Cook, Brendan2022-08-292022-08-292022-05https://hdl.handle.net/11299/241372University of Minnesota Ph.D. dissertation. 2022. Major: Mathematics. Advisor: Jeff Calder. 1 computer file (PDF); 105 pages.In this thesis we explore two applications of partial differential equations to data science. In Part I we establish a convergence rate for the continuum limit of the nondominated sorting process. In Part II we show how the Poisson Equation can form the basis for "Poisson Learning," a new graph-based semi-supervised machine learning algorithm which excels at low label rates.enThesis or Dissertation