An inverse problem in reaction kinetics

Fadil Santosa, Benjamin Weitz

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper we investigate the problem of extracting information about chemical reactions involving multiple species from the time history of the concentration of each species. The mathematical model of the kinetic system leads to a system of ordinary differential equations. Our focus is to examine whether the species' concentrations as functions of time are sufficient to determine what chemical reactions, and at what reaction rates, have occurred. We show that within the limitation of our model, there may be many candidate reaction systems that could explain the data. Using the notion of sparsity, we provide a quantitative assessment of the question of distinguishability. We further demonstrate that sparsity enforcing approaches, such as minimizing the ℓ1 or the ℓ0 norms are not reliable. Our conclusion is that additional knowledge about the kinetic system will be necessary to reliably solve this inverse problem.

Original languageEnglish (US)
Pages (from-to)1507-1520
Number of pages14
JournalJournal of Mathematical Chemistry
Issue number8
StatePublished - Sep 1 2011


  • Inverse problems
  • Reaction kinetics

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