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Synthesizing ReLU neural networks with two hidden layers as barrier certificates for hybrid systems

Barrier certificates provide safety guarantees for hybrid systems. In this paper, we propose a novel approach to synthesizing neural networks as barrier certificates. Candidate networks are trained from a special structure: ReLU neural networks consisting of two hidden layers. Then, the problem of identifying real barrier certificates from candidates is transformed into a group of mixed integer linear programming problems and a mixed integer quadratically constrained problem. Taking full advantage of the recent advance in optimization, barrier certificates validation can be performed effectively. We implement the tool SyntheBC and evaluate its performance over 3 hybrid systems and 8 continuous systems up to 12-dimensional state space. The experimental results show that our method is more scalable and effective than the classical polynomial barrier certificate method and the existing neural network based method.