pCODE: Estimating Parameters of ODE Models

The ordinary differential equation (ODE) models are prominent to characterize the mechanism of dynamical systems with various applications in biology, engineering, and many other areas. While the form of ODE models is often proposed based on the understanding or assumption of the dynamical systems, the values of ODE model parameters are often unknown. Hence, it is of great interest to estimate the ODE parameters once the observations of dynamic systems become available. The parameter cascade method initially proposed by (Ramsay et al. 2007) is shown to provide an accurate estimation of ODE parameters from the noisy observations at a low computational cost. This method is further promoted with the implementation in the R package CollocInfer by (Hooker et al. 2016). However, one bottleneck in using CollocInfer to implement the parameter cascade method is the tedious derivations and coding of the Jacobian and Hessian matrices required by the objective functions for doing estimation. We develop an R package pCODE to implement the parameter cascade method, which has the advantage that the users are not required to provide any Jacobian or Hessian matrices. Functions in the pCODE package accommodate users for estimating ODE parameters along with their variances and tuning the smoothing parameters. The package is demonstrated and assessed with four simulation examples with various settings. We show that pCODE offers a derivative-free procedure to estimate any ODE models where its functions are easy to understand and apply. Furthermore, the package has an online Shiny app at https://pcode.shinyapps.io/pcode/.

Haixu Wang (Simon Fraser University) , Jiguo Cao (Simon Fraser University)

Supplementary materials

Supplementary materials are available in addition to this article. It can be downloaded at RJ-2023-018.zip

G. Hooker, J. Ramsay and L. Xiao. CollocInfer: Collocation inference in differential equation models. Journal of Statistical Software, Articles, 75(2): 1–52, 2016. URL https://www.jstatsoft.org/v075/i02.
J. Ramsay, G. Hooker, D. Campbell and J. Cao. Parameter estimation for differential equations: A generalized smoothing approach. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 69(5): 741–796, 2007.



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For attribution, please cite this work as

Wang & Cao, "pCODE: Estimating Parameters of ODE Models", The R Journal, 2023

BibTeX citation

  author = {Wang, Haixu and Cao, Jiguo},
  title = {pCODE: Estimating Parameters of ODE Models},
  journal = {The R Journal},
  year = {2023},
  note = {https://doi.org/10.32614/RJ-2023-018},
  doi = {10.32614/RJ-2023-018},
  volume = {14},
  issue = {4},
  issn = {2073-4859},
  pages = {291-304}