Optimized Dynamic Mode Decomposition for Reconstruction and Forecasting of Atmospheric Chemistry Data

The paper explicitly models forecasts as x(t)=Φ exp(Ω t) b (a finite sum of exponentials) and observes empirically that allowing eigenvalues with positive real part produces exponentially growing forecasts, while constraining the spectrum to the closed left-half plane stabilizes forecasts; these claims are documented in their diagnostics and discussion (see the representation in Eq. (1) and surrounding text, and the constraint statements and empirical outcomes) . The candidate solution provides a clean, rigorous proof of boundedness under Re(ωk)≤0 and divergence when some Re(ωk)>0 (with a careful treatment of ties and cancellations). Thus, both align on substance; the paper provides empirical/algorithmic justification while the model gives a formal argument.