Related papers: Projected Regression Methods for Inverting Fredhol…

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…

We address the problem of analytic continuation of imaginary-frequency Green's functions, which is crucial in many-body physics, using machine learning based on a multi-level residual neural network. We specifically address potential biases…

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…

Physics-informed machine learning typically integrates physical priors into the learning process by minimizing a loss function that includes both a data-driven term and a partial differential equation (PDE) regularization. Building on the…

Solving Fredholm equations of the first kind is crucial in many areas of the applied sciences. In this work we adopt a probabilistic and variational point of view by considering a minimization problem in the space of probability measures…

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…

The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…

The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open…

The term analytic continuation emerges in many branches of Mathematics, Physics, and, more generally, applied Science. Generally speaking, in many situations, given some amount of information that could arise from experimental or numerical…

In this paper we study a linear inverse problem with a biological interpretation, which is modeled by a Fredholm integral equation of the first kind. When the kernel in the Fredholm equation is represented by step func- tions, we obtain…

Previous results pertaining to algebraic state and parameter estimation of linear systems based on a special construction of a forward-backward kernel representation of linear differential invariants are extended to handle large noise in…

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…

In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…

Magnetic particle imaging (MPI) is a relatively new imaging modality. The nonlinear magnetization behavior of nanoparticles in an applied magnetic field is employed to reconstruct an image of the concentration of nanoparticles. Finding a…

Many safety failures in machine learning arise when models are used to assign predictions to people (often in settings like lending, hiring, or content moderation) without accounting for how individuals can change their inputs. In this…

We develop a novel identification strategy as well as a new estimator for context-dependent causal inference in non-parametric triangular models with non-separable disturbances. Departing from the common practice, our analysis does not rely…

A characteristic of existing predictive process monitoring techniques is to first construct a predictive model based on past process executions, and then use it to predict the future of new ongoing cases, without the possibility of updating…

Many real-world time series exhibit strong periodic structures arising from physical laws, human routines, or seasonal cycles. However, modern deep forecasting models often fail to capture these recurring patterns due to spectral bias and a…

Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…