Surrogate Models for Optimization of Dynamical Systems
This work addresses computational bottlenecks in optimization of complex dynamical systems, such as inverse and optimal control problems, but is incremental as it builds on existing surrogate modeling techniques.
The paper tackles the computational expense of solving differential equations in optimization by constructing low-dimensional surrogate models using proper orthogonal decomposition and radial basis functions, reducing optimization time while preserving accuracy, with examples showing dominance over variable order methods in computational efficiency.
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.