Advances in artificial intelligence (AI) implemented with neural networks and other machine learning techniques have transformed what computers can accomplish. Despite their potential, AI has had comparatively less impact on cyber-physical systems (CPS). Many CPS interact with the physical world where safety is important, so a solution with superior performance 99.9% of the time may still be unacceptable for a CPS. Unfortunately, AI systems are hard to prove correct ? it is difficult to trust the systems will always do what they are designed to do. The goal of this research is to advance the foundations of formal methods in order to make formal verification of AI-based CPS practical. If successful, the work will enable a justified trust in AI systems and allow AI to be applied within safety-critical processes that interact with the physical world. The project investigates approximation approaches where an AI component is replaced by an approximation with similar performance that is easier to verify.