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 ...

Inverse problems research lies at the intersection of pure and applied mathematics. The forward problem corresponding to an inverse problem is usually a well defined problem in physics, engineering or ...

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 ...

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 ...