One-shot learning for the complex dynamical behaviors of weakly nonlinear forced oscillators
For engineers characterizing nonlinear microsystems (e.g., MEMS), this method drastically reduces data acquisition burden by enabling extrapolative prediction from a single measurement.
The paper introduces MEv-SINDy, a one-shot learning method that identifies global frequency-response curves of weakly nonlinear forced oscillators from a single excitation time history, accurately predicting softening/hardening effects and jump phenomena across a wide range of excitation levels.
Extrapolative prediction of complex nonlinear dynamics remains a central challenge in engineering. This study proposes a one-shot learning method to identify global frequency-response curves from a single excitation time history by learning governing equations. We introduce MEv-SINDy (Multi-frequency Evolutionary Sparse Identification of Nonlinear Dynamics) to infer the governing equations of non-autonomous and multi-frequency systems. The methodology leverages the Generalized Harmonic Balance (GHB) method to decompose complex forced responses into a set of slow-varying evolution equations. We validated the capabilities of MEv-SINDy on two critical Micro-Electro-Mechanical Systems (MEMS). These applications include a nonlinear beam resonator and a MEMS micromirror. Our results show that the model trained on a single point accurately predicts softening/hardening effects and jump phenomena across a wide range of excitation levels. This approach significantly reduces the data acquisition burden for the characterization and design of nonlinear microsystems.