Keith Rudd, an IGERT WISENet Trainee in the Mechanical Engineering and Materials Science department at Duke University, successfully passed his Ph.D. defense August 26, 2013 under the supervision of Dr. Silvia Ferrari. Keith’s dissertation “Solving Partial Differential Equations Using Artificial Neural Networks" presents a method for solving partial differential equations (PDEs) using artificial neural networks. The method uses a constrained-backpropagation (CPROP) approach for preserving prior knowledge during incremental training for solving nonlinear elliptic and parabolic PDEs adaptively, in non-stationary environments.