# Efficient Local Computation of Differential Bisimulations via Coupling and Up-to Methods

arXiv: https://arxiv.org/abs/2104.13160 · HTML: https://mlsanity.com/paper/2104.13160/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2021.

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

- [Efficient Shield Synthesis via State-Space Transformation](https://mlsanity.com/paper/2407.19911/) (2024)
- [Scaling Weisfeiler-Leman Expressiveness Analysis to Massive Graphs with GPUs](https://mlsanity.com/paper/2607.02603/) (2026)

## Abstract (arXiv)

We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial differential equations, a ubiquitous model of dynamical systems across science and engineering. The algorithm enjoys polynomial time complexity and complements classical partition-refinement approaches because: (a) it implements a local exploration of the system, possibly yielding equivalences that do not necessarily involve the inspection of the whole system of differential equations; (b) it can be enhanced by up-to techniques; and (c) it allows the specification of pairs which ought not to be included in the output. Using a prototype, these advantages are demonstrated on case studies from systems biology for applications to model reduction and comparison. Notably, we report four orders of magnitude smaller runtimes than partition-refinement approaches when disproving equivalences between Markov chains.