Tracking governing equations with nonlinear adaptive filters

In the current advent of empirical system modeling, numerous approaches have been introduced to model nonlinear dynamical systems from measurement data. One well-established method is to reconstruct the governing system equations using sparse identification of nonlinear dynamics (SINDy). However, such models are not suitable for continuous streams of measurement data that may also include changing system dynamics e.g. due to aging, as is realistic for applications in the field. Therefore, this work introduces a novel data-driven adaptive filter model that utilizes the capabilities of SINDy to address this shortcoming. Additionally, we also introduce a method to monitor the steady-state behaviour of our filters and consequently improve tracking capabilities. The proposed approach is validated on a variety of chaotic attractor examples from the dyst database, highlighting both interpretability and accurate adaption to governing equation changes.