Georgia Institute of Technology College of Sciences

Exploring Parametrized Systems of Real Polynomial Equations with Neural Networks

We investigate the use of machine learning techniques to assist in the solution of parametrized systems of real polynomial equations. In particular, we discuss the problem of jointly predicting the number of real solutions to a problem and approximating the paramter-to-solution map. Throughout, we emphasize interactions between the algebraic geometry of the underlying problem and considerations in deep learning.
This is based on ongoing work with Julianne Barnhart, Jonathan Hauenstein, Ikenna Nometa, Margaret Regan, Trong-Thuc Trang, and Charles Wampler.