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Regime switching is ubiquitous in many complex dynamical systems withmultiscale features, chaotic behavior, and extreme events. In this paper, acausation entropy boosting (CEBoosting) strategy is developed to facilitate thedetection of regime switching and the discovery of the dynamics associated withthe new regime via online model identification. The causation entropy, whichcan be efficiently calculated, provides a logic value of each candidatefunction in a pre-determined library. The reversal of one or a few suchcausation entropy indicators associated with the model calibrated for thecurrent regime implies the detection of regime switching. Despite the shortlength of each batch formed by the sequential data, the accumulated value ofcausation entropy corresponding to a sequence of data batches leads to a robustindicator. With the detected rectification of the model structure, thesubsequent parameter estimation becomes a quadratic optimization problem, whichis solved using closed analytic formulae. Using the Lorenz 96 model, it isshown that the causation entropy indicator can be efficiently calculated, andthe method applies to moderately large dimensional systems. The CEBoostingalgorithm is also adaptive to the situation with partial observations. It isshown via a stochastic parameterized model that the CEBoosting strategy can becombined with data assimilation to identify regime switching triggered by theunobserved latent processes. In addition, the CEBoosting method is applied to anonlinear paradigm model for topographic mean flow interaction, demonstratingthe online detection of regime switching in the presence of strongintermittency and extreme events.

CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting