Fig. 3: Flow behind a cylinder ROM problem.
From: State estimation of a physical system with unknown governing equations
a, Predictions for the first ten latent states over the testing time interval t = [256.2, 260.2]. The black lines show the test states and the coloured lines indicate samples from the predictive posterior. b, Velocity magnitude and flow lines at t = 260.2. Test (left), mean prediction (centre) and standard deviation (right). In this example, we train a neural SDE on trajectories projected onto the POD basis to construct a ROM. Although a neural SDE is less interpretable than a symbolic model, it is useful in cases in which the state is either (1) high dimensional or (2) it is not clear which basis functions might be appropriate for the problem at hand. We see that the error bars are higher in regions in which the mean prediction seems to differ from the test velocity.
