Fig. 5: Recovering long-time statistics.
From: Learning dynamical systems with hit-and-run random feature maps
Comparison of the marginal densities obtained by the original systems and the surrogate models. The respective Wasserstein W2 distances are indicated at the top of the kernel density plots. A L63 system (5) with marginal densities for each component x, y and z. We used the best models marked with the *-symbol in Fig. 2A and in Supplementary Table 1 to generate the data. The mean VPT for these models are 9.8, 10.6 and 12.0 from left to right. B L96 system (7). We employ translational symmetry and use all 40 components to estimate the densities. We used the best models marked with the *-symbol in Fig. 2B and in Supplementary Tables 3 and 4 to generate the data. The mean VPT for these models are 2.3, 2.8, 6.8, 7.2, and 7.3 from left to right. C KS system (8). We employ translational symmetry and use all 512 components to estimate the densities. We used the best models marked with the *-symbol in Fig. 2C and in Supplementary Table 5 to generate the data. The mean VPT for both of these models is 5.0.
