Suppressing unknown disturbances to dynamical systems using machine learning

Identifying and suppressing unknown disturbances to dynamical systems is a problem with applications in many different fields. Here we present a model-free method to identify and suppress an unknown disturbance to an unknown system based only on previous observations of the system under the influence of a known forcing function. We find that, under very mild restrictions on the training function, our method is able to robustly identify and suppress a large class of unknown disturbances. We illustrate our scheme with the identification of both deterministic and stochastic unknown disturbances to an analog electric chaotic circuit and with numerical examples where a chaotic disturbance to various chaotic dynamical systems is identified and suppressed. Identifying and mitigating unknown disturbances to complex systems poses a critical challenge in a wide range of disciplines. Here, the authors use machine learning to identify unknown disturbances made to unknown systems and a methodology to suppress these disturbances to recover the undisturbed system.