# Data-Driven Reachability Analysis with Christoffel Functions

arXiv: https://arxiv.org/abs/2104.13902 · HTML: https://mlsanity.com/paper/2104.13902/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2021.

## Built on by (most cited first, 12 of 12)

- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023)
- [Data-driven Reachability using Christoffel Functions and Conformal Prediction](https://mlsanity.com/paper/2309.08976/) (2023)
- [Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shift](https://mlsanity.com/paper/2407.11609/) (2024)
- [Data-Driven Reachability analysis and Support set Estimation with Christoffel Functions](https://mlsanity.com/paper/2112.09995/) (2021)
- [Machine Learning for Smart and Energy-Efficient Buildings](https://mlsanity.com/paper/2211.14889/) (2022)
- [Pedestrian Motion Prediction Using Transformer-based Behavior Clustering and Data-Driven Reachability Analysis](https://mlsanity.com/paper/2408.15250/) (2024)
- [Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes](https://mlsanity.com/paper/2504.01007/) (2025)
- [RESCORE: LLM-Driven Simulation Recovery in Control Systems Research Papers](https://mlsanity.com/paper/2604.04324/) (2026)
- [Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemics](https://mlsanity.com/paper/2111.04704/) (2021)
- [Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets](https://mlsanity.com/paper/2210.01919/) (2022)
- [Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees](https://mlsanity.com/paper/2604.00283/) (2026)

## Abstract (arXiv)

We present an algorithm for data-driven reachability analysis that estimates finite-horizon forward reachable sets for general nonlinear systems using level sets of a certain class of polynomials known as Christoffel functions. The level sets of Christoffel functions are known empirically to provide good approximations to the support of probability distributions: the algorithm uses this property for reachability analysis by solving a probabilistic relaxation of the reachable set computation problem. We also provide a guarantee that the output of the algorithm is an accurate reachable set approximation in a probabilistic sense, provided that a certain sample size is attained. We also investigate three numerical examples to demonstrate the algorithm's capabilities, such as providing non-convex reachable set approximations and detecting holes in the reachable set.