Paramatrized intrusive POD-based reduced-order models applied to advection-diffusion-reaction problems

Parametrized problems involve high computational costs when looking for the proper values of their input parameters and solved with classical schemes. Reduced-order models (ROMs) based on the proper orthogonal decomposition act as alternative numerical schemes that speed up computational times while maintaining the accuracy of the solutions. They can be used to obtain solutions in a less expensive way for different values of the input parameters. The samples that compose the training set determine some computational limits on the solution that can be computed by the ROM. It is highly interesting to study what can be done to overcome these limits. In this article, the possibilities to obtain solutions to parametrized problems are explored and illustrated with several numerical cases using the two-dimensional (2D) advection-diffusion-reaction equation and the 2D wildfire propagation model.