Uncertainty Quantification via Invariant-Measure Conformal Prediction

Abstract: Uncertainty quantification for learned stochastic dynamical systems is essential in safety-critical tasks such as control and monitoring. Standard conformal prediction provides finite-sample coverage guarantees under exchangeability, but this assumption is typically violated in dynamical systems because trajectory data are temporally dependent, state distributions evolve, and recursive prediction errors accumulate. This paper proposes an invariant-measure conformal prediction (imCP) framework that calibrates uncertainty using independent samples from an invariant measure of the Markov process induced by the dynamics. This aligns calibration with the stationary operating regime and restores the statistical symmetry needed for rolling one-step split conformal guarantees. For recursive multi-step prediction, imCP combines conformal calibration with Lipschitz error propagation through the learned predictor to obtain explicit horizon-dependent bounds.These pre-deployment uncertainty tubes are suitable for rolling and receding-horizon applications, such as self-triggered control and fault detection, where uncertainty bounds must be computed before future residuals are observed. Numerical experiments show that imCP yields reliable bounds, while non-invariant calibration can become misaligned during deployment.