# Data-driven memory-dependent abstractions of dynamical systems

arXiv: https://arxiv.org/abs/2212.01926 · HTML: https://mlsanity.com/paper/2212.01926/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2022.

## Built on by (most cited first, 2 of 2)

- [Data-driven abstractions via adaptive refinements and a Kantorovich metric [extended version]](https://mlsanity.com/paper/2303.17618/) (2023)
- [Increasing Information for Model Predictive Control with Semi-Markov Decision Processes](https://mlsanity.com/paper/2501.17256/) (2025)

## Abstract (arXiv)

We propose a sample-based, sequential method to abstract a (potentially black-box) dynamical system with a sequence of memory-dependent Markov chains of increasing size. We show that this approximation allows to alleviating a correlation bias that has been observed in sample-based abstractions. We further propose a methodology to detect on the fly the memory length resulting in an abstraction with sufficient accuracy. We prove that under reasonable assumptions, the method converges to a sound abstraction in some precise sense, and we showcase it on two case studies.