From PDE-Constrained Optimization to DNNs

In the present work we explore numerical methods inspired by optimal control theory to train image classifiers. In a first step, we consider a prototypical formulation of a variational optimization problem governed by an elliptic dynamical system. We will discuss the numerical treatment and study some of the mathematical operators. Subsequently, we present the optimal control formulation for training DNNs and derive some expressions for the associated optimality conditions. In our future work, we plan to extend these optimality conditions and device a numerical scheme for the DNN training problem, similar to the scheme developed for the prototypical problem.Mathematics, Department ofHonors Colleg