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

2026-04-16

AI Summary

This work addresses the challenge of predicting frequency response characteristics in weakly nonlinear forced oscillators, which typically demands extensive datasets. The authors propose a one-shot learning approach capable of extrapolating the global frequency response from a single excitation–response measurement. By integrating multi-frequency evolutionary modeling with sparse identification for the first time, the method employs the MEv-SINDy algorithm in conjunction with the generalized harmonic balance technique to extract slowly varying evolution equations from a single-point time series and reconstruct the governing equations of the non-autonomous system. Experimental validation on MEMS nonlinear beam resonators and micromirror systems demonstrates that the approach accurately captures softening/hardening behaviors and jump phenomena, substantially reducing the data requirements for nonlinear characterization of microsystems.

Technology Category

• Machine Learning: Evolutionary Learning
• Search and Optimization: Evolutionary Computation
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and 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.

Problem

• one-shot learning
• nonlinear dynamics
• forced oscillators
• frequency-response curves
• MEMS

Innovation

• one-shot learning
• MEv-SINDy
• nonlinear dynamics
• Generalized Harmonic Balance
• MEMS