One-shot learning for the complex dynamical behaviors of weakly nonlinear forced oscillators

• URL: http://arxiv.org/abs/2604.15181v1
• Date: Thu, 16 Apr 2026 16:10:44 GMT
• Title: One-shot learning for the complex dynamical behaviors of weakly nonlinear forced oscillators
• Abstract summary: We introduce MEv-SINDy (Multi-frequency Sparse Identification of Evolutionary Dynamics) to infer the governing equations of non-autonomous and multi-frequency systems.<n>We validated the capabilities of MEv-SINDy on two critical Micro-Electro-Mechanical Systems.
• Score: 10.038220687588117
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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