<ul><li>Recent approaches to leveraging deep learning for computing reachable sets of continuous-time dynamical systems have gained popularity over traditional level-set methods.</li><li>The introduction of an epsilon-approximate Hamilton-Jacobi Partial Differential Equation (HJ-PDE) establishes a relationship between training loss and accuracy of the true reachable set.</li><li>Satisfiability Modulo Theories (SMT) solvers are used to bound the residual error of the HJ-based loss function, allowing for formal certification of the approximation.</li><li>Certified Approximate Reachability (CARe) is the first approach to provide soundness guarantees on learned reachable sets of continuous dynamical systems.</li></ul>

Certified Approximate Reachability (CARe): Formal Error Bounds on Deep Learning of Reachable Sets

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