# Stochastic Hybrid Model

Simulation of stochastic hybrid systems previously handled only discrete nondeterministic choices, while an action allowed to fire anywhere in a time interval gives a single state infinitely many options. The new method discretizes each action's time interval separately, learns a scheduler with Q-learning over the finite abstraction, and uses precomputed symbolic reachable states to steer simulation and prune unreachable regions in a correct-by-construction way. On the water tank benchmark the simulation reproduces the maximum reachability probabilities reported by an existing method; on a water tank variant with a low-probability underflow objective, guidance makes learning clearly faster than unguided simulation and yields a reachability probability of at least 45%.

Simulation of stochastic hybrid systems previously handled only discrete nondeterministic choices, while an action allowed to fire anywhere in a time interval gives a single state infinitely many options. The new method discretizes each action's time interval separately, learns a scheduler with Q-learning over the finite abstraction, and uses precomputed symbolic reachable states to steer simulation and prune unreachable regions in a correct-by-construction way. On the water tank benchmark the simulation reproduces the maximum reachability probabilities reported by an existing method; on a water tank variant with a low-probability underflow objective, guidance makes learning clearly faster than unguided simulation and yields a reachability probability of at least 45%.