Mining Point-of-No-Return Boundaries in Constrained Dynamical Systems via Counterfactual Auditing

Abstract

Safety-critical failures in constrained dynamical environments are often detected only after a violation occurs, while outcome metrics (e.g., success rate, time-to-failure) conflate structural inevitability with decision-induced errors. We formulate failure diagnosis as recoverability boundary discovery and define the Point-of-No-Return (PoNR) as the last recoverable snapshot before violation becomes unavoidable under an audited intervention class. We introduce Counterfactual PoNR Auditing (CPA), a snapshot-replay framework that produces matched counterfactual rollouts and is accelerated by a neural operator surrogate (UNO) for a 3.09× end-to-end speedup. CPA yields Evidence Objects (EOs) that support structural--policy decomposition and enable Failure Atlas mining via contrastive analysis of event sequences within the policy-induced gap. CPA also serves as an offline supervision generator, allowing lightweight predictors to learn early inevitability signals beyond static observational baselines. Experiments on a high-fidelity hydrodynamic control testbed and a canonical bistable system show that PoNR precedes observable violation, remains stable under up to 30% multiplicative surrogate noise, and reduces auditing cost through surrogate-guided search.