PreprintCC0arXiv
Equation free data-driven modelling of chaotic processes
Abstract
We introduce a method for constructing predictive models of non cyclic physical processes directly from time-series data, without assuming an underlying differential equation. The observations define a discrete evolution rule whose recurrent behaviour captures the essential dynamics of the process. Analysing this behaviour across multiple geometric scales leads to probabilistic models in the form of Markov chains. Hyperbolicity criteria identify when these models provide a consistent statistical description of the data. The method is inspired by, and illustrated through, the analysis of a biological imaging data set referred to as the Cell Process.
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BibTeX
@misc{poggi2026equation,
title = {{Equation free data-driven modelling of chaotic processes}},
author = {Aurora Poggi and Marco Martens and Hjalmar Brismar and Ozan Oktem and Liviana Palmisano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08530},
eprint = {2609.08530},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08530},
note = {CC0},
}
RIS
TY - UNPB
TI - Equation free data-driven modelling of chaotic processes
AU - Aurora Poggi
AU - Marco Martens
AU - Hjalmar Brismar
AU - Ozan Oktem
AU - Liviana Palmisano
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08530
UR - https://arxiv.org/abs/2609.08530
AB - We introduce a method for constructing predictive models of non cyclic physical processes directly from time-series data, without assuming an underlying differential equation. The observations define a discrete evolution rule whose recurrent behaviour captures the essential dynamics of the process. Analysing this behaviour across multiple geometric scales leads to probabilistic models in the form of Markov chains. Hyperbolicity criteria identify when these models provide a consistent statistical description of the data. The method is inspired by, and illustrated through, the analysis of a biological imaging data set referred to as the Cell Process.
ER -