Fig. 3: Different MIDST variants predictions on a previously unseen trajectory.

GT denotes ground-truth; Fresh-start denotes a newly trained MIDST model; Pre-trained auto-encoder (AE) denotes a fixed pre-trained AE and a newly trained propagator K; Pre-trained AE + Dynamics denotes training only the B matrix in the propagator. a Predictions are for horizon H = 1 across the entire test set. b Zoom-in on the right blue box. c Auto-regressive predictions for H = 20 (displaying first 15 points for clarity), zoom-in on the left blue-box. Colors correspond to Lyapunov time (i.e., \(\frac{1}{{\lambda }_{L}}\), where λ_L ≈ 0.9056⁴⁶ is the largest Lyapunov exponent of the Lorenz system). Importantly, note that while a macro view shows no visible differences (a), by utilizing previously learned dynamics (i.e., dynamics sharing), our model forecasts are both more accurate for H = 1 (b and Fig. S3), and better encapsulate the true system dynamics when applied auto-regressively for longer time-horizons (c). Specifically, c shows that the only model actually obeying the true system dynamics for more than a single prediction step, is the one utilizing dynamics sharing.