Synthesis of Parametric Hybrid Automata from Time Series

TL;DR

This paper introduces an algorithm for synthesizing parametric hybrid automata from time series data, producing a family of models that approximate the data within a specified error margin, and selecting the most precise model efficiently.

Contribution

It presents a novel algorithm that generates a family of hybrid automata models from time series, ensuring data approximation within a controllable error margin.

Findings

Efficient algorithm for model synthesis demonstrated in case studies.

Models accurately capture time series data within specified error bounds.

Ability to select the most precise model from the family.

Abstract

We propose an algorithmic approach for synthesizing linear hybrid automata from time-series data. Unlike existing approaches, our approach provides a whole family of models. Each model in the family is guaranteed to capture the input data up to a precision error {\epsilon}, in the following sense: For each time series, the model contains an execution that is {\epsilon}-close to the data points. Our construction allows to effectively choose a model from this family with minimal precision error {\epsilon}. We demonstrate the algorithm's efficiency and its ability to find precise models in two case studies.