Related papers: PETAL: Physics Emulation Through Averaged Lineariz…

Recovering a source signal from indirect measurements often requires estimating latent parameters, such as wireless channel states or MRI coil sensitivities, that cannot be directly observed. Here, we introduce Physics-Embedded Inverse…

Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Inverse problems exist in a wide variety of physical domains from aerospace engineering to medical imaging. The goal is to infer the underlying state from a set of observations. When the forward model that produced the observations is…

Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…

This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and…

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…

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…

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…

We discuss the possibility to learn a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularised reconstructions. This paper discusses the…

Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…

Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…

We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…

Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

We present an efficient, effective, and generic approach towards solving inverse problems. The key idea is to leverage the feedback signal provided by the forward process and learn an iterative update model. Specifically, at each iteration,…

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

This paper proposes an active learning (AL) algorithm to solve regression problems based on inverse-distance weighting functions for selecting the feature vectors to query. The algorithm has the following features: (i) supports both…