Fig. 2: Benchmarking summary with 20 independent trials per system.
From: State estimation of a physical system with unknown governing equations
a, State-estimation results with perfect knowledge of the dynamics. b, State-estimation results with minor corruption of the dynamics. c–e, Before and after adding a small probabilistic corruption for the coupled linear oscillator (c), the cubic oscillator (d) and the Hopf bifurcation (e) (10–90th quantiles shown). f–h, Probabilistic forecast with 64 (f), 512 (g) and 1,024 (h) data points. We see that our method (SVISE) performs similarly to the PF when the governing equations are known exactly. In the presence of only mild modelling error, our method outperforms the PF on average. Moreover, after training, our method enables us to make probabilistic forecasts. Expectedly, the predictive posterior shrinks as the amount of data is increased.
