  Driven by increased complexity of dynamical systems, the solution of system
of differential equations through numerical simulation in optimization problems
has become computationally expensive. This paper provides a smart data driven
mechanism to construct low dimensional surrogate models. These surrogate models
reduce the computational time for solution of the complex optimization problems
by using training instances derived from the evaluations of the true objective
functions. The surrogate models are constructed using combination of proper
orthogonal decomposition and radial basis functions and provides system
responses by simple matrix multiplication. Using relative maximum absolute
error as the measure of accuracy of approximation, it is shown surrogate models
with latin hypercube sampling and spline radial basis functions dominate
variable order methods in computational time of optimization, while preserving
the accuracy. These surrogate models also show robustness in presence of model
non-linearities. Therefore, these computational efficient predictive surrogate
models are applicable in various fields, specifically to solve inverse problems
and optimal control problems, some examples of which are demonstrated in this
paper.
