Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guarantees

2026-01-03

arXiv.org

AI Summary

This work addresses the challenge of efficiently and reliably computing closed-loop reachable sets for unknown nonlinear dynamical systems. The authors propose a data-driven safety verification framework that integrates Koopman operator theory with conformal prediction. By leveraging neural networks to learn a lifting map, the nonlinear system is approximated as a linear one in an augmented space, where a linear controller is designed to track reference trajectories. Reachable sets computed in this lifted space are then mapped back to the original state space using neural network verification tools. To account for model mismatch, conformal prediction is employed to quantify approximation errors and provide statistically valid probabilistic coverage guarantees. This approach achieves, for the first time, scalable, generalizable, and probabilistically sound reachability analysis without repeated computation in high-dimensional systems—including an 11-dimensional Hopper, a 28-dimensional Swimmer, and a 12-dimensional quadrotor—demonstrating significantly improved coverage, computational efficiency, and reduced conservativeness.

Technology Category

• Natural Language Processing: Safety and Robustness
• Intelligent Robots: State Estimation
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We propose a scalable reachability-based framework for probabilistic, data-driven safety verification of unknown nonlinear dynamics. We use Koopman theory with a neural network (NN) lifting function to learn an approximate linear representation of the dynamics and design linear controllers in this space to enable closed-loop tracking of a reference trajectory distribution. Closed-loop reachable sets are efficiently computed in the lifted space and mapped back to the original state space via NN verification tools. To capture model mismatch between the Koopman dynamics and the true system, we apply conformal prediction to produce statistically-valid error bounds that inflate the reachable sets to ensure the true trajectories are contained with a user-specified probability. These bounds generalize across references, enabling reuse without recomputation. Results on high-dimensional MuJoCo tasks (11D Hopper, 28D Swimmer) and 12D quadcopters show improved reachable set coverage rate, computational efficiency, and conservativeness over existing methods.

Problem

• reachability analysis
• nonlinear dynamics
• safety verification
• conformal prediction
• Koopman operators

Innovation

• Koopman operator
• conformal prediction
• data-driven reachability
• neural network lifting
• safety verification