficient for a two-dimensional generalized diffusion equation. These problems are ill-posed in the Hadamard sense, where small perturbations in the data can lead to uncontrolled variations in the solution. From a analytic viewpoint we provide existence and uniqueness results for the...
