PCA-DDReach: Efficient Statistical Reachability Analysis of Stochastic Dynamical Systems via Principal Component Analysis

Navid Hashemi, Lars Lindemann, Jyotirmoy V. Deshmukh
Proceedings of the International Conference on Neuro-symbolic Systems, PMLR 288:693-707, 2025.

Abstract

This paper proposes a scalable data-driven algorithm for reachability analysis of complex cyber-physical systems (CPS) without requiring parametric models. Traditional methods rely on known physical dynamics, which are often unavailable due to system complexity or variability. Instead, we treat such systems as black boxes and use trajectory data to learn predictive models. To quantify prediction uncertainty and ensure safety, we integrate conformal inference (CI) — a statistical tool for probabilistic guarantees — with Principal Component Analysis (PCA) to reduce conservatism and enhance scalability. Our method constructs probabilistic reachable sets that are less conservative under distribution shifts compared to prior CI-based methods. We validate the approach on high-dimensional systems, including a 12D quadcopter and a 27D powertrain model, demonstrating improved accuracy and computational efficiency over existing techniques.

Cite this Paper

BibTeX
@InProceedings{pmlr-v288-hashemi25a, title = {PCA-DDReach: Efficient Statistical Reachability Analysis of Stochastic Dynamical Systems via Principal Component Analysis}, author = {Hashemi, Navid and Lindemann, Lars and Deshmukh, Jyotirmoy V.}, booktitle = {Proceedings of the International Conference on Neuro-symbolic Systems}, pages = {693--707}, year = {2025}, editor = {Pappas, George and Ravikumar, Pradeep and Seshia, Sanjit A.}, volume = {288}, series = {Proceedings of Machine Learning Research}, month = {28--30 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v288/main/assets/hashemi25a/hashemi25a.pdf}, url = {https://proceedings.mlr.press/v288/hashemi25a.html}, abstract = {This paper proposes a scalable data-driven algorithm for reachability analysis of complex cyber-physical systems (CPS) without requiring parametric models. Traditional methods rely on known physical dynamics, which are often unavailable due to system complexity or variability. Instead, we treat such systems as black boxes and use trajectory data to learn predictive models. To quantify prediction uncertainty and ensure safety, we integrate conformal inference (CI) — a statistical tool for probabilistic guarantees — with Principal Component Analysis (PCA) to reduce conservatism and enhance scalability. Our method constructs probabilistic reachable sets that are less conservative under distribution shifts compared to prior CI-based methods. We validate the approach on high-dimensional systems, including a 12D quadcopter and a 27D powertrain model, demonstrating improved accuracy and computational efficiency over existing techniques.} }
Endnote
%0 Conference Paper %T PCA-DDReach: Efficient Statistical Reachability Analysis of Stochastic Dynamical Systems via Principal Component Analysis %A Navid Hashemi %A Lars Lindemann %A Jyotirmoy V. Deshmukh %B Proceedings of the International Conference on Neuro-symbolic Systems %C Proceedings of Machine Learning Research %D 2025 %E George Pappas %E Pradeep Ravikumar %E Sanjit A. Seshia %F pmlr-v288-hashemi25a %I PMLR %P 693--707 %U https://proceedings.mlr.press/v288/hashemi25a.html %V 288 %X This paper proposes a scalable data-driven algorithm for reachability analysis of complex cyber-physical systems (CPS) without requiring parametric models. Traditional methods rely on known physical dynamics, which are often unavailable due to system complexity or variability. Instead, we treat such systems as black boxes and use trajectory data to learn predictive models. To quantify prediction uncertainty and ensure safety, we integrate conformal inference (CI) — a statistical tool for probabilistic guarantees — with Principal Component Analysis (PCA) to reduce conservatism and enhance scalability. Our method constructs probabilistic reachable sets that are less conservative under distribution shifts compared to prior CI-based methods. We validate the approach on high-dimensional systems, including a 12D quadcopter and a 27D powertrain model, demonstrating improved accuracy and computational efficiency over existing techniques.
APA
Hashemi, N., Lindemann, L. & Deshmukh, J.V.. (2025). PCA-DDReach: Efficient Statistical Reachability Analysis of Stochastic Dynamical Systems via Principal Component Analysis. Proceedings of the International Conference on Neuro-symbolic Systems, in Proceedings of Machine Learning Research 288:693-707 Available from https://proceedings.mlr.press/v288/hashemi25a.html.

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