Related papers: A conceptual framework for discrete inverse proble…

We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…

In electromagnetic inverse scattering, the goal is to reconstruct object permittivity using scattered waves. While deep learning has shown promise as an alternative to iterative solvers, it is primarily used in supervised frameworks which…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

Model calibration consists of using experimental or field data to estimate the unknown parameters of a mathematical model. The presence of model discrepancy and measurement bias in the data complicates this task. Satellite interferograms,…

In this paper we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the…

Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…

We briefly review some of the scientific challenges and epistemological issues related to climate science. We discuss the formulation and testing of theories and numerical models, which, given the presence of unavoidable uncertainties in…

The behaviors and skills of models in many geosciences (e.g., hydrology and ecosystem sciences) strongly depend on spatially-varying parameters that need calibration. A well-calibrated model can reasonably propagate information from…

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…

The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…

This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…

The astounding success of these methods has made it imperative to obtain more explainable and trustworthy estimates from these models. In hydrology, basin characteristics can be noisy or missing, impacting streamflow prediction. For solving…

In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…

Weather extremes are a major societal and economic hazard, claiming thousands of lives and causing billions of dollars in damage every year. Under climate change, their impact and intensity are expected to worsen significantly.…

This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…

Models of physical systems are used to explain and predict experimental results and observations. When students encounter discrepancies between the actual and expected behavior of a system, they revise their models to include the newly…