Verifying Neural Network Controlled Systems by Combining Forward and Backward Reachability Analysis

With the advancement of neural networks, neural network controlled systems (NNCSs) are increasingly deployed in safety-critical scenarios, making the safety verification of NNCSs imperative. Traditional verification methods based on overapproximated reachability analysis introduce precision loss during the verification process, which may lead to “Unknown” results. Moreover, standalone forward reachability analysis often fails to incorporate target safety properties into its verification process, while backward reachability analysis does not account for input constraints. To address these challenges, this paper proposes an iterative refinement approach by combining forward and backward reachability analysis. For a given safety property, our method guides state space partitioning and pruning on-the-fly by making use of the target safety constraints when verification results remain “Unknown”. By partitioning the state space into smaller subspaces, the precision loss due to overapproximation is significantly mitigated. Additionally, integrating forward and backward reachability analysis further counteracts these overapproximation effects through pruning, ultimately yielding more accurate verification outcomes. We demonstrate that our approach successfully verifies the system's safety properties with a 100% success rate across four benchmarks, whereas other verification tools for NNCSs such as Reach-LP-GSG, BReach-LP, and DRIP-Hpoly either return “Unknown” results or require up to $29 \%, 60 \%$, and 232% more time.