Abstract:

Sparse identification of nonlinear dynamics (SINDy) has made significant progress in data-driven dynamics modeling. However, determining appropriate hyperparameters and addressing the time-consuming symbolic regression process remain substantial challenges. This study proposes the adaptive backward stepwise selection of fast SINDy (ABSS-FSINDy), which integrates statistical learning-based estimation and technical advancements to significantly reduce simulation time. This approach not only provides insights into the conditions under which SINDy performs optimally but also highlights potential failure points, particularly in the context of backward stepwise selection (BSS). By decoding predefined features into textual expressions, ABSS-FSINDy significantly reduces the simulation time compared with conventional symbolic regression methods. We validate the proposed method through a series of numerical experiments involving both planar/spatial dynamics and high-dimensional chaotic systems, including Lotka-Volterra, hyperchaotic Rössler, coupled Lorenz, and Lorenz 96 benchmark systems. The experimental results demonstrate that ABSS-FSINDy autonomously determines optimal hyperparameters within the SINDy framework, overcoming the curse of dimensionality in high-dimensional simulations. This improvement is substantial across both low- and high-dimensional systems, yielding efficiency gains of one to three orders of magnitude. For instance, in a 20D dynamical system, the simulation time is reduced from 107.63 s to just 0.093 s, resulting in a 3-order-of-magnitude improvement in simulation efficiency. This advancement broadens the applicability of SINDy for the identification and reconstruction of high-dimensional dynamical systems.

Key words: data-driven dynamics modeling, backward stepwise selection (BSS), sparse identification of nonlinear dynamics (SINDy), sparse regression, hyperparameter determination, curse of dimensionality