Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve very different scales or highly sensitive parameters), they become extremely difficult to solve. This is especially relevant in inverse problems, where scientists try to deduce unknown physical laws from observed data.

PDF | We give a one-sentence proof of McLaughlin and Rundell's inverse uniqueness theorem. | Find, read and cite all the research you need on ResearchGate

Solving non-convex regularized inverse problems is challenging due to their complex optimization landscapes and multiple local minima. However, these models remain widely studied as they often yield high-quality, task-oriented solutions, particularly in medical imaging, where the goal is to enhance clinically relevant features rather than merely minimizing global error. We propose incDG, a hybrid framework that integrates deep learning with incremental model-based optimization to efficiently approximate the $\ell_0$-optimal solution of imaging inverse problems. Built on the Deep Guess strategy, incDG exploits a deep neural network to generate effective initializations for a non-convex variational solver, which refines the reconstruction through regularized incremental iterations. This design combines the efficiency of Artificial Intelligence (AI) tools with the theoretical guarantees of model-based optimization, ensuring robustness and stability. We validate incDG on TpV-regularized op

Spectral identities for Schrödinger operators - Volume 68 Issue 2

Abstract. We show that inverse square singularities can be treated as boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenval

Estimation of parameters in physical processes often demands costly measurements, prompting the pursuit of an optimal measurement strategy. Finding such strategy is termed the problem of optimal exper...