Approximate Constrained Lumping of Polynomial Differential Equations

Alexander Leguizamon-Robayo*, Antonio Jiménez-Pastor, Micro Tribastone, Max Tschaikowski, Andrea Vandin

*Corresponding author for this work

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review


In life sciences, deriving insights from dynamic models can be challenging due to the large number of state variables involved. To address this, model reduction techniques can be used to project the system onto a lower-dimensional state space. Constrained lumping can reduce systems of ordinary differential equations with polynomial derivatives up to linear combinations of the original variables while preserving specific output variables of interest. Exact reductions may be too restrictive in practice for biological systems since quantitative information is often uncertain or subject to estimations and measurement errors. This might come at the cost of limiting the actual aggregation power of exact reduction techniques. We propose an extension of exact constrained lumping which relaxes the exactness requirements up to a given tolerance parameter ε. We prove that the accuracy, i.e., the difference between the output variables in the original and reduced model, is in the order of ε. Furthermore, we provide a heuristic algorithm to find the smallest ε for a given maximal approximation error. Finally, we demonstrate the approach in biological models from the literature by providing coarser aggregations than exact lumping while accurately capturing the original system dynamics.

Original languageEnglish
Title of host publicationComputational Methods in Systems Biology : 21st International Conference, CMSB 2023, Luxembourg City, Luxembourg, September 13–15, 2023, Proceedings
EditorsJun Pang, Joachim Niehren
Number of pages18
Publication date2023
ISBN (Print)978-3-031-42696-4
ISBN (Electronic)978-3-031-42697-1
Publication statusPublished - 2023
EventProceedings of the 21st International Conference on Computational Methods in Systems Biology, CMSB 2023 - Luxembourg City, Luxembourg
Duration: 13 Sept 202315 Sept 2023


ConferenceProceedings of the 21st International Conference on Computational Methods in Systems Biology, CMSB 2023
CityLuxembourg City
SeriesLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14137 LNBI

Bibliographical note

Funding Information:
The work was partially supported by the DFF project REDUCTO 9040-00224B, the Poul Due Jensen Grant 883901, the Villum Investigator Grant S4OS, the PRIN project SEDUCE 2017TWRCNB and the co-funding of European Union-Next Generation EU, in the context of The National Recovery and Resilience Plan, Investment 1.5 Ecosystems of Innovation, Project Tuscany Health Ecosystem (THE), CUP: B83C22003920001.

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.


  • Approximate reduction
  • Constrained lumping
  • Dynamical systems


Dive into the research topics of 'Approximate Constrained Lumping of Polynomial Differential Equations'. Together they form a unique fingerprint.

Cite this