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Jérôme Feret.
Model reduction of infinite rule-based models.
In Proceedings of the Thirty-nineth SIGSIM Principles of Advanced Discrete Simulation, PADS'25. Santa Fe, New Mexico, USA, A. Uhrmacher (Ed), To appear in ACM Conference Proceedings.
© ACM, USA.

Abstract:

We propose a systematic approach to approximate the behav- ior of models of unbounded polymers. Our technique consists in discovering time-dependent ranges for the quantities of some patterns of interest. These ranges are obtained by ap- proximating the state of the system by a hyper-box (i.e. a rectangle in 𝑛-dimensions), with differential equations defin- ing the evolution of the coordinates of each of its hyper-faces (e.g. each of its (𝑛−1)-faces). Each equation pessimistically bounds the time derivative of the corresponding coordinate, when the state of the system ranges over this hyper-face.

To synthesize these bounds, we focus on the models writ- ten in the Kappa language. Kappa provides symbolic equali- ties and inequalities which intentionally may be understood as algebraic constructions over patterns, and extensionally as sound properties about the quantities of the biomolecular species that contain these patterns. 
@inproceedings{10.1145/3726301.3728414, 
  author = {Feret, Jerome}, 
  title = {Model reduction of infinite rule-based models}, 
  year = {2025}, 
  isbn = {9798400715914}, 
  publisher = {Association for Computing Machinery}, 
  address = {New York, NY, USA}, 
  url = {https://doi.org/10.1145/3726301.3728414}, 
  doi = {10.1145/3726301.3728414}, 
  location = {Santa Fe, NM, USA}, 
  series = {SIGSIM-PADS '25} }
  author       = {J{\'{e}}r{\^{o}}me Feret},
  editor       = {Adelinde Uhrmacher}
}