Alistair Sirman, Fleur Conway, Jessica Ciupa et al.
Neural network controllers for autonomous decision-making are well-established in cyber-physical systems, yet their deployment in safety-critical healthcare settings remains largely unverified. This paper presents a methodology and case study for the formal verification of a neural network controller for antibiotic dosing, motivated by the challenge of systems that must be simultaneously adaptive and provably safe across unbounded time horizons. We construct a simplified yet clinically-interpretable model that tracks drug concentration, body temperature, and white blood cell count. Vancomycin is selected as a representative antibiotic, widely prescribed for severe infections yet carrying a narrow therapeutic window, where supratherapeutic concentrations risk nephrotoxicity and subtherapeutic dosing risks treatment failure. A supervised neural network controller is trained on synthetic clinician-style dosing data. We establish formal verification of input-output safety properties, specifically verifying a property of a neural network that implies an infinite-horizon proof that automated dosing never exceeds the supratherapeutic boundary. This system property is proven in Rocq using the Vehicle interactive theorem prover back-end to integrate the different proof systems. The end result is a verification pipeline that allows for a wide variety of treatment approaches whilst maintaining safety for each specific patient.