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Table 3 Overview of the regressor- and response matrices used in the regression analyses and the test sets used for the three application examples

From: Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

Application Design variables (D) Regressor matrix (X) Response matrix (Y) Test set used
Gene regulatory networks 125 initial conditions for the three state variables X1, X2 and X3 (at time zero) in a 53 FFD (dimensions: 125 × 3) [D sin(D) cos(D)] The concatenated time series for the state variables X1, X2 and X3 (Yi = 3 × 300 time points,
i = 1 to nr. of observations)
33% of the observations in D (randomly chosen), and the corresponding Y-values
Mammalian circadian clock model Nine model parameters in an OMBR design using eight levels for each parameter
(dimensions: 8192 × 9)
[D cross-terms of D D2] 16 state variable time series modelled separately (for each state variable Yi = 200 time points,
i = 1 to nr. of observations)
8192 new parameter combinations generated by random Monte Carlo sampling (here the entire matrix D was used for calibration) and corresponding Y-values
Mouse ventricular myocyte model Ten model parameters in a 310 FFD
(dimensions: 59049 × 10)
[D cross-terms of D D2]* 35 state variable time series modelled separately (for each state variable Yi = 200 time points,
i = 1 to nr. of observations)*
33% of the observations in D that did not fail (randomly chosen), and the corresponding Y-values
  1. *The three parts of the mouse ventricular myocyte data set separated according to the stimulus period were analysed separately, and only the simulations that did not fail were used.