  Big data has become a critically enabling component of emerging mathematical
methods aimed at the automated discovery of dynamical systems, where first
principles modeling may be intractable. However, in many engineering systems,
abrupt changes must be rapidly characterized based on limited, incomplete, and
noisy data. Many leading automated learning techniques rely on unrealistically
large data sets and it is unclear how to leverage prior knowledge effectively
to re-identify a model after an abrupt change. In this work, we propose a
conceptual framework to recover parsimonious models of a system in response to
abrupt changes in the low-data limit. First, the abrupt change is detected by
comparing the estimated Lyapunov time of the data with the model prediction.
Next, we apply the sparse identification of nonlinear dynamics (SINDy)
regression to update a previously identified model with the fewest changes,
either by addition, deletion, or modification of existing model terms. We
demonstrate this sparse model recovery on several examples for abrupt system
change detection in periodic and chaotic dynamical systems. Our examples show
that sparse updates to a previously identified model perform better with less
data, have lower runtime complexity, and are less sensitive to noise than
identifying an entirely new model. The proposed abrupt-SINDy architecture
provides a new paradigm for the rapid and efficient recovery of a system model
after abrupt changes.
