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 ...

Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly ...

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 ...

Inverse problems for magnetic Schrödinger operators are at the forefront of mathematical physics and analysis, as they address the challenge of determining unknown magnetic and electric potentials ...

Recent advances at the intersection of neural networks and inverse scattering problems have transformed traditional approaches to imaging and material characterisation. Inverse scattering involves ...

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 ...