Certifying Simulation-Based Inference for Nonlinear Scientific Models

Simulation-based inference (SBI) learns information for posterior inference from simulator outputs when likelihood evaluation is unavailable or expensive. In scientific applications, however, statistical accuracy of the learned posterior does not guarantee that every retained parameter value defines a mathematically well-posed continuous model, nor that an approximate solver is close to that model's solution. We introduce certified SBI, an estimator-agnostic layer that conditions a learned posterior on parameters passing a deterministic model-validity certificate. The framework covers both time-dependent models described by fixed-point maps and steady-state models described by residual equations. For certified parameters, we prove sample-wise existence and uniqueness, residual-to-error bounds for approximate solvers, stability of posterior conditioning, and end-to-end bounds that propagate certification and posterior-approximation errors to downstream posterior summaries and Bayes decisions. The certification interface is compatible with neural posterior, likelihood, or ratio estimation and with classical or learned PDE solvers. A controlled nonlinear inverse problem demonstrates the resulting validity–coverage–cost trade-off.