Model selection for hybrid dynamical systems via sparse regression
Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations solely from measurement data. In this article, we develop a new methodology, Hybrid-Sparse Identification of Nonlinear Dynamics (Hybrid-SINDy), which identifies separate nonlinear dynamical regimes, employs information theory to manage uncertainty, and characterizes switching behavior.
The high-fidelity characterization of complex systems is of paramount importance to manage modern infrastructure and improve lives around the world. However, when a system exhibits nonlinear behavior and switches between dynamical regimes, as is the case for many large-scale engineered and human systems, model identification is a significant challenge. These hybrid systems are found in a diverse set of applications including epidemiology , legged locomotion , cascading failures on the electrical grid , and security for cyber infrastructure.
Steps for local validation and selection of models. For each cluster from the training set, we identify validation time-series points that are local to the training cluster centroid (black dots, panel 1). We simulate time-series for each model in the cluster library, starting from each point in the validation cluster (teal, gold and purple dots) and calculate the error from the validation time-series. Using this error we calculate a relative AICc value and rank each model in the cluster (panel 2). We collect the models with significant support into a library, keeping track of their frequency across clusters. The highest frequency models across clusters are shown in panel 3. Note that the colors associated with each model in panel 3 are consistent across panels.