Extended Data Fig. 2: Experiment on discovering governing equations for a high-dimensional system with a low-rank observation matrix.
From: State estimation of a physical system with unknown governing equations
a, Visualization of Lorenz ’96 full underlying state data with 1,024 states. b, Reconstruction error for varying observation matrix ranks. c, Number of mismatched terms for varying observation matrix ranks. In this experiment, we assumed that the governing equations were a sparse linear combination of basis functions from the dictionary of quadratic polynomial functions of the node state and its four closest neighbours to the left and right of the node. We were able to successfully recover the exact functional form of the Lorenz ’96 governing equations using an observation matrix whose rank was half that of the full underlying state.
