In the context of inverse problems, a mathematical model of the measurements is called the direct problem. To understand this term, let us consider a model for obstetric sonography. An ultrasonic ...

Inverse problems involve deducing the underlying characteristics of a system from observational data, rather than from direct measurement. In the realm of differential operators, this approach focuses ...

Inverse scattering problems are concerned with deducing the characteristics of an object or medium from the scattered waves produced when an incident field interacts with it. This domain spans ...

Computational Inverse Problems are all about the application. The driving question is how to extend the thorough theory of an Inverse Problem to an algorithm, which can be implemented and ultimately ...

Check back in Fall 2025. Abstract: Constitutive or material models provide a mathematical description of how solids respond to mechanical stimuli. For example, an isotropic linear elastic constitutive ...

Dozens of machine learning algorithms require computing the inverse of a matrix. Computing a matrix inverse is conceptually easy, but implementation is one of the most difficult tasks in numerical ...

Dr. James McCaffrey of Microsoft Research presents a full-code, step-by-step tutorial on an implementation of the technique that emphasizes simplicity and ease-of-modification over robustness and ...