Sparse identification of nonlinear dynamics with library optimization mechanism: Recursive long-term prediction perspective

The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given basis functions. A major challenge in SINDy is the design of a library, which is a set of candidate basis functions, as the appropriate library is not trivial for many dynamical systems. To overcome this difficulty, this study proposes SINDy with library optimization mechanism (SINDy-LOM), which is a combination of the sparse regression technique and the novel learning strategy of the library. In the proposed approach, the basis functions are parametrized. The SINDy-LOM approach involves a two-layer optimization architecture: the inner-layer, in which the data-driven model is extracted as the sparse linear combination of the candidate basis functions, and the outer-layer, in which the basis functions are optimized from the viewpoint of the recursive long-term (RLT) prediction accuracy; thus, the library design is reformulated as the optimization of the parametrized basis functions. The dynamical model obtained by SINDy-LOM has good interpretability and usability, as this approach yields a parsimonious closed-form model. The library optimization mechanism significantly reduces user burden. The RLT perspective improves the reliability of the resulting model compared with the traditional SINDy approach that can only ensure the one-step-ahead prediction accuracy. The effectiveness of the proposed approach is verified through numerical experiments.