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January 22, 2026ACM communications in computer algebra0 citations

Symbolic-Numeric Pipeline for Reachability Analysis of Differential Equations with B-Series

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JSJulien Alexandre dit Sandretto

Key Points

  • The aim is to develop a pipeline for effectively performing reachability analysis on ordinary differential equations using B-series.
  • Develop a symbolic step to generate B-series and assess truncation errors.
  • Optimize the truncation error to minimize over-estimation during set computations.
  • Evaluate the B-series using affine arithmetic and intervals to create a reachable tube.
  • The proposed pipeline shows reduced over-estimation in reachability analysis.
  • B-series evaluations yield guaranteed reachable sets.
  • Optimization techniques enhance accuracy in computations.

Abstract

An in-progress pipeline based on B-series is proposed to solve reachability analysis of ordinary differential equations. First, a symbolic step generates a B-series and its associated truncation error. This later is symbolically optimized in order to reduce the over-estimation introduced by computation with sets. Finally, the B-series is evaluated with affine arithmetic and intervals to produce a guaranteed reachable tube.

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Cite This Study

Julien Alexandre dit Sandretto (2025) studied this question.

synapsesocial.com/papers/6971bd26642b1836717e1d75https://doi.org/10.1145/3787957.3787961
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