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Researchers should cite this work as follows:

• Campbell, D. (2023). 2012-Campbell-EtAl-Parameter estimation in differential equation models with constrained states. SIMIODE, QUBES Educational Resources. doi:10.25334/N9MZ-VT46

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Campbell, David A.,  Giles Hooker, and   Kim B. McAuley. 2012. Parameter estimation in differential equation models with constrained states. Journal of Chemometrics. Special Issue Article.

See http://people.stat.sfu.ca/~dac5/Dave_Campbell/Research_files/Parameter%20estimation%20in%20differential%20equation%20mode.pdf . Accessed 29 March 2023.

Abstract: We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non‐negative states. We motivate the methodology using a real data chemical engineering example and show that a variety of restrictive constraints from earlier analyses do not address the problem of interpretability. Our proposed method estimates parameters using a smoothing‐based relaxation of the model to enforce interpretability of the observed and unobserved system states.