  In this work, we study the numerical solution of inverse eigenvalue problems
from a machine learning perspective. Two different problems are considered: the
inverse Strum-Liouville eigenvalue problem for symmetric potentials and the
inverse transmission eigenvalue problem for spherically symmetric refractive
indices. Firstly, we solve the corresponding direct problems to produce the
required eigenvalues datasets in order to train the machine learning
algorithms. Next, we consider several examples of inverse problems and compare
the performance of each model to predict the unknown potentials and refractive
indices respectively, from a given small set of the lowest eigenvalues. The
supervised regression models we use are k-Nearest Neighbours, Random Forests
and Multi-Layer Perceptron. Our experiments show that these machine learning
methods, under appropriate tuning on their parameters, can numerically solve
the examined inverse eigenvalue problems.
