Abstract: The single frequency nature of magnetic resonance imaging (MRI) allows the design and optimization of fast and robust algorithms for computational electromagnetics, based on integral equations. The fast and accurate estimation of the electromagnetic interactions in an MRI setup is critical to solve inverse problems based on MRI measurements. For example, rapid integral equations methods can be used to solve the inverse form of Maxwell’s equations and estimate tissue electrical properties. In addition, the speed advantages of integral equations allows the generation of thousands of realistic simulated data to train machine learning algorithms. In this talk, I will describe my contributions to the area of electrical property reconstruction and present results from three different approaches, based on optimization methods and machine learning algorithms.