This paper investigates the joint optimization of power allocation and antenna activation in sparse extremely large aperture array systems operating under power amplifier non-linearities. We first derive an analytical expression for the achievable spectral efficiency (SE) of point-to-point MIMO channels affected by non-linear distortions using the Bussgang decomposition. To address the combinatorial and non-convex nature of the energy-efficiency (EE) maximization problem, we employ an unsupervised deep neural network (DNN) that learns the non-linear mapping between the channel state information and the optimal EE operating point. The DNN jointly predicts distortion-aware power allocation, total transmit power scaling, and modular sub-array activation based on singular-value and geometric channel features. Numerical results demonstrate that the proposed DNN-based arrays achieve significant EE gains over the conventional sparse arrays.