Table 2 List of symbols used in Algorithm 4

ρ

group of model parameters {a(t),b,σ};

\(c_{k}\)

number of parameters selected adaptively based on surrogate modeling;

V

solution obtained by solving a full order model;

\(c_{0}\)

Number of randomly selected parameter groups to initiate the algorithm;

ε

error estimator;

\(\varepsilon ^{k}\)

set comprised of error estimator values at kth iteration;

\(e_{\mathrm{sg}}\)

set composed of all error estimator values at the kth iteration;

ε̄

surrogate error model;

P̂

parameter set used to obtain the optimal parameter group;

\(\rho _{I}\)

optimal parameter group which maximizes the error estimator;

e

relative error between a reduced and full model;

V̄

solution obtained using a reduced order model;

V̂

snapshot matrix;

\(E_{p}\)

error set;

ē

error model as an approximate error for the exact error e;

\(e^{\mathrm{max}}_{\mathrm{tol}}\)

tolerance for the relative error, greedy iterations terminates if \(\bar{e} < e^{\mathrm{max}}_{\mathrm{tol}}\);

\(\gamma _{e}\)

slope of the error model;

τ̂

intersection with the logarithmic axis log(y).