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

arXiv: https://arxiv.org/abs/2601.01076 · HTML: https://mlsanity.com/paper/2601.01076/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 3 Jan 2026.

## Builds on (most cited first, 24 of 24)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Reachability Analysis of Neural Feedback Loops](https://mlsanity.com/paper/2108.04140/) (2021)
- [Formal Verification and Control with Conformal Prediction](https://mlsanity.com/paper/2409.00536/) (2024)
- [Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constants](https://mlsanity.com/paper/2010.08993/) (2020)
- [FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planning](https://mlsanity.com/paper/1703.07373/) (2017)
- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems](https://mlsanity.com/paper/2104.08695/) (2021)
- [A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis](https://mlsanity.com/paper/2112.05745/) (2021)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (2022)
- [One-Shot Reachability Analysis of Neural Network Dynamical Systems](https://mlsanity.com/paper/2209.11827/) (2022)
- [PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator](https://mlsanity.com/paper/2306.12962/) (2023)
- [Efficient Interaction-Aware Interval Analysis of Neural Network Feedback Loops](https://mlsanity.com/paper/2307.14938/) (2023)
- [Robust Tracking with Model Mismatch for Fast and Safe Planning: an SOS Optimization Approach](https://mlsanity.com/paper/1808.00649/) (2018)
- [Numerical Verification of Affine Systems with up to a Billion Dimensions](https://mlsanity.com/paper/1804.01583/) (2018)
- [Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization](https://mlsanity.com/paper/2105.00886/) (2021)
- [Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shift](https://mlsanity.com/paper/2407.11609/) (2024)
- [Constraint-Aware Refinement for Safety Verification of Neural Feedback Loops](https://mlsanity.com/paper/2410.00145/) (2024)
- [Reachability Analysis for Black-Box Dynamical Systems](https://mlsanity.com/paper/2410.07796/) (2024)
- [Explicit Error Bounds for Carleman Linearization](https://mlsanity.com/paper/1711.02552/) (2017)
- [Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilization](https://mlsanity.com/paper/2509.19688/) (2025)
- [Reachability of weakly nonlinear systems using Carleman linearization](https://mlsanity.com/paper/2108.10390/) (2021)

## Built on by (most cited first, 1 of 1)

- [Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees](https://mlsanity.com/paper/2604.00283/) (2026)

## Abstract (arXiv)

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.