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

TL;DR

This paper introduces MEv-SINDy, a one-shot learning method that uses a single excitation response to accurately identify nonlinear dynamics in MEMS devices, reducing data needs.

Contribution

The novel MEv-SINDy approach combines harmonic balance and sparse identification to infer governing equations from minimal data in complex nonlinear systems.

Findings

Accurately predicts nonlinear effects like softening/hardening from a single response.

Validated on MEMS resonator and micromirror with successful results.

Reduces data collection effort in nonlinear microsystem characterization.

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.