Inverse problems are pivotal in a variety of applications, such as target identification, non-destructive testing, and parameter estimation. Among these, the inverse scattering problem in inhomogeneous media poses significant challenges, as it seeks to estimate unknown parameters from available measurement data. To understand the mathematics of machine learning approaches for inverse scattering, we develop a…

Recent advancements in deep learning have led to a surge in research focused on solving scientific problems under the "AI for Science." Among these efforts, Scientific Machine Learning (SciML) aims to address domain-specific data challenges and extract insights from scientific datasets through innovative methodological solutions. A particularly active area within SciML involves using neural operators…

Natural gas production and distribution in the US is interconnected continent-wide, and hence the simulation of fluid flow in pipeline networks is a problem of scientific interest. While the problem of steady, unidirectional flow of fluid in a single pipeline is simple, it ceases to be so when we consider fluid flow in a large…