Fig. 6: Identifying the conserved spatial phase for the oscillating Turing pattern system.
From: Discovering conservation laws using optimal transport and manifold learning
a An example trajectory, with randomly sampled states u(x) and v(x) plotted, illustrates the high dimensional nature of the problem. b The heuristic score (with cutoff 0.6) identifies two relevant components, but on further examination, c we see that there is just a single conserved angle, corresponding to the spatial phase η of the Turing pattern, that needs to be embedded in two dimensions due to its topology.
