Observability Gramian of a Rxn-Diffusion System
Pseudocolor plot of the fifty-first most observable mode of a reaction-diffusion system. Given an initial configuration of a linear dynamical system with a linear readout of the internal states, the Observability Gramian completely characterizes the resulting energy of the resulting output signal. By computing a spectral decomposition of the Observability Gramian, one can identify the most relevant components of the state space needed to reconstruct the output signal. Novel numerical linear algebra techniques allow fast low-rank adaptive approximation of the Gramian quickly getting good resolution of the important directions while ignoring the others.