Reduced Order Model

For any given parabolic partial differential equation (PDE) can be written as

\[ \dot{a} = F(a) \]

where \(F\) could be linear or nonlinear operator. To obtain Direct Numerical Simulation (DNS) of that PDE requires lots of degrees of freedom i.e., \( \mathcal{O}(10^6) \). Although DNS solution is accurate, it is not efficient in terms of computational cost.

In Reduced Order Models (ROMs), we aim to decrease the computational cost \( \mathcal{O}(10^1) \) without losing accuracy.