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Recent work has shown that it is possible to learn neural networks withprovable guarantees on the output of the model when subject to inputperturbations, however these works have focused primarily on defending againstadversarial examples for image classifiers. In this paper, we study how theseprovable guarantees can be naturally applied to other real world settings,namely getting performance specifications for robust virtual sensors measuringfuel injection quantities within an engine. We first demonstrate that, in thissetting, even simple neural network models are highly susceptible to reasonablelevels of adversarial sensor noise, which are capable of increasing the meanrelative error of a standard neural network from 6.6% to 43.8%. We thenleverage methods for learning provably robust networks and verifying robustnessproperties, resulting in a robust model which we can provably guarantee has atmost 16.5% mean relative error under any sensor noise. Additionally, we showhow specific intervals of fuel injection quantities can be targeted to maximizerobustness for certain ranges, allowing us to train a virtual sensor for fuelinjection which is provably guaranteed to have at most 10.69% relative errorunder noise while maintaining 3% relative error on non-adversarial data withinnormalized fuel injection ranges of 0.6 to 1.0.

Neural Network Virtual Sensors for Fuel Injection Quantities with Provable Performance Specifications