# Research

## 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.