Towards Certified Sim-to-Real Transfer via Stochastic Simulation-Gap Functions
Abstract
This paper introduces the notion of stochastic simulation-gap function, which formally quantifies the gap between an approximate mathematical model and a high-fidelity stochastic simulator. Since controllers designed for the mathematical model may fail in practice due to unmodeled gaps, the stochastic simulation-gap function enables the simulator to be interpreted as the nominal model with bounded state- and input-dependent disturbances. We propose a data-driven approach and establish a formal guarantee on the quantification of this gap. Leveraging the stochastic simulation-gap function, we design a controller for the mathematical model that ensures the desired specification is satisfied in the high-fidelity simulator with high confidence, taking a step toward bridging the sim-to-real gap. We demonstrate the effectiveness of the proposed method using a TurtleBot model and a pendulum system in stochastic simulators.
Cite
@article{arxiv.2603.20672,
title = {Towards Certified Sim-to-Real Transfer via Stochastic Simulation-Gap Functions},
author = {P Sangeerth and Abolfazl Lavaei and Pushpak Jagtap},
journal= {arXiv preprint arXiv:2603.20672},
year = {2026}
}