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Neural State Classification for Hybrid Systems

### Dung Phan, Nicola Paoletti, Timothy Zhang, Radu Grosu, Scott A. Smolka, and Scott D. Stoller

We introduce the State Classification Problem (SCP) for continuous
and hybrid systems, and present Neural State Classification (NSC) as an efficient solution technique. SCP generalizes the model checking problem as it entails classifying each state s of a hybrid automaton as either positive or negative,
depending on whether or not s satisfies a given time-bounded reachability specification. This is an interesting problem in its own right, which NSC solves using
machine-learning techniques, Deep Neural Networks in particular. State classifiers produced by NSC tend to be very efficient (run in constant time and space),
but may be subject to classification errors. To quantify and mitigate such errors,
our approach comprises: i) techniques for certifying, with statistical guarantees,
that an NSC classifier meets given accuracy levels; ii) tuning techniques, including a novel technique based on adversarial sampling, that can virtually eliminate
false negatives (positive states classified as negative), thereby making the classifier more conservative. We have applied NSC to six nonlinear hybrid system
benchmarks, achieving an accuracy of 99.25% to 99.98%, and a false-negative
rate of 0.0033 to 0, which we further reduced to 0.0015 to 0 after tuning the
classifier. We believe that this level of accuracy is acceptable in many practical
applications, and that these results demonstrate the promise of the NSC approach.

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