Fig. 7: Identifying three local conserved quantities of the Korteweg–De Vries (KdV) equation.
From: Discovering conservation laws using optimal transport and manifold learning
a An example trajectory from the KdV dataset shows the high dimensional raw sampled states u(x). b To focus on local conserved quantities, we extract a distribution of the local features u(x), Δu(x) from the raw states, removing the explicit spatial label. The plot shows the local feature distributions for a few sample states. c The heuristic score (with cutoff 0.6) correctly identifies three relevant components corresponding to d–f the three local conserved quantities (Eq. (14)).
