Fig. 3: Identifying unknown disturbances: Rössler and Lorenz 96 systems.
From: Suppressing unknown disturbances to dynamical systems using machine learning
a, b Unknown and reconstructed disturbance functions [gx(t), gy(t)] (black curve) and [ux(t), uy(t)] (red curve) along with the training forcing functions [fx(t), fy(t)] (blue curves). For each case the reservoir was trained with \([{f}_{x}(t),{f}_{y}(t)]=[\cos (0.05t),\sin (0.05t)]\) and disturbed with (a) Lorenz dynamics and (b) sinusoidal functions. c, d Time series for the unknown (solid black) and recovered (dashed red) disturbance functions in the second component, gy(t) and uy(t) (or \({g}_{{x}_{2}}(t)\) and \({u}_{{x}_{2}}(t)\)).
