  In this work, we propose Wasserstein distributionally robust shallow convex
neural networks (WaDiRo-SCNNs) to provide reliable nonlinear predictions when
subject to adverse and corrupted datasets. Our approach is based on a new
convex training program for ReLU shallow neural networks which allows us to
cast the problem as an exact, tractable reformulation of its order-1
Wasserstein distributionally robust equivalent. Our training procedure is
conservative by design, has low stochasticity, is solvable with open-source
solvers, and is scalable to large industrial deployments. We provide
out-of-sample performance guarantees and show that hard convex physical
constraints can be enforced in the training program. WaDiRo-SCNN aims to make
neural networks safer for critical applications, such as in the energy sector.
Finally, we numerically demonstrate the performance of our model on a synthetic
experiment and a real-world power system application, i.e., the prediction of
non-residential buildings' hourly energy consumption. The experimental results
are convincing and showcase the strengths of the proposed model.
