Okay, so I am using DMD to formulate a low rank model of a system I'm working on. Everything works fine thus far, and I can reconstruct the states for the time I have measurements - so for t \in [0, 10000] seconds. However, I wanna forecast for the next pred_steps = 100 seconds or so, and I know that the algorithm can do that, I am just not sure which formula I should use...
So the book by Brunton and Kutz shows two formulas, and I am confused as to which one is the correct one / the one I should use in my case?
The formulas in the book are: A) $x_{k=1} = A x_{k}$ B) $x(t) = \Phi exp(\Omega t) b$
A third formula is shown on a paper from Kutz et. al. : C) $V(t_{j+1}) = A V(t_j)$, V being the right singular vector matrix
I understand that one is in discrete-time and the other in continuous-time spaces, but I am not sure as to which I should use... Are they equivalent?
Thank you in advance!!
I have already tried implementing both, and to be honest the forecast results are veery different from one to the other. So i have am not sure which one would be the "correct" approach...