Characterizing the nonlinear behavior of dynamical systems near their stability boundary is a critical step toward understanding and designing systems with desired dynamics. A robust approach to investigate the reduced dynamics of nonlinear systems exhibiting instabilities is based on center manifold theory in conjunction with the theory of normal forms near local bifurcations. However, the traditional derivation of the reduced dynamics on the center manifold requires an accurate model of the system as well as considerable algebra using the nonlinear system equations. This is especially challenging for nonlinear systems with more than just a few dimensions because the algebraic complexity of the model increases dramatically. In this talk, we introduce a deep learning structure that can uncover the reduced dynamics on the center manifold for a class of systems prone to instabilities using measurements of the system dynamics from random perturbations. The approach returns a parameter dependent closed form model of the system dynamics on the center manifold and automatically generates the coordinate transformations from the physical coordinates to the coordinates on the identified center manifold and vice versa. Application of this approach in stability analysis of several classes of nonlinear systems prone to instabilities will be discussed. Authors: Amin Ghadami and Bogdan Epureanu, University of Michigan