  Recent work has shown that it is possible to learn neural networks with
provable guarantees on the output of the model when subject to input
perturbations, however these works have focused primarily on defending against
adversarial examples for image classifiers. In this paper, we study how these
provable guarantees can be naturally applied to other real world settings,
namely getting performance specifications for robust virtual sensors measuring
fuel injection quantities within an engine. We first demonstrate that, in this
setting, even simple neural network models are highly susceptible to reasonable
levels of adversarial sensor noise, which are capable of increasing the mean
relative error of a standard neural network from 6.6% to 43.8%. We then
leverage methods for learning provably robust networks and verifying robustness
properties, resulting in a robust model which we can provably guarantee has at
most 16.5% mean relative error under any sensor noise. Additionally, we show
how specific intervals of fuel injection quantities can be targeted to maximize
robustness for certain ranges, allowing us to train a virtual sensor for fuel
injection which is provably guaranteed to have at most 10.69% relative error
under noise while maintaining 3% relative error on non-adversarial data within
normalized fuel injection ranges of 0.6 to 1.0.
