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

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 acros...

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Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 14
Main Authors: Bacci, Giorgio, Bacci, Giovanni, Larsen, Kim G., Tribastone, Mirco, Tschaikowski, Max, Vandin, Andrea
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Couplings
Differential equations
Heuristic algorithms
Probabilistic logic
Prototypes
Runtime
Systems biology
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Abstract 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 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.
AbstractList 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 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.
Author Bacci, Giorgio
Bacci, Giovanni
Tschaikowski, Max
Larsen, Kim G.
Vandin, Andrea
Tribastone, Mirco
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  givenname: Giorgio
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  surname: Bacci
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  organization: Aalborg University,Department of Computer Science,Denmark
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  givenname: Kim G.
  surname: Larsen
  fullname: Larsen, Kim G.
  organization: Aalborg University,Department of Computer Science,Denmark
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  givenname: Mirco
  surname: Tribastone
  fullname: Tribastone, Mirco
  organization: IMT Lucca,SysMA Research Unit,Italy
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  givenname: Max
  surname: Tschaikowski
  fullname: Tschaikowski, Max
  organization: Aalborg University,Department of Computer Science,Denmark
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  givenname: Andrea
  surname: Vandin
  fullname: Vandin, Andrea
  organization: Scuola Superiore Sant'Anna,Institute of Economics,Italy
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Snippet We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can...
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SubjectTerms Couplings
Differential equations
Heuristic algorithms
Probabilistic logic
Prototypes
Runtime
Systems biology
Title Efficient Local Computation of Differential Bisimulations via Coupling and Up-to Methods
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